Delay Representation in the Sensorimotor System. Guy Avraham

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1 Thesis submitted in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY by Submitted to the Senate of Ben-Gurion University of the Negev 31-Oct-16 Beer-Sheva

2 Thesis submitted in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY by Submitted to the Senate of Ben-Gurion University of the Negev Approved by the advisors Approved by the Dean of the Kreitman School of Advanced Graduate Studies 31-Oct-2016 Beer-Sheva

3 This work was carried out under the supervision of Dr. Ilana Nisky, Dr. Lior Shmuelof and Prof. Amir Karniel Date of death: June 2 nd, 2014 In the Department of Biomedical Engineering Faculty of Engineering

4 I, whose signature appears below, hereby declare that (Please mark the appropriate statements): I have written this Thesis by myself, except for the help and guidance offered by my Thesis Advisors. The scientific materials included in this Thesis are products of my own research, culled from the period during which I was a research student. This Thesis incorporates research materials produced in cooperation with others, excluding the technical help commonly received during experimental work. Therefore, I am attaching another affidavit stating the contributions made by myself and the other participants in this research, which has been approved by them and submitted with their approval. Date: 31-Oct-2016 Student's name: Signature:

5 Acknowledgements I wish to thank Amir, who made me love science. His ambition and innovative ideas were inspiring. He made me realize how great it is to have a controversial research, which simply means it is interesting. He set a high standard of both professionalism and kindness, and, knowingly or not, guided me to follow his lead. To Ilana, for being a perfect mentor. She had a tremendous role in making my transition from life science to engineering as smooth as possible. She taught me about perfectionism in scientific research, and was a role model in every professional aspect. For Ilana, every crazy thought and idea were welcomed and intriguing, and conversations usually evolved into how we can make them real. Fortunately, when things seemed to fall apart, Ilana showed me how they actually happened for the best. To Lior, who undertook the responsibility to fulfill my wishes to study new scientific approaches, and for providing the missing link to the field in which I grew in. He introduced me to the novel and interesting studies that were most influential for desirable future academic paths. Lior always encouraged me to think deeper about the meaning of my findings; he asked the important questions that led me to meaningful insights. Both Ilana and Lior took me under their wings following the tragic loss of Prof. Amir Karniel. Thanks to them, each lab was (not only felt like) home. I would also like to thank Prof. Opher Donchin for guidance and support in this transition, for your insightful advices, and for your most valuable scientific contribution to this work. To Prof. Sandro Mussa-Ivaldi, for serving as an additional advisor de facto, for hosting me in his lab for prolonged visits and for the fruitful Skype calls. I gained a lot from his vast knowledge and experience. Thanks to all the members of the Computational Motor Control Lab, the Biomedical Robotics Lab and the Brain and Action Lab in the past and in the present, for making it truly enjoyable to come to the lab every day. Special thanks to my dear friends and colleagues Firas, Raz, Amit and Mor for sharing your admirable skills and for all the fun that we had together. To Dorit for opening the doors of the biomedical department for me and for her warm support throughout my entire graduate studies. To my friend Shai, for the long talks that guided me through the decisions that brought me here. I owe a great deal to my beloved family: Mom, Dad, Chen, Niv and Lior, for your unconditional love. I was supported by the Negev Fellowship, and the study was supported by the Binational United-States Israel Science Foundation.

6 To my parents, who have showed me the way and still do.

7 Table of Contents Abstract... 2 Chapter 1: General Introduction Delay representations in the sensorimotor system Internal representations in motor control Effects of the schedule and magnitude of the presented delay perturbations Organization of this Thesis... 8 Chapter 2: Ghosts from the Past and the Present Representing Delayed Force Feedback as a Combination of Delayed and Current States Chapter 3: Running Behind Time State-Based Delay Representation and Its Transfer from a Game of Pong to Reaching and Tracking Chapter 4: The Magnitude and the Schedule of Presentation of a Visuomotor Delay Affect Adaptation and its Transfer Chapter 5: General Discussion What did we learn? What do we think we learned? What do we still not know? Implications From time (delay) to time References...169

8 Abstract To coordinate movements and adapt to changes in our body or the surrounding environment, our brain integrates signals from different sensory modalities. As a result of differences in information transmission rates between modalities, the integration processes must account for delays between the signals. The mechanisms by which these delays are represented and compensated are unclear. In this thesis, we investigated how the sensorimotor system represents delayed feedback from the external world. First, we explored how humans represent delayed force feedback. Participants adapted to force perturbations that were applied on their moving hand by a robotic device that were proportional to the velocity of the hand some time beforehand. We developed computational models to account for the ways in which these delayed perturbations can be represented in the sensorimotor system; namely, either with a time-base representation of the actual time lag or with an approximation of the delay using current state information. We tested these models by measuring the forces participants applied at the end of adaptation and during generalization to faster movements. We found that the best representation model consisted of the current position and velocity together with the delayed velocity. Second, we examined the way humans represent a delayed visual feedback. We used a virtual game of pong in which the paddle is delayed with respect to the participant s hand movement, and explored how participants adapt to this delay. A time representation of delay would use the actual time lag between hand and paddle movements, whereas a state representation would use only current state variables. Following prolonged exposure to the delayed pong, participants made larger movements during blind reaching and tracking. We developed a computational model that explains this hypermetria as an attribution of the delay to the dynamics of a mechanical system (mass, spring, and damper) connecting the paddle to the hand. Next, we examined this state-based representation in depth: we tested the effects of playing pong in the presence of different delay magnitudes which were presented either gradually or abruptly on movement kinematics during the game, and during transfer to the blind reaching 2

9 task. We found increases in the amplitude and duration of the movements during the game with increasing delay, and showed that the apparent transfer of hypermetria to the blind reaching task was incomplete. We also found that participants performance in the game declined with increased delays. These results provide further support for our proposed representation model of visuomotor delay as a mechanical system equivalent. Finally, we explored various effects of visual delay on interception kinematics which could lead to future approaches examining the representation of delayed feedback in an ecological motor task. We conclude the thesis by listing questions about delay representations in the sensorimotor system, and discuss in what ways the results presented here contribute to responding to them. The findings may pave the way to future studies that can fill in the gaps in our understanding of the learning process for delay representation and the neural structures that underpin this process. Understanding the way delay is represented is essential for understanding how the sensorimotor system forms predictions and integrates different sensory signals. It is also important for studying pathological conditions that are characterized by delayed information transmission, such as Multiple Sclerosis. It also has numerous practical applications, such as remote teleoperation. Keywords: adaptation, delay, force field, motor primitives, reaching, representation, tracking, transfer, visuomotor perturbations 3

10 Chapter 1: General Introduction 1.1 Delay representations in the sensorimotor system When a ball lands on a child's hand, her sensory system is stimulated by inputs from different modalities. Her eyes register the image of the collision, she hears its thud, and she feels the tactile sensation on the palm of her hand. All of these signals are transmitted at different rates through the nervous system (Murray and Wallace, 2011) but she still perceives them as happening at the same time. Studies have suggested that the brain achieves simultaneity by actuating temporal adjustment processes that synchronize the signals (Miall et al., 1993; Spence and Squire, 2003; Harrar and Harris, 2008; Vroomen and Keetels, 2010; Pressman et al., 2012) through neural structures ( clocks ) that can represent time (Creelman, 1962; Treisman, 1963; Allan, 1979; Ivry, 1996). Recent studies have challenged this claim and have reported that within the milliseconds range of intermodal delay, time is measured through changes in the network state rather than with a linear measure predicted by a neural clock (Mauk and Buonomano, 2004; Karmarkar and Buonomano, 2007). Thus, the debate over the underlying mechanisms implemented by the nervous system to represent the timing of intermodal events is far from being resolved. Simultaneity is not only important for enabling a reliable perception of the world, but also to properly act in it. To catch a basketball, a player must have a highly accurate estimation of the state of her own body in addition to the estimated state of the approaching ball. However, because the brain sends a motor command to the muscles of the arms to move them in preparation for the catch, this can take more than 100 ms for the command to reach the muscles, generate forces, and for the emerging sensory feedback to return upstream for processing and integration (Franklin and Wolpert, 2011). Thus, if the state estimation used by the brain to control movements relies solely on the out-of-date sensory feedback, the player will probably miss the ball (Miall et al., 2007). There is a general consensus that to deal with such delays, an efference copy of the motor command is sent to a controller a forward model which predicts the sensory consequences of the action, and makes it possible to estimate the future state of the arm and 4

11 the ball given their current state (Jordan and Rumelhart, 1992; Wolpert et al., 1995; Wolpert and Ghahramani, 2000; Miall et al., 2007; Shadmehr and Krakauer, 2008; Wolpert et al., 2011). Previous studies have suggested that the construction of forward models is based on an explicit representation of time (Miall et al., 1993; Miall and Wolpert, 1995). This is in line with the ample evidence that forward models operate in the cerebellum (Wolpert et al., 1998; Miall et al., 2007; Nowak et al., 2007), which is regarded as a part of the brain that has internal clocks (Ivry, 1996; Spencer et al., 2003; Ivry and Schlerf, 2008). Thus, in the control of movement, inherent feedback delays can be compensated for by generating predictions based on representations of actual time lags. However, it is not clear whether the sensorimotor system can represent time explicitly (Conditt and Mussa-Ivaldi, 1999; Karniel and Mussa-Ivaldi, 2003; Karniel, 2011), and specifically when experiencing delayed feedback. On the one hand, people can adapt to force perturbations that are applied to their moving arm and that are delayed with respect to its velocity (Levy et al., 2010). Also, when interacting with virtual objects, people adjust their grip force to match a delayed load force (Witney et al., 1999; Leib et al., 2015). On the other hand, delaying the force feedback when probing virtual objects biases the perception of their stiffness (Pressman et al., 2007; Nisky et al., 2008; Nisky et al., 2010; Di Luca et al., 2011; Leib et al., 2015; Leib et al., 2016). In addition, a delay in visual feedback alters the perceived dynamics of the controlled objects (Sarlegna et al., 2010; Takamuku and Gomi, 2015), and affects movements (Pressman, 2012) and grip force control (Sarlegna et al., 2010). These perceptual and motor biases suggest that the brain cannot realign the original temporal relationship between the motor command and its delayed consequences; possibly, it attributes the altered dynamics to changes in the mechanical properties of the interactions. Therefore, it is not clear whether the sensorimotor system represents delayed feedback as an actual time lag or rather approximates it using the available information of current state variables. This is the question that we address in this thesis. 1.2 Internal representations in motor control Over the past decades, the motor control field has gained much of its understanding about the 5

12 way the sensorimotor system controls movements and adapt to changes in the environment using computational modelling (Pouget and Snyder, 2000; Wolpert and Ghahramani, 2000; Shadmehr and Krakauer, 2008; Karniel, 2011). Computational approaches were used to successfully characterize the typical bell-shaped speed profiles of reaching movements (Flash and Hogan, 1985; Uno et al., 1989; Ben-Itzhak and Karniel, 2008), to explain how internal representation are formed in the context of control theory (Shadmehr and Mussa-Ivaldi, 1994; Wolpert et al., 1995) and how performance is optimized (Todorov and Jordan, 2002; Körding and Wolpert, 2004). In addition, state-space systems were modeled to describe various phenomena in motor adaptation, such as generalization (Donchin et al., 2003), savings (Smith et al., 2006; Herzfeld et al., 2014) and associated cognitive processes (McDougle et al., 2015). Thus, computational approaches provide powerful tools for understanding sensorimotor processing. To control movements, it is commonly (Asatryan and Feldman, 1965) accepted that the brain constructs internal models; i.e., neural structures that represent the musculoskeletal system and the external world (Shadmehr and Mussa-Ivaldi, 1994; Wolpert et al., 1995; Kawato, 1999; Wolpert and Ghahramani, 2000; Shadmehr and Krakauer, 2008; Karniel, 2011). Internal models serve to predict the sensory consequences of a motor command (forward models) and to plan a motor command based on a desired movement trajectory (inverse models). When the environment changes (for example, the size or the weight of the basketball that needs to be caught), the sensorimotor system updates the parameters of these representations (Karniel, 2011) and thereby adapts to the novel conditions. We use here computational modelling to understand delay representation. We formulate predictions about whether the sensorimotor system uses time-based representation of a delayed feedback, or rather calculates an approximation of the delayed dynamics using the available current state information. We validate these predictions experimentally, and also use simulations to explain behavioral data. The processes by which the sensorimotor system constructs internal representations have been studied extensively by observing the movements of humans when they adapt to external perturbations. The vast majority of these studies have examined adaptation to two types of perturbations: force fields, in which a force is applied to the moving arm, which depends on the 6

13 state of the arm (Lackner and Dizio, 1994; Shadmehr and Mussa-Ivaldi, 1994), and visuomotor perturbations, where the spatial mapping between the moving hand and the visual feedback is distorted (Flanagan and Rao, 1995; Krakauer et al., 2000). For both these dynamic (force field) and the kinematic (visuomotor) perturbations, participants exhibit a similar adaptation pattern; namely, when a perturbation is suddenly presented, participants experience an error between the expected and the actual feedback, and with adaptation, this error is reduced. Upon sudden removal of the perturbation, participants show an aftereffect in the form of an error in the opposite direction, indicating that an internal representation of the perturbation had been formed. However, adaptation to force field and visuomotor perturbations while performing movements are distinct processes. Whereas the errors resulting from dynamic perturbations are computed in an intrinsic coordinate system of joints and muscles (Shadmehr and Mussa-Ivaldi, 1994), kinematic errors are computed in an extrinsic coordinate system of arm endpoints (Flanagan and Rao, 1995; Wolpert et al., 1995). This is consistent with the evidence that learning one type of perturbation does not interfere with the learning of the other type (Krakauer et al., 1999). Furthermore, different brain areas are associated with adaptation to visuomotor and force field perturbations (Rabe et al., 2009; Donchin et al., 2012). Thus, it is not enough to obtain inferences about internal representations in the sensorimotor system from only one of these adaptation paradigms; rather, the integration from both provides a more thorough picture (Krakauer et al., 1999). In this thesis, to comprehensively examine delay representation in the sensorimotor system, protocols that embrace both the dynamic and kinematic approaches were designed. To characterize the changes in internal representations of both dynamic and kinematic perturbations, studies have examined how adaptation is transferred to a different context (Shadmehr and Mussa-Ivaldi, 1994; Krakauer et al., 2000). One highly productive approach is to test how motor performance changes as a result of adaptation in a context where the perturbation is not present. In the case of adaptation to force fields, presenting participants with virtual force channels that constrain their movements to a straight line can be used to measure the forces they apply on the channel walls to counteract just presented force perturbations 7

14 (Scheidt et al., 2000), and decompose these forces into state-based components of different weights (Sing et al., 2009). For visuomotor perturbations, omitting the visual feedback can be used to examine how feedforward mechanisms are influenced by the adaptation of the new mapping between the motor command and the resulting feedback (Pressman, 2012; Botzer and Karniel, 2013). Here we adopted the use of such transfer paradigms to reveal how the sensorimotor system constructs representations of delayed feedback. 1.3 Effects of the schedule and magnitude of the presented delay perturbations An adapted perturbation may be represented differently depending on its schedule of presentation and its magnitude. Studies have shown that the transfer of adaptation is stronger when the perturbation is presented gradually rather than abruptly (Kluzik et al., 2008; Torres- Oviedo and Bastian, 2012). One possible explanation for this difference is that participants are more aware of the perturbation when it is presented abruptly (Baraduc and Wolpert, 2002; Kluzik et al., 2008) since the magnitude of the experienced error is larger than when it is presented gradually (Criscimagna-Hemminger et al., 2010; Gibo et al., 2013; Patrick et al., 2014), and therefore they assign the change to the environment rather than to their own body (Berniker and Kording, 2008). Thus, abrupt/large perturbations may result in a different representation of external delayed feedback than gradual/small perturbations. Alternatively, since the sensorimotor system deals constantly with inherent delays, and unlike current state-based perturbations, animals do not naturally experience external delayed feedback, participants may assign the change to their body regardless of the schedule or magnitude of the perturbation. 1.4 Organization of this Thesis This goal of this thesis is to study representation in humans of both delayed force and visual feedback during performance of a motor task. It examines how people represent delayed feedback by formulating predictions using computational models of different representations, and compares them to the participants performance in the experiments. 8

15 Chapter 2 investigates the representation of delayed force feedback. Participants adapted to force perturbations that depended on either the current or the delayed (70 or 100 ms) velocity of the hand while performing reaching movements. Using force-channel trials, we measured the forces participants applied to cope with the perturbations. We found that the delayed forces are counteracted by forces that can be reconstructed according to the information of the current position, velocity and the delayed velocity; we also documented the evolution of this information with repeated exposure to the perturbations; in addition, we revealed similar force patterns when participants performed faster movements following adaptation. These results suggest a representation of the delayed force feedback as a combination of current and delayed states. Chapter 3 studies the representation of visuomotor delay. Participants adapted to a delay of up to 100 ms between their hand and the paddle while playing in an ecological motor task a virtual game of pong. We examined the way they represented the delayed feedback using transfer to simpler tasks blind reaching and tracking. Following adaptation to delay, participants made longer movements in these transfer tasks. Comparing these results to simulations of different representation models revealed an internal representation of the visuomotor delay as a mechanical system equivalent, rather than as an actual time lag. Additionally, similar transfer results were observed when the delay was introduced abruptly or gradually, suggesting that the schedule of the delay presentation does not influence the representation. Chapter 4 examines the state-based representation of visuomotor delay in depth. The study tested the effects of playing pong in the presence of up to 300 ms delays which were either presented gradually or abruptly, on movement kinematics during the game, and on performance in the blind reaching task that was presented in different stages of the game. The results showed that the delays caused an increase in movement amplitude and duration during the game, and that the hypermetria transferred to the blind reaching task as of the early stages of exposure to delay. Furthermore, participants performance in the game deteriorated with increased delays. These results further strengthens the conclusion that the brain does not represent the correct temporal dynamics between the hand and the delayed paddle but rather approximate it using current state information. Also, by providing an extensive exploration of various effects of delay 9

16 on interception kinematics in the game, this chapter opens a variety of questions to explore in future studies. In Chapter 5 we conclude the thesis with a general discussion. We formulate questions about delay representation in the sensorimotor system and answer them in light of our findings. We conclude that humans can adapt to external delayed feedback, but the sensorimotor system cannot represent it correctly. We also suggest reasons for the presence of delayed state information in the representation of the delayed force but not in the delayed visual feedback. In addition, we propose conjectures regarding to the learning process that drives adaptation to delayed feedback and where it is represented in the brain. Lastly, we discuss the relation between representations of delayed state and time in the sensorimotor system. 10

17 Chapter 2: Ghosts from the Past and the Present Representing Delayed Force Feedback as a Combination of Delayed and Current States Submitted for publication Avraham G 1,2, Mawase F 3, Karniel A 1,2, Shmuelof L 4,2, Donchin O 1,2, Mussa-Ivaldi FA 5,6,7 and Nisky I 1,2 1. Department of Biomedical Engineering, Ben-Gurion University of the Negev, Beer-Sheva, Israel. 2. Zlotowski Center for Neuroscience, Ben-Gurion University of the Negev, Be'er Sheva, Israel 3. Department of Physical Medicine and Rehabilitation, Johns Hopkins School of Medicine, Baltimore, MD, USA. 4. Department of Brain and Cognitive Sciences, Ben-Gurion University of the Negev, Beer-Sheva, Israel. 5. Northwestern University and Rehabilitation Institute of Chicago, Chicago, IL, USA 6. Department of Biomedical Engineering, Northwestern University, Evanston, IL, USA 7. Sensory Motor Performance Program, Rehabilitation Institute of Chicago, Chicago, IL, USA Keywords: adaptation, delay, force field, motor primitives, reaching Acknowledgments: The authors wish to thank Amit Milstein and Chen Avraham for the assistance in data collection. The study is supported by the Binational United-States Israel Science Foundation (grant no ), by the Israeli Science Foundation (grant 823/15), and by the Helmsley Charitable Trust through the Agricultural, Biological and Cognitive Robotics Initiative of Ben-Gurion University of the Negev, Israel. GA was supported by the Negev Fellowship. The authors declare no competing financial interests. Contribution: G.A, F.M., A.K., L.S., F.A.M.I. and I.N designed the study. G.A. and F.M. performed the experiments. G.A. analyzed the data. G.A., F.M., L.S., O.D, F.A.M.I. and I.N. interpreted the results and wrote the paper. 11

18 Abstract To adapt to deterministic force perturbations that depend on the current state of the hand, we build internal representations of the relations between the experienced forces and our motions. However, information from multiple modalities travels with different rates, resulting in intermodal delays that require compensation to develop the internal representations. To understand how these delays are represented by the brain, we presented participants with delayed velocity-dependent force fields forces that depend on hand velocity either 70 or 100 ms beforehand. We found that for both delayed forces, the best model of the internal representation consists of a delayed velocity and current position and velocity. We show that participants rely initially on the current state, and with adaptation, the contribution of the delayed representation to adaptation increases. When the participants were asked to make faster movements following adaptation, they applied forces that were consistent with current position and velocity as well as delayed velocity representations. This suggests that delayed force feedback is represented by the sensorimotor system using current and delayed state primitives. This representation can be further used in generalization to a higher velocity, for which the delayed force field was never experienced. 2.1 Introduction To effectively move, the brain must compensate for the ongoing kinematic and dynamic changes in the environment and in body state, which are transmitted as afferent signals that propagate through the sensory system. It is widely accepted that to do so, we construct and exploit internal models neural structures that hold a causal link between the motor commands and the state of the body and the forces that are acting on it (Shadmehr and Mussa-Ivaldi, 1994; Wolpert et al., 1995; Kawato, 1999; Wolpert and Ghahramani, 2000; Shadmehr and Krakauer, 2008; Karniel, 2011). In a well-established experimental paradigm, participants make point-to-point reaching movements in the presence of perturbations that include either an altered visual feedback or the application of external forces that depend linearly on movement variables, such as position and velocity (Shadmehr and Mussa-Ivaldi, 1994; Tong et al., 2002). By updating the internal models 12

19 parameters, our sensorimotor system is able to adapt to such novel environments (Karniel, 2011). For example, it was suggested that participants cope with state-dependent force perturbations by adjusting combinations of movement primitives, where each primitive (position, velocity, etc.) produces a force that is linearly related to the respective state. For example, a position primitive is a force that is linearly related to the current hand position. The adjustment of such primitive combinations attempt to increase the weight of the primitive on which the perturbing force depends while decreasing the weights of the others (Shadmehr and Mussa-Ivaldi, 1994; Thoroughman and Shadmehr, 2000; Sing et al., 2009; Yousif and Diedrichsen, 2012). However, signals from different modalities are transmitted at different rates across the nervous system (Murray and Wallace, 2011), and thus, the information that is available for constructing internal models entails delays between the signals. This raises the question how internal models are formed in light of these delays; namely, how the brain represents delayed feedback. Recent studies demonstrated that when sensory feedback is delayed, perception of impedance (Pressman et al., 2007; Nisky et al., 2008; Nisky et al., 2010; Di Luca et al., 2011; Leib et al., 2015; Leib et al., 2016) and object dynamics (Sarlegna et al., 2010; Honda et al., 2013; Takamuku and Gomi, 2015) are biased. In addition, a delay in the visual feedback of a virtual object affects proprioceptive state representation (Mussa-Ivaldi et al., 2010; Pressman, 2012) and interferes with adaptation to space-based visuomotor perturbations (Held et al., 1966; Honda et al., 2012). On the other hand, it was demonstrated that participants can adapt to delayed velocitydependent force perturbations, in which the force depends linearly on the hand velocity a certain time beforehand (Levy et al., 2010). Furthermore, in this experiment, after the delayed force was suddenly removed, participants exhibited aftereffects that were shifted in time compared to those after the non-delayed perturbations, suggesting that perhaps some representation of the delay was used. Here, we explore how the brain represents delayed force feedback. We study adaptation to delayed velocity-dependent force perturbations, compare the effectiveness of different candidate representations in accounting for the observed compensations for the delayed forces, 13

20 and examine the dynamics of the formation of these representations and their aftereffects. We asked healthy participants to perform point-to-point reaching movements, and applied forces that were either non-delayed or delayed with respect to movement velocity (Fig. 2.1a). We examined participants internal representations of each type of perturbation by measuring forces they applied in Force Channel trials trials in which a lateral force was applied on participants hand that was equal and opposite to the force applied by the participant that were randomly presented throughout the experiment (Scheidt et al., 2000). Based on previous studies (Sing et al., 2009; Yousif and Diedrichsen, 2012), we expected that in the non-delayed case, participants would represent the perturbation as a combination of position and velocity primitives, with a higher weight to the velocity primitive (Fig. 2.1b). For the delayed case, we entertained two competing hypotheses: if participants have access to a representation of delayed velocity, they would learn to use it to predict the force (Fig. 2.1c, left panel). Alternatively, if such a delayed velocity representation is not available, they would build a prediction based on current state, possibly trying to approximate the delay as a combination of current state variables (Fig. 2.1c, right panel). Such a state-based representation is expected to allow for a successful coping with small delays (relative to the movement duration), but may deteriorate for increasing magnitude of delay. Surprisingly, we found that throughout adaptation to both 70 and 100 ms delayed velocitydependent force perturbations, participants build a representation that is based on the delayed velocity together with the current position and velocity information. With the higher delay, the temporal separation between the constructing delayed and current velocity profiles is higher. Also, adaptation to the delayed force is generalized to faster movements for which the delayed force field was never experienced, and the forces participants exhibit during the faster movements are also consistent with a combined representation of current and delayed velocity. 2.2 Methods Notations 14

21 Delay Representation in the Sensorimotor System We use lower-case letters for scalars, lower-case bold letters for vectors, and upper-case bold letters for matrices. Upper-case non-bold letters indicate the dimensions of vectors/matrices of sampled data points and of vectors/matrices that were calculated from sampled data points. The letter n specifies trial index. Lower-case Greek letters indicate regression coefficients. x is the Cartesian space position vector, with x and y position coordinates (for the right-left and forward-backward directions, respectively). N indicates the number of participants in a group. Figure 2.1. Models of force representation. (a) Schematic illustration of the force applied by the haptic device during Adaptation in the non-delayed (blue) and delayed (beige) conditions, using the same representative velocity profile (dotted grey) in both conditions. (b) The representation of non-delayed force (solid dark blue) is modelled as a combination of position (dotted orange) and velocity (dotted green). (c) Possible representations of delayed force (solid brown): left panel based on representation of position and delayed velocity (dotted dark blue), right panel based only on current state position, velocity and acceleration (dotted purple). 15

22 2.2.2 Participants and experimental setup Thirty eight healthy volunteers (ages [18-29], twenty females) participated in two experiments: thirty participated in Experiment 1 and eight in Experiment 2. No statistical methods were used to predetermine sample sizes, but the minimum sample size per condition that we used was the same as the test group in a previous study (Levy et al., 2010), and the effects in our study were expected to be of similar size. Both experiments were conducted after the participants signed the informed consent form as stipulated by the Institutional Helsinki Committee (Experiment 1) or by the Human Subjects Research Committee (Experiment 2) of Ben-Gurion University of the Negev, Be'er-Sheva, Israel. The experiments were administered in a virtual reality environment in which the participants controlled the stylus of a six degrees-of-freedom PHANTOM Premium TM 1.5 haptic device (Geomagic ). Seated participants held the handle of the haptic device with their right hand while looking at a screen that was placed transversely above their hand (Fig. 2.2a), and with a distance of ~10 cm from participants chin. The hand was hidden from sight by the screen, and a sheet covered the upper body of the participants. The movement of the haptic device was mapped to the movement of a cursor that indicated the participants hand location. Participants were instructed to make point-to-point reaching movements in a transverse plane. Hand position was maintained in the transverse plane by forces generated by the robot that resisted any vertical movement. These forces were implemented by applying a one-dimensional spring ( 500 ) and a damper ( 5 ) above and below the plane. The update rate of the control loop was 1,000 Hz Task Ns m A trial was initiated when the participants placed a yellow cursor, 1.6 cm diameter, inside a white circle, 2.6 cm diameter, which is defined as the start area. The cursor center position inside the white circle specified the movement initial position. Participants were required to keep the cursor within the start area for 1.5 s. When they did, a red target, also 2.6 cm diameter, appeared on the screen at a distance of 10 cm away from the center of the start area along the sagittal axis, instructing the participants to perform a fast reaching movement and to stop when they saw the N m 16

23 cursor reach the target. The target location was constant throughout the entire experiment, and across participants. The start area, the cursor, and the target were all displayed during the entire movement (Fig. 2.2a). Target reach time was defined to be the moment when the center of the cursor was within the target. Movements could be completed if the cursor reached the target or passed the target s y position. If movements were not completed within 700 ms, they were considered completed at that time. After the movement was completed, the target disappeared and participants were asked to return to the start area and to prepare for the appearance of the next target. 17

24 Figure 2.2. Experiment 1: experimental setup and protocol (a) An illustration of the experiment task: participants sat and held the handle of a Phantom Premium 1.5 haptic device (Geomagic ). A screen that was placed transversely covered the hand and displayed the task scene. Participants controlled the movement of a cursor (yellow dot) and performed reaching movements from a start location (white dot) to the target (red dot). Drawing by Raz Leib. (b) Schematic display of the experimental protocol: the experiment was composed of three sessions during the Baseline session (100 trials), no perturbation was applied; during the Adaptation session (200 trials), reaching movements were perturbed with a velocity-dependent force field; and during the Washout session (100 trials), the perturbations were removed. Green bars represent Force Channel trials that appeared pseudo-randomly in ~11 percent of the trials. Three groups of participants performed the experiment, each experienced different perturbations throughout the Adaptation session: movements of Group ND participants were perturbed with a non-delayed velocity-dependent force field (blue bar), and movements of Group D70 and Group D100 participants were perturbed with a 70 ms (yellow bar) and 100 ms (red bar) delayed velocity-dependent force field, respectively. (c) During Force Channel trials, high-stiffness forces were applied by the haptic device that constrained the hand to move in a straight path, enabling to measure the lateral forces applied by the participants. Following completion of each reaching movement, participants were provided with an on-screen text as feedback based on movement duration and accuracy. The purpose of this feedback was to equalize as much as possible movements durations and velocities within and between participants and to make the trajectories and the applied forces consistent and suitable for averaging across trials and participants within a group. In Experiment 1, we set a single range of movement duration between ms. In Experiment 2, the feedback about the movement duration served an additional purpose: it enabled to train participants to move at different velocities and to test generalization of adaptation to the applied perturbation from slow to fast movements. We defined two trial types in Experiment 2: Slow and Fast. We set the ranges of movement duration for the Slow and the Fast types to be ms and ms, respectively. To inform participants about the required movement duration in each trial, we set a different display background color for each type (Slow cyan, Fast purple), and instructed them before the experiment to move accordingly with the displayed color. In both Experiment 1 and Experiment 2, for movements where the cursor reached the target within the trial duration range, the word "Exact" was displayed. If participants passed the target s y position during this range, they were requested to Stop on The Target. For movements where participants did not reach the target by the maximum set duration, the words "Move Faster" were displayed. For 18

25 movements where participants reached the target in less than the minimum set duration, the words "Move Slower" were displayed Protocol Experiment 1 The experiment consisted of three sessions: Baseline, Adaptation, and Washout (Fig. 2.2b). In the Baseline session (100 trials), no perturbation was applied on the hand of the participant. In the Adaptation session (200 trials), the participant experienced a velocity-dependent force field in which a force was applied in the rightward direction with a magnitude linearly related to the forward-backward velocity. The Washout session (100 trials) was similar to the Baseline session and was without perturbations. Forty five (~11%) trials (five trials during Baseline, twenty five during Adaptation, and fifteen during Washout) were Force Channel trials. Force channel trials were similar to other trials in the sense that the participants did not receive different instructions; however, in these trials, the haptic device constrained participants movement by enclosing the straight path between the center of the cursor at trial initiation and the end location within highstiffness virtual walls (Scheidt et al., 2000; Gibo et al., 2014) (Fig. 2.2c). The virtual walls were implemented by applying a one-dimensional spring ( 500 ) and a damper ( 5 Ns m ) around the channel. Although we could not achieve a perfect straight path in Force Channel trials, maximum perpendicular displacement from a straight line to the target was held smaller than 0.77 cm and averaged 0.10 cm in magnitude (considering all the Force Channel trials in the experiment). The virtual walls served the dual purpose to prevent lateral motions and to measure lateral forces that the participant applied during the reach. We refer to these forces as the actual forces. The rationale of this paradigm is that if participants have an internal model of the perturbing forces and a representation of the forces that they have to apply to be able to reach the target properly, and if this internal model was adapted to the new environment containing a lateral force perturbation, it would be reflected in the forces that they apply on the Force Channel as a mirrored profile of the perturbation s representation (Scheidt et al., 2000; Joiner and Smith, 2008; Castro et al., 2014). The Force Channel trials were presented in a pseudo-random and predetermined order that was identical across participants in all three groups. 19 N m

26 The participants were assigned randomly to three groups: Group ND ( N 10 ), Group D70 ( N 10 ) or Group D100 ( N 10 ). The groups were different from each other in the forces that the participants experienced during the Adaptation session (Fig. 2.2b). Group ND adapted to a non-delayed force field, in which the applied force perturbation, f NoDelay (t), was temporally aligned with their hand velocity, x(t) : NoDelay (2.1) f ( t) B x ( t), Pert where B Pert 0 0 b Pert ; b Nms Pert 60 cm 0, and since movements are executed in a twodimensional plane x, y, NoDelay f ( t) NoDelay x x ( t) f ( t) and x ( t). Group D70 and Group D100 NoDelay f y ( t) y ( t) adapted to a delayed force field, in which the applied force perturbation, f Delay70 ( t ) in Group D70 and f Delay100 ( t ) in Group D100, was proportional to the movement velocity either 70 or 100 ms before time t, respectively: Delay (2.2) f ( t) B x ( t ), Delay 70 Delay where for Group D70, 70 ms and f ( t) f ( t), and for Group D100, 100 ms and Pert Delay100 Delay f ( t) f ( t). Similarly to the non-delayed case, x ( t ) x ( t ). y ( t ) Delay f ( t) Delay x f ( t) and Delay f y ( t) Due to the update rate of the control loop (1,000 Hz), during the non-delayed case, there was a delay of 1 ms in the force feedback. The experimentally manipulated delay in the delay conditions was added on top of this delay Experiment 2 One group of volunteers, Group D70_SF ( N 8 ), participated in Experiment 2. The experiment consisted of three sessions: Baseline, Adaptation, and Washout (Fig. 2.8a). In the Baseline session 20

27 (100 trials), no perturbation was applied on the hand of the participant. The Baseline session started with twenty Slow type trials, followed by twenty Fast type trials. In the remaining sixty trials of the session, the Slow and Fast types were presented in a pseudo-random and predetermined order that was identical across the participants. In the Adaptation session (200 trials), the participant experienced a 70 ms delayed velocity-dependent force field ( f ( ) Delay70 t the right direction. All the trials in the Adaptation session were of a Slow type. Twenty-nine trials (~10% of the total trial number of both Baseline and Adaptation sessions: four during Baseline and twenty-five during Adaptation) were Force Channel trials, all of them of a Slow type. To examine generalization of adaptation to the delayed force perturbation from slow to fast movements, the Washout session (100) was consisted of only Force Channel trials of both Slow and Fast type trials (Joiner et al., 2011). The Slow and Fast trials were evenly split in each set of ten consecutive Washout trials, and were presented in a pseudo-random and predetermined order that was identical across the participants Data collection and analysis Haptic device position, velocity, and the forces applied were recorded throughout the experiment and were sampled at 200 Hz. They were analyzed off-line using custom-written MATLAB code (The MathWorks, Inc., Natick, MA, USA). To calculate acceleration, the velocity was numerically differentiated and filtered using the Matlab function filtfilt() with a 2 nd order low-pass Butterworth filter with a cutoff frequency of 10Hz. For the purposes of data analysis, we defined movement onset and movement end time at the first time the velocity rose above and decreased below five percent of its maximum value, respectively. We included in the analysis the data from 100 ms before movement onset to 200 ms after movement end time Adaptation analysis To assess adaptation, we calculated the positional deviation from all the trials that are not Force Channel trials and the adaptation coefficient at Force Channel trials succeeding Force Field trials. We calculated the positional deviation as the maximum lateral displacement (perpendicular to movement direction). A positional deviation to the right is defined positive and a positional ) in 21

28 deviation to the left is defined negative. A large positional deviation indicates that the movement is not straight. We calculated the adaptation coefficient,, as the slope of the linear regression between the actual force that the participants applied during a Force Channel trial n, f ( n) Actual, and the perturbation force during the preceding Force Field trial velocity profile (Eqs. 2.1 and 2.2): n 1, f ( n1) Perturb, as calculated from the ( n) ( n1) (2.3) f f ε. Actual Perturb Both f ( n) Actual and f ( n1) Perturb are N s 1 column vectors for N s sampled data points. is the intercept of the regression line and ε is the residual error, minimized by the regression procedure. The rationale for using this metric is that since reduction in the positional deviation throughout adaptation to a lateral force field can be achieved by various strategies (for example, by increasing arm stiffness), it does not necessarily imply the existence of an internal representation of the perturbation. Instead, the adaptation coefficient indicates that a representation is likely formed when there is an increasing correlation between the actual forces and the perturbing forces. According to this view, during early stages of adaptation, before an internal representation of the force field is formed, the correlation between the perturbation and the actual force participants apply on the Force Channel would be low (adaptation coefficient close to zero). As participants adapt and improve their compensation for the perturbation, the adaptation coefficient approaches a value of one (Smith et al., 2006) Representation analysis Local peaks of actual forces To analyze quantitatively the shape of the actual forces following adaptation to the different force perturbations, we calculated probability histogram of number of force peaks (local maxima) in a single trial. In addition, we calculated probability histograms of the timing of the local actual forces peaks within the movement. We first filtered the actual forces, from each of the analyzed Force Channel trial, with a 2 nd order low-pass Butterworth zero-lag filter with a cutoff frequency of 10Hz implemented with the Matlab function filtfilt(). We extracted the number of peaks, their 22

29 values, and their times within the movement from each of the filtered actual forces profiles using the Matlab function findpeaks(). To exclude peaks that are not related to the representation of the perturbations, and that likely to result from non-specific force fluctuations, we calculated for each participant the mean of the maximum applied forces from the Force Channel trials of the Baseline session and set it as the minimum height of a peak (see for example the inset in Fig. 2.4d). We calculated probability histograms of number of force peaks in a single trial according to: j Nt P( j) ; j 1,2,3,4,5, where N N t j N t is the number of trials in which j peaks were detected (five was the maximum number of peaks in all the trials that were analyzed), N is the number of participants in a group, and N t is the number of the trials per participant that were analyzed. In the end of the Adaptation session (in both Experiment 1 and Experiment 2), N 10. In the early Washout session in Experiment 2, N 5 for each of the Slow and Fast types. t To calculate the probability histograms of the timing of the local actual forces peaks within the movement, we segmented each actual force trajectory into bins of 25 ms each. For each bin, we calculated the probability as the number of peaks that were found in that bin across trajectories and participants, and divided it by the total number of peaks found for all the trajectories and participants in the group Primitives We follow the assumption that the internal representation of the environment forces during a t single movement, f ( t), is constructed from a linear combination of Rep p ( t), and that each primitive corresponds to a specific state variable: i L movement primitives (2.4) f Rep ( t) Cipi ( t). L i1 23

30 For movements executed in a two-dimensional plane x, y, the vectors f Rep ( t) x f Rep ( t) and f Rep ( t) y pi ( t) x p i ( t) are the represented forces and primitive profiles in both movement directions. p ( t) i y The matrix cxx cxy C defines the gains of each primitive that contributes to the c c yx yy representation of the force in each dimension (first subscript component) and for each dimensional component of the movement (second subscript component). For example, representation of non-delayed velocity-dependent force field was suggested to be constructed from a linear combination of position and velocity primitives (Sing et al., 2009), and accordingly, we can formulate such a representation as follows: (2.5) f ( t) K x( t) B x ( t), Rep where K and B are the gain matrices of the position and velocity primitives, respectively. Since in our experimental design, the participants are required to move in the y direction and the perturbation is applied in the x direction, for each primitive, we chose to estimate only the gain component c xy associated with the respective movement and force dimensions. To simplify notations, we designate this gain component as c in the general case. Thus, the internal representation of the forces in the x direction, f Rep ( t), can be described as follows: x (2.6) f Rep ( t) ci pi ( t), y x L i1 Where i (t) indicates the p y y direction trajectory of the i th primitive. Here, we examine the possible contribution of four types of primitives to the representation: position ( y (t) ), velocity ( y (t) ), delayed velocity ( y ( t ) ) and acceleration ( y(t ) ), and we designate their gains as k, b, b and m, respectively. 24

31 The actual lateral force that the participants apply during a Force Channel trial, f Actual, is a proxy for the representation of the forces in the environment, f Rep ( t) (Sing et al., 2009; Sing et al., 2013). Therefore, to test the predictions in Fig. 2.1, and to assess which motor primitives participants use to represent the experienced force perturbation in Experiment 1, we used a repeated-measures linear regression analysis. We fitted a repeated-measures linear regression model between the forces that were applied by the participants during a Force Channel trial n of N s sampled data points, f ( n) Actual x ( N 1), and various combinations of motor primitives s position, velocity, delayed velocity, and acceleration from the preceding Force Field trial n 1. We chose to fit the model using the primitives of the preceding movements because movement kinematics were slightly influenced by the force channel. Specifically, we found that the velocity trajectory during Force Channel trials are slightly skewed towards the beginning of the movement, possibly due to an effect of a feedback component. Therefore, to reduce as much as possible such distortions in the trajectories that may be a result of an online control mechanism, we chose to use the primitives from the preceding Force Field trial for the regression. Each of the representation models tested is defined as a specific weighted linear combination of the columns of the movement primitives matrix movement primitives in a model). Each of the columns of ( n1) P with dimensions N s L (where L is the number of ( n1) P is one primitive variable (position y ( n1) ( 1) y, velocity n, delayed velocity ( 1) y and acceleration n ), constructed from the ( n 1) y trajectories of the trials that precede each of the Force Channel trials. The weights are determined by an gains designated as, L 1 gains vector γ,, and, which consists of a combination of one or more of the associated with each primitive in the model. For example, for a model consisting of only the position and velocity primitives, ( n1) P is the N s 2 ( 1) ( 1) matrix [ y n y n ] and the corresponding γ is a 2 1 vector [ ]. For each representation model, the resulting force representation estimation in trial n, a N 1 ˆ n Rep ( ) column vector f, (Representation Model profiles in Fig. 2.5), was calculated as: s 25

32 (2.7) fˆ ( n ) ( n ) P 1 γ Rep The primitives matrix ( n1) P in the regression analysis described in Equation 2.7 may consist of different types of state variables (position, velocity and acceleration), each have specific units that are also different from the force units. As a result, the gains in γ have non-comparable units. Thus, to assess the weighted contribution of each primitive in a representation model, we calculated normalized gains: (2.8) g ; g ; g ; qp qv qv g q a where g, g, g and g are the normalized gains of the position, velocity, delayed velocity and acceleration primitives, respectively. The normalizing factors q p, q v and q a were chosen to equate peak perturbing forces between force fields that depends linearly on a single state variable (Sing et al., 2009). qv 60 was chosen to be equal to the damping constant Nms cm b Pert (Eq. 2.1,2.2) for all groups. To determine the other normalizing factors, for each group, we estimated the mean maximum velocity of all participants during Force Field trials (Group ND: v cm v cm, Group D70: max ms ms, Group D100: max v max cm ) and ms approximated a mean maximum velocity-dependent perturbation force (Group ND: f bpert v 3. 8 N max, Group D70: fmax 3. 2 N, Group D100: fmax 2. 6 N ). Since max participants were required to move a pmax 10 cm distance (see Protocol), equivalent positiondependent force fields that produce the above peak forces would have an elasticity constant f k max Pert. Accordingly, we set N p cm pmax q for Group ND, q N cm for Group D70 p and q for Group D100. Similarly, accordingly with the mean maximum acceleration p N cm 4 (Group ND: a.81 cm 4 2, Group D70: a.70 cm 2, Group D100: a 4 max cm 2 ms max 6 10 ms max 4 10 ms ) as was estimated from the acceleration traces, to produce the same amount of maximum force, an equivalent acceleration-dependent force field would have a mass 26

33 f max 3 2 mpert. Accordingly, we set q N ms cm a a max 3 2 for Group ND, Nms cm for q a Group D70 and q a Nms cm for Group D100 (Sing et al., 2013). The specific combinations of primitives that we considered as models for the representation of the perturbing force field in each of the groups ND, D70 and D100 are specified in Table 2.1. For the models that included a delayed velocity primitive, for model simplicity, we set the value of the delay to be consistent with the delay in the perturbing force, 70 ms in Group D70 and 100 ms in Group D100 (but see Discussion). The duration and time course of the movement trajectories were roughly similar within and between participants in each group, and therefore, no manipulation (such as time scaling) on the data was necessary to make the force profiles and the primitives consistent and suitable for averaging across trials and participants within a group. To determine the lower cutoff of the duration of the trials that were used for the analysis (Force Channel trials and each of the preceding Force Field trials), we calculated the tenth percentile of the trial durations for each group (ND: 545 ms, D70: 585 ms, and D100: 620 ms). Trial pairs (Successive Force Field and Force Channel trials) in which at least one trial was completed faster were removed from the analysis (15.8% of trial pairs from the overall of all three groups). To equalize the duration of the displayed profiles between the groups (Fig. 2.4 and 2.5), we used the minimum cut off duration of the three groups (545 ms). We used the Bayesian Information Criterion ( BIC ) (Schwarz, 1978) to compare between the different representation models based on their goodness-of-fit and parsimony: (2.9) BIC d ln( T) 2 LogL Where d is the number of predictors associated with the linear regression for each representation model, T is the number of observations, and LogL is the logarithm of the optimal likelihood for the regression model (a smaller value of BIC indicates a better model). The comparison between the representation models was performed separately for each group. 27

34 We first performed this analysis on the last ten pairs of successive Force Field and Force Channel trials in the Adaptation session, all pooled into a single regression model. We ran the analysis on the entire data from these trials, putting together the actual forces and primitives from each pair in the same regression model and extracting the goodness of fit ( and D100 during the end of the Adaptation. We calculated the regression again, this time separately for each participant for each of the last ten Force Field - Force Channel trials pair in the Adaptation. We then averaged the resulting normalized gains from these trials for each participant Statistical analysis Statistical analysis was performed using custom written Matlab functions, Matlab Statistics Toolbox, and IBM SPSS. 28 R 2 ) and a single BIC value for each model (Table 2.1). Then, to examine the trial-to-trial dynamics of the different primitives normalized gains throughout the experiment, for the best models in each of the groups, we recalculated the regression separately for each Force Field - Force Channel trials pair in the experiment. For the latter analysis, we eliminated trials in which we identified high multicollinearity between the primitives. Multicollinearity in a regression analysis occurs when there is a high correlation between predictors in the model, which limits our capability to draw conclusions about the contribution of each predictor in accounting for the variance. To evaluate multicollinearity, we calculated for each participant and for each Force Field - Force Channel trials pair the variance inflation factor (VIF) of the model primitives. Trial pairs in which the VIF was greater than 10 were removed from the analysis (Myers, 1990) (3.9% of trial pairs from the overall of all three groups). Importantly, these trials were removed only for the presentation of the trial-to-trial dynamics of the different primitives normalized gains, and therefore, all the conclusions that were drawn about the fit of the different representation models are valid also without the elimination of these trials. We then compared between the normalized gain of the velocity primitive ( g ) from the position velocity representation model in Group ND and the normalized gains of the delayed velocity primitive ( g ) from the position velocity delayed velocity representation model in Groups D70

35 We used Lilliefors test to determine whether our measurements are normally distributed (Lilliefors, 1967). In repeated-measures ANOVA models, we used Mauchly s test to examine whether the assumption of sphericity is met. When it did not, F-test degrees of freedom were corrected using Greenhouse-Geisser adjustment for violation of sphericity. We denote the p values that were calculated using these adjusted degrees of freedom as p. For the factors that were statistically significant, we performed planned comparisons, and corrected for familywise error using Bonfferoni correction. We denote the Bonfferoni-corrected p values as For adaptation analysis, we first examined whether there are differences in the positional deviation between different stages of the experiment. We evaluated for each participant the mean positional deviation of four Force Field trials at the following stages of the experiment: Late Baseline, Early Adaptation, Late Adaptation and Early Washout. We fit a two-way mixed effects ANOVA model, with the mean positional deviation as the dependent variable, one between participants independent factor (Group: 3 levels ND, D70 and D100), and one within participants independent factor (Stage: 4 levels Late Baseline, Early Adaptation, Late Adaptation and Early Washout). Mauchly s test indicated a violation of the assumption of sphericity for the statistical analysis on the mean positional deviation in Experiment 1 ( 2 (5) , p ), and thus, we applied the Greenhouse-Geisser correction factor ( ˆ 0.466) to the degrees of freedom of the main effect of experiment Stage and to the Group- Stage interaction effect. To analyze adaptation according to positional deviation in Group D70_SF (Experiment 2), we fit a one-way repeated-measures ANOVA model, with the mean positional deviation as the dependent variable and one within subjects independent factor (Stage: 3 levels Late Baseline, Early Adaptation and Late Adaptation). Mauchly s test indicated a violation of the assumption of sphericity ( 2 (2) , p ), and thus, we applied the Greenhouse-Geisser correction factor ( ˆ ) to the degrees of freedom of the main effect of experiment Stage. The second analysis of adaptation was done to test for an increase in the adaptation coefficient between early and late stages of Adaptation. We first computed for each participant the p B. 29

36 adaptation coefficient (Equation 3) for each of the Force Channel preceding Force Field trial pairs in the Adaptation session, and averaged these values separately for the first (Early Adaptation) and the last (Late Adaptation) five trials of adaptation. Following a Lilliefors test for normality, we fit a two-way mixed effect ANOVA model, with as the dependent variable, one between participants independent factor (Group: 3 levels ND, D70 and D100), and one within subjects independent factor (Stage: 2 levels Early Adaptation and Late Adaptation). For Group D70_SF, we used a two-tailed paired-samples t-test to compare between the mean adaptation coefficient during Early Adaptation and Late Adaptation stages. To compare between the normalized gain of the velocity primitive ( g ) from the position velocity representation model in Group ND and the normalized gain of the delayed velocity primitive ( g ) from the position velocity delayed velocity representation model in Group D70 and Group D100 during the end of the Adaptation, we fit a one-way ANOVA model, with the respective normalized gain as the dependent variable, and the Group as the independent factor (3 levels ND, D70 and D100). To compare the mean maximum velocity of the movements in Force Channel trials during the Late Adaptation stage between Group D70 and Group D70_SF, we used a two-tailed independent-samples t-test. Throughout the paper, statistical significance was determined at the p 0.05 threshold. 2.3 Results Experiment 1 In Experiment 1, participants performed fast reaching movements from an initial location to a target presented in front of them while holding a haptic device that recorded their movements and applied forces that depended on the state of their hand (Fig. 2.2a). After a Baseline session, during which they moved with no external force perturbing their hand, we introduced an 30

37 Adaptation session in which a velocity-dependent force field was presented, and persisted throughout the entire session. During Washout, the perturbation was removed and the environment was as in Baseline (Fig. 2.2b) Participants adapted to both non-delayed and delayed velocity-dependent force perturbations by constructing an internal representation of the environment dynamics Figure 2.3 summarizes the analysis of adaptation for Group ND (blue), Group D70 (yellow) and Group D100 (red). Figure 2.3a presents the mean positional deviation of all trials that are not Force Channel trials (the latter are indicated by the green bars) for each of the three groups. The positional deviation is defined as the maximum lateral displacement (perpendicular to movement direction), with positive and negative signs for displacements to the right and left, respectively. Individual movements from non-force Channel trials of a single participant from each group are presented in the insets of Figure 2.3a at locations that correspond to the experimental stage in which they were taken from. In the last trial of the Baseline session Late Baseline participants movements were similar to a straight line. In the first trial of the Adaptation session Early Adaptation the movements were disturbed by a velocity-dependent force to the right, resulting in a deviation from the straight line in a direction corresponding to the direction of the perturbation. In the last trial of the Adaptation session Late Adaptation participants recover the straight paths they exhibited during Baseline. Finally, during the first trial of the Washout session, immediately after the removal of the perturbations Early Washout participants from all groups exhibit an aftereffect, meaning a deviation from the straight line, in the opposite direction to the force field that was applied. These qualitative observations are also supported by a statistical analysis of the mean positional deviation from four trials during each of the four experimental stages mentioned above (Fig. 2.3c). For all three groups, the mean positional deviation significantly change throughout the these stage (main effect of Stage: F , p ). It greatly increases from Late ( 1.398,37.747) Baseline to Early Adaptation as a result from the initial exposure to the perturbation ( p B ), and as participants adapt, the mean positional deviation show a decreased and declined closer to zero during Late Adaptation ( p ). Immediately after the perturbation is removed B 31

38 during Early Washout, the observed positional deviation becomes negative and significantly different from both Late Adaptation ( p ) and Late Baseline ( p ), implying the B existence of an aftereffect. These results indicate that the participants from all three groups adapted to applied force field. B 32

39 Figure 2.3. Experiment 1: adaptation to non-delayed and delayed velocity-dependent force fields (a) Time course of the peak positional deviation, averaged over all participants in each group (Group ND blue, Group D70 yellow, Group D100 red). Vertical dashed gray lines separate the Baseline, Adaptation and Washout sessions of the experiment. Green bars indicate Force Channel trials. Insets present individual movements of a single participant from each group during a single non Force Channel trial from the Late Baseline (LB), Early Adaptation (EA), Late Adaptation (LA) and Early Washout (EW) stages of the experiment. (b) Time course of the average adaptation coefficient during the Adaptation session. The adaptation coefficient represents the slope of the regression line extracted from a linear regression between the actual force participants apply during a Force Channel trial and the applied perturbation force during the preceding Force Field trial. Shading represents 95% confidence interval in both a and b. (c) Mean positional deviation of four trials from four stages of the experiment (LB, EA, LA and EW) averaged over all participants in each group. (d) Mean adaptation coefficient of the first (EA) and last (LA) five trials pairs of adjacent Force Field and Force Channel trials of the Adaptation session. Error bars represent 95% confidence interval. ***p< The magnitude of the experienced delay in the force (0, 70 and 100 ms) does not affect the overall positional deviation (main effect of Group: F , p ), nor the change in the ( 2,27) positional deviation throughout the stages of the experiment (Stage-Group interaction effect: F 1.880, p ( 2.796,37.747) between the groups. ), indicating that there is no difference in the extent of adaptation On random trials, the haptic device applied a high-stiffness attractor to a straight line path (Force Channel trials, Fig. 2.3b, c). These trials allowed for measuring the actual forces that the participants applied and for estimating the adaptation coefficient,, from the linear regression between each of these force trajectories and the force trajectories that were applied by the haptic device during the preceding Force Field trials (Equation 2.3). If participants update their internal representation of the external forces, the value of this adaptation coefficient should increase and approach one when participants adapt completely. In Figure 2.3b, the adaptation coefficients are presented against the sequential numbers of Force Channel trials in the Adaptation session. For all three groups, there is an increase in the adaptation coefficient throughout the adaptation session. The mean adaptation coefficient during Late Adaptation is significantly higher than during Early Adaptation and is closer to one. ( F , p ( 1,27) ) (Fig. 2.3d), indicating that participants learn to apply lateral forces that oppose the perturbing forces. The magnitude of the experienced delay in the force affects the overall adaptation

40 coefficient (main effect of Group: F, ( 2,27) coefficient of Group D100 being smaller than that of Group ND ( p 0.014), with the mean adaptation p 0.031) and Group D70 ( p ), but it does not affect the change in the mean adaptation coefficient between the early and late stages of adaptation (Stage-Group interaction effect: F , p ). ( 2,27) The adaptation analysis suggests that participants adapt to both 70 and 100 ms delayed velocitydependent force fields, similarly to the adaptation observed when they experience non-delayed fields. The existence of an aftereffect and the increase in the adaptation coefficient both suggest that this adaptation is a result of an adaptive process that uses a representation of the external forces The actual forces that are applied following adaptation to the delayed velocity-dependent force fields do not fully correspond to the perturbations To assess the way participants represent the forces that they adapted to, we examined the actual forces that participants exhibited at the end of the Adaptation session (Fig. 2.4). The mean actual forces profile that Group ND participants exhibited is roughly a scaled version of the mean perturbation forces applied during the preceding Force Field trials (Fig. 2.4a): the onset of the mean actual forces and the time of its peak correspond to the onset and the peak time of the mean perturbation force, respectively; both profiles decline together after they have reached their respective peak (which is smaller for the mean actual forces profile). For the participants in both Group D70 and Group D100 (Fig. 2.4b-c), the onset of their mean actual forces occurs before the onset of the mean perturbation forces, similar to the time within the movement in which the onset of the mean actual forces of Group ND participants occurs. However, the peak of their mean actual forces corresponds to the time in which the mean of the perturbation forces for each of these groups (which is a scaled version of the delayed velocity) reaches its maximum value. Also, the mean actual forces in both groups does not return to zero. In the mean actual force of Group D70, we could identify that the decrease in the mean actual forces becomes milder, resulting in a tail when approaching to the end of the movement (Fig. 2.4b, left). 34

41 Figure 2.4. Experiment 1: actual forces at the end of adaptation (a-c) The left panel depicts the mean perturbation profiles (solid) and mean actual forces (dashed) of all the participants in each group Group ND (a), Group D70 (b) and Group D100 (c). The depicted actual forces are forces that participants applied during the last ten Force Channel trials of the Adaptation session to cope with the applied perturbations presented in the preceding Force Field trials. Shading represents 95% confidence intervals. The right panel presents the mean actual forces for each participant from the group on the left. (d-f) Histograms depict the distribution of the actual forces peaks within the movements for each group (d ND, e D70 and f D100). Bars insets depict the probability of the actual forces profiles from late Adaptation that consist of the number of peaks in the abscissa. The trajectory inset in (d) is an example of a single actual force trajectory (solid blue) and a peak (gray dot) that was identified above a baseline actual force threshold (dashed black line). A closer examination of each participant s mean actual forces at the end of the Adaptation (Fig. 2.4a-c, right panels) reveals that while the forces applied by Group ND consist of a single distinct peak, the forces applied by Group D70 and Group D100 participants consist of mainly two peaks. 35

42 There is however a degree of inter-participants variability in the relative contribution of the peaks. Therefore, we also analyzed quantitatively the shape of the actual forces following adaptation to the different force perturbations to emphasize the existence of multiple peaks within a single trajectory rather than their size. The histograms in the insets of Figure 2.4d-f show that for all the actual force profiles at the end of Adaptation in group ND, the actual forces that has a single peak are with the highest probability ( P ( 1) 0. 43). For Group D70 and Group D100, the probability of the actual forces that have a single peak is lower (D70: P ( 1) 0. 25, D100: P ( 1) 0.12), and is the highest for the actual forces that consist of two peaks (D70: P( 2) 0. 51, D100: P ( 2) ). The histograms of the timing of the local actual forces peaks within the movement show that one of them, usually the dominant peak, occurs around the time of the peak perturbation, and the other occurs before, closer to the time of the peak perturbation in Group ND (which corresponds to the current velocity) (Fig. 2.4d-f). These results indicate that, unlike in adaptation to non-delayed velocity-dependent force fields, the actual forces that participants apply to cope with the delayed force fields correspond only partially to the applied perturbation. Although there seems to be a component in the actual forces that matches the perturbing force, at least one additional component exists that does not directly relate to the perturbing force The representation of the delayed velocity-dependent force perturbations can be reconstructed best using a combination of current position, velocity, and delayed velocity primitives. To evaluate the fit of different representation models with the actual forces, we calculated a repeated-measures linear regression between the forces that were applied by the participants during Force Channel trials, and various combinations of motor primitives position, velocity, delayed velocity, and acceleration from the respective preceding Force Field trials. The durations of the movements from these trials were similar within and between participants in each group ([ mean SD ], ND: ms, D70: ms, D100: ms ), and 36

43 thus, we did not need to perform any manipulation on the profiles to make them consistent for averaging across trials and participants within a group. v(t) Representation Model p(t), v(t) v( t ) p(t) p(t) p(t),,, v( t ) v(t), v(t), a(t) v( t ) R 2 Group ND D70 D100 D70_SF BIC ( 10 4 ) R 2 BIC ( 10 4 ) R 2 BIC ( 10 4 ) R 2 BIC ( 10 4 ) Table 2.1. Evaluation of the goodness-of-fit with the correlation coefficient (R2) and Bayesian Information Criterion (BIC) for the representation models that were examined in each group according to the actual forces at the end of adaptation. Values of R 2 closer to 1 and smaller values of BIC indicate a better model. Our evaluation of the ability of different combinations of motor primitives to explain the internal representation of the non-delayed and delayed velocity-dependent force fields is presented in Table 2.1. The closer the R 2 is to one, and the smaller the value of BIC is, the better the model explains the actual forces that the participants applied at the end of the Adaptation session. Consistent with prior studies (Sing et al., 2009; Yousif and Diedrichsen, 2012), the actual forces applied by the participants in Group ND are best fitted by a representation model that is based on current position and velocity primitives (Fig. 2.5a), with a large positive normalized gain for the velocity primitive and a small positive normalized gain for the position primitive, rather than a model based solely on a velocity primitive (Table 2.1). Surprisingly, this was not the case in the D70 and D100 groups. The qualitative evaluation of the mean actual forces profile (Fig. 2.4) suggests that a model based on current position and velocity or on current position and delayed velocity would both not be able to explain well the representation of the delayed velocity-dependent force fields. Indeed, an examination of these 37

44 models (Fig. 2.5b-e) and their goodness-of-fit evaluation (Table 2.1) supports this observation. The current position and velocity model fails to capture the shifted peak in the actual forces (Fig. 2.5b,c), and the current position and delayed velocity model fails to capture the early initiation of forces (Fig. 2.5d,e). Therefore, we conclude that participants do not represent the delayed velocity-dependent force field using a combination of position and either current or delayed velocity primitives alone. Next, we examined whether a representation model that includes a current position primitive and a state-based approximation of the delayed velocity, using current velocity and acceleration, can provide a better fit for the performance of Group D70 and Group D100 participants. This model is characterized by a better fit than the representation models mentioned above (Table 2.1), but an examination of the representation model s trajectories shows that they still do not match very well to the actual forces, especially in the case of the larger delay (Fig. 2.5f,g). We tested an additional simple model that combines current position and velocity as well as delayed velocity movement primitives (Fig. 2.5h,i). The components of this combination yield a representation model that more closely resembles the prominent features of the actual force trajectory than any other model of similar complexity, as evident by the R 2 and BIC values in Table 2.1, as well as a visual examination of Figure 2.5h,i. The mean onset of the actual force trajectory is close to the mean onset of the velocity trajectory. The time of the peak of the trajectory is similar to the time in which the delayed-velocity trajectory reached a maximum value. Finally, the force tail at the end of the movement proposes an involvement of a position component, although this may also arise from a feedback. This model provides the best fit to the actual forces that Group D70 and Group D100 participants applied during Force Channel trials at the end of the Adaptation session (among all the models that we tested in this study) while remaining attractive due to its simplicity. Note however that a close examination of Figure 2.5h,i reveals that this model does not match the applied forces accurately. We discuss potential sources of discrepancies and additional, more complicated, alternative models in the Discussion section. 38

45 39

46 Figure 2.5. Experiment 1: actual forces and fitted representation models. The representation models are constructed according to different combinations of motor primitives. (a) The actual forces applied by Group ND participants are well fitted by a representation model (solid dark blue) that is based on position (dotted orange) and velocity (dotted green) movement primitives; bar plots present the normalized gain of each primitive, estimated from the linear regression between the actual forces and the specific primitives combination. (b-e) The actual forces that were applied by both Group D70 (b, d) and Group D100 (c, e) participants do not correspond well either to a representation model (solid brown and solid dark red, respectively) that is based on current position and velocity movement primitives (b-c), or to a model based on position and delayed velocity (dotted dark blue) movement primitives (d-e). (f-i) a representation model based on current position, velocity and acceleration (dotted purple) movement primitives shows a better fit to the actual forces of Group D70 and Group D100 participants (f-g), but a representation model based on current position and velocity, and delayed velocity movement primitives provides the best fit (h-i) (compared to the other models that we tested). Shading and error bars represent 95% confidence intervals The gain of the delayed velocity primitive evolves throughout adaptation to delayed velocity-dependent force perturbations To examine the dynamics of the forming of the internal representation for the non-delayed and both the delayed velocity-dependent force fields, after choosing the best candidate representation model from each group, we calculated the normalized gain of each primitive in these models in each Force Channel trial. The time course of the evolution of these normalized gains throughout the Baseline, Adaptation, and Washout sessions of the experiment are depicted in Fig Consistent with the fact that participants did not experience external perturbing forces during Baseline, in the last Force Channel trial in Baseline, in all Group ND (Fig. 2.6a), Group D70 (Fig. 2.6c) and Group D100 (Fig. 2.6e), the normalized gains of the current position and velocity primitives were close to zero, as well as the normalized gain of the delayed velocity primitive in both the delay groups. For all groups, the first Force Channel trial of the Adaptation session appeared after a single Force Field trial was presented. After experiencing the perturbation for the first time, Group ND participants (Fig. 2.6a,b) apply a force that reflects an initial representation consisting of a small contribution of both position and velocity primitives, with similar normalized gains. Since the perturbing force depends linearly on the velocity, throughout 40

47 adaptation, there is a sharp increase in the velocity normalized gain (Fig. 2.6a, green triangles; Fig. 2.6b, ordinate) in parallel with a mild decrease in the position normalized gain (Fig. 2.6a, orange dots; Fig. 2.6b, abscissa). In Group D70 and Group D100 (Fig. 2.6c-f), participants started in a similar initial representation consisted of position and velocity normalized gains that were similar to Group ND, and with no contribution of a delayed velocity primitive. Similarly to the Group ND, the position normalized gains mildly decreased throughout adaptation (Fig. 2.6c,e, orange dots; Fig. 2.6d,f, left and middle panels, abscissa). The normalized gains of the velocity primitive (Fig. 2.6c,e, green triangles; Fig. 2.6d,f, left panel and right panels, ordinate and abscissa, respectively) mildly increased during early adaptation and then decreased during late adaptation, such that their final value was similar to that at the beginning. Importantly, in both Group D70 and Group D100, the normalized gains of the delayed velocity primitive increased (Fig. 2.6c,e dark blue squares; Fig. 2.6d,f, middle and right panels, ordinate). However, they did so slower and reached to values that were significantly smaller than those of the velocity normalized gain in Group ND (main effect of Group: F , p ; ND-D70: p , ND-D100: p ), likely due ( 2,27) to the remaining non-delayed velocity primitive in the representation. There was no statistically significant difference between the delayed velocity normalized gains of Group D70 and Group D100 at the end of the Adaptation ( p ), suggesting that the weighted contribution of the B delayed velocity primitive to the representation is not influenced by the delay magnitude. During Washout, the position and velocity normalized gains of Group ND showed an early decay response to the removal of the perturbation (Fig. 2.6a), and then they reached close to zero in the last Force Channel trial of the session. In Group D70 and Group D100, the position and velocity normalized gains exhibit a similar immediate response to that of Group ND (Fig. 2.6c,e) and eventually approach zero. Interestingly, the delayed velocity normalized gains of both the delay groups remained similar to its mean value at the end of Adaptation, and even showed a slight increase from the first to the second Force Channel trials of the Washout session. Only then, it dropped to a smaller value until reaching zero at the end of the washout. B B 41

48 Delay Representation in the Sensorimotor System Figure 2.6. Experiment 1: the dynamics of movement primitives normalized gains The gains are presented for the models that best explain the actual force patterns that each group exhibits during Force Channel trials. (a) Time course of the position (orange dots) and velocity (green triangles) normalized gains throughout the experiment for Group ND. Shading represents 95% confidence interval. Vertical dashed gray lines separate the Baseline, Adaptation and Washout sessions of the experiment. The color gradient bar represents the progression of Force Channel trials from early (dark) to late (light) adaptation. (b) The normalized gains from the Adaptation session in (a) are plotted in a position-velocity normalized gain space. Each dot represents the primitives gain combination in each trial, and the color codes the trial number. (c, e) Time course of the position, velocity and delayed velocity (dark blue squares) normalized gains throughout the experiment for Group D70 (c) and Group D100 (e). (d, f) The normalized gains from the Adaptation sessions in (c) and (e) (respectively) are plotted in position-velocity (left), position-delayed velocity (middle) and velocity-delayed velocity (right) normalized gain spaces. 42

49 2.3.2 Experiment Generalization of adaptation to a delayed force field from slow to fast movements a support for an internal representation of a delayed velocity-dependent force field as a combination of current position, velocity, and delayed velocity primitives In Experiment 1, we showed that the representation model that is constructed from position, velocity and acceleration primitives provides a relatively good fit to the actual forces of Group D70 participants, and its predicted trajectory is quite similar to that of the position, velocity and delayed velocity representation model (Fig. 2.5f,h). Compared to Group D70, the actual forces that Group D100 participants apply exhibit clearer dual-peak trajectories. These two peaks are likely associated with the better separated in time current and delayed velocity primitives. However, based on Experiment 1, it is impossible to reject a hypothesis that the clearly distinct delayed velocity primitive is specific to adaptation to a larger delay. Therefore, it is not clear if the actual forces that counteract the 70 ms delayed velocity-dependent force field are a result of a representation that is composed of current state primitives or a combination of current and delayed primitives. In addition, it is not clear if the representation that is formed at a particular velocity generalizes to a different velocity. To address these two open questions, we designed Experiment 2 a generalization study to a faster velocity. The predictions of the actual force trajectories during a generalization to a faster velocity are different for a representation model that is composed of position, velocity, and acceleration and a model that is composed of position, velocity, and delayed velocity (Fig. 2.7). We simulated the actual forces applied following adaptation to 70 ms delayed velocitydependent force fields for both the position-velocity-acceleration (Fig. 2.7, upper panel) and the position-velocity-delayed velocity (Fig. 2.7, lower panel) representation models during slow (Fig. 2.7, left panel) and fast movements (Fig. 2.7, right panel). We determined the gain of each primitive in our simulation based on their relative contribution in the representation analysis of Group D70 in Experiment 1 (Fig. 2.5f,h). The simulation results show that during slow movements, the actual force predicted by the position-velocity-acceleration model is similar to the actual force predicted by the position-velocity-delayed velocity model (Fig. 2.7, cyan). 43

50 However, the same representations predict considerably different actual force trajectories during fast movements (Fig. 2.7, purple). The position-velocity-acceleration representation predicts a trajectory with a small initial decrease in the actual force, followed by a steep increase with a single peak. The position-velocity-delayed velocity representation predicts an actual force trajectory that has two positive peaks which correspond to each of the velocity primitives. Note that if the adaptation to the delayed velocity-dependent force is indeed generalized to a higher velocity, the temporal separation between the velocity and the delayed velocity primitives should be better since each trajectory is higher and narrower. In this sense, and in this sense only, examining the generalization to a higher velocity is somewhat similar to examining the representation of a higher delay. In Experiment 2, we tested experimentally how constructing a representation of 70 ms delayed velocity-dependent force field while executing slow movements would generalize to faster movements. In this experiment, a group of participants (Group D70_SF) performed the same task as they did in Experiment 1, but the protocol was modified (Fig. 2.8a). During Baseline, participants moved with no external force perturbing their hand, and we trained them to reach the target within two different duration ranges, and thereby to move either at low (Slow) or high speed (Fast). The participants were informed about the required movement speed using a different display background color for each trial mode. During Adaptation, a velocity-dependent force field was presented and persisted throughout the entire session. All the trials in the Adaptation session were of a Slow type. The applied force influences the positional deviation of the participants (Fig. 2.8b), which significantly changes throughout the Late Baseline, Early Adaptation and Late Adaptation stages of the experiment (main effect of Stage: F , p ( 1.023,7.159) ). There is an increase in the positional deviation from Late Baseline to Early Adaptation as a result from the sudden introduction of the perturbation ( p 0.017). With the repeated exposure to the force, the positional deviation decreases ( B p B 0.046) and it declines closer to zero during Late Adaptation. These results indicate that Group D70_SF participants adapted to the delayed force field. 44

51 Figure 2.7. Predicted actual force during a generalization to faster movements During slow movements (left panel), the predicted actual forces (solid cyan) that are constructed according to a position-velocity-acceleration representation model (upper panel) are similar to the predicted actual forces of a position-velocity-delayed velocity representation model (lower panel). During fast movements (right panel), the same position-velocity-acceleration representation model predicts substantially different actual force profiles (solid purple) than the actual force profiles predicted by the position-velocity-delayed velocity representation model: in the former, there is an initial increase in the actual force to the same direction towards which the perturbing force is applied (a negative force) followed by a steep increase to the opposite direction (a positive force), whereas in the latter, the actual force profiles have two positive peaks. Similar to Experiment 1, in Experiment 2 we also included Force Channel trials that were presented randomly throughout the Baseline and the Adaptation sessions. All the Force Channel trials in these sessions were of the Slow type, and they allowed for measuring the actual forces that participants apply to counteract the perturbations. An evidence that participants built an internal representation of the perturbation is provided by the increase in the adaptation 45

52 coefficient throughout the Adaptation session (Fig. 2.8c), with a significantly higher mean adaptation coefficient during Late Adaptation than during Early Adaptation ( p 0.002). t, ( 7) To assess the way participants represent the forces that they adapted to, we examined the actual forces that they exhibited during Late Adaptation (Fig. 2.8d). The mean actual forces trajectory that Group D70_SF participants in Experiment 2 exhibited is similar in its shape to the mean actual forces trajectory of Group D70 participants in Experiment 1 (Fig. 2.4b). That is, the onset of the mean actual forces occurs before the onset of the mean perturbation forces, and the peak of the mean actual forces corresponds to the time of the peak mean perturbation forces. Since the durations range within which Group D70_SF participants were required to move during the Adaptation session was smaller than and within the upper range of the movement durations range in Group D70, they moved slower. The mean maximum velocity of Group D70_SF during Late Adaptation ([ mean 95% CI ], m s ) was significantly smaller than that of Group D70 ( m )( t , p ), and therefore, overall perturbations s ( 16) and actual forces were all down-scaled. To examine generalization of adaptation to the delayed force perturbation from slow to fast movements, the Washout session was consisted of only Force Channel trials of both Slow and Fast type trials (Joiner et al., 2011). We included the Slow Force Channel trials to compare the actual forces during Fast trials with the actual forces during Slow trials from the same experimental stage (Early Washout). The actual forces (both group s average and individuals means) during the Slow trials at the Early Washout stage (Fig. 2.8e) show wide trajectories with an initial increase around the onset of the actual forces during Late Adaptation (Fig. 2.8d) and a peak mean force around the time of the peak mean perturbation. This profile is consistent with the simulated actual force trajectory of both the position-velocity-acceleration and the positionvelocity-delayed velocity representation models (Fig 2.7, left panel, solid cyan). The actual forces during the Fast trials at the Early Washout stage (Fig. 2.8f) has clear dual-peak trajectories that are consistent with the position-velocity-delayed velocity representation model (Fig 2.7, lower right panel, solid purple). It also does not show the initial decline that is predicted by the position- 46

53 velocity-acceleration representation model (Fig 2.7, upper right panel, solid purple). The existence of the two peaks in the force profiles is further supported by an analysis of the histograms of force peak probability. During the Slow Force Channel trials at Late Adaptation and Early Washout, the distribution of the number of actual forces trajectories with certain amounts of peaks is similar to that in Group D70 (insets in Figs. 2.4b, 2.8g and 2.8h), with a high probability for the actual forces that consist of two or three peaks (Slow Late Adaptation: P ( 2) 0. 34, P ( 3) 0.19; Slow Early Washout: P ( 2) 0. 33, P ( 3) 0. 38). Although for Late Adaptation, the histogram of the peaks probability in each time bin within the movement suggests that they are mainly composed of a delayed velocity (Fig. 2.8g), for Early Washout, there is also a high probability for a peak to occur closer to movement initiation ( ~ 200 ms ), suggesting a contribution of the current velocity (Fig. 2.8h). Importantly, the simulated actual forces of the position-velocity-acceleration representation model during generalization to faster movements predicts an amplification of a delayed peak (as a result of both the velocity and acceleration primitives contributions), but without the presence of any additional preceding peak. However, the probability of the actual forces from the Fast type trials that consist of a single peak was low (inset in Fig. 2.8i, P ( 1) 0. 08), and the probabilities of the actual forces that consist of two or three peaks remained high ( P ( 2) 0. 48, P ( 3) ). Also, the high probabilities of peak occurrences at ms, ms and 400 ms (Fig. 2.8i) are consistent with the contributions of the current velocity, the delayed velocity and the current position, respectively. Overall, the generalization from slow to fast movements further strengthens our suggestion that indeed a delayed velocity primitive was used to adapt to the delayed velocity-dependent force perturbations. 47

54 48

55 Figure 2.8. Experiment 2: generalization to faster movements experimental design and results The experimental setup of this experiment was the same as in Experiment 1. (a) Schematic display of the experimental protocol. During the Baseline session (100 trials), no perturbation was applied and participants were trained to reach in two velocity ranges either Slow or Fast. During the Adaptation session (200 trials), movements were perturbed with a 70 ms delayed velocity-dependent force field, and participants were presented only with the Slow reaching type trials. The cyan bars represent Force Channel trials during which participants were requested to move in a Slow type. The Washout session (100 trials) consisted of only Force Channel trials that were pseudo-randomly alternated between a Slow and a Fast (purple) type. (b) Time course of the peak positional deviation, averaged over all the participants in Group D70_SF. Vertical dashed gray lines separate the Baseline, Adaptation and Washout sessions of the experiment. Cyan and purple bars indicate Force Channel trials. (c) Time course of the average adaptation coefficient during the Adaptation session. (d) Mean perturbation profiles (solid) and mean actual forces (dashed) from the end of adaptation of all the participants in Group D70_SF (upper panel). The mean actual forces for each participant are presented in the lower panel. (e,f) Mean actual forces of the first five Slow (e, cyan) and Fast (f, purple) trials in the Washout session, averaged over all the participants in the group. The mean actual forces for each participant from each of these trial types are presented in the lower panels. Shadings in (b-f) represents 95% confidence interval. (g,h,i) Insets present for each stage and trial type (g LA; h EW, Slow; i EW, Fast) the probability of the actual forces profiles that consist of the number of peaks in the abscissa. Histograms present the distribution of the actual forces peaks within the movements. 2.4 Discussion To explore how internal models are formed in light of sensory transmission delays, we examined the representation of delayed velocity-dependent force perturbations. Consistent with prior studies, participants adapted to delayed and non-delayed perturbations similarly (Scheidt et al., 2000; Levy et al., 2010). Interestingly, unlike in the non-delayed case where the current position and velocity movement primitives provide a good fit for participants actual forces (Sing et al., 2009), models based on the current position with the current or the delayed velocity are insufficient to explain the forces applied in the delayed case. Instead, among the models that we tested, the best model consists of current position, velocity and delayed velocity primitives. Moreover, this representation that consists of current and delayed states generalizes to a higher velocity, for which the delayed force field was never experienced. 49

56 Prior studies are equivocal about delayed feedback representation. On one hand, when the simultaneity is disrupted during interactions with elastic force fields by force feedback delays, stiffness perception is biased (Pressman et al., 2007; Nisky et al., 2008; Pressman et al., 2008; Nisky et al., 2010; Di Luca et al., 2011; Nisky et al., 2011; Leib et al., 2016). This suggests that the brain does not employ a delay representation that realigns the position signal with the delayed force signal. On the other hand, humans can adapt to delayed velocity-dependent force perturbations (Levy et al., 2010) and adjust their grip force to a delayed load force during toolmediated interactions with objects (Witney et al., 1999; Leib et al., 2015). By explicitly measuring, using force channels, the forces that participants apply to directly counterbalance delayed force perturbations, we provide the first evidence for exploiting the delayed state information a delayed velocity primitive together with the current state information in the control of arm movements. We also quantitatively evaluate the relative contribution of the current and delayed state primitives in the representation, determine their evolution and washout dynamics, and examine their generalization. The coexistence of the delayed and current state primitives in the representation is in line with studies that found evidence for a mixed representation of the actual delay and a state-based estimation of the delay (Diedrichsen et al., 2007; Leib et al., 2015). Diedrichsen et al. showed that when two tasks are overlapping in time, participants use a state-dependent control the motor command in one task depends on the arm state in the other task, but when they are separated, they use a time-dependent control (Diedrichsen et al., 2007). The delays in our experiments were within their identified transition range, where a mixture of both was used. This mixture may result from the similarity between the current and delayed velocity primitives, which hinders the ability to assign the perturbation to one or the other, and larger delays may lead to a better separation (Witney et al., 1999). However, the delays in our experiment are bounded by the short durations of ballistic reaches. Indeed, when analyzing the primitives dynamic throughout the experiment in the group that experienced 100 ms delay (Fig. 2.6e), the regression analysis of some trials revealed a high correlation between the delayed velocity and the position primitives. Also, larger delays may potentially break down the association between the movement and the 50

57 perturbing force. Thus, we believe that 100 ms is probably close to the maximal delay magnitude that can be used in our experiment. Our results indicate that it is most likely that the sensorimotor system uses a delayed velocity rather than an acceleration primitive. Despite the fact that we are continuously experiencing inertial forces, previous studies demonstrated slow adaptation and poor generalization of acceleration-dependent compared to velocity-dependent force fields (Hwang and Shadmehr, 2005; Hwang et al., 2006), and indeed, force field adaptation studies focused mainly on primitives depending on position and velocity (Thoroughman and Shadmehr, 2000; Donchin et al., 2003; Sing et al., 2009; Yousif and Diedrichsen, 2012). However, this may be a consequence of the difficulty in acceleration estimation in experiments. Therefore, the capability of the sensorimotor system to utilize an acceleration primitive when responding to environmental dynamics requires further investigation. We suggest that specifically when coping with a delayed velocitydependent force feedback, acceleration is not used. Our best model is not perfect in predicting the forces that participants applied at the end of adaptation. The inconsistencies may be related to un-modeled mechanisms, such as increasing arm stiffness to cope with delay-induced instability (Milner and Cloutier, 1993; Burdet et al., 2001). Both the 70 and 100 ms delay groups in Experiment 1 exhibit aftereffects and an increase in the adaptation coefficient. This suggests that increased stiffness is not the main coping mechanism (Shadmehr and Mussa-Ivaldi, 1994; Burdet et al., 2001). However, while we did not find a statistically significant difference in the size of the aftereffect and the adaptation coefficients between the groups, there was a systematic decrease in both of them as the delay increased. Therefore, it may be that the contribution of increased stiffness is larger with increasing delay. Also, we observed a systematic increase in the movement duration with the higher delay, which may imply that one strategy for dealing with the delayed force is to move slower; and indeed, as the delay increased, the velocity dependent applied perturbations were weaker, and the size of the aftereffect is directly related to the magnitude of the forces participants adapt to. Other un-modeled factors could be additional higher-order derivatives or lateral movement primitives. In addition, we assumed an accurate delay for the delayed velocity 51

58 primitive, but the participants may have a noisy estimation of the delay. We chose not to improve the fit of the model with additional primitives or by optimizing the delay parameter to avoid overfitting. We wished to keep the models that we tested as simple as possible and to examine only primitives that were included in our original predictions. The inconsistencies may also result from the absence of well-established priors in the sensorimotor system for the delayed perturbation. The slow increase in the delayed velocity gain, relatively to the current velocity gain (Fig. 2.6a,c,e), is consistent with previous results suggesting that new temporal relationships between actions and their consequences are learned by generating a novel rather than adapting an original predictive response (Witney et al., 1999). Possibly, the slow process of constructing the new representation did not complete within the adaptation duration in our study. Indeed, the gain of the delayed velocity primitive did not clearly reach a plateau and did not decrease instantaneously following perturbation removal. Finding out whether participants could construct an accurate representation if they had more trials to do so is beyond the scope of this study. Instead, we focus on comparing the adaptation to nondelayed and delayed perturbations and on the evolution of the current and delayed primitives for the same number of trials. Inferring the gains of the primitives is practically an estimation of the stiffness (for the position primitive) and viscosity (for the current and delayed velocity primitives) of the environment. As delayed force feedback biases perception of stiffness (Pressman et al., 2007; Nisky et al., 2008; Di Luca et al., 2011; Leib et al., 2015), it may also influence the explicit assessment of the viscosity. Such biases may consequently affect the estimation of the correct contribution of each primitive while constructing the representation that generates the actual forces. Perceptual biases do not necessarily align with effects on actions (Goodale and Milner, 1992), and specifically in the response to delayed force feedback (Leib et al., 2015). However, future studies may examine the influence of such perceptual biases by probing the explicit component of adaptation (Taylor et al., 2014) in both the non-delayed and delayed conditions, and extract the primitive gains from the implicit process alone. 52

59 Interestingly, the primitives gains continue changing throughout the entire adaptation while performance, as measured by the peak hand deviation from a straight line movement, reaches an asymptote after less than 100 trials. This suggests that the error that drives the change in primitives gains is not the hand deviation, but maybe a continuous optimization process driven by other variables (Mazzoni and Krakauer, 2006; Smith et al., 2006; McDougle et al., 2015). The questions still remain open which signals are used to construct the delayed velocity primitive, and what is the mechanism of its construction. The construction of a delayed primitive that is used for action may depend on the presence of the delay in the force feedback. Studies that examined action with visual feedback delays (Mussa-Ivaldi et al., 2010; Sarlegna et al., 2010; Takamuku and Gomi, 2015) did not find an evidence for a representation of the delayed signals. However, studies of action with force feedback delays found evidence for delay representation (Witney et al., 1999; Leib et al., 2015). It may be that the formation of a delayed state primitive depends on the activity of sensory organs that respond to force, such as the Golgi tendon organ (Houk and Simon, 1967) or mechanoreceptors in the skin of the fingers (Zimmerman et al., 2014). The formation of the delayed velocity primitive may involve an explicit representation of time. It is not clear though whether the nervous system is capable of representing time (Karniel, 2011). Humans can adapt to state-dependent, but not time-dependent, force perturbations while performing movements (Karniel and Mussa-Ivaldi, 2003), and time-dependent forces can be misinterpreted as state-dependent (Conditt and Mussa-Ivaldi, 1999). However, time and not state representation explains the perceived timings of events during a task involving discrete impulsive forces (Pressman et al., 2012). If humans can employ time representation, our best model is consistent with evidence for neural representation of both time and state. Structures that represent time were linked to the basal ganglia (Ivry, 1996; Rao et al., 2001) and to the supplementary motor area (Halsband et al., 1993; Macar et al., 2006). The posterior parietal cortex was proposed to hold state estimation (Desmurget et al., 1999; Makin et al., 2007). The cerebellum was suggested to play a role in time representation (Ivry et al., 2002; Spencer et al., 2003), but also in state estimation, especially in light of feedback delays (Ebner and Pasalar, 2008) by hosting forward models (Miall et al., 1993; Wolpert et al., 1998; Miall et al., 2007; Nowak et 53

60 al., 2007). Lobule V of the cerebellum was linked to state-dependent control whereas the left planum temporale to time-dependent control (Diedrichsen et al., 2007). Importantly, the observation that a model that includes the delayed velocity primitive can best account for the actual forces does not necessarily mean that the sensorimotor system uses an actual representation of the delayed velocity. Participants could estimate the delayed velocity as a function of the time relative to movement duration rather than absolute time. In fact, visual examination of the temporal distance between the force peaks, corresponding to the current and delayed velocity, is not constant between slow and fast movements (Fig. 2.8e, f); rather, it appears to scale with movement duration. This suggests a delayed velocity representation that is equivalent to a constant phase shift of the movement velocity. Furthermore, since along a typical reaching movement, the position and time are closely coupled, our results may be also consistent with a use of the extent of motion in the construction of the delayed velocity representation. Thus, to dissociate between the two options, future experiments might examine generalization to movements that are distinctly different in terms of the shape of the velocity trajectory (e.g. a sequence of discrete movements along the same path). In addition, participants could have represented the perturbing force as an explicit function of time, but previous evidence for limited capability to represent time-dependent forces (Conditt and Mussa-Ivaldi, 1999; Karniel and Mussa-Ivaldi, 2003) suggests that this is unlikely. Lastly, adaptation can take place by memorizing the shape of the experienced force along the trajectory; however, the brain does not seem to employ such rote learning mechanism when experiencing novel environmental dynamics (Conditt et al., 1997). Understanding adaptation to environment dynamics in the presence of delayed causality is critical for understanding forward models and sensory integration. It is also important for studying pathologies with transmission delays like Multiple Sclerosis (Trapp and Stys, 2009), or with disordered neural synchronization, like Parkinson s disease (Hammond et al., 2007), essential tremor (Schnitzler et al., 2009), and epilepsy (Scharfman, 2007), specifically if treatment is attempted by tuning the delay in the feedback loop to control the neural synchronization (Rosenblum and Pikovsky, 2004; Popovych et al., 2005). Finally, it may also be useful for the 54

61 design of efficient teleoperation technologies in which feedback is delayed (Nisky et al., 2011; Nisky et al., 2013). To conclude, understanding delay representation is important for understanding healthy and diseased neural processes, for developing treatments for timingrelated neural disorders, and for developing efficient teleoperation technologies. 55

62 Chapter 3: Running Behind Time State-Based Delay Representation and Its Transfer from a Game of Pong to Reaching and Tracking Submitted for publication Title of submitted article: State-based delay representation and its transfer from a game of pong to reaching and tracking 1,2, Raz Leib 1,2, Assaf Pressman 1,2,3, Lucia S. Simo 4, Amir Karniel 1,2, Lior Shmuelof 5,6,2, Ferdinando A. Mussa-Ivaldi 4,7,3 and Ilana Nisky 1,2 1. Department of Biomedical Engineering, Ben-Gurion University of the Negev, Be'er Sheva, Israel 2. Zlotowski Center for Neuroscience, Ben-Gurion University of the Negev, Be'er Sheva, Israel 3. Sensory Motor Performance Program, Rehabilitation Institute of Chicago, Chicago, IL, USA 4. Department of Physiology, Feinberg School of Medicine, Northwestern University, Chicago, IL, USA 5. Department of Brain and Cognitive Sciences, Ben-Gurion University of the Negev, Be'er Sheva, Israel 6. Department of Physiology and Cell Biology, Ben-Gurion University of the Negev, Be'er Sheva, Israel 7. Department of Biomedical Engineering, Northwestern University, Evanston, IL, USA Keywords: delay, reaching, tracking, transfer, representation Acknowledgments: The authors would like to thank Ali Farshchiansadegh and Felix Huang for their help in constructing the experimental setups, and Matan Halevi for assistance in data collection. The study is supported by the Binational United-States Israel Science Foundation (grant no ), and by the Helmsley Charitable Trust through the Agricultural, Biological and Cognitive Robotics Initiative of Ben-Gurion University of Negev, Israel. GA was supported by the Negev Fellowship. Contribution: GA, RL, AP, LSS, AK, LS and FI designed the experiments; GA and AP analyzed the data; GA, RL, AP, LSS, AK, LS, FI and IN interpreted the results; GA, RL, AP, LSS, LS, FI and IN wrote the manuscript. 56

63 Abstract To accurately estimate the state of the body, the sensorimotor system needs to account for delays between sensory signals from different modalities. To investigate how such delays may be represented in the brain, we asked participants to play a virtual pong game, in which the movement of the virtual paddle was delayed with respect to their hand movement. We found that the effects of a prolonged exposure to the delayed feedback transfer to blind reaching and tracking tasks and cause participants to exhibit hypermetric movements. These results, together with simulations, suggest that delay is not represented based on time, but rather based on equivalent mechanical elements. This is the first evidence of adaptation to a visuomotor delay in an ecological motor task the game of pong using a mechanical system equivalent representation that is uncovered by kinematic changes during transfer to different contexts. 3.1 Introduction It is unclear whether the brain represents time explicitly (Karniel, 2011) using "neural clocks" (Ivry, 1996; Spencer et al., 2003; Ivry and Schlerf, 2008). Evidence suggest that no such clock is involved in the control of movement. For example, humans are able to adapt to state-dependent, but not time-dependent, force perturbations (Karniel and Mussa-Ivaldi, 2003), and timedependent forces are in some cases misinterpreted as state-dependent (Conditt and Mussa- Ivaldi, 1999). Instead, for timing of movements, the sensorimotor system may use the temporal dynamics of state variables that are associated with the performance of actions. Time representation is important for sensory integration and for movement planning and execution. Sensory signals are characterized by different transmission delays (Murray and Wallace, 2011), and movement planning and execution require additional processing time. Therefore, to enable animal s survival, the brain must take these delays into consideration. Current literature is equivocal on how delay is represented. On the one hand, humans can adapt to visuomotor delays (Miall and Jackson, 2006; Botzer and Karniel, 2013) and to delayed force feedback (Witney et al., 1999; Levy et al., 2010; Leib et al., 2015). On the other hand, delayed 57

64 sensory feedback biases perception of impedance (Pressman et al., 2007; Nisky et al., 2008; Nisky et al., 2010; Di Luca et al., 2011; Kuling et al., 2015; Leib et al., 2016) and resistance (Takamuku and Gomi, 2015), suggesting that the brain does not realign the signals to obtain accurate estimations of the environment. Here, we examine how the sensorimotor system represents a visuomotor delay. Imagine you play a game of pong with a slow computer, controlling a paddle with the computer mouse and attempting to intercept a moving ball. Since the computer is slow, there is a delay between the movement of the hand and the movement of the controlled paddle. A representation of such a delay can be Time-based or State-based (Rohde and Ernst, 2016). A Time Representation of the delay is a representation of the actual time lag between the movements of the hand and the paddle. Thus, to compensate using Time Representation, you would precede the movement of the hand by the appropriate amount of time so that the paddle would hit the ball at the planned location. Since with such a representation, the execution of the motor command is different only by its timing and not by its magnitude, the movement of the hand would be the same as if the computer is fast and there is no delay. Alternatively, a State Representation is a representation of delay using current state variables. You may believe that your brand new computer could not possibly be slow, and attribute the lag to a mechanical resistance at the mouse inertia, viscosity, and stiffness. You may also believe that you missed the ball because you failed to aim far enough, and interpret the distance between the paddle and the ball originating from the delay as a spatial shift. Unlike Time Representation, the State Representation would influence the state of the movement of the hand. Previous studies presented evidence supporting the mechanical system representation of visuomotor delay, and explained effects on perception (Takamuku and Gomi, 2015), and on grip force control (Sarlegna et al., 2010). However, it is unclear whether these effects were a result of a change in an internal representation of hand-cursor dynamics, or an online effect of perceptual illusions. In this study, we use simulations to illustrate the specific effects of Time and State Representations on movements execution, and examine them experimentally. 58

65 We hypothesized that following adaptation to delay, humans form an internal State-based Representation using a mechanical equivalent. To test this hypothesis, we asked participants to play a pong game and control a paddle to hit a continuously moving ball (Reichenthal et al., 2016) (Fig. 3.1a). Such an ecological task provides the opportunity to examine how the sensorimotor system performs in a more natural environment than was previously studied: it is composed of multiple interception movements that start and end at various locations of the workspace, and the movement of the target (the ball) is altered by the paddle hits. The participants played the pong game when the paddle moved in coincidence with the movement of the hand (Fig. 3.1b, left No Delay), and when the paddle movement was delayed with respect to the movement of the hand (Fig. 3.1b, right Delay). 59

66 Figure 3.1. The pong game and the representation models for hand-paddle delay (a) An illustration of the experimental setup and the pong game: participants sat and held the handle of a robotic arm. A screen that was placed transversely above their hand covered the hand and displayed the scene of the experiment. During the pong game, participants controlled the movement of a paddle (red bar) and were required to hit a moving ball (green dot) towards the upper wall of the pong arena, which is delineated by the black rectangle. (b) The paddle movement was either concurrent (left No Delay) or delayed (right Delay) with respect to the hand movement (the red arrow indicates the paddle movement direction). (c) Participants may represent the hand location based on the delayed paddle using Time Representation (left) or State Representation (right). In Time Representation, participants estimate the actual time lag,, and represent the hand location at time t as the location of the paddle at (blurred paddle). In State Representation, participants may represent either a Mechanical System that connects the two and includes a spring ( K ), a mass ( M ) and a damper ( B ), or a Spatial Shift ( ) between the hand and the paddle. x t To computationally formalize the possible predictions for delay representation, we assume that to control movements, the participants formed an estimation of their hand location ˆ ( t) x h that was based on the state of the displayed paddle x p (t) and its time derivatives (Pressman, 2012). A Time-based Representation of delay would lead to an estimate of hand location including explicitly the actual time lag ( ) between hand and paddle movements: (3.1) xˆ ( t) x ( t ˆ ) where x p ( t ˆ ) is the location of the paddle at estimated h 60 p (ˆ ) time ahead (Fig. 3.1c, left panel). A State-based Representation of the delay may follow one of two alternative models (Fig. 3.1c, right panel): participants may use a Taylor s series approximation of the expression in Equation 3.1 around the position of the delayed paddle: 2 ˆ (3.2) xˆ ˆ h( t) xp( t ˆ) xp( t) x p( t) x p( t). 2 Such an approximation is based only on the current state position, velocity and acceleration B of the paddle. By substituting ˆ and K ˆ2 2 M K, we can view the dynamics between the hand and the paddle as a Mechanical System equivalent representation that consists of a spring ( K ), a mass ( M ) and a damper ( B ):

67 B M (3.3) xˆ h ( t) x p ( t) x p ( t) x p ( t). K K According to this view, the cursor is a damped mass that is connected to the hand with a spring. Note that while it may appear that the Mechanical System model has three free parameters, this is not the case. The mechanical elements K, M and B are all derived from the Taylor s approximation, and thus, the Mechanical System model has only a single free parameter, as the other models that we consider. Another State-based alternative is a representation of the current location of the hand according to the current location of the paddle spatially shifted by A common approach to characterize changes of internal representations is to examine transfer of adaptation to other contexts (Shadmehr and Mussa-Ivaldi, 1994; Krakauer et al., 2000; Krakauer et al., 2006). While various terminologies are used in different fields, here we define transfer as a change in performance in one task following the experience of another task. To investigate whether participants represent the experienced dynamics between the hand and the delayed paddle using each of the abovementioned representation models Time, Mechanical System and Spatial Shift (Fig. 3.1c) we examined transfer to blind reaching and blind tracking tasks that required movement without visual feedback. Transfer to these well-understood movements allowed for comparing our experimental observations to simulations of the three representation models. By omitting the visual feedback, we could examine the performance of the participants when they had to rely only on a feedforward mechanism and a proprioceptive feedback, and thereby, capture the representation following exposure to either the non-delayed or the delayed pong game. In prior adaptation studies, the schedule by which perturbations are presented abrupt or gradual affected transfer, favoring a stronger transfer following gradual presentation (Kluzik et al., 2008; Torres-Oviedo and Bastian, 2012). Different explanations were proposed to explain these differences, including the influence of awareness (Baraduc and Wolpert, 2002; Taylor and Ivry, 2011) and the assignment of the change to the body of the participant rather than to an 61 x (3.4) xˆ ( t) x ( t) x. h p as a result of the delay (Spatial Shift):

68 external source (Berniker and Kording, 2008). We hypothesized that a gradual increase of the delay during the pong game would enhance the behavioral effect in our transfer tasks compared to an abrupt increase of the delay. In this paper, we simulate the computational models of our suggested representations of visuomotor delay to construct behavioral predictions, and test these predictions with experiments. We found that, regardless of the schedule of delay presentation during the pong game, the transfer to blind reaching is consistent with a State-based rather than a Time-based representation of the delay. Further, the transfer to blind tracking supports a Mechanical System representation. 3.2 Results Experiment 1 Transfer of hypermetria following a delayed pong game to a blind reaching task suggests State rather than Time Representation of the delay We designed an experimental protocol in which a group of participants, the Delay group (N=9), played two Pong sessions (Fig. 3.2a): the first Pong session was introduced with no delay (Pong No Delay), where the paddle moved together with the hand, and the second Pong session was introduced with a delay of 0.1 s between hand and paddle movements (Pong Delay). In each trial of pong, participants were asked to hit the moving ball as many times as they can towards the upper wall of the arena. A second group of participants served as the Control group (N=8). They experienced a protocol similar to the Delay group, with the exception that during the Pong Delay session, the magnitude of the delay was zero, and thus, in terms of hand-paddle dynamics, it was the same as the Pong No Delay session. 62

69 63

70 Figure 3.2. Experimental protocols In all experiments, participants hand (gray) was hidden from sight the entire time. (a) Experiment 1: Delay vs. Control, transfer to reaching. Sessions were alternating between a pong game and a reaching task. During a Reach trial, a target (gray square) appeared in one out of three locations in space, ahead from a start location (black square), and participants were asked to reach and stop at the target. An experiment started with a Reach Training session in which participants received full visual feedback of the hand location using a cursor on the screen (dark gray filled square). After training, participants were presented with a Pong game session (No Delay), in which the paddle was moving instantaneously with the hand movement, followed by a Blind Reach session where no visual feedback was presented at any point during the trial (Post No Delay, blue frame). The second Pong game session (Delay) was introduced with (Delay group) or without a delay (Control group) between hand and paddle movements, and it was followed by another Blind Reach session (Post Delay, orange frame). (b) Experiment 2: Abrupt vs. Gradual delay, transfer to reaching. The experimental protocol was similar to Experiment 1, but with an addition of a Blind Reach Training session: the cursor was omitted during the movement, but was displayed at the movement stop location. In the second Pong game session, we introduced either an abruptly (Abrupt group) or gradually (Gradual group) increasing delay. (c) Experiment 3: Abrupt vs. Gradual delay, transfer to tracking. Sessions were alternating between a pong game and a tracking task. During a Track trial, participants were asked to track a target that moved along a figure-of-eight path (dashed gray. The path was not presented to the participants) in a direction that is illustrated by the dotted dark gray arrow. An experiment started with a Track Training session in which participants received full visual feedback of the hand location (dark gray filled square). After training, participants were presented with a Pong game session with no delay (No Delay), followed by a Blind Track session (Post No Delay, purple frame). Next, a Pong game session was introduced with either an abruptly (Abrupt group) or gradually (Gradual group) increasing delay (Delay), and was followed by another Blind Track session (Post Delay, green frame). To evaluate performance in the pong game, we calculated paddle-ball hit rate and analyzed its change throughout the experiment in both the Delay and Control groups (Fig. 3.3). The change in hit rate throughout the stages of the experiment was different between the groups (Stage- Group interaction effect: F , p ). The hit rate of the Control group remained ( 2,30) the same throughout the experiment (Late No Delay Early Delay: p ; Late No Delay Late Delay: p ; Early Delay Late Delay: p ). However, as a result of the sudden B presentation of the delay, the hit rate of the participants from the Delay group decreased drastically ( p ), and then increased with continued exposure to delay ( p ). B Albeit, they did not reach the same hit rate as without delay ( p ), nor as the Control group at the corresponding Late Delay stage ( p ). Hence, participants from the Delay B B B B B 64

71 group improved their performance after sufficient exposure to the delay, but this improvement was mild, suggesting a difficulty in adapting to the perturbation. Figure 3.3. Experiment 1: paddle-ball hit rate in the presence of delayed and non-delayed feedback Analysis of the change in hit rate is presented for each of the Abrupt (a, c, filled markers and bars) and Control (b, c, hollow markers and bars) groups. (a,b) Time courses of the mean hit rate of all participants in each group. The grey dashed vertical line separates the Pong No Delay (triangles) and the Pong Delay (circles) sessions. Shading represents 95% confidence interval. Colored areas represent the stages that were selected for statistical analysis: Late No Delay (dark blue), Early Delay (beige) and Late Delay (dark red). (c) On the left, mean hit rate of the Late No Delay, Early Delay and Late Delay stages, averaged over all the participants in each group (Delay: N=9, Control: N=8). The right black bars present the differences in the mean hit rate between the different stages, averaged over all the participants in each group. The dots represent individuals differences. Error bars represent 95% confidence interval. *p<0.05. **p<0.01. ***p< Both the Delay and the Control groups had to perform sessions of a blind reaching task after each of two Pong conditions: Post No Delay and Post Delay (Fig. 3.2a, blue and orange frames, respectively). During blind reaching, participants did not receive any visual feedback about the location of their hand, and they were asked to imagine as if there is a cursor. This enabled us to examine transfer to a task where participants had to rely only on a feedforward mechanism and 65

72 a proprioceptive feedback, and thereby, to capture the representation of their hand following exposure to either the non-delayed or the delayed pong game. In each trial, a target appeared in one out of three locations in the space, 10 cm away from a start location in the forward direction, and participants were requested to reach with their hand which was hidden from sight the entire experiment and to stop at a location that would place the imagined cursor at the target. At the beginning of the experiment, participants were familiarized with a reaching task with full visual feedback of the hand location using a cursor that was displayed during the entire session (Fig. 3.2a, Reach Training). Analysis of participants performance in the blind reaching task revealed that participants from the Delay group, but not the Control group, made longer (hypermetric) reaching movements following the play with the delayed pong. Figure 3.4a presents the reaching endpoints the locations of movements terminations during the Post No Delay and Post Delay blind reaching sessions from a representative participant from each group. While for the participant from the Delay group, Post Delay movements endpoints reached farther away from the start location than the Post No Delay movements endpoints (Fig. 3.4a, left), for the participant from the Control group, the blind reaching movements from the Post No Delay and Post Delay sessions ended around the same location (Fig. 3.4a, right). We extracted the reaching amplitude from all movements in each session (Fig. 3.4b). Playing pong in the presence of delay affected the reaching amplitudes (Session-Group interaction effect: F 4.717, p ). For participants from the Delay group, the reaching amplitude ( 1,15) significantly increased from the Post No Delay to the Post Delay session (Post Delay Post No Delay: [mean difference, 95% CI], cm,[ ], p ) (Fig 3.4b, left). Such an increase was not seen in the Control group ( cm,[ ], p ) (Fig. 3.4b, right). Overall, these statistical analyses suggest that the specific experience with the delayed pong caused the participants to perform larger blind reaching movements. B B 66

73 Delay Representation in the Sensorimotor System Figure 3.4. Experiment 1: reaching experimental results and representation models simulation results suggest a State-based rather than a Time-based Representation of delay. (a) Single participant s experimental results from each of the Delay (left, filled markers) and Control (right, hollow markers) groups. Movements start location is indicated by the black square and targets locations are marked by the gray squares. Markers represent the end point locations of the hand at movements terminations during the Post No Delay (blue triangles) and Post Delay (orange circles) Blind Reach sessions. (b) Experimental results group analysis. Colored bars represent the mean reaching movement amplitudes of each participant, and for each of the Blind Reach sessions, averaged over all the participants in each group (Delay: left, N=9, Control: right, N=8) and following subtraction of each group s average baseline amplitude (during the Blind Reach Post No Delay session). Black bars represent the difference in mean amplitude between the Post Delay and the Post No Delay blind reaching sessions for each participant, averaged over all participants in each group. The dots represent individuals differences. Error bars represent 95% confidence interval. (c) Simulation results of reaching end points in the Delay group (Post No Delay black outlined blue triangles, Post Delay black outlined orange circles) for Time Representation (left) and State Representation (right) of the delay. **p<

74 We observed that participants performed longer movements towards the right target than they did towards the other targets (main effect of Target: F , p ). For both groups, ( 2,30) the reaching amplitudes to the right target was larger than to the left ( p ) and to the middle ( p ) targets. In addition, only for the right target (Target-Session interaction B effect: F , ( 2,30) p 0.001), there was a statistically significant increase in movement amplitude between the Post No Delay and the Post Delay blind reaching sessions ( p ). No such differences were found for the left ( p ) and for the middle targets ( B ). Importantly, these differences in the reaching amplitudes between the targets did not stem from the applied delay (Group-Target-Session interaction effect: F , B ( 2,30) B p B p 0.744). Thus, we reasoned that they are a result of the difficulty in performing reaching to visual targets without visual feedback of the hand, and potentially, due to an insufficient training on this blind reaching task. Therefore, in Experiment 2, we added an additional session in the beginning of the experiment to train the participants to the blind reaching task. To understand which of the representation models described in Figure 3.1c explains the observed results, we simulated reaching movements towards targets for the Post No Delay and Post Delay conditions (Bakker et al., 2014) of the Delay group based on three representation models: Time Representation, State Representation Mechanical System and State Representation Spatial Shift. Reaching movements were simulated according to the minimum jerk trajectory (Flash and Hogan, 1985). To be consistent with the presentation of the experimental results, we added noise to the endpoint of each simulated movement. The noise was drawn from a normal distribution with zero mean and 1 cm standard deviation. Such noise may correspond to the noise that is present in various stages of sensorimotor control (Franklin and Wolpert, 2011). The simulation results are presented in Figure 3.4c. Post No Delay endpoints are closely distributed around targets locations. For Time Representation of the delay, in which an estimation of the actual time delay is available (ˆ in Eq. 3.1), the Post Delay endpoints are also distributed around the targets locations, and this result is not influenced by the value chosen for the estimated delay parameter ˆ. Hence, we cannot find a parameter value in the Time Representation model that would provide simulation results that are consistent with the reaching 68

75 overshoot observed in the experimental results. In contrast, for both types of the State Representation models, the Mechanical System and the Spatial Shift, we could find a parameter value that, similarly to the experimental observations, result in simulated Post Delay overshoots. For example, the simulation results shown in Figure 3.4c for the Mechanical System model were generated with a free parameter of the Taylor s series approximation ˆ 69 (Eq. 3.2) equal to 0.1 s, similarly to the delay in the experiment, and the results for the Spatial Shift model were generated with the free parameter x (Eq. 3.4) equaled to 1.5cm. Therefore, State Representation and not Time Representation can explain the increase in movement amplitude following the experience with the delayed pong Experiment 2 Transfer of hypermetria following a delayed pong game to a blind reaching task is not influenced by the schedule of delay presentation The group that experienced the delay in Experiment 1, and that showed, as a result, hypermetric movements during transfer to a blind reaching task, was presented with an abrupt delay perturbation. Since adaptation through the experience of gradually increasing perturbations was shown to enhance transfer (Kluzik et al., 2008; Torres-Oviedo and Bastian, 2012), we hypothesized that presenting participants with a gradually increasing delay during the Pong Delay session would result in an increase in the reaching movement amplitude during the blind transfer task compared with the abrupt case. To examine this hypothesis, we performed a second experiment (Experiment 2). The general protocol of Experiment 2 was similar to that of Experiment 1 except that during the Pong Delay session, one group of participants (Gradual, N=10) was exposed to a gradually increasing delay (from 0 to 0.1 s) during the first twenty five trials in the session and then remained constant at 0.1 s during the remaining five trials; and the other (Abrupt, N=10) was exposed to a constant 0.1 s delay from the beginning of the Pong Delay session (similarly with the Delay group in Experiment 1). The analysis of the paddle-ball hit rate (Fig. 3.5) revealed that the change in the hit rate throughout the delayed pong session was different between the groups (Group-Stage interaction effect: F , p ). Participants from the Abrupt group improved their ( 1,18) performance in the presence of the delay ( p ). In contrast, since the Gradual group did B

76 not experience an abrupt change in the delay, the mean hit rate of the participants from this group was higher than that of the Abrupt group at the beginning of the Pong Delay session ( p 0.001). As the delay increased, there was a decrease in their performance ( p ). B Altogether, while these results suggest that the Abrupt group adapted to the delay, in the Gradual protocol, we could not detect an improvement. This could be due to the gradual increase in delay that may conceal such an improvement. B Figure 3.5. Experiment 2: paddle-ball hit rate in the presence of abruptly- and gradually-introduced delayed feedback (a) Time courses of the mean hit rate of all participants in each group of the Abrupt (left, filled markers) and Gradual (right, hollow-dotted markers) groups. The grey dashed vertical line separates the Pong No Delay (triangles) and the Pong Delay (circles) sessions. Shading represents 95% confidence interval. Colored areas represent the stages that were selected for statistical analysis: Early Delay (beige) and Late Delay (dark red). (b) Colored bars represent the mean hit rate of the Early Delay and Late Delay stages, averaged over all the participants in each group (Abrupt: filled, N=10, Gradual: diagonal lines, N=10). The right black bars present the differences in the mean hit rate between the Early Delay and Late Delay stages, averaged over all the participants in each group. The dots represent individuals differences. Error bars represent 95% confidence interval. ***p< To examine transfer for each type of schedule of delay presentation, both the Abrupt and Gradual groups had to perform sessions of a blind reaching task after each of the Pong sessions: Post No Delay and Post Delay (Fig. 3.2b, blue and orange frames, respectively). In each blind reaching trial, participants were requested to reach and to stop at a location that would place the imagined cursor at the target that appeared in one out of three locations in the space, 12 cm away from a start location in the forward direction. To improve baseline performance in blind reaching, and to reduce non-specific variability between the targets, following a familiarization session with the reaching task (Reach Training), we added a session of Blind Reach Training. During this session, 70

77 we exposed participants to the blind reaching task but provided end point feedback at a location where they stopped after completing the movement. The two training sessions enabled us to make sure that the participants are able to reach the targets, and to train them to be accurate when no visual feedback is provided during the movement. The mean reaching amplitude during the Blind Reach Training session was larger by ~6% ([ mean, 95% CI ], cm,[ ] ) than the distance between start and targets locations. Analysis of participants performance in the blind reaching task revealed that, regardless of whether the delay was presented abruptly or gradually, participants made longer reaching movements following the play with the delayed pong, and the effect size was similar between the two groups. Figure 3.6a presents the reaching endpoints during the Post No Delay and Post Delay blind reaching sessions from a representative participant from each group. In both participants, while Post No Delay movements endpoints reached close to the targets, Post Delay movements endpoints overshot them. We analyzed the change in reaching amplitude due to the delayed pong and compared between the Abrupt and Gradual groups (Fig. 3.6b). Playing with the delayed pong resulted in an increase in reaching amplitudes in both groups (main effect of the Session: F , p ,[mean difference, 95% CI], cm,[ ] ) (Fig. 3.6b). ( 1,18) Although the overall mean reaching amplitude of the Gradual group was larger than that of the Abrupt group (main effect of Group: F , p ), we did not find an effect of the ( 1,18) play with the delayed pong on the change in reaching amplitudes between the groups (Session- Group interaction effect: F , p ). These results suggest that the hypermetric ( 1,18) blind reaching movements following the experience with the delayed pong are not influenced by the schedule of the delay presentation. We did not find a significant difference in the reaching amplitudes between the targets (main effect of Target: F , p 0. 75). Also, there was no difference in the change in ( 1.327,23.887) reaching amplitudes throughout the experiment between the targets (Target-Session interaction effect: F , p ), and no difference between the Abrupt and Gradual ( 1.517,27.313) groups (Group-Target-Session: F , p ). Thus, the increase in the blind ( 1.517,27.313) 71

78 reaching amplitudes following the play with the delayed pong was similar across the different targets. Figure 3.6. Experiment 2: comparison between the reaching results of the Abrupt and Gradual groups suggests that the schedule of delay presentation does not influence the representation of delay. (a) Single participant s experimental results from each of the Abrupt (left, filled markers) and Gradual (right, hollow-dotted markers) groups. Movements start location is indicated by the black square and targets locations are marked by the gray squares. Markers represent the end point locations of the hand at movements terminations during the Post No Delay (blue triangles) and Post Delay (orange circles) Blind Reach sessions. (b) Experimental results group analysis. Colored bars represent the mean reaching movement amplitudes of each participant, and for each of the Blind Reach sessions, averaged over all the participants in each group (Abrupt: filled, N=10, Gradual: diagonal lines, N=10). The right black bar represents the difference in mean amplitude between the Post Delay and the Post No Delay blind reaching sessions for each participant, averaged over all the participants from both groups. The dots represent individuals differences. Error bars represent 95% confidence interval. ***p< Experiment 3 Transfer of hypermetria to a blind tracking task suggests State Representation as a Mechanical System equivalent rather than a Spatial Shift Although the comparison between the blind reaching experimental and simulation results suggests that State and not Time variables are used to represent the delayed feedback, the blind reaching task have two limitations: (1) the increase in blind reaching amplitude following the experience with the delay indicates that the delay affects the representation of the state of the hand, but it may also mask some extent of time representation. Since the reaching task is mainly spatial, if a partial representation of the time lag exists, we cannot find it with this transfer task. (2) The blind reaching cannot differentiate between the suggested types of State Representations. Both the Mechanical System and the Spatial Shift models predict reaching 72

79 overshoot following the experience with the delayed Pong. Thus, to determine which model best explains delay representation, we conducted an additional experiment in which we examined transfer to a blind tracking after each of the Pong conditions: Post No Delay and Post Delay (Fig. 3.2c, purple and green frames, respectively). Similarly to the blind reaching task, during blind tracking, participants did not receive any visual feedback on the location of their hand and they were asked to imagine as if there was a cursor. As with the transfer to blind reaching, the absence of visual feedback in the transfer to blind tracking enable us to capture the representation of the participants when they had to rely only on a feedforward mechanism and a proprioceptive feedback. In each trial, a target was moving along a figure-of-eight path (which was not visible). The path was the same between trials, but the point within the path from which the target started moving randomly alternated between five different locations on the path. When the target started moving along the path, participants were required to track and maintain the imagined cursor within the target. In the beginning of the experiment, we familiarized the participants with the blind tracking task by providing them with a full visual feedback of the hand location using a cursor that was displayed the entire session (Fig. 3.2c, Track Training). Importantly, we designed the tracking task so that it would be predictive, thereby to enable revealing any temporal component that may exist in the representation (for both the Time and Mechanical System Representation models) (Rohde et al., 2014). To test whether the transfer is influenced by the schedule of delay presentation, participants were again assigned to one of two groups: Gradual (N=10) and Abrupt (N=10), which were different in the schedule of delay presentation during the Pong Delay session. 73

80 Figure 3.7. Experiment 3: blind tracking predictions Predicted tracking performance for each representation model: Time Representation (left), State Representation Mechanical System (middle) and State Representation Spatial Shift (right). The upper panel depicts schematic illustrations of a sinusoidal target trajectory (bold black) and hand trajectories during a tracking task following a non-delayed (Post No Delay, dashed gray) and a delayed (Post Delay, dotted gray) Pong game. The lower panel depicts the target-hand position space plots for the post nondelayed (Post No Delay, purple) and post delayed (Post Delay, green) conditions, each corresponds to the target and hand trajectories presented above it. An accurate performance in the Post No Delay condition would be reflected in an alignment between hand and target positions during tracking. For Time Representation of the delay, the hand trajectory is predicted to precede the target trajectory, resulting in an ellipse in the target-hand position space, with its major axis (dashed-dotted dark green) coincides with the Post No Delay target-hand position space line. For the State Representation Mechanical System model, the hand trajectory is predicted to precede the target trajectory while increasing in its amplitude, bringing about an ellipse that has a major axis tilted such that its slope is greater than the slope of the Post No Delay target-hand position space line. For the State Representation Spatial Shift model, the hand trajectory is predicted to be shifted away with respect to the target trajectory, resulting in an upward shift in the target-hand position space line. Figure 3.7 presents the predicted blind tracking performance in a single dimension and for a complete and single cycle of the figure-of-eight path during Post No Delay and Post Delay sessions for each of the representation models. The figure displays both the predicted target and hand position trajectories (upper panels) and the corresponding target-hand position space plots 74

81 (lower panels). The latter panels depict the position of the hand as a function of the position of the target for each sample during the movement. For the Post No Delay session, we defined an accurate tracking performance as a perfect spatial alignment and temporal synchronization between hand and target movements. Such an accurate performance would result in a linear relation with a zero intercept and a unity slope between hand and target positions (purple solid lines). For the Post Delay session, if participants cope with the delay using Time Representation, the movement of their hand will be shifted in time with respect to the movement of the paddle, preceding the path according to the represented time lag. When viewed in terms of the relationship between hand and target, this would result in an ellipse in the target-hand position space. The major axis of this ellipse is expected to overlap with the Post No Delay target-hand position space line. Alternatively, a representation of the delay as a Mechanical System will result in a hand trajectory that will slightly precede the target trajectory (but much less than in the Time Representation case), and importantly, its amplitude will be larger. In terms of the relationship between hand and target, this will result in an ellipse that has a major axis tilted such that its slope is greater than the slope of the Post No Delay target-hand position space line. Finally, if participants represent the delay as a Spatial Shift, the entire path of the hand will be shifted farther away from the body of the participant relative to the target. This would result in an upward shift of the target-hand position space line, and thus, a higher ordinate intercept value with respect to that of the Post No Delay target-hand position space line, and without any change in its slope. We analyzed participants blind tracking performance by examining the hand and target positional trajectories in both the frontal (right-left) and sagittal (front-back) dimensions of the movements. We evaluated the dynamics between hand and target movements by mapping the hand position to the target position for each sample, and by fitting an ellipse to the scatter of each trial. Figure 3.8a presents examples of target-hand position space scatters and their corresponding fitted ellipses of a single participant from two blind tracking trials one from a Post No Delay session (purple) and one from a Post Delay session (green) and for a single cycle in the sagittal dimension. The results demonstrate that the major axis of the Post Delay ellipse has a greater slope than that of the Post No Delay ellipse. Such a change in the slope is consistent 75

82 with the Mechanical System representation model, and not with the Time or Spatial Shift representations models. For a quantitative analysis of the dynamics between the hand and the target in each of the frontal (Fig. 3.8b) and the sagittal (Fig. 3.8c) dimensions, we extracted from each trial three measures: the delay between the target and the hand (Target-Hand Delay), the slope of the major axis of the ellipse (Slope), and the intercept of the major axis (Intercept). The Target-Hand Delay was evaluated by finding the lag for which the cross-correlation between the movements of the target and the hand was maximal. Positive values of Target-Hand Delay indicate that the hand movement preceded the movement of the target. The delayed pong did not cause participants to precede their hand movement with respect to the target movement in the blind tracking task. In both the frontal and sagittal dimensions of the task, the mean Target-Hand Delay was not significantly different between the Post No Delay and the Post Delay blind tracking sessions (Table 3.1, Session main) ([mean difference, 95% CI], frontal: 0.005,[ ], sagittal: 0.013,[ ] ) (Fig. 8b,c, left). This suggests that participants did not use Time Representation of the experienced delay. Also, participants hand did not move farther away from the target in a consistent manner due to the experience of the delayed pong. There was no significant difference in the mean Intercept between the Post No Delay and the Post Delay sessions (Table 3.1, Session main) (frontal: 0.541,[ ], sagittal: 0.608,[ ] ) (Fig. 3.8b,c, right. Note that for consistency with the presentation of the reaching amplitude in Figs. 3.4 and 3.6, we present the Intercept following subtraction of each group s average baseline Intercept). This suggests that it is unlikely the State Representation Spatial Shift model explains participants performance. In contrast, playing with the delayed pong caused participants to perform longer hand movements during the blind tracking task. We found a significantly higher Slope during the Post Delay than during the Post No Delay session (Table 3.1, Session main) (frontal: 0.114,[ ], sagittal: 0.162,[ ] ) (Fig. 3.8b,c, middle). These results are consistent with the State Representation Mechanical System model. We did not find an overall difference between the groups in any of these three measures (Table 3.1, Group main), and no difference in the influence of the delayed pong between the groups 76

83 (Table 3.1, Session-Group interaction). These results suggest that, similarly with the transfer to reaching case (Experiment 2), the schedule of the delay presentation does not influence tracking performance. 77

84 Figure 3.8. Experiment 3: tracking experimental results suggest State Representation of delay as a Mechanical System equivalent rather than a Spatial Shift. (a) Single participant s results. Target-hand position space of a single sagittal cycle from each of the Post No Delay (purple triangle) and Post Delay (green circles) Blind Track sessions. The left panel presents data points sampled at 11.8 Hz. The right panel presents data points sampled at 28.6 Hz and the fitted ellipses for entire data distribution (sampled at 200 Hz) from each of the Post No Delay (purple) and Post Delay (green) tracking sessions, together with the corresponding major axis lines (dashed-dotted dark purple and dashed-dotted dark green, respectively). (b,c) Group analyses for the frontal cycle (b) and for the sagittal cycles (c) of the delay between the hand and the target (left), and of the major axes slopes (middle) and intercepts (following subtraction of each group s average Post No Delay intercept, right), extracted from participants tracking performances. Colored bars represent each participant s mean, from each of the Post No Delay (purple) and Post Delay (green) tracking sessions, averaged over all the participants in each group (Abrupt: filled, N=10, Gradual: diagonal lines, N=10). Black bars represent the difference in the mean of each measure between the Post Delay and the Post No Delay sessions for each participant, averaged over the participants in the experiment. The dots represent individuals differences. Error bars represent 95% confidence interval. **p<0.01. Effect Session main Group main Session-Group interaction Measure Dimension Target-Hand Delay Slope Intercept F (1,18) p F (1,18) p F (1,18) p Frontal Sagittal Frontal Sagittal Frontal Sagittal Table 3.1. Statistical analyses of the blind tracking task For each of the Target-Hand Delay, the Slope, and the Intercept measures, and for each of the frontal and sagittal dimensions of the tracking path, we fit a two-way mixed effect ANOVA model, with the measure as the dependent variable, one between-participants independent factor (Group: two levels, Abrupt and Gradual), and one within-participants independent factor (Session: two levels, Post No Delay and Post Delay). The reported values for each measure are the F ratio, with the corresponding factor and residuals degrees of freedom in parentheses (left column), and the corresponding p-value (right column). 78

85 3.3 Discussion We exposed participants to a delayed feedback in an ecological task a pong game. Following a prolonged experience with the delay, regardless of whether the delay was introduced gradually or abruptly, and during subsequent blind reaching and tracking, their movements became hypermetric. Simulations explain this hypermetria as an outcome of a representation of delay as a mechanical system equivalent rather than a temporal or a spatial shift Delay representation time-based or state-based? There is an inherent difficulty in deciphering the representation of delay because it is a temporal perturbation that causes spatial effects. For example, visuomotor delay increased driving errors (Cunningham et al., 2001) and the size of drawn letters and shapes (Kalmus et al., 1960; Morikiyo and Matsushima, 1990). The ability to reveal the representation of the delay in these ecological tasks is limited by their complexity. Although our pong game is not entirely natural (the task scene is in 2D and the manipulated objects are not real), it is more complex and dynamic than the motor tasks that are usually being used for studying the sensorimotor system. To overcome the difficulty in extracting the change in representation from such a task, we examine transfer to simple and well-understood tasks. The transfer of hypermetria indicates that the participants used a state-based representation of the visuomotor delay. This may also explain the limited transfer of adaptation to delay to timing-related tasks (de la Malla et al., 2014). Conversely, recent studies reported evidence for a time-based representation of delay. In a tracking task, participants adapted to a visuomotor delay by time-shifting the motor command (Rohde et al., 2014), even in highly redundant tasks (Farshchiansadegh et al., 2015). Contrary to our ecological pong game, the tracking tasks in these studies were highly predictable. Also, the reported time-shift was observed during the adaptation or when examining aftereffect with the same, but non-perturbed, task. If our participants represented time, it only partially contributed to the adaptation, and was not transferred to the blind reaching and tracking. Similar temporal adjustments were also observed with delayed force feedback (Witney et al., 1999; Levy et al., 2010; Leib et al., 2015), and it may be that such adjustments are based on the capability of sensory organs that respond to force such as the Golgi tendon organ (Houk and Simon, 1967) 79

86 or mechanoreceptors in the skin of the fingers (Zimmerman et al., 2014) to represent delay as a time lag Adaptation to delay versus spatial perturbations There is an apparent similarity between a visuomotor delay and a spatial shift. In prior studies of reach movements, both displaced and delayed feedback caused overshoots that were reduced following adaptation, and a surprising removal of the perturbations caused undershoots (Smith and Bowen, 1980; Botzer and Karniel, 2013). There, participants were required to stop at stationary targets, whereas in the interception task of the pong game, movement endpoints were not constrained. Importantly, in Smith and Bowen (1980), the transfer to movements to the opposite direction was different: overshoot in displacement, and undershoot in delay. This supports our results that delay is not represented as a spatial shift. Another related perturbation is a visuomotor gain. In both gain and delay, the target and cursor locations at movement onset are unaltered, the magnitude of the spatial effects depends on the movement, and the aftereffects are similar (Krakauer et al., 2000; Paz et al., 2005). Indirect evidence for the relationship between gain and delay comes from interference studies. The interference paradigm suggests that successive (Krakauer et al., 1999; Tong et al., 2002; Caithness et al., 2004) or simultaneous (Tcheang et al., 2007; Sing et al., 2009) presentation of competing tasks disrupts learning and consolidation. Delayed visual feedback disrupts adaptation to visuomotor rotation and displacement (Held et al., 1966; Honda et al., 2012), but gain and rotation did not interfere with each other (Prager and Contreras-Vidal, 2003). This comparison suggests that gain and delay are processed and represented separately. However, representation of delay as gain is still a viable option. Because a mechanical system is essentially a frequencydependent gain and phase shift, evaluating the frequency dependency of the representation is critical for distinguishing between the gain and the mechanical system representations. Future studies are needed to directly examine this question Mechanical system representation of delay 80

87 The hypermetria during tracking is consistent with a mechanical system equivalent representation of delay. Meaning, the movement of the hand reflects a policy of controlling the delayed paddle as if the lag is a result of a damped paddle with an inertia that is attached to the hand by a spring. Such dynamic systems approach was suggested in a previous objectmanipulation study (Sarlegna et al., 2010). There, due to the visuomotor delay, participants changed their grip force control consistently with a visually-induced illusion of a mechanical system, but the effect vanished immediately with delay removal. We explored adaptation during the pong game and tested the representation in a transfer to the tracking task, capturing the representation independently from the online delayed feedback. The mechanical system equivalent explains effects of delayed visual feedback on perception increased mass (Honda et al., 2013) or resistance (Takamuku and Gomi, 2015). The anecdotal verbal responses of our participants were consistent with this view and with previous reports (Smith, 1972; Vercher and Gauthier, 1992) stating that the paddle is harder to maneuver, sluggish, or mechanical. The mechanical system model predicts that the hand should slightly lead the target. Such lead requires predictability of target s movement (Rohde et al., 2014), and was not observed in our results. This may be because, contrary to our expectation, participants did not fully predict the future location of the target in our tracking task. Nevertheless, since the hypermetria strongly distinguishes the mechanical system model from the other models that we tested, we think that the hypermetria is sufficient to support the mechanical system model Similar transfer of adaptation between abrupt and gradual schedules Both in reaching and tracking, the strength of transfer did not depend on whether delay was introduced abruptly or gradually. Other studies showed no difference in the influence of the schedule of perturbations presentation on motor learning of other types of perturbations, both in healthy (Wang et al., 2011; Joiner et al., 2013; Patrick et al., 2014) and in impaired participants (Gibo et al., 2013; Schlerf et al., 2013). In contrast, abruptly-introduced perturbations were shown to strengthen interlimb transfer (Malfait and Ostry, 2004). Also, gradually-introduced perturbations strengthen transfer of adaptation to other contexts (Kluzik et al., 2008; Torres- 81

88 Oviedo and Bastian, 2012). This is despite the fact that for the same duration of adaptation and for the same maximum magnitude of the perturbation, participants experience a smaller integral of the perturbation in a gradual compared to an abrupt protocol. In that sense, by comparing the transfer effects with respect to the overall experienced perturbation, and not with respect to its terminal/maximum value, we may view the influence of the gradual presentation of the perturbation on transfer to another context as stronger than the abrupt presentation. In any case, differences between abrupt and gradual presentation of perturbations may be attributed to the presence or absence of an awareness to the perturbations (Kluzik et al., 2008). Awareness was proposed to affect the assignment of the perturbation to extrinsic rather than intrinsic sources (Berniker and Kording, 2008), and to elicit explicit rather than implicit learning (Mazzoni and Krakauer, 2006; Taylor et al., 2014). Thus, we speculate that the delay was assigned to an intrinsic source, and that the adaptation to the delayed feedback is a result of an implicit process. This is likely because our brain naturally deals with intrinsic transmission and processing delays. However, we should be careful with this conjecture because we probed the delay representation only before and after the delayed pong session, and therefore, we may have missed differences between the abrupt and gradual groups during adaptation The learning rule for adaptation to the delayed pong We did not deal here with the learning mechanisms in adaptation to the delay. Since participants were instructed to hit the ball as many times as possible within the time duration of each trial, and were provided with a feedback according to this performance measure, we chose to report their hit rate throughout the experiments. These hits can be considered as rewarding signals that influence future interception attempts in a reinforcement learning mechanism (Izawa and Shadmehr, 2011; Wolpert et al., 2011; Shmuelof et al., 2012; Nikooyan and Ahmed, 2015). Although we saw a significant improvement in the hit rate in the groups that experienced an abrupt and constant delay (Figs. 3.3a,c, 3.5), the effects were not strong. Also, due to the dynamic nature of the gradual protocol, we could not report for adaptation in the Gradual groups. Importantly, an absence of an improvement in a motor task does not entail that an internal representation of the environment and body state was not constructed. It is evident by the 82

89 change in performance during both transfer tasks that an internal representation was indeed constructed throughout the participants experience with the delayed environment and independently of whether they have improved or not in the game. It might be that adaptation can be identified with other measures (Sternad, 2006; Faisal and Wolpert, 2009; Reichenthal et al., 2016). If the adaptation is error-based (Thoroughman and Shadmehr, 2000; Donchin et al., 2003; Smith et al., 2006; Herzfeld et al., 2014), the candidate error signals need to be identified, for example, the distance between the hand and the paddle at meaningful events during the game such as ball-paddle hits. Further studies are required to understand how the state-based representation of the delay is constructed. 3.4 Methods Notations We use lower-case letters for scalars, lower-case bold letters for vectors, and upper-case bold letters for matrices. x is the Cartesian space position vector, with x and y position coordinates (for the right-left / frontal and forward-backward / sagittal directions, respectively). f vector, with f and x Experiments f y Participants and experimental setup 83 is the force force coordinates. N indicates the number of participants in a group. Fifty seven right handed healthy volunteers (ages [21-41], 29 females) participated in three experiments: seventeen participated in Experiment 1, twenty in Experiment 2, and twenty in Experiment 3. No statistical methods were used to predetermine sample sizes, but the sample size per condition that we used was similar to the reported sample size in a previous study (Pressman, 2012), and for the similar test groups, the effects in our study were expected to be of similar size. All experiments were conducted after the participants signed an informed consent form approved by the Institutional Helsinki Committee of Ben-Gurion University of the Negev, Be'er-Sheva, Israel (Experiment 1), the Institutional Review Board of Northwestern University,

90 Chicago, USA (Experiment 2), or by the Human Subjects Research Committee of Ben-Gurion University of the Negev, Be'er-Sheva, Israel (Experiment 3). The experiments were administered in a virtual reality environment in which the participants controlled the handle of a robotic device, either a six degrees-of-freedom PHANTOM Premium TM 1.5 haptic device (Geomagic ) (Experiment 1), a two degrees-of-freedom MIT Manipulandum (Experiment 2) or a six degrees-of-freedom PHANTOM Premium TM 3.0 haptic device (Geomagic ) (Experiment 3). Figure 3.1a illustrates the experimental setup. Seated participants held the handle of the device with their right hand while looking at a screen that was placed transversely above their hand, and with a distance of ~10 cm bellow participants chin. They were instructed to move in a transverse plane. In Experiments 1 and 3, hand position was maintained in this plane by forces generated by the device that resisted any vertical movement. The update rate of the control loop was 1,000 Hz. Since the Manipulandum is planar, this was not required in Experiment 2. In Experiments 1 and 2, a projector that was suspended from the ceiling projected the scene onto a transverse white screen placed above the participant's arm. In Experiment 3, a flat LED television was suspended approximately 20 cm above a reflective screen, placing the visual scene approximately 20 cm below the screen, on the transverse plane in which the hand was moving. The hand was hidden from sight by the screen, and a dark sheet covered the upper body of the participants to remove all visual cues about the arm configuration. When visual feedback of the hand location was provided, the movement of the device was mapped to the movement of a cursor; when it was not perturbed by the delay, the cursor movement was consistent with the hand movement Tasks Each experiment consisted of two tasks: a pong game task and another blind task. During the latter, no visual feedback about the hand location was provided. In Experiments 1 and 2, the blind task was a reaching task, and in Experiment 3, it was a tracking task. The purposes of the blind tasks were to examine transfer and to capture the participants representation of their hand following an exposure to either the non-delayed or delayed pong game. Pong game 84

91 In the pong game, participants observed the scene that is illustrated in Figure 3.1b. The rectangle delineated by the black walls (Experiments 1 and 3: [sagittal frontal dimensions] cm, Experiment 2: cm) indicates the pong arena. The red horizontal bar marks the location of the paddle and corresponds to the hand location. As described below (see Protocol), each experiment consisted of two Pong game sessions. We name the first Pong session Pong No Delay, and the second Pong session Pong Delay. In the Pong No Delay session, the paddle moved synchronously with the hand. In the Pong Delay session, the paddle movement was delayed with respect to the hand movement (only for the Control group in Experiment 1, the delay in the Pong Delay session was equal to zero, and hence, the dynamics between the hand and the paddle in this session was equivalent to the dynamics during the Pong No Delay session). To apply the delay, we saved the location of the hand in a buffer that was updated with the update rate of the control loop, and displayed the paddle at the location of the hand time before. was set to values between 0 and 0.1 s, depending on the protocol and the stage within the session. The green dot indicates a ball which bounces off the walls and the paddle as it hits them. The duration of each Pong trial was t Trial 60 s. Information about the elapsed time from the beginning of the trial was provided to the participants by a magenta colored timer bar. A feedback about the performance in each trial was also provided using a blue hit bar that progressed accordingly with the recorded paddle-ball hits from trial initiation. In Experiments 1 and 3, during each trial, we updated the hit bar on every hit. The total amount of hits required to fill the bar completely ( ) was set to 80 in Experiment 1 and to 60 in Experiment 3, and it remained constant the entire experiment. In Experiment 2, during each trial, we updated the hit bar every time the participants achieved 5% of full n hit full n hit full. During the Pong No Delay session, we set n 90. After the last trial of the Pong No Delay session has completed, we calculated for each participant the average hitting hit rate of that trial, n hit t Trial, where n hit is the number of hits in the last trial of the Pong No Delay session. In the first trial of the second Pong Delay session, we matched the progression rate of the hit bar for each participant according to her performance at the end of the Pong No Delay session, such that n n. Then, in order to encourage participants to improve in the task, we full hit hit decreased the progression rate of the hit bar by 5% for each successive trial. 85

92 The ball was not displayed between trials. The initiation of a trial was associated with the appearance of the ball in the arena. In Experiments 1 and 2, a trial was initiated when participants moved the paddle to a restart zone a green rectangle (Experiment 1: 1 4 cm, Experiment 2: 2 10 cm) that was placed 3 cm below the bottom (proximal) border of the arena. Throughout the entire experiment, including the Pong Delay session, the paddle was never delayed between trials. Since the displayed paddle movement between trials was always instantaneous with hand movement, we were concerned that the effect of delay on state representation is attenuated by a recalibration of the hand location according to the non-delayed paddle. Thus, in Experiment 3, we did not display the paddle between trials, and participants were instructed to initiate a trial by moving the handle of the robotic device backward (towards their body). When the invisible paddle crossed a distance of 3 cm from the bottom border of the arena, the trial was initiated. In Experiments 1 and 3, the initial velocity of the ball in the first Pong trial was 20 cm/s, and in every other Pong trial, it was the same as the velocity at the end of the previous trial. In Experiment 2, the initial velocity of the ball in each Pong trial was 28 cm/s. The participants were instructed to hit the ball towards the upper (distal) border as many times as possible. When the ball hit a border, its movement direction was changed to the reflected arrival direction, keeping the same absolute velocity (consistent with the laws of elastic collision). To encourage the participants to explore the whole arena and to eliminate a drift to stationary strategies, the reflection of the upper border (and not the other borders) included some random jitter. Introducing the jitter effectively corresponded to setting a compromise between playing against a wall and playing against an opponent. We did it by adding the jitter component j to the frontal component of ball s velocity before the collision with the upper border that: where postub preub (3.5) x x j. b b preub x b, such postub x b is the frontal component of ball s velocity following the collision with the upper preub border. In Experiments 1 and 3, j y b tan( j ), where preub y b is the sagittal component of 2 ball s velocity before the collision with the upper border and j ~ N(, ) N(0,0.05 ). 86

93 2 and denote for the mean and variance of a normal distribution N, respectively. In Experiment 2, j U( a, b) U( 13 cm,13 cm ), where U two arguments. ~ s s is the uniform distribution between its The velocity of the ball is also influenced by the paddle s velocity at the time of a hit. We determined the relations between the velocity of the ball following a paddle hit ( according to the velocity of the ball before the hit ( reaching the ball ( was computed according to: x p x b prep x b postp ) and the velocity of the paddle when ). For the frontal dimension, the ball s velocity after bouncing the paddle postp prep (3.6) x b 0.7 x b x p. For the sagittal dimension, we enabled the hit to occur only when the paddle was moving upward and the ball was moving downward. In all other cases, the ball passed through the paddle as if they were moving over different planes. The purpose of allowing hits to occur only in the upward direction was to enable a separation between the effects of the Time and State Spatial Shift representation models. In our design, we follow the assumption that a change in representation occurs mainly during meaningful events in the pong game paddle-ball hits. According to this view, allowing hits to occur in both the upward and downward directions could have cancel out the State Representation Spatial Shift effect, limiting our capability to distinguish it from the Time Representation model. In this dimension, after a hit occurred, the ball's movement direction was always reversed, and its velocity was computed according to: postp prep (3.7) y b 0.7 y b y p. In our setup, the upward movement direction had a positive velocity, and the downward direction was negative. Note that since a hit occurred only when prep y b was negative and y p was ) positive, the resulting postp y b was always positive. This way, the ball's movement direction following the hit was reversed, moving towards the upper border. A possible strategy to cope with the delay was to slow down, and thus, for the delay to be effective, we wished to encourage participants to maintain their movement velocity as much as possible during the game despite 87

94 the change in delay. Therefore, we determined the coefficients absolute values of prep y b and y p (Eq. 3.7) to be between 0 and 1, such that they would reduce the effect of these velocities on the velocity of the ball after the hit. Thus, to maintain the ball s speed after the hit as it was before the hit or to make it faster, y p needed to be at least prep ~ In addition to the constraint y b on the paddle to move upward, participants were informed that they should control the paddle to move fast enough at the moment of a hit, otherwise the ball would slow down, reducing the number of opportunities to hit it. Once participants hit the ball with the paddle, a haptic pulse was delivered by the device simultaneously with the displayed collision. The pulse f postp was applied according to: where m b is the ball s mass and (3.8) f postp postp mb ( x b x b t prep t is the duration of the applied force. The specific parameters of the magnitude and durations of the haptic pulses were tuned for each of the devices that were used in the different experiments such that a relatively similar haptic stimulation was applied despite the differences in the specifications of the devices. In Experiments 1 and 3,, and we calculated ). m b kg postp f as the maximum applied force according to a time interval of t s. However, the haptic pulse was applied for 0.05 s, in which it gradually and linearly postp increased from zero to f for the first s (since the update rate of the control loop in this setup was 1,000 Hz, this is equivalent to 25 sample intervals) and then decreased back to zero in a similar manner for the remaining s. In Experiment 2, m b kg, and the force was applied during a single sample interval of t s. Reaching At the beginning of a reaching trial, the entire display was turned off, and the device applied a spring-like force that brought the hand to a start location, which was at the center of the bottom border of the pong arena (that was displayed only during the pong trials) and 1 cm (Experiment 1) or 3 cm (Experiment 2) below it. A trial began when a target (a hollow square, cm 88

95 inner area) appeared in one out of three locations in the plane, which were distant by 10 cm (Experiment 1) or 12 cm (Experiment 2) from the start location in the forward direction, and separated from each other by 45 0 (Fig. 3.2a,b, 3.4a and 3.6a). Throughout a reaching session, each of the three targets appeared fifteen times and in a random and predetermined order. The appearance of the target was the cue for the participants to reach fast and to stop at the target. During each reaching trial in the experiment, we determined movement initiation as the time when the hand was distant by 3 cm from the start location (Experiment 1) or when the sagittal component of hand s velocity ( y h ) rose above 25 cm/s (Experiment 2). Movement stop was defined at 0.5 s after y h went below 10 cm/s (Experiment 1) or 0.2 s after it went below 15 cm/s (Experiment 2). After identifying that a reaching movement was initiated and completed, the device returned the hand to the start location in preparation for the next target to appear. We had three types of Reaching sessions that were different from each other by the visual feedback that was provided to the participants (Fig. 3.2a and 3.2b). During a Reach Training session, participants received full visual feedback of the hand location using a cursor (filled square, cm) on the screen throughout the entire movement. They were instructed to put the cursor inside the hollow target. During a Blind Reach Training session, the cursor was not presented during the movement, and participants were requested to imagine as if there was a cursor, and to stop when the invisible cursor is within the target. When they stopped, we displayed the cursor, providing the participants with a feedback about their movement endpoint with respect to the location of the target. During the Blind Reach sessions that were presented after each of the Pong sessions, participants did not receive any visual feedback about their performance during or after the trial. Tracking At the beginning of a tracking trial, the entire display was turned off, and the device applied a spring-like force that brought the hand to a start location, which was at the center of the bottom border of the Pong arena and 2 cm below it. During each trial, participants were asked to track a target (a hollow square, cm inner area) that moved along an invisible figure-of-eight 89

96 path (Fig. 3.2c). This path was constructed as a combination of the following cyclic trajectories in the two-dimensional plane: where A 8 cm 2 t xt ( t) Asin( ) (3.9) T, 4 t yt ( t) Asin( ) T is the path amplitude, and T 5 s is the cycle time. The center of the figure-ofeight path was located 15 cm ahead from the location of the hand at trial initiation (start location). A trial began when a target appeared in one out of five locations in the plane: either in the center of the figure-of-eight path (15 cm ahead from the start location), or in each of the four sagittal extrema (9 and 24 cm ahead). Throughout a Tracking session, the five targets appeared in equal amounts and in a random and predetermined order. The appearance of the target was the cue for the participants to reach fast and to stop at the target. Reaching initiation was determined as the time when either the frontal ( x h ) or sagittal ( y h ) components of hand s velocity rose above 10 cm/s. Reaching stop was defined at 0.5 s after both x h and y h went below 5 cm/s. When the reaching movement stopped, the target started moving along the figure-ofeight path until it reached back to its initial location. The targets were moving in the same direction along the path (as illustrated by the dotted arrow in Fig. 3.2c), regardless of their initial location. A trial was completed after the device returned the hand to the start location in preparation for the next target to appear. Each experiment included two types of Tracking sessions that were different from each other by the visual feedback that was provided to the participants (Fig. 3.2c). During a Track Training session, participants received full visual feedback of the hand location using a cursor (filled square, cm) on the screen throughout the entire movement. They were instructed to keep the cursor inside the hollow target. During a Blind Track session, the cursor was not presented during the entire duration of the trial, and participants were requested to imagine as if there was a cursor, and to keep the imagined cursor within the moving target. 90

97 Protocol Experiment 1 In each experiment, sessions alternated a pong game and a reaching task (Fig. 3.2a). Each Reach session consisted of forty-five trials (fifteen for each target). An experiment started with a Reach Training session. The purpose of this session was to familiarize participants with the Reaching task. After training, participants were presented with the Pong No Delay session for ~10 min. This was followed by a Blind Reach session (Post No Delay). Next, participants experienced the Pong Delay session for ~30 min. In the Delay group (N=9), we introduced a delay of 0.1 s between hand and paddle movements at the first trial of the Pong Delay session that remained constant throughout the entire session. In the Control group (N=8), no delay was applied throughout the entire Pong Delay session. The Pong Delay session was followed by another Blind Reach session (Post Delay). Experiment 2 In each experiment, sessions alternated a pong game and a reaching task (Fig. 3.2b). An experiment started with a Reach Training session that consisted of six trials (two for each target). The purpose of this session was to familiarize participants with the reaching task. The next session was a Blind Reach Training session that consisted of forty-five trials (fifteen for each target). Since during this session, visual feedback was provided only after the movement ended, this enabled us to train participant to reach accurately to the targets when they do not have any visual indication of their hand location throughout the movement. After training, participants were presented with a Pong No Delay session, consisting of ten trials. This was followed by a Blind Reach session (Post No Delay) with forty-five trials. Next, participants experienced a Pong Delay session, consisting of thirty trials. In the Abrupt group (N=10), we introduced a delay of 0.1 s between hand and paddle movements at the first trial of the Pong Delay session that remained constant throughout the entire session. In the Gradual group (N=10), we introduced a delay of s at the first trial of the Pong Delay session and gradually increased it by s on every trial until the 25 th trial of the session, where it reached 91

98 to 0.1 s ; then, the delay was kept constant for the remaining five trials of the session. The experiment ended with another Blind Reach session (Post Delay) of forty five trials. Experiment 3 In each experiment, sessions alternated a pong game and a tracking task (Fig. 3.2c). An experiment started with a Track Training session that consisted of thirty trials (six for each target). The purpose of this session was to familiarize participants with the Tracking task and to train them to the predictable figure-of-eight path. After training, participants were presented with a Pong No Delay session, consisting of ten trials. This was followed by a Blind Track session (Post No Delay) that consisted of fifteen trials (three for each target). Next, participants experienced a Pong Delay session, consisting of thirty trials. The time course of change in delay throughout the experiment in the Abrupt (N=10) and Gradual (N=10) groups was the same as in Experiment 2. The experiment ended with another Blind Track session (Post Delay) of forty-five trials Data analysis Metrics Device position, velocity, and the forces applied were recorded throughout the experiment at 200 Hz. They were analyzed off-line using custom-written MATLAB code (The MathWorks, Inc., Natick, MA, USA). Pong: Hit rate To examine performance in the pong game, we analyzed the change in paddle-ball hit rate throughout the experiment. As mentioned above, during a hit, a haptic pulse was delivered by the device. No force was generated by the device when no hits occurred. Thus, we identified the number of hits off-line by extracting the number of haptic pulses from the force data. Since the duration of each of the Pong sessions in Experiment 1 was varied between participants, to analyze the change in the average hit rate of all participants in each group, for each participant, we pulled the data of a session and divided it into bins of equal duration. The Pong No Delay 92

99 session was divided into five bins, and the Pong Delay session was divided into twenty bins. Hit rate was calculated as n hit t Bin, where n hit is the number of hits in a bin. In Experiments 2 and 3, the duration of the Pong sessions was equal between participants, consisting of the same number of trials, each with a duration of t Trial 60 s. Thus, in these experiments, hit rate was calculated as n hit t Trial, where n hit is the number of hits in a trial. Reaching: Amplitude For the purpose of data analysis, we defined movement onset at the first time the velocity rose above two percent of its maximum value. Movement end time was determined to be at 0.1 s after the time the velocity dropped below five percent of its maximum value, and thus, reaching end-point is defined as hand location ( x h ) at that time point. Reaching amplitude was calculated as the Euclidean distance between x h at movement onset and movement end-point. Tracking: Target-Hand Delay, Slope, and Intercept As mentioned above, during each Tracking trial, the tracking task began immediately after the participant reached towards a target within the figure-of-eight path and stopped. Thus, we separated the tracking movement from the reaching movement by defining tracking onset as the first sampled time point in which the target started moving. To evaluate the tracking accuracy, we calculated for each Tracking trial an (Nagengast et al., 2009): 2 R value according to (3.10) R 2 var( xh xt ) var( yh yt ) 1, var( x ) var( y ) h h where var is the variance of the expression in the parentheses. We calculated for each participant the mean 2 R was smaller than 6 2 R of each Tracking session. In 12% of the individual Blind Track trials, the 0., and we removed them from further analysis. Since the pong game was two dimensional, we analyze the effect of the game on both the x h (t) and y h (t) components of the hand movement that tracked the two-dimensional target s path 93

100 (Eq. 3.9). To measure Target-Hand Delay, for each dimension, we calculated the cross correlation between target and hand positions ( (t) x t and x h (t) for the frontal dimension, and (t) y t and y h (t) for the sagittal dimension) in each trial, and found the lag for which the cross correlation was maximal. Positive values of Target-Hand Delay indicate that the hand movement preceded the movement of the target. The purpose of this measure was to examine whether participants used a Time-based Representation to cope with the delay. If they did, the predicted effect would be an increase in the Target-Hand Delay from the Post No Delay to the Post Delay tracking session. As illustrated in Figures 3.7 and 3.8, we examined the relationship between the target and the hand during tracking by projecting the sampled position of each in a target-hand position space. Then, we fitted an ellipse to the data points with the following form (Fitzgibbon et al., 1999; Chernov, 2009): 2 2 (3.11) a x 2b x x c x 2d x 2e x f 0, e t e t h e h e t e h e where x t and x h are the Euclidean space coordinates of the target and hand frontal movement direction in a single trial, respectively. The same was done also for y t and y h the Euclidean space coordinates of the target and hand sagittal movement direction. Note that the figure-ofeight is constructed from a single frontal sine cycle and two sagittal cycles, but for each dimension we fitted a single ellipse for all the data points. Then, we extracted the Slope and the Intercept of the ellipse s major line. To do this, we derived the coordinates of the center of the ellipse ( o t, o h ) according to: (3.12) o t c d b e e b d e e e e e e e e, oh. 2 2 be ae ce be ae ce a The counterclockwise angle of rotation ( ) between the x t or the line is: y t axis and the ellipse s major 94

101 (3.13) ae ce cot ( ) 2 2be 1 1 ae ce cot ( ) 2 2 2be for for for for b 0, a e e e e e b 0, a e b 0, a e b 0, a e c e c e c e c e or or b 0, a e e e b 0, a e c. e c e The ellipse s major line Slope ( s maj ) and Intercept ( i maj ) were calculated according to: (3.14) s tan( ), i maj (3.15) maj oh smaj ot. The Slope and Intercept measures enabled us to assess how State Representation of delay takes place; an increase in the Slope is consistent with a delay representation as a Mechanical System, whereas an increase in the Intercept suggests a representation of delay in the form of a Spatial Shift Statistical analysis Statistical analyses were performed using custom written Matlab functions, Matlab Statistics Toolbox, and IBM SPSS. We used Lilliefors test to determine whether our measurements were normally distributed (Lilliefors, 1967). For ANOVA models that included a within-participants independent factor with more than two levels, we used Mauchly s test to examine whether the assumption of sphericity was met. When it was not, F-test degrees of freedom were corrected using Greenhouse-Geisser adjustment for violation of sphericity. We denote the p values that were calculated using these adjusted degrees of freedom as p. For the factors that were statistically significant, we performed planned comparisons, and corrected for family-wise error using Bonferroni correction. We denote the Bonferroni-corrected p values as In Experiment 1, to analyze the change in hit rate throughout the experiment for each of the Delay and Control groups, we calculated for each participant the mean hit rate of the last four p. B 95

102 bins in the Pong No Delay session (Late No Delay), and the first (Early Delay) and last (Late Delay) four bins in the Pong Delay session. Then, we fit a two-way mixed effect ANOVA model, with the mean hit rate as the dependent variable, one between-participants independent factor (Group: two levels, Delay and Control), and one within-participants independent factor (Stage: three levels, Late No Delay, Early Delay and Late Delay). In Experiment 2, to analyze the change in hit rate throughout the Pong Delay session and to compare between the Abrupt and Gradual groups, we calculated for each participant the mean hit rate of the first (Early Delay) and last (Late Delay) five trials in the Pong Delay session. Then, we fit a two-way mixed effect ANOVA model, with the mean hit rate as the dependent variable, one between-participants independent factor (Group: two levels, Abrupt and Gradual), and one within-participants independent factor (Stage: two levels, Early Delay and Late Delay). To analyze the effect of the delayed pong on reaching amplitude, we evaluated for each participant the mean reaching amplitude during the Post No Delay and Post Delay sessions. We fit a three-way mixed effects ANOVA model, with the mean reaching amplitude as the dependent variable, one between-participants independent factor (Group: two levels, Experiment 1: Delay and Control, Experiment 2: Abrupt and Gradual), and two within-participants independent factor (Session: two levels, Post No Delay and Post Delay. Target: three levels, Right, Middle and Left). Mauchly s test indicated a violation of the assumption of sphericity for the main effect of Target on the reaching amplitude in Experiment 2 ( 2 (2) , p ), and for the Session and Target interaction effect ( 2 (2) , p ). Thus, we applied the Greenhouse-Geisser correction factor to the Target factor s degrees of freedom in the former ( ˆ ), and to the Session-Target and the Session-Target-Group interactions degrees of freedom in the latter ( ˆ 0.759). To analyze the effect of the delayed Pong on tracking performance, we evaluated for each participant the mean Target-Hand Delay, Slope and Intercept measures for each movement dimension during the Post No Delay and Post Delay sessions. For each measure, we fit a twoway mixed effect ANOVA model, with the measure as the dependent variable, one between- 96

103 participants independent factor (Group: two levels, Abrupt and Gradual), and one withinparticipants independent factor (Session: two levels, Post No Delay and Post Delay). Throughout the paper, statistical significance was determined at the p 0.05 threshold. 97

104 Chapter 4: The Magnitude and the Schedule of Presentation of a Visuomotor Delay Affect Adaptation and its Transfer 1,2, Lior Shmuelof 3,4,2, Ferdinando A. Mussa-Ivaldi 5,6,7 and Ilana Nisky 1,2 1. Department of Biomedical Engineering, Ben-Gurion University of the Negev, Be'er Sheva, Israel 2. Zlotowski Center for Neuroscience, Ben-Gurion University of the Negev, Be'er Sheva, Israel 3. Department of Brain and Cognitive Sciences, Ben-Gurion University of the Negev, Be'er Sheva, Israel 4. Department of Physiology and Cell Biology, Ben-Gurion University of the Negev, Be'er Sheva, Israel 5. Department of Physiology, Feinberg School of Medicine, Northwestern University, Chicago, IL, USA 6. Department of Biomedical Engineering, Northwestern University, Evanston, IL, USA 7. Sensory Motor Performance Program, Rehabilitation Institute of Chicago, Chicago, IL, USA Keywords: delay, reaching, transfer, representation Acknowledgments: The authors would like to thank Ali Farshchiansadegh and Felix Huang for their help in constructing the experimental setups. This study was supported by the Binational United-States Israel Science Foundation (grant no ), and by the Helmsley Charitable Trust through the Agricultural, Biological and Cognitive Robotics Initiative of Ben-Gurion University of Negev, Israel. GA was supported by a Negev Fellowship. Contribution: GA, LS, FMI and IN designed the experiments; GA analyzed the data; GA, LS, FMI and IN interpreted the results; GA, LS, FMI and IN wrote the manuscript. 98

105 Abstract Our previous results indicated that for delays of up to 100 ms, prolonged experience with a visuomotor delay in a game of pong causes hypermetric movements in subsequent blind reaching and tracking tasks. These results are consistent with a model that suggests a representation of delay as a mechanical system equivalent rather than as an actual time lag. Here, we examined this state-based representation in depth: we tested the effects of playing pong in the presence of up to 300 ms delays which were presented either gradually or abruptly on movement kinematics during the game and during transfer to the blind reaching task. We also explored the dynamics of the transfer of the delay effects by presenting the blind reaching task multiple times throughout the experiment. We found that increasing delays cause increases in movement amplitude and duration during the pong game; however, the delay does not affect the maximum velocity of the pong movements. These effects were apparent even during the very early stages of exposure to delay. The hypermetria transfers to the blind reaching task (albeit in a limited manner), and is associated with either an increase in the maximum velocity or duration of the movements. The data also showed that participants performance in the game declined with increased delays. These results, together with a comparison of the delay perturbations (for the different delay magnitudes) and their equivalent mechanical system models in the frequency domain, provide further support for our proposed state-based representation model of visuomotor delay. Our analyses also shed light on the kinematic characteristics of movements during the pong game with and without delays of varying magnitudes. They raise a series of questions that can guide future research that should lead to a better understanding the effects of delayed feedback in a dynamic ecological motor task. 4.1 Introduction Previously, we examined the way experience with visuomotor delays of up to 100 ms during a game of pong affected the movement amplitude during transfer to blind reaching and tracking tasks. We found that the delay caused participants to perform hypermetric (longer) movements in the transfer tasks than they did before their experience with the delay. These hypermetric 99

106 movements were consistent with a representation of the delay as an equivalent to the mechanical system. In this series of experiments we further explore the state-based representation of the delay by presenting participants with visuomotor delays of up to 300 ms while they play the pong game (Fig. 4.1). We examine the way various movement kinematics are affected by the magnitude of the delay and its presentation schedule. To investigate the dynamics of the delay effects throughout the experiments, we analyzed participants performance both while attempting to intercept the ball in the pong task and during the transfer to the blind reaching task, which was presented multiple times throughout the delayed pong session. The representation of visuomotor delay in the sensorimotor system may depend on the magnitude of the delay. Typically, delays in visuomotor integration processes range from 150 to250 ms (Miall and Wolpert, 1995; Kawato, 1999; Franklin and Wolpert, 2011), and numerous results suggest that humans can cope with such internal delays through neural structures that predict the sensory outcomes of a motor command (Miall et al., 1998; Miall et al., 2001; Imamizu, 2010). The delays that were applied between the hand and paddle movements in the experiments described previously did not exceed 100 ms. These magnitudes are smaller than the inherent delays typically dealt with by the sensorimotor system, which could have adopted the appropriate coping mechanisms without modulation. However, higher delays are likely to result in new coping strategies (Sheridan and Ferrell, 1963; Ferrell, 1965). From a computational point of view, for a given frequency of a cyclic movement, the magnitude of the delay should influence the movements that are predicted by a delay representation as a mechanical system equivalent. As described in Chapter 3, the mechanical system representation model is derived from an approximation of a Taylor series of the dynamics between the hand and the delayed paddle, with the estimated time delay (ˆ ) as a single free parameter in the model. One prediction of the mechanical system model is an increase in the amplitude of the movement of the hand; with a higher delay, the predicted amplitude is expected to be larger. Another prediction of the mechanical system representation is a slight temporal lead of the hand with respect to the perceived paddle. For small delays, the temporal phase shift resulting from the 100

107 delay should be similar in magnitude to the lag of the equivalent mechanical system. However, as the delay between the hand and the paddle gets higher, the less the mechanical system equivalent can approximate the dynamics between them, unless the participants slow down. Thus, an approximation of visuomotor delays as a mechanical system equivalent may be valid solely for delays that are small compared to the cycle of the movement. This may explain why the participants were able to improve in the game despite the incorrect representation. If we represent the delay using a mechanical system equivalent, at higher delays performance in the game should deteriorate (either because of an invalid delay approximation or as a consequence of slowing down). In addition, for large enough delays, this mechanical system representation is likely to break down, and the sensorimotor system will either use another representation, or will no longer be able to build an internal representation of the delay. It is important to analyze the movement kinematics of the participants during the game and to the changes between the non-delayed and the delayed conditions. Exploring the transfer of delay effects to blind reaching and tracking tasks was used to compare performance on these wellunderstood movements and the simulated predictions of the different representation models. This comparison showed that the delay was mainly represented as a mechanical system equivalent. However, it is still possible that part of the representation of the delay is time-based and cannot be identified solely by analyzing the transfer tasks. This is because the reaching task is purely spatial. Second, if participants can represent the actual time lag but the tracking task is not sufficiently predictable, they would still fail to precede their movement with respect to the moving target (Rohde et al., 2014). Finally, the time representation of the delay may have been specific to the task in which the delay was introduced (the pong game) and does not transfer (de la Malla et al., 2014). Some of the effects of the mechanical system representation such as the increase in movement amplitude and the temporal lead of the hand may also be lost during the transfer. Therefore, examining the kinematic changes that may occur during the game due to the delay could shed new light on the representation of visuomotor delay. 101

108 Delay Representation in the Sensorimotor System Figure 4.1. The pong game and the experimental protocols (a) An illustration of the experimental setup and the pong game: participants sat and held the handle of a robotic arm. A screen that was placed transversely above their hand covered the hand and displayed the scene of the experiment. During the pong game, participants controlled the movement of a paddle (red bar) and were required to hit a moving ball (green dot) towards the upper wall of the pong arena, which is delineated by the black rectangle. The paddle movement was either concurrent (No Delay) or delayed (Delay) with respect to the hand movement (the red arrow indicates the paddle movement direction). (b, c) Experimental protocols. In each experiment, sessions alternated a pong game (colored solid lines) and a blind reaching task, where no visual feedback was presented at any point during the trial. In the first pong session (No Delay, purple line), the paddle moved instantaneously with the hand movement, followed by a Blind Reach session (Post No Delay, black bar). The next sessions (Delay, blue scale lines) began with a delay between hand and paddle movements, and each of these was followed by a Blind Reach session (Post Delay, gray scale bars). Two groups, Abrupt 100 (N=10) and Gradual 100 (N=10) experienced a single No Delay session and a single Delay session (b). For comparisons between different stages of the experiment, we divided the Delay session into six stages of five minutes each. Three groups, Abrupt 150 (N=8), Abrupt 300 (N=9) and Gradual 300 (N==9), experienced six alternating Delay (pong) and Post Delay (blind reaching) sessions (c). Throughout the Delay session, the Abrupt 100, Abrupt 150 and Abrupt 300 groups experienced a constant delay of 100, 150 and 300 ms, respectively. The Gradual 100 and Gradual 300 groups were exposed to a gradual increase of the delay from 0 to 100 or 300 ms, respectively. As shown in the legend scales, the color intensities represent the maximum experienced delay in each of the delayed pong session (blue) and for the subsequent blind reaching session (gray); darker colors represent higher delays. 102

109 In the study reported in Chapter 3, we also found no influence of the schedule of delay presentation on movement amplitude during the transfer tasks since the increase in movement amplitude was comparable between the gradual and abrupt presentations. However, if the effect is immediate and directly related to the magnitude of the recently experienced delay, we should find differences between the presentations during the early stages of playing with the delayed pong, both during the game and in the transfer. Thus, in this work, in addition to the examination of movements during the pong game throughout the experiment, we introduced multiple sessions of the blind reaching task interspersed within the delayed pong game. This served to examine the dynamics of the transfer of delay effects at different exposure durations. The results are divided to two main sections. The first section presents an analysis of the effects of the delay magnitude and the schedule of presentation on movement kinematics during the pong game, and on the transfer of these effects to the blind reaching task. The data suggest that regardless of their presentation schedule, increasing delays cause increases in movement amplitude and duration during the pong game, which further strengthens our mechanical system representation model for visuomotor delay. The data also show that differences in the pong movements under a different delay presentation schedule do not transfer to the blind reaching task. In addition, the blind reaching results reveal inter-participant variability in the change in movement maximum velocity and duration. The second section focuses on performance in the pong task and shows a decline in performance in the game with increasing delay. It also characterizes the effect of delay on various interception kinematics. It provides ideas and future directions for analyses of motor behavior during an ecological interception task, and attempts to identify the mechanisms by which the sensorimotor system learns to cope with visuomotor delays. 103

110 4.2 Results Section 1: the magnitude and the schedule of presentation of a visuomotor delay during a game of pong affect movement kinematics, and these effects only partially transfer to a blind reaching task Visuomotor delay causes hypermetric movements during the pong game that transfer to the blind reaching task Participants played a game of pong, in which they were asked to hit the moving ball as many times as they could towards the upper wall of the arena (Fig. 4.1a). There were two types of pong sessions: the first session was always played with no delay (Pong No Delay), where the paddle moved together with the hand. In the second type, the game incorporated a delay between hand and paddle movements (Pong Delay). After the pong session, the participants played a session of a blind reaching task in which they did not receive any visual feedback about the location of their hand (Fig. 3.2a, b in Chapter 3). In each blind reaching trial, a target appeared in one out of three locations in the space, 12 cm away from a start location in the forward direction, and participants were requested to reach with their hand which was hidden from sight for the entire experiment and stop at the location that would place the imagined cursor at the target. To train participants for this task, at the beginning of the experiment, participants took part in a Blind Reach Training session during which they were provided with end point feedback on the location where they stopped after completing the movement. To examine how playing pong with delays of up to 100 ms and how the schedule of the delay presentation affect movement amplitudes during the game (pong amplitude, Fig. 4.2a), and its relationship to performance during transfer (reaching amplitude), we revisited the Abrupt and Gradual groups in Experiment 2 that were described in the previous chapter. For our purposes, these groups were dubbed Abrupt 100 (N=10) and Gradual 100 (N=10), respectively (Fig. 4.1b). Both groups took part in a single No Delay pong session and a single Delay pong session, each of which was followed by a Blind Reach session (Post No Delay and Post Delay, respectively). Throughout the Delay session, the Abrupt 100 group experienced a constant 100 ms delay whereas the Gradual 100 was exposed to a gradual increase in the delay from 0 to 100 ms. For 104

111 Delay Representation in the Sensorimotor System comparisons between different stages of the experiment, we divided the Delay pong session into six sessions of five minutes each. Figure 4.2. Examples of pong movements and kinematic measures (a) An example of the hand movement path of an individual participant (Abrupt 150 group) during ~ 5 sec of a single pong trial (the last trial of the No Delay session). The Black rectangle represents the walls of the pong arena. The dark parts of the movement are discrete interception attempts for which we extracted movement kinematics. (b) Sagittal position (upper panel) and velocity (lower panel) trajectories of the movements in (a). Playing with the delayed pong caused participants from the Abrupt 100 and Gradual 100 groups to increase their movement amplitude during the delayed pong (Fig. 4.3a) (main effect of Session: F(1.524, ) , p ). There was an overall increase in the movement amplitude from the late No Delay pong (No Delay) session to the last Delay pong (Delay 6) session ( pb ). In addition, the schedule of delay presentation affected the change in participants pong amplitude (Session-Group interaction: F(1.524, ) , p ). In the Abrupt 100 group, with the sudden presentation of the delay, the pong amplitude showed a prompt increase and was significantly higher during the first Delay pong (Delay 1) session than during No Delay ( 105

112 p B 0.001) (Fig. 4.3c, upper panel). Although the pong amplitude during Delay 6 was not significantly different than during the late No Delay stage ( p ), it did not differ from the Delay 1 ( p ) stage. In the Gradual 100 group, the pong amplitude increased gradually B (Fig. 4.3a). It did not change significantly from No Delay to Delay 1 ( p ), probably since the delay that was experienced during Delay 1 was still short (<20 ms). However, the pong amplitude was significantly higher during Delay 6 than during both No Delay ( p ) and Delay 1 ( p ). In addition, during Delay 6, the pong amplitude of the Gradual 100 group B was higher than in the Abrupt 100 group ( p ). B As we showed in the Chapter 3, Hypermetric movements were also observed during the transfer to the blind reaching task ( F , ( 1,18) between the groups (Session-Group interaction: F , 106 B B p 0.001) (Fig. 4.3a). This increase was similar ( 1,18) p 0.235), suggesting that the schedule of the delay presentation did not affect transfer (Fig. 4.3c, lower panel). Overall, these results indicate that a 100 ms delay causes an increase in movement amplitude both during the pong game and the transfer to the blind reaching task. The gradual introduction of the 100 ms delay had a greater effect on participants pong amplitude than an abrupt introduction of the delay, but this difference between the schedules did not transfer to the blind reaching task Larger delays cause greater hypermetria of the movements during the pong game but not during transfer to the blind reaching task To examine whether the effect of the delay on movement amplitude also persisted for larger delays, we designed additional protocols and recruited a group of participants (Fig. 4.1c) for each. Following a No Delay pong session, all protocols consisted of six Delay pong sessions of five minutes each. Two groups, Abrupt 150 (N=8) and Abrupt 300 (N=9), experienced a constant delay of 150 ms and 300 ms, respectively during the Delay sessions. The time courses of the movement amplitude suggest a more prominent increase in the pong amplitude due to the delay in these groups (Fig. 4.3b, upper panel) than in the Abrupt 100 group (Fig. 4.3a, upper panel). Indeed, the increase in pong amplitude from the late No Delay stage (No Delay) to the last Delay B

113 pong session (Delay 6) was significantly different across the three abrupt groups ( F ( , p 0.001) (Fig. 4.3d, upper panel). Although we did not find a significant increase in the pong amplitude between these sessions in the Abrupt 100 group, significant increases were found in both the Abrupt 150 ( p ) and Abrupt 300 ( p ) groups. During Delay 6, the pong B amplitude in the Abrupt 100 was significantly lower than in both the Abrupt 150 ( p ) and the Abrupt 300 ( p ) groups, but it was not different between the latter two ( p B B 1.000). These results suggest that for visuomotor delays of up to 150 ms, the increase in the magnitude of the delay causes an increase in movement amplitudes during the game. However, between 150 to 300 ms delays, the increase in the delay did not affect the pong amplitude, possibly due to ceiling effects related to physical or computational constraints (see discussion). Unlike the effect of the magnitude of the delay on the change in pong amplitude, it did not affect the increase in the reaching amplitude (Fig. 4.3d, lower panel). While there was an overall increase in the reaching amplitude from the Blind Reach session that followed the No Delay pong session (Post No Delay) to the Blind Reach session that followed the last Delay pong session (Post Delay 6) for all three abrupt groups (main effect of Session: F , p ), this B ( 1,24) increase was not significantly different across the three groups (Session-Group interaction: F 0.857, p ). The inconsistencies in the effects of the delay magnitude on the ( 2,24) increase in the movement amplitude between the pong and the reaching suggest that the transfer of the delay effect was not complete. A comparison of the delay-induced increase in movement amplitude between the pong and the reaching did not reveal a significant overall difference between the tasks (main effect of Task: F , p ) and in any of the ( 1,24) groups (Task-Group interaction: F , p ). However, since the pong and the ( 2,24) blind reaching are very different tasks, inferences from such a direct comparison should be treated with caution. 2,24) B 107

114 Figure 4.3. The effects of the delay magnitude and its presentation schedule on movement amplitude during pong and blind reaching. The analysis results of the movement amplitude are presented both for the pong game (colored lines and bars) and the blind reaching task (black and gray bars), and for each of the Abrupt 100 (N=10, filled bars), Gradual 100 (N=10, ascending lines bar), Abrupt 150 (N=8, dotted bars), Abrupt 300 (N=9, hollow bars) and Gradual 300 (N=9, descending lines bar) groups. The color code is as in Figure 4.1. (a) Time courses of the mean movement amplitudes for the Abrupt 100 (upper panel) and Gradual 100 (bottom panel) groups during the No Delay (purple) and the Delay (light blue) pong sessions and in each of the subsequent blind 108

115 reaching sessions (Post No Delay black, Post Delay light gray). (b) Time courses of the mean movement amplitudes for each of the Abrupt 150 (upper-left panel), Abrupt 300 (upper-right panel) and Gradual 300 (bottom panel) groups during the pong and the blind reaching sessions. (c-f) Various comparisons of movement amplitudes between groups and sessions, both for the pong game (upper panels) and for the blind reaching task (lower panels). Each bar represents the mean amplitude during a specific session in the experiment (abscissa), averaged over all the participants in each group. All means are presented after subtraction of each group s average baseline amplitude (during the No Delay pong session or the Post No Delay reaching session). Shading and error bars represent the 95% confidence interval. *p<0.05. ***p< The schedule of presentation of larger delays does not affect the transfer of hypermetria to the blind reaching task, either during the early or late stages of the experience. As reported above, the effect of the abrupt introduction of the 100 ms delay on pong amplitude was quite prompt. Such a prompt response can be also seen in the time courses of the Abrupt 150 and Abrupt 300 groups (Fig 4.3b, upper panel). This suggests that the state-based representation of the delay was constructed during the early stages of the Delay pong session. To observe the dynamics of the transfer effects throughout the experience with the delay, we incorporated Blind Reach sessions after each of the Delay pong sessions (Fig. 4.1c). Since we were mainly interested in testing whether the transfer occurred during the early stages of the experience with the delay, we focused our analysis on the Blind Reach session that followed the first Delay pong session (Post Delay 1). We were also concerned that we may have missed differences in the transfer of gradual and abrupt presentations because the effects of the 100 ms delay were too small. Thus, to examine whether differences in the effect of the schedules of delay presentation on movement amplitude would become more pronounced for higher delays, another group of participants, Gradual 300 (N=9), was exposed to a gradually increasing delay (from 0 to 300 ms) during the first five Delay sessions, which remained constant at 300 ms during the remaining last Delay session (Fig. 4.1c). In addition to observing the transfer dynamics, the multiple Blind Reach sessions enabled us to compare the Gradual 300 to each of the Abrupt groups (150 and 300) for a similar duration of playing pong and for similar experienced delay magnitudes. 109

116 When comparing the Abrupt 150 and the Gradual 300 groups, we analyzed the change in pong amplitude from the No Delay pong session to the first (Delay 1) and third (Delay 3) Delay sessions. Thus enabled us to examine both the effect of the delay during the early stages of experience (No Delay Delay 1 comparison) and the effect of the schedule of its presentation subsequent to min of playing pong (Delay 3) for the same mean delay (150 ms in the Abrupt 150 group, and ms in the Gradual 300 group). We found that for delays of up to 150 ms, the pong amplitude was directly related to the magnitude of the experienced delay. Although the Abrupt 150 group (Fig. 4.3b, upper-left panel) showed an abrupt increase in the pong amplitude on the abrupt presentation of the delay which then remained constant for the rest of the Delay sessions, in the Gradual 300 group (Fig. 4.3b, lower panel), the increase in amplitude was gradual (Session-Group interaction: F , ( 2,30) p 0.001) (Fig. 4.3e, upper panel). During Delay 3, when both groups experienced the same mean delay, the pong amplitude was comparable ( p ). Therefore, unlike the 100 ms delay, the experience with a 150 ms delay caused participants to increase their pong amplitudes to comparable sizes regardless of whether the delay was introduced abruptly or gradually. Similar to the effects of up to 100 ms delay on movement amplitude, the different dynamics between the schedules of delay presentation observed during the pong was not manifested during the transfer to the reaching task (Session-Group interaction: F , p ) B ( 2,30) (Fig. 4.3e, lower panel). When comparing the corresponding reaching sessions, the only overall increase (main effect of Session: F , p ) in the reaching amplitude was from ( 2,30) Post No Delay to Post Delay 3 ( p ). Once again, the differences between the schedules B of delay presentation on the pong amplitude but not on the reaching amplitude may be consistent with the existence of a partial transfer of the delay effects to the blind reaching task. To compare the Abrupt 300 and the Gradual 300 groups, we analyzed the changes in pong amplitude from the No Delay pong session (No Delay) to the first (Delay 1) and last (Delay 6) Delay sessions. Again, these comparisons made it possible to examine the effects of delay during 110

117 the early stages of the experience (No Delay Delay 1) and the effects of the schedule of presentation for the same delay (300 ms) subsequent to min of playing pong (Delay 6). When the 300 ms delay was presented abruptly, the change in the pong amplitude evolved gradually during early stages (Fig. 4.3b, upper-right panel). Note that during the first Delay session (Delay 1), the Abrupt 300 group experienced delays that were more than five times higher than the Gradual 300 groups, and the time-course of the Abrupt 300 group suggested a fairly rapid effect of the delay. However, there was no significant difference between the groups (Session-Group interaction: F , ( 2,32) p ), possibly due to the noisy dynamics of the pong amplitude exhibited by the Abrupt 300 group during this stage. Throughout the experiment, both groups displayed an overall increase ( F , ( 2,32) p 0.001) (Fig. 4.3f, upper panel) in pong amplitude from No Delay to Delay 1 ( p ) and then from Delay 1 to the last Delay session (Delay 6) ( p ). B B The delay effects on movement amplitude in the Abrupt 300 and Gradual 300 transferred to the reaching task relatively early (main effect of Session: F , p ) (Fig. 4.3f, ( 1.261,20.172) lower panel). During Post Delay 1, it was already higher than during Post No Delay ( p ), and comparable to the reaching amplitude during Post Delay 6 ( p ). Similar to the effect on the pong amplitude, the increase in the reaching amplitude was not influenced by the schedule of the delay presentation (Session-Group interaction: F , p ). B ( 1.261,20.172) These results suggest that for delays of up to 300 ms, the construction of the state-based representation of the delay occurred during the first five minutes of the game, regardless of whether the delay was introduced gradually or abruptly, and remained comparable to the representation during the later stages of the game. B 111

118 Delay-induced hypermetric movements are associated with an increase in movement duration during pong and with increases in either movement duration or maximum velocity during blind reaching The incomplete transfer of hypermetria to the reaching task suggests that the context of the task influenced the control mechanism of the movements. Thus, to further characterize the effects of visuomotor delay on the movement amplitude, we examined the way it influences other movement kinematics; namely, the maximum velocity and the duration of the movement (Fig. 4.2b). The observed increase in movement amplitude could be accompanied by an increase in either one or both of these measures. Note that the amplitude is not strictly determined by the maximum velocity, rather it is average velocity, but while pong movements are largely periodic and with a single velocity peak for each cycle (Fig. 4.2b), the integration with movements duration should be generally correlated with the amplitude. A qualitative examination of the time courses of movement maximum velocity in the Abrupt 100 and Gradual 100 suggested a small increase in both groups due to the delay, both during the pong and the transfer to the blind reaching task (Fig. 4.4a). We found a significant effect of the delay on pong maximum velocity (main effect of Session: F , p ) (Fig. 4.4c, ( 2,36) lower panel) regardless of whether the delay was introduced abruptly or gradually (Session- Group interaction effect: F , p ) (Fig. 4.4c, upper panel). The pong maximum ( 2,36) velocity during the last Delay session (Delay 6) was significantly higher than during both the No Delay ( p ) and the first Delay session (Delay 1) ( p ). This effect of the delay also B transferred to the blind reaching task, where the maximum velocity of the movement during Post Delay 6 was higher than during Post No Delay (main effect of Session: F , p ). B ( 1,18) The time courses of the pong movement duration in the Abrupt 100 group indicated a slight increase upon the appearance of the delay and a gradual decrease with repeated exposure to the delay (Fig. 4.5a, upper panel), while in the Gradual 100 group, the pong movement duration gradually increased with the increasing delay (Fig. 4.5a, lower panel). A statistical analysis revealed significant differences between the groups (Session-Group interaction effect: 112

119 F , ( 2,36) p 0.001) (Fig. 4.5c, upper panel). Despite the seeming dynamics in the pong movement duration of the Abrupt 100 group, there were no significant differences between the sessions (No Delay Delay 1, p ; No Delay Delay 6, p ; Delay 1 Delay 6, p B B 0.058). However, in the Gradual 100 group, the pong movement duration did not change from No Delay to Delay 1 ( p ), but then increased from Delay 1 to Delay 6 ( p ). B In contrast to the pong, the delay did not affect the duration of the reaching movements (main effect of Session: F , ( 1,18) p 0.321). B B The effect of up to 100 ms delay can be summarized as follows. During the pong game, the increase in the pong amplitude was accompanied by an increase in movement maximum velocity in both the Abrupt 100 and the Gradual 100 groups, and by an increase in movement duration mainly in the Gradual 100 group (although a possible contribution of the duration to movement amplitude was also present in the Abrupt 100 during the early stages of experience with the delay). During the blind reaching task, the overall increase in the reaching amplitude in both groups was correlated with the increase in the maximum velocity but not with the duration. In general, the effects of these small delays on movement maximum velocity and duration in both the pong and the reaching tasks were quite small, and examination of the effects on these measures in the groups that experienced longer delays may provide a clearer picture. The presence of delays of up to 300 ms did not alter the maximum velocity of the movements during the pong game. The time courses of the pong maximum velocity in the Abrupt 150 and Abrupt 300 groups suggest a small increase due to the delay in the Abrupt 150 group, a small decrease in the Abrupt 300 group, and no change in the Gradual 300 group (Fig. 4.4b). However, comparing the No Delay and the Delay 6 sessions for the abrupt groups (including Abrupt 100) did not reveal an overall significant effect of the delay on pong maximum velocity (main effect of Session: F , p ), regardless of the magnitude of the delay (Session-Group ( 1,24) interaction: F , p ) (Fig. 4.4d, upper panel). Similarly, the schedule ( 1,24) presentation of these delays did not affect the pong maximum velocity (Session-Group interaction Abrupt 150 Gradual 300: F , p ; Abrupt 300 Gradual 300: ( 2,30) 113

120 F 1.951, ( 2,32) p ) (Fig. 4.4e, f, upper panels). These results suggest that for higher delays, the increase in the pong amplitude was not associated with an increase in the maximum velocity of the movements. Figure 4.4. The effects of the delay magnitude and its presentation schedule on movement maximum velocity during pong and blind reaching. 114

121 The analysis results for movement maximum velocity are presented both for the pong game (colored lines and bars) and the blind reaching task (black and gray bars), and for each of the Abrupt 100 (N=10, filled bars), Gradual 100 (N=10, ascending lines bar), Abrupt 150 (N=8, dotted bars), Abrupt 300 (N=9, hollow bars) and Gradual 300 (N=9, descending lines bar) groups. The color code is as in Figure 4.1. (a) Time courses of the mean movement maximum velocities for the Abrupt 100 (upper panel) and Gradual 100 (bottom panel) groups during the No Delay (purple) and the Delay (light blue) pong sessions and in each of the subsequent blind reaching sessions (Post No Delay black, Post Delay light gray). (b) Time courses of the mean movement maximum velocities for each of the Abrupt 150 (upper-left panel), Abrupt 300 (upper-right panel) and Gradual 300 (bottom panel) groups during the pong and the blind reaching sessions. (c-f) Various comparisons of movement maximum velocities between groups and sessions, both for the pong game (upper panels) and for the blind reaching task (lower panels). Each bar represents the mean maximum velocity during a specific session in the experiment (abscissa), averaged over all the participants in each group. All means are presented after subtraction of each group s average baseline maximum velocity (during the No Delay pong session or the Post No Delay reaching session). Shading and error bars represent the 95% confidence interval. *p<0.05. **p<0.01. The maximum velocity of the reaching movements were not substantially affected by the experience of the 300 ms delayed pong either. There was a small overall increase in the maximum velocity of the abrupt groups due to the delay (main effect of Session: F , ( 1,24) p 0.039) (Fig. 4.4d, lower panel), but comparisons with the Gradual 300 group did not reveal any change in reaching maximum velocity due to either the 150 ms ( F , p ) ( 2,30) (Fig. 4.4e, lower panel) or the 300 ms ( F , p ) (Fig. 4.4e, lower panel) ( 1.181,18.897) delay. This indicates that the increase in the reaching amplitude due to the higher delay was not accompanied by an increase in the maximum velocity. Unlike the maximum velocity, the durations of the pong movements became considerably longer in the presence of ms delays (Fig. 4.5b, upper panel). Comparing the change in the pong movement duration between the No Delay and the last Delay session (Delay 6) to the change in the Abrupt 100 group revealed a significant effect of the magnitude of the delay (Session-Group interaction: F , p ). During Delay 6, movement duration became longer than ( 2,24) during the No Delay in both the Abrupt 150 ( p ) and Abrupt 300 ( p ) groups B (Fig. 4.5d, upper panel). This increase was not observed in the Abrupt 100 group ( p ), B B 115

122 and the durations of the pong movements during Delay 6 in this group were significantly shorter than those of the Abrupt 150 ( p ) and Abrupt 300 ( p ) groups. There was no B significant difference in the movement duration between the Abrupt 150 and the Abrupt 300 groups during this session ( p ), suggesting a ceiling effect, similar to the effect of delay on the pong amplitude. B B 116

123 Figure 4.5. The effects of the delay magnitude and its presentation schedule on movement duration during pong and blind reaching. The analysis results of the movement duration are presented both for the pong game (colored lines and bars) and the blind reaching task (black and gray bars), and for each of the Abrupt 100 (N=10, filled bars), Gradual 100 (N=10, ascending lines bar), Abrupt 150 (N=8, dotted bars), Abrupt 300 (N=9, hollow bars) and Gradual 300 (N=9, descending lines bar) groups. The color code is as in Figure 4.1. (a) Time courses of the mean movement durations for the Abrupt 100 (upper panel) and Gradual 100 (bottom panel) groups during the No Delay (purple) and the Delay (light blue) pong sessions and in each of the subsequent blind reaching sessions (Post No Delay black, Post Delay light gray). (b) Time courses of the mean movement durations for each of the Abrupt 150 (upper-left panel), Abrupt 300 (upper-right panel) and Gradual 300 (bottom panel) groups during the pong and the blind reaching sessions. (c-f) Various comparisons of movement durations between groups and sessions, both for the pong game (upper panels) and for the blind reaching task (lower panels). Each bar represents the mean duration during a specific session in the experiment (abscissa), averaged over all the participants in each group. All means are presented after subtraction of each group s average baseline duration (during the No Delay pong session or the Post No Delay reaching session). Shading and error bars represent the 95% confidence interval. *p<0.05. **p<0.01. ***p< In conditions with an abrupt presentation of either the 150 ms or the 300 ms delay, the movement duration immediately increased and remained constant throughout the entire Delay pong session (Fig. 4.5b, upper panel). In particular, a gradual presentation of the 300 ms delay caused a gradual increase in the duration of the pong movements, and for the same mean delay, the duration was similar to the abrupt groups (Fig. 4.5b, lower panel). Comparisons between the Gradual 300 group and each of the abrupt groups supported these different dynamics, both for 150 ms (Session-Group interaction: F , p ) and 300 ms ( F , ( 2,30) ( 2,32) p 0.002) delays (Fig. 4.5e, f, upper panels). Movement durations were significantly longer during Delay 1 than during No Delay in both the Abrupt 150 ( p ) and the Abrupt 300 ( p B 0.001) groups, and they remained comparable to the movement durations during the Delay 3 (Abrupt 150: p ) or the Delay 6 (Abrupt 300: p ) sessions. In the Gradual 300 B group, the pong movement durations during Delay 1 (0-60 ms delay) were no different than during No Delay ( p ) and they were shorter than the durations in the Abrupt 150 ( B p 0.003) and the Abrupt 300 ( p ) groups during the same session. During sessions B B B B 117

124 where participants from the Gradual 300 group experienced similar delays as each of the Abrupt 150 and Abrupt 300 groups for a similar playing duration (Delay 3 and Delay 6, respectively), the pong movement durations were comparable between the groups (Abrupt 150 Gradual 300: p 0.178; Abrupt 300 Gradual 300: p ). These results may indicate that the increase B B in the pong amplitude was associated with an increase in the duration of the movements. The prominent effects of the ms delays on the durations of the pong movements were not observed in the transfer to the blind reaching task (Fig. 4.5b). We did not find an overall effect of the delay ( F , ( 1,24) p ), regardless of its magnitude ( F , ( 2,24) p (Fig. 4.5d, lower panel) or presentation schedules (Abrupt 150 Gradual 300: main effect of Session F , ( 2,30) p ; Session-Group interaction F , ( 2,30) p ) ; Abrupt 300 Gradual 300: Session F , ( 1.476,23.610) p ; Session-Group F ( ,23.610), p ). The absence of a substantial influence of the delay on the pong movement velocity, along with its clear effect on the durations of the pong movement suggests that the latter is the main cause of their spatially longer movements. However, since the longer movement amplitudes transferred to the blind reaching task, the absence of a clear effect for either reaching maximum velocity or duration is puzzling. However, there was considerable variability among participants in the mean reaching maximum velocity (Fig. 4.4) and duration (Fig. 4.5). As mentioned above, an increase in movement amplitude may result from various combinations of changes in movement velocity or duration (Fig. 4.6). During the pong game, for most of the participants, the increase in movement amplitude due to the delay was primarily accompanied by an increase in the movement duration (Fig. 4.6a, c, e). In contrast, during the blind reaching task, some participants exhibited an increase in movement duration, others in movement maximum velocity, and others in both (Fig. 4.6b, d, f). Thus, the seemingly comparable movement maximum velocity and duration between the Post No Delay and the Post Delay blind reaching sessions, despite the overall increase in amplitude, should be ascribed to the variability in the changes in these movement properties across participants. 118

125 Delay Representation in the Sensorimotor System Figure 4.6. Dynamics of movement amplitude, maximum velocity and duration during pong and blind reaching. Dynamics of the delay effects are presented in the Duration Maximum Velocity space for the pong game (a, c, e) and the blind reaching task (b, d, f), and for each of the Abrupt 150 (N=8) (a, b), Abrupt 300 (N=9) (c, d) and Gradual 300 (N=9) (e, f) groups. Gray scale contours represent the respective movement amplitudes for each duration and maximum velocity combination, calculated according to the minimum jerk trajectory. The darker the contour, the higher the amplitude. Markers represent individuals mean maximum velocity and mean duration of each session. Individuals are distinguished by a different marker color and shape. The color intensity represents a different session, where darker colors are for later sessions. The straight lines link the markers of the No Delay / Post No Delay sessions to those of the Delay 6 / Post Delay 6 in each individual. 119

126 The increase in movement duration during the delayed pong game is consistent with a representation of the delay as a mechanical system equivalent. In the previous chapter, we defined a Time Representation of the delay between the hand and the paddle as an estimation of hand location that explicitly uses the actual time lag ( ) between their movements: (4.1) xˆ ( t) x ( t ˆ ) h p where x p ( t ˆ) is the location of the paddle at an estimated (ˆ ) time ahead. Also, we suggested a specific model for a Mechanical System Representation derived from a Taylor series approximation of the expression in Equation 1 around the position of the delayed paddle: 2 ˆ (4.2) xˆ ˆ h ( t) x p ( t) x p ( t) x p ( t). 2 To examine whether the increase in the durations of the movements during the delayed pong game were consistent with our proposed model of a Mechanical System Representation of the delay, we looked at the frequency responses of each of these dynamical systems (Fig. 4.7). Since the design of our pong game encourages participants to repetitively hit the ball towards the upper wall of the arena, the sagittal movements in the game are periodic and can be well approximated by a sinusoid (4.2). We defined the main movement frequency ( freq ) as 1 freq, where c is the cycle time. c c was approximated as c 2 T. is directly related to the movement duration (T ) and As was shown in the previous chapter, the increase in movement amplitude was consistent with the Mechanical System Representation of the delay, and not with the Time Representation. This is illustrated in the dependency of the output magnitude (the absolute ratio between paddle and hand amplitudes) on the frequency of each of these representations (Fig 4.7a, c, e). The Time Representation model does not predict a change in the relative amplitudes. However, for the typical baseline movement frequency (1.32 Hz), the Mechanical System Representation shows a reduction in the gain between paddle and hand movements. In other words, with the latter 120

127 Delay Representation in the Sensorimotor System representation, the paddle moves in smaller amplitudes with respect to the hand amplitudes. Thus, to compensate for this small gain, participants increase their hand movement amplitudes. Figure 4.7. Frequency responses for Time Representation and Mechanical System Representation of various visuomotor delay magnitudes Predicted magnitude (a, c, e) and phase (b, d, f) as a function of movement frequency during the pong game for 100 (a, b), 150 (c, d) and 300 ms (e, f) delay. The frequency responses are presented for Time Representation (yellow solid lines) and for a Mechanical System Representation (using Taylor s approximation of the delay, green solid lines) on the same graph. Dashed lines mark the actual mean frequency of the participants movements during No Delay (purple) and Delay (light to dark blue). 121

128 Interestingly, increasing the duration of movement is also a reasonable approach to cope with the delay if it is represented as a mechanical system equivalent. As described above, a mechanical system is an adequate approximation of small delays, partly since the temporal phase shift between the hand and the paddle resulting from the delay is similar in magnitude to the lag of the equivalent mechanical system. For example, for a 100 ms delay, and for the baseline movement frequency (1.32 Hz), the phase difference between the Mechanical System Representation and the Time Representation (which reflects the accurate delayed dynamics) was (Fig. 4.7b). However, even with the 100 ms delay, participants tended to slightly increase their movement duration (decreasing its frequency to 1.22 Hz), which resulted in a decrease in the phase difference between the representations ( ). As the delay between the hand and the paddle got higher, the phase shift of the Time Representation increased, and became farther away from the phase shift of the Mechanical System equivalent that was bounded at (i.e. a lag that is half of the movement time cycle): with the baseline movement frequency, the phase differences between the models was for 150 ms delay (Fig. 4.7d) and for 300 ms delay (Fig. 4.7f). Thus, we predicted that participants would not be able to use the Mechanical System Representation for the higher delays. However, by increasing the movement duration they effectively decreased the phase differences between the representations: for the 150 ms delay, the mean movement frequency was 0.96 Hz, which resulted in a phase difference of ( ); for 300 ms delay, participants moved at a mean frequency of 0.89 Hz, which enabled them to bring the phase of the Mechanical System Representation closer by to that of the Time Representation. This suggests that participants used a strategy that preserved the use of the Mechanical System Representation in the presence of delays that were as high as 300 ms Section 2: deteriorated performance in the presence of delay and altered interception kinematics To understand the processes that drive the choice of the sensorimotor system to increase movement amplitude and duration during the pong game due to the delay, we now focus on performance on the pong task. Because the task is very different from the well-controlled tasks that are typically used in the study of computational motor control, we do not have sufficient 122

129 prior literature to form structured hypotheses, and hence, this section is mostly exploratory. It suggests signals the participants use to attempt to cope with the delay and to improve as much as possible in the game despite the incorrect state-based representation. Thus, rather than an exhaustive description of the results for all the comparisons between the groups, we only report a subset of the conditions and groups as examples of the effects. However, for the interested reader and for completeness of the report we provide the full statistical analysis in Tables and in the related figures The probability of hitting the ball decreases with increasing delay First, we analyzed how the magnitude of the delay and its presentation schedule affected the probability of paddle-ball hit occurrences (Fig. 4.8). The Hit Probability was calculated as the ratio between the counted hits and the number of interception attempts on each trial. For delays of up to 100 ms, the Hit Probability changed in a different manner between abrupt and gradual schedules (Tables 4.1 and 4.2) (Fig. 4.8a, c). The Abrupt 100 group showed a decrease in the Hit Probability due to the sudden introduction of the delay and then an increase by the last Delay session, suggesting they had adapted to the delay. The Gradual 100 group showed a small decrease in the Hit Probability as the delay increased. The progressive increase in the delay in Gradual protocols may have concealed a possible progressive improvement, and thus, we cannot account for the adaptation in the Gradual 100 group. Examination of the groups that experienced delays of up to 300 ms revealed significantly deteriorated performance due to the higher delays (Tables 4.1 and 4.2)(Fig. 4.8b, d-f). Analysis of the Hit Probability indicated that all three abrupt groups showed an overall decrease in the Hit Probability when the delay was suddenly introduced. Although they exhibited an overall improvement by the end of the Delay session (the Hit Probability increased by 19% from the first Delay session) (Fig. 4.8d), they did not regain their baseline performance. In fact, they achieved success rate of 74% compared to their baseline success scores. Moreover, the higher the delay participants experienced the worse they performed. Both during the Delay 1 and the Delay 6 sessions, we found significant decreases in the Hit Probability with the increased delay. Similarly, 123

130 the Gradual 300 group also showed a decrease in the Hit Probability as the delay gradually increased throughout the Delay session (Tables 4.1 and 4.2) (Fig. 4.8b, lower panel, e, f). Figure 4.8. The effects of the delay magnitude and its presentation schedule on paddle-ball hit probability during pong. The analysis results of the hit probability are presented for each of the Abrupt 100 (N=10, filled bars), Gradual 100 (N=10, ascending lines bar), Abrupt 150 (N=8, dotted bars), Abrupt 300 (N=9, hollow bars) and Gradual 300 (N=9, descending lines bar) groups. The color code is as in Figure 4.1. (a) Time courses for the mean hit probability for the Abrupt 100 (upper panel) and Gradual 100 (bottom panel) groups. (b) Time courses for the mean hit probability for each of the Abrupt 150 (upper-left panel), Abrupt 300 (upper-right panel) and Gradual 300 (bottom panel) groups. (c-f) Various comparisons of hit probabilities between groups and sessions. Each bar represents the mean hit probability during a specific session in 124

131 the experiment (abscissa), averaged over all the participants in each group. Shading and error bars represent the 95% confidence interval. *p<0.05. **p<0.01. ***p< ANOVA Model Abrupt 100 Gradual 100 Abrupt 100 Abrupt 150 Abrupt 300 Abrupt 150 Gradual 300 Abrupt 300 Gradual 300 Effect Model Results DOF F p Session (2,36) Session Group (2,36) <0.001 Group (1,18) Session (2,48) <0.001 Session Group (4,48) <0.001 Group (2,24) <0.001 Session (2,30) <0.001 Session Group (2,30) <0.001 Group (1,15) Session (2,32) <0.001 Session Group (2,32) <0.001 Group (1,16) Table 4.1. Statistical analyses of the Hit Probability during the pong game. DOF, F and p represent the Degrees of Freedom, the F ratio, and the p-value of the ANOVA model, respectively. Bold fonts represent significance at the 0.05 level. The deterioration in participants performance with the increased delay lends further support to our findings that the delay is not represented correctly as an actual time lag. Only compensation for the full time delay in the timing of the hand movement during the interception attempts could have enabled participants to regain their baseline performance. 125

132 ANOVA Model Effect Groups Sessions Abrupt 100 Gradual 100 Abrupt 100 Abrupt 150 Abrupt 300 Abrupt 150 Gradual 300 Abrupt 300 Gradual 300 Session Group Session Session Group Group Session Session Group Session Session Group Abrupt 100 Gradual 100 Abrupt 100-Abrupt150 Mean Diff (% Change) No Delay-Delay (16%) <0.001 No Delay-Delay (7.6%) Delay 1-Delay (10%) No Delay-Delay (7.9%) No Delay-Delay (0.7%) Delay 1-Delay (6.7%) No Delay-Delay (38%) <0.001 No Delay-Delay (26%) <0.001 Delay 1-Delay (19%) <0.001 Abrupt 100-Abrupt300 No Delay (5.4%) pb (8.4%) Abrupt 150-Abrupt (3.2%) Abrupt 100-Abrupt (28%) <0.001 Abrupt 100-Abrupt300 Delay (61%) <0.001 Abrupt 150-Abrupt (46%) <0.001 Abrupt 100-Abrupt (23%) Abrupt 100-Abrupt300 Delay (49%) <0.001 Abrupt 150-Abrupt (33%) Abrupt 100-Abrupt (19%) Abrupt 100-Abrupt (37%) <0.001 Abrupt 150-Abrupt (22%) Abrupt 150 Gradual 300 Abrupt 300 Gradual 300 No Delay-Delay (18%) <0.001 No Delay-Delay (26%) <0.001 Delay 1-Delay (11%) No Delay-Delay (34%) <0.001 No Delay-Delay (26%) <0.001 Delay 1-Delay (12%) No Delay-Delay e-5 (0%) No Delay-Delay (26%) <0.001 Delay 1-Delay (26%) <0.001 No Delay-Delay (34%) <0.001 No Delay-Delay (52%) <0.001 Delay 1-Delay (27%) <0.001 No Delay-Delay (66%) <0.001 No Delay-Delay (50%) <0.001 Delay 1-Delay (50%) No Delay-Delay e-5 (0%) No Delay-Delay (61%) <0.001 Delay 1-Delay (61%) <

133 Table 4.2. Hit Probability: pairwise comparisons for the significant effects in the ANOVA models from Table 4.1. p B represents the Bonferroni-corrected p-value for multiple comparisons. Bold fonts represent significance at the 0.05 level. From now on, we focus our description on the Abrupt 150 group. We chose this group for two reasons: (1) since it experienced a constant perturbation, any change in our performance measures can be attributed to an adaptive change in behavior that is not influenced by increasing difficulty (as was the case for the Gradual groups); and (2) 150 ms was the minimum delay that caused the largest increase in the amplitude and the duration of the pong movements Delay causes a directional increase in the frontal distance between the paddle and the ball on interception attempts To characterize participants' deteriorated performance, we extracted kinematic measures that are related to the participants attempts to hit the ball. The decrease in the probability of hitting the ball due to the delay indicates that there were more unsuccessful interception attempts in which the paddle and the ball passed each other without an impact. The participants were informed that they could only hit the ball in cases where the ball moved downward and the paddle moved upward, regardless of the frontal movement (rightward/leftward) direction of both. Since the delay caused a lag in the movement of the paddle with respect to the movement of the hand, the frontal direction from which the hand approaches the ball would primarily influence the side from which the paddle would pass it. Consider the simple case in which the ball moves straight down and the participant moves her hand up in the rightward direction. If she does not represent the delay and she is accurate in reaching with her hand to the ball, because of the delay, at the moment when the hand and the ball are at the same location, the paddle is behind, somewhere down and to the left side. Since a hit does not occur, the ball continues its downward movement and it would pass by the sagittal location of the moving paddle on its right. 127

134 Figure 4.9. The effects of the delay on the frontal distance between the ball and the paddle when they are at the same sagittal location (X Distance) during pong. (a, b) Examples of rightward paddle movements during interception attempts from an individual participant (Abrupt 150 group), taken from the last trial of the No Delay session (a) and from the first trial of the Delay session (b). The highest points of the movements represent the time in which the paddle and the ball (black circle) reached the same sagittal location; all of them are vertically aligned to this location. The gray dashed line represents the size of the paddle with respect to the ball, and thus, the range within which the movements resulted in successful hits. (c) Time courses of the X-Distance for each interception attempt (Hit Try) for the Abrupt 100 (upper panel) and Gradual 100 (bottom panel) groups. (c) Time courses of X-Distance for each of the Abrupt 150 (upper-left panel), Abrupt 300 (upper-right panel) and Gradual 300 (bottom panel) groups. The color code is as in Figure

135 This phenomenon is illustrated in the examples of rightward paddle movements during interception attempts from a single participant (Abrupt 150 group), taken from the last trial of the No Delay session (Fig. 4.9a) and the first trial of the Delay session (Fig. 4.9b). In the absence of a delay, the paddle came close to the ball, but when a delay was presented, rightward movements resulted in a directional deviation between the paddle s and the ball s frontal locations. To quantify this effect, we calculated the frontal distance between the paddle and the ball (X-Distance) when they were in the same sagittal location after approaching each other (Reichenthal et al., 2016). A positive value of the X-Distance indicates that the ball passed by the paddle to the right for rightward movements and to the left for leftward movements. In fact, playing pong with the delay resulted in more hit attempts in which the X-Distance exceeded the size of the paddle (Fig. 4.9 c,d), which effectively caused misses. In addition, the time courses of all groups suggest that in the presence of a delay, the X-Distance deviated farther toward the positive range. This indicates that most misses were direct consequences of the applied delay and the incapability to represent it correctly Delay causes failure to hit the ball at the time of the paddle s maximum velocity The pong task was designed in a way that encouraged the participants to hit the ball with high velocity; otherwise, the ball would slow down, decreasing the number of opportunities to hit it (see methods). The findings that the maximum velocity of the movements during the pong was not substantially influenced by the delay (Fig. 4.4) suggest that the motor system controls this for the purpose of the task. Thus, for each successful hit, we examined the time of the hit with respect to the time of the maximum velocity within the duration of the paddle movement (Max Vel - Hit Lag, Fig. 4.10a). When participants played pong without a delay, their Max Vel - Hit Lag was close to zero, indicating that participants attempted (and succeeded) at hitting the ball at maximum velocity (Fig. 4.10b-g). Interestingly, in the presence of a delay, participants did not hit the ball close to the time of the paddle s maximum velocity, but typically before the paddle reached its maximum velocity (Tables 4.3 and 4.4). For example, in the Abrupt 150 group (Fig. 4.10c, upper-left panel), there was an immediate increase in the Max Vel - Hit Lag with the sudden presentation of the 129

136 delay, which persisted as well during the later stages. Thus, participants failed to realign the time of the hit with the maximum velocity of the delayed paddle. Figure The effects of the delay magnitude and its presentation schedule on the time lag between the paddle s maximum velocity and the time of the hit (Max Vel - Hit Lag) during pong. 130

137 (a) An example of hand (gray) and paddle (red) trajectories during a play in a presence of 300 ms delay. The filled orange circle represents an occurrence of paddle ball hit. The Max Vel - Hit Lag is calculated for a successful attempt, as the time lag between the time of a hit (t Hit) and the time of paddle s maximum velocity (t MaxVel) normalized by the movement duration. The analysis results of the Max Vel Hit Lag are presented for each of the Abrupt 100 (N=10, filled bars), Gradual 100 (N=10, ascending lines bar), Abrupt 150 (N=8, dotted bars), Abrupt 300 (N=9, hollow bars) and Gradual 300 (N=9, descending lines bar) groups. The color code is as in Figure 4.1. (b) Time courses of the mean Max Vel - Hit Lag for the Abrupt 100 (upper panel) and Gradual 100 (bottom panel) groups. (c) Time courses of the mean Max Vel - Hit Lag for each of the Abrupt 150 (upper-left panel), Abrupt 300 (upper-right panel) and Gradual 300 (bottom panel) groups. (d-g) Various comparisons of Max Vel - Hit Lag between groups and sessions. Each bar represents the mean Max Vel - Hit Lag during a specific session in the experiment (abscissa), averaged over all the participants in each group. Shading and error bars represent the 95% confidence interval. *p<0.05. **p<0.01. ***p< ANOVA Model Abrupt 100 Gradual 100 Abrupt 100 Abrupt 150 Abrupt 300 Abrupt 150 Gradual 300 Abrupt 300 Gradual 300 Effect Model Results DOF F p Session (2,36) <0.001 Session Group (2,36) <0.001 Group (1,18) <0.001 Session (2,48) <0.001 Session Group (4,48) Group (2,24) Session (2,30) <0.001 Session Group (2,30) <0.001 Group (1,15) Session (2,32) <0.001 Session Group (2,32) Group (1,16) Table 4.3. Statistical analyses of the Max Vel Hit Lag during the pong game. DOF, F and p represent the Degrees of Freedom, the F ratio, and the p-value of the ANOVA model, respectively. Bold fonts represent significance at the 0.05 level. 131

138 ANOVA Model Effect Groups Sessions Abrupt 100 Gradual 100 Abrupt 100 Abrupt 150 Abrupt 300 Abrupt 150 Gradual 300 Abrupt 300 Gradual 300 Session Session Group Abrupt 100 Gradual 100 Mean Diff (% Change) No Delay-Delay (646%) <0.001 No Delay-Delay (853%) <0.001 Delay 1-Delay (28%) No Delay-Delay (465%) <0.001 No Delay-Delay (390%) <0.001 Delay 1-Delay (13%) No Delay-Delay (460 %) No Delay-Delay (2.e3%) <0.001 Delay 1-Delay (433%) <0.001 Group Abrupt 100-Gradual (70%) <0.001 Session Session Session Group Abrupt 150 Gradual 300 No Delay-Delay (326%) <0.001 No Delay-Delay (351%) <0.001 Delay 1-Delay (6%) No Delay-Delay (244%) <0.001 No Delay-Delay (412%) <0.001 Delay 1-Delay (49%) No Delay-Delay (260%) <0.001 No Delay-Delay (272%) <0.001 Delay 1-Delay (3.4%) No Delay-Delay (154%) No Delay-Delay (1.e3%) <0.001 Delay 1-Delay (382%) <0.001 Group Abrupt 150-Gradual (63%) Session No Delay-Delay (281%) No Delay-Delay (627%) <0.001 Delay 1-Delay (90%) Group Abrupt 300-Gradual (62%) pb Table 4.4. Max Vel Hit Lag: pairwise comparisons for the significant effects in the ANOVA models from Table 4.3. p B represents the Bonferroni-corrected p-value for multiple comparisons. Bold fonts represent significance at the 0.05 level. 132

139 Delay causes a decrease in the velocity of the hits The finding that participants did not change their maximum velocity in the presence of a delay (Fig 4.4), together with their failure to hit the ball at the moment of maximum velocity due to the delay (Fig. 4.10), suggest that the velocity of the hit decreased (Fig. 4.11a). In this case, participants possibly tried to regain their baseline performance as much as possible by increasing the velocity during the hit. Analysis of the hit velocity indeed revealed an overall decrease in the Hit Velocity with increased delay (except for a small increase in the 100 ms delay cases, which was possibly due the overall increase in their movement velocity) (Fig. 4.11b-g, Tables 4.5 and 4.6). As illustrated by the change in the Hit Velocity of the Abrupt 150 group (Fig. 4.11c, upperleft panel), when participants were suddenly introduced to the delay, the Hit Velocity immediately decelerated. The time course suggests that participants gradually increased their hit velocity throughout the Delay session, but this was not statistically significant. ANOVA Model Abrupt 100 Gradual 100 Abrupt 100 Abrupt 150 Abrupt 300 Abrupt 150 Gradual 300 Abrupt 300 Gradual 300 Effect Model Results DOF F p Session (2,36) Session Group (2,36) Group (1,18) Session (1.584,38.004) <0.001 Session Group (3.167,38.004) <0.001 Group (2,24) Session (2,30) Session Group (2,30) Group (1,15) Session (2,32) <0.001 Session Group (2,32) <0.001 Group (1,16) Table 4.5. Statistical analyses of the Hit Velocity during the pong game. DOF, F and p represent the Degrees of Freedom, the F ratio, and the p-value of the ANOVA model, respectively. Bold fonts represent significance at the 0.05 level. 133

140 ANOVA Model Effect Groups Sessions Abrupt 100 Gradual 100 Abrupt 100 Abrupt 150 Abrupt 300 Abrupt 150 Gradual 300 Abrupt 300 Gradual 300 Session Mean Diff (% Change) No Delay-Delay (2.1%) No Delay-Delay (8.2%) Delay 1-Delay (10%) Group Abrupt 100-Gradual 100 No Delay-Delay (19%) Session Session Group Session Session Group Session Session Group Abrupt 100 Abrupt150 Abrupt300 Abrupt 150 Gradual 300 Abrupt 300 Gradual 300 No Delay-Delay (23%) <0.001 No Delay-Delay (12%) Delay 1-Delay (13%) <0.001 No Delay-Delay (6.2%) No Delay-Delay (6.5%) Delay 1-Delay (13%) No Delay-Delay (20%) No Delay-Delay (11%) Delay 1-Delay (11%) No Delay-Delay (38%) <0.001 No Delay-Delay (28%) <0.001 Delay 1-Delay (17%) No Delay-Delay (3.8%) No Delay-Delay (7.5%) Delay 1-Delay (5.5%) No Delay-Delay (20%) No Delay-Delay (16%) Delay 1-Delay (4.7%) No Delay-Delay (8.8%) No Delay-Delay (5.1%) Delay 1-Delay (13%) No Delay-Delay (15%) No Delay-Delay (23%) Delay 1-Delay (9.0%) No Delay-Delay (38%) <0.001 No Delay-Delay (28%) Delay 1-Delay (17%) No Delay-Delay (8.8%) No Delay-Delay (17%) Delay 1-Delay (24%) pb Table 4.6. Hit Velocity: pairwise comparisons for the significant effects in the ANOVA models from Table 4.5. p B represents the Bonferroni-corrected p-value for multiple comparisons. Bold fonts represent significance at the 0.05 level. 134

141 Figure The effects of the delay magnitude and its presentation schedule on the hit velocity during pong. (a) An example of hand (gray) and paddle (red) trajectories during play in the presence of 300 ms delay. The filled orange circle represents an occurrence of paddle ball hit. The hit velocity is the velocity of the paddle (ẋ Paddle) during a hit (t Hit). The analysis results of the hit velocity are presented for each of the Abrupt 100 (N=10, filled bars), Gradual 100 (N=10, ascending lines bar), Abrupt 150 (N=8, dotted bars), Abrupt 300 (N=9, hollow bars) and Gradual 300 (N=9, descending lines bar) groups. The color code is as in Figure 135

142 4.1. (b) Time courses of the mean hit velocities for the Abrupt 100 (upper panel) and Gradual 100 (bottom panel) groups. (c) Time courses of the mean hit velocities for each of the Abrupt 150 (upper-left panel), Abrupt 300 (upper-right panel) and Gradual 300 (bottom panel) groups. (d-g) Various comparisons of hit velocities between groups and sessions. Each bar represents the mean hit velocity during a specific session in the experiment (abscissa), averaged over all the participants in each group. Shading and error bars represent the 95% confidence interval. *p<0.05. **p<0.01. ***p< Delay can alter the symmetry of the velocity trajectory As was shown above, during the delayed pong, participants consistently hit the ball before the paddle reached its maximum velocity (Fig. 4.10). Thus, in order to hit the ball with an adequate velocity, they may have developed a strategy that changed the control of the movement such that the ascending part of the velocity profile took longer than when no delay was present. Since it is evident that participants could not represent the actual time delay, and thus misinterpreted the true dynamics, this strategy could provide a wider range of time points in which the velocity was high enough for the hit to occur. To examine how the shape of the velocity profile during the game is affected by the delay, we calculated the Velocity Symmetry: for each movement in which a hit occurred, we measured the duration between the movement onset and the time of maximum velocity, and the duration between the time of maximum velocity and the movement end time, and we calculated the ratio between them (Fig. 4.12a). The velocity is symmetrical when this ratio equals one. For a Velocity Symmetry more than one, the accelerating part of the velocity profile takes longer than the decelerating part, and vice versa for Velocity Symmetry less than one. During baseline, the velocity symmetry was around two (Fig. 4.12, b-g), which indicates that the movements in the game were also not symmetric when there was no delay. This is due to the fact that the pong movements are better modeled as slicing (out-and-back) than reaching movements (Gottlieb, 1998; Scheidt and Ghez, 2007). Though the time courses suggest an increase in the mean Velocity Symmetry measure with increased delay; i.e., the ascending portion of the velocity became longer than the descending portion, there was only a clear effect in the Abrupt 150 group (Tables 4.7 and 4.8). A qualitative examination of the velocity trajectories suggests that the change in 136

143 symmetry is not due to an increase in the number of velocity peaks, but rather a change in the skewness of the velocity profile. Figure The effects of the delay magnitude and its presentation schedule on the symmetry of the velocity trajectory during pong. 137