Recruitment of Degrees of Freedom based on. Multimodal Information about Interlimb Coordination. A dissertation submitted to the.

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2 Recruitment of Degrees of Freedom based on Multimodal Information about Interlimb Coordination A dissertation submitted to the Graduate School of the University of Cincinnati in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the Department of Psychology of the McMicken College of Arts and Sciences by Laura E. Bachus M.A. University of Cincinnati June 2011 Committee Chair: Kevin Shockley, Ph.D. i

3 Abstract The present experiments were designed to determine whether degree of freedom (df) recruitment serves to stabilize coordination, whether there is a tradeoff between df recruitment and coordination stability, and to further explore the role of vision and biomechanics on interlimb coordination. Participants moved their hands in the transverse plane, which caused corresponding motion of a virtual marker in the coronal plane. The participants goal was to trace symmetric or asymmetric elliptical shapes on a projection screen with the virtual marker. Experiment 1 decoupled biomechanical symmetry from visual symmetry by implementing a translational gain. Both visual and biomechanical asymmetries resulted in increased df recruitment with no changes in coordination stability. Experiment 2 decoupled visual phase from biomechanical phase by reversing the marker mapping of one motion sensor. When visual information matched biomechanical information, coordination stability and df recruitment were higher. Similarly, biomechanically anti-phase conditions had less stability and more df recruitment than inphase conditions. The third set of experiments manipulated feedback by either giving participants feedback about their accuracy in the x-y plane (i.e., motion around the targets; Experiment 3a) or feedback about their movement in the z-plane (i.e., df recruitment; Experiment 3b). Experiment 3a showed opposite results of Experiment 1(no df recruitment but a decrease in stability), again suggesting the same relationship between df recruitment and coordination stability. Experiment 3b showed that feedback about motion in the z- plane did suppress df recruitment. There were no differences in coordination stability across trials; however, performance accuracy was generally poor. Results of Experiment 3b were inconclusive. The present results collectively suggest that df recruitment does ii

4 stabilize coordination, and that there is a tradeoff between df recruitment and coordination stability. It remains unclear, however, under which conditions df recruitment occurs (i.e., why actors elect to stabilize coordination via df recruitment in some circumstances but not others). The present results also suggest that both vision and biomechanics influence interlimb coordination dynamics. Visual and biomechanical symmetry both seem to stabilize coordination, presuming that df recruitment indexes threats to coordination stability. Similarly, both visual phase and biomechanical phase seemed to influence coordination. In Experiment 2, when visual information conflicted with biomechanical information (i.e., mismatch conditions) coordination stability was compromised compared to when the visual and biomechanical information matched. However, in addition to an influence of information congruence, biomechanical phase also influenced stability such that biomechanically anti-phase conditions had lower stability than biomechanically inphase conditions. iii

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6 Acknowledgments First and foremost, I would like to thank my mentor, Dr. Kevin Shockley, for his knowledge, expertise, patience, and advice as I wrote my dissertation and throughout my academic training. He has guided me through graduate school, and I could not imagine having taken this journey without him. I would also like to thank Dr. Michael Richardson, Dr. Richard Schmidt, and Charles Coey for the use of their Matlab Code that significantly helped my data analysis. Dr. Richardson has further assisted me as a committee member, teacher, and sounding board, for which I am very grateful. My thanks are also extended to Dr. Michael Riley for serving as a committee member and teacher. His attention to detail and insight helped hone my research goals and have pushed me to work and think harder. Thank you also to Dr. Sarah Cummins-Sebree for serving as a committee member and teaching mentor. She has helped and inspired me throughout graduate school and into my future career path. I would like to thank my fellow graduate students, both past and present, for their friendship, support, and feedback. Finally, I would like to thank my family. Thank you to my parents for believing in me and encouraging me to succeed. Thank you to my sister, for her constant love, support, and listening ear. And finally, thank you to my husband for his extreme patience; throughout this process he both learned to cook and put up with an extraordinary amount of takeout. v

7 Table of Contents CHAPTER 1: INTRODUCTION... 1 The Informational Basis of Interlimb Coordination... 2 The Role of Biomechanics in Coordination Stability... 3 Recruitment of Degrees of Freedom... 4 The Present Research Question... 5 The Pilot Study... 7 The Current Study CHAPTER 2: General Method Participants Apparatus Procedure Data Analyses Measures of Task Performance Measures of Stability CHAPTER Experiment 1: Visual and Biomechanical Asymmetry Method Participants Apparatus Procedure Results Task Performance Movement Amplitude Movement Frequency Relative Phase Recruitment of df Coordination Stability Tradeoff between df Recruitment and Coordination Stability Discussion CHAPTER Experiment 2: Reversal of virtual marker mapping vi

8 Method Participants Apparatus Procedure Results Task Performance Movement Amplitude Movement Frequency Relative Phase Summary of relative phase analysis Recruitment of df Manipulated hand Unmanipulated hand Coordination Stability X-axis Y-axis Z-axis The Influence of Congruence of Visual and Biomechanical Motion Movement Frequency X-axis Y-axis Z-axis Relative Phase Recruitment of df Coordination Stability Tradeoff between df Recruitment and Coordination Stability Discussion CHAPTER Experiment 3: Feedback Experiment 3a: Feedback in the x-y plane Method Participants Apparatus vii

9 Procedure Results Task Performance Movement Amplitude Movement Frequency Relative phase Recruitment of df Coordination Stability Tradeoff between df Recruitment and Coordination Stability Discussion Experiment 3b: Feedback in the z-plane Method Participants Apparatus Procedure Results Task Performance Movement Amplitude Movement Frequency Relative Phase Recruitment of df Coordination Stability Tradeoff between df Recruitment and Coordination Stability Discussion CHAPTER 6: GENERAL DISCUSSION Does df recruitment serve to stabilize coordination? Tradeoff between df recruitment and coordination stability? Visual or Biomechanical Basis of Coordination Stability? Attention and Coordination? Future Directions References viii

10 List of Tables Table 1. Mean and standard deviation for xdiff for each hand in each condition, and results of paired t-tests to determine whether each hand was moving differently. Bolded conditions were expected to be significantly different. All df = 26. Table 2. T-values for paired t-tests comparing values of xdiff for the manipulated hand to determine task accuracy. Bolded entries were expected to be significantly different. All df = 26. Table 3. T-values for paired t-tests comparing values of xdiff for the unmanipulated hand to determine task accuracy. There were no expected significant differences since all display targets were circles. All df = 26. Table 4. Mean and standard deviation for ydiff for each hand in each condition, and results of paired t-tests to determine whether each hand was moving differently. No conditions were expected to be significantly different since all target asymmetries were in the x-axis. All df = 26. Table 5. T-values for paired t-tests comparing values of ydiff for the manipulated hand to determine task accuracy. All df = 26, all p >.05. Table 6. T-values for paired t-tests comparing values of ydiff for the unmanipulated hand to determine task accuracy. All df = 26. Table 7. Mean and standard deviation for xdiff for each hand in each condition, and results of paired t-tests to determine whether each hand was moving differently. No conditions ix

11 were expected to be significantly different since all target motions were circular. All df = 17, all p >.05. Table 8. T-values for paired t-tests comparing values of xdiff for the manipulated hand to determine task accuracy. All df = 17, all p >.05. Table 9. T-values for paired t-tests comparing values of xdiff for the unmanipulated hand to determine task accuracy. All df = 17. Table 10. Mean and standard deviation for ydiff in each hand in each condition, and results of paired t-tests to determine whether each hand was moving differently. No conditions were expected to be significantly different since all target motions were circular. All df = 17, all p >.05 Table 11. T-values for paired t-tests comparing values of ydiff for the manipulated hand to determine task accuracy. All df = 17. Table 12. T-values for paired t-tests comparing values of ydiff for the unmanipulated hand to determine task accuracy. All df = 17, all p >.05. Table 13. Mean and standard deviation for xdiff for each hand in each condition, and results of paired t-tests to determine whether each hand was moving differently. Bolded entries were expected to be significantly different from each other. All df = 14. Table 14. T-values for paired t-tests comparing values of xdiff for the manipulated hand to determine task accuracy. Bolded entries were expected to be significantly different from each other. All df = 14. x

12 Table 15. T-values for paired t-tests comparing values of xdiff for the unmanipulated hand to determine task accuracy. There were no expected differences since all targets were circular. All df = 14. Table 16. Mean and standard deviation for ydiff for each hand in each condition, and results of paired t-tests to determine whether each hand was moving differently. No conditions were expected to be significantly different since all manipulations were in the y-axis. All df = 14. Table 17. T-values for paired t-tests comparing values of ydiff for the manipulated hand to determine task accuracy. All df = 14. Table 18. T-values for paired t-tests comparing values of ydiff for the unmanipulated hand to determine task accuracy. All df = 14, all p >.05 Table 19. Mean and standard deviation for xdiff for each hand in each condition, and results of paired t-tests to determine whether each hand was moving differently. Bolded entries were expected to be significantly different from each other. All df = 19. Table 20. T-values for paired t-tests comparing values of xdiff for the manipulated hand to determine task accuracy. Bolded entries were expected to be significantly different. All df = 19. Table 21. T-values for paired t-tests comparing values of xdiff for the unmanipulated hand to determine task accuracy. No entries were expected to be significantly different. All df = 17. xi

13 Table 22. Mean and standard deviation for ydiff for each hand in each condition, and results of paired t-tests to determine whether each hand was moving differently. No conditions were expected to be significantly different since all manipulations were in the x-axis. All df = 19. Table 23. T-values for paired t-tests comparing values of ydiff for the manipulated hand to determine task accuracy. All df = 19. Table 24. T-values for paired t-tests comparing values of ydiff for the unmanipulated hand to determine task accuracy. All df = 19, all p >.05. xii

14 List of Figures Figure 1. Experimental setup. Movement in the transverse plane (depicted by dashed lines) causes corresponding motion in the coronal plane (i.e., on the screen). Figure 2. Movement into the z-plane under visual manipulations of symmetry. Figure 3. Standard deviation of the relative phase angle (SDɸ), a measure of stability for the x, y, and z axes under visual manipulations of symmetry. Figure 4. Overhead view of participant movement (a)., side view of participant movement showing upward movement (b), and time series of movement displacement over time (with peaks and valleys denoted by asterisks) for the x-axis (c) and y-axis (d). Figure 5. Results of the frequency analysis for each axis of movement. Error bars represent standard error of the mean. Figure 6. Amount of movement in the z-plane (zdiff) for each condition. Error bars represent standard error of the mean. Figure 7. Amount of movement in the z-plane (zdiff) separated by hand for the biomechanically symmetric and asymmetric conditions. Error bars represent standard error of the mean. Figure 8. SDɸ for each axis. Error bars represent standard error of the mean. Figure 9. Scatterplot comparing SDɸ for the z-axis to zdiff for the manipulated hand (a) and unmanipulated hand (b). Figure 10. Visual and biomechanical motion depicted in the visual phase biomechanical phase design (a) and in the match type biomechanical phase design (b). xiii

15 Figure 11. Frequencies (Hz) for the visual phase biomechanical phase interactions for the y-axis analysis (a) and z-axis analysis (b). Figure 12. Values of ɸ for all conditions (a), as well as for the visual phase biomechanical phase interactions along the x-axis (b), y-axis (c), and z-axis (d). Error bars represent standard error of the mean. Figure 13. Amount of movement in the z-plane for the visual phase biomechanical phase hand interaction. Error bars represent standard error of the mean. Figure 14. SDɸ for the visual phase biomechanical phase interactions for all axes (a), along the x-axis (b), y-axis (c) and z-axis (d). Error bars represent standard error of the mean. Figure 15. Frequencies (Hz) for the biomechanical phase and match main effects for the y- axis analysis (a) and z-axis analysis (b). Figure 16. Values of ɸ for the main effects of biomechanical phase and match type (a) and the axis match type interaction (b). Error bars represent standard error of the mean. Figure 17. Amount of movement in the z-plane for the match type hand interaction for the match type hand biomechanical phase designs (a) and SDɸ for the match type axis interaction for the match type axis biomechanical phase designs (b). Error bars represent standard error of the mean. Figure 18. Amount of movement in the z-plane (a) and SDɸ (b) for the match type and biomechanical phase main effects. Error bars represent standard error of the mean. xiv

16 Figure 19. Scatterplot comparing SDɸ for the z-axis to zdiff for the manipulated hand (a) and unmanipulated hand (b). Figure 20. Results of the frequency analysis along each axis. Error bars indicate standard error of the mean. Figure 21. Average values of SDɸ for each axis(a) and all asymmetric and symmetric conditions (b). Error bars represent standard error of the mean. Figure 22. Scatterplot comparing SDɸ across all conditions for the z-axis to zdiff across all conditions for the manipulated hand (a) and unmanipulated hand (b). Figure 23. Scatterplot of the values of SDɸ for the x-axis and zdiff for the unmanipulated hand (a) and a scatterplot of the values of SDɸ for the y-axis and zdiff for the unmanipulated hand (b). Higher values of zdiff were significantly correlated with lower values of SDɸ. Figure 24. Movement frequencies (Hz) for each axis separated by symmetry condition. Error bars represent standard error of the mean. Figure 25. Amount of movement in the z-plane (zdiff) for all trials with and without feedback about z-axis movement. Error bars represent standard error of the mean. Figure 26. Values of SDɸ for each axis separated by conditions with and without feedback about z-axis movement. Error bars represent standard error of the mean. Figure 27. Scatterplot comparing SDɸ for the z-axis to zdiff for the manipulated hand (a) and unmanipulated hand (b). xv

17 CHAPTER 1: INTRODUCTION When people are asked to pat their heads while rubbing their bellies they tend to have trouble doing both at the same time because the natural tendency is for rhythmically moving limbs to coordinate with one another. People therefore often end up doing something like a rolling pat of the head and a patting rub of the belly (i.e., they move in unintended directions when the limbs are tasked with performing different movement patterns). At issue in the present research is what permits stable patterns of movement when coordination would ordinarily be unstable resulting from the limbs being required to move in different ways from one another. Kelso (1984) introduced a bimanual coordination task where he had participants oscillate their fingers along the horizontal plane in either muscular in-phase, where flexion and extension of each finger occurs at the same time, or muscular anti-phase, where fingers are flexing at opposite times and move parallel to each other. Haken, Kelso, and Bunz (1985) modeled the dynamics of Kelso s rhythmic bimanual coordination task in terms of self-organized, coupled oscillators. They found that at low frequencies, participants could produce both muscular in-phase movements and muscular anti-phase movements. However, when starting in an anti-phase mode, increasing the movement frequency yielded a spontaneous transition to an in-phase mode (the only stable mode at high frequencies). As frequency increases, anti-phase movements become less stable and are accompanied by critical fluctuations, which are quantified by an increased standard deviation of the continuous relative phase (a measure quantifying the coordination between two limbs) of the two oscillating fingers (Kelso, Scholz, & Schӧner, 1986). In other 1

18 words, as a system becomes less stable and approaches a transition to more stable state of movement, coordination between the two limbs begins to break down and becomes more variable. Further, increased standard deviation of the relative phase is an indication of reduced coordinative stability. Although the stable and unstable modes of interlimb coordination have been well investigated (Haken et al., 1985), the informational basis that supports stable coordination is not as well understood. The Informational Basis of Interlimb Coordination Schmidt, Carello and Turvey (1990) showed that interlimb coordination has an informational, rather than purely biomechanical, basis by using an interpersonal version of Kelso s (1984) task. They had two participants sit next to each other and swing their lower legs to a paced frequency in in-phase (i.e., symmetric) and anti-phase (i.e., asymmetric) movements. Consistent with the findings of intrapersonal interlimb coordination, they found that in-phase modes were more stable than anti-phase modes and that participants involuntarily switched from anti-phase to in-phase movements at high-frequencies. This showed that coordinative control systems are not simply based on intrapersonal biomechanics, but have a visual informational basis since there was no physical link between the two coordinating effectors. When the visual information about interlimb coordination indicates a stable mode (e.g., in-phase), and even when the muscular phase relationship exhibits an unstable relationship, actors can produce patterns that they otherwise would not be able to produce. Mechsner, Kerzel, Knoblich, and Prinz (2001), for example, had participants circle two visible flags by moving cranks occluded by a table. If the participants moved the cranks at a 2

19 4:3 frequency ratio (i.e., one hand completed four movement cycles during the same time the other completed three), which is typically an unstable, practically impossible movement for individuals to produce, the flags appeared to be moving in-phase. Participants were able to perform the difficult coordination task, even at relatively high coupled movement frequencies, as long as the visual information remained available. Visual information indicating a stable coordination pattern was sufficient for individuals to perform otherwise impossible interlimb movements (Experiment 3). Rather than having a purely muscular or motor basis, interlimb coordination seems to have an informational basis. The Role of Biomechanics in Coordination Stability Levin, Suy, Huybrechts, Vangheluwe, and Swinnen (2004) also studied the role of biomechanics in bimanual coordination. They had participants perform bimanual flexion and extension tasks with homologous joint combinations (i.e., movement about both shoulder joints or both elbow joints) or heterologous joint combinations (i.e., one arm moves about the shoulder while the other moves about the elbow) involving full arm movements. Participants moved their limbs at a preferred isofrequency (1:1 frequency ratio) or less preferred (and inherently less stable) multifrequency (1:2 frequency ratio). During isofrequency conditions, coordination patterns were more stable and accurate during homologous joint combinations compared to heterologous joint combinations. However, during multifrequency conditions, heterologous joint combinations were more stable and accurate than homologous joint combinations. This suggests that there may be a link between instability and flexibility such that limb combinations that have less coupling 3

20 and are less stable (i.e., heterologous joint combinations) may have greater flexibility when performing unfamiliar coordination tasks. Similarly, Swinnen et al. (2003) studied the influence of visual and kinesthetic information on bimanual coordination to determine which was primary in control of movement organization. They used a line drawing task, where the left hand was instructed to draw a vertical line while the right hand transitioned between different line orientations in a star shape. There were several visual manipulation conditions such that participants had normal vision, were blindfolded, watched their right-hand motion on a display screen that had no transformation, and watched the display with rotated motion. Regardless of visual information, participants showed no difference in degree or pattern of movement, suggesting vision is not primary in limb coordination. However, the influences of kinesthetic information were not entirely clear either. They used a similar task as in the visual manipulation experiment, but put vibration at different locations on the right limb to interfere with kinesthetic information. The only effects on orientation were very small, but other effects such as limb drift and reduced movement amplitude were aligned with prior research indicating the importance of kinesthetic information on upper limb movements; as such, the authors concluded that upper limb coordination during directionally differing movements is mediated by kinesthetic influences rather than visual influences. Recruitment of Degrees of Freedom The nature of coordination stability has also been investigated using spatially incompatible movements of the two limbs. Buchanan and Kelso (1999) had participants swing two hand-held pendulums in an anti-phase coordinative mode. As pacing frequency 4

21 increased, participants movements switched from planar (2D) to elliptical (3D); these elliptical motions were accompanied with increasing amounts of forearm motion. However, the coordinative mode did not switch to in-phase which suggests that systems recruiting df may enhance coordination stability thereby reducing the need for pattern switching. Richardson, Campbell, and Schmidt (2009) further studied the role of df recruitment in coordination in an interpersonal task where a participant synchronized arm movements in the vertical or horizontal plane to a confederate s movements. In congruent conditions, both participant and confederate moved in the same plane. In incongruent conditions participants moved in the plane orthogonal to the confederate s movements. During incongruent conditions participants produced increased movement in the non-instructed plane of movement. They found that participants produced coherent oscillations in the non-instructed plane, and that these oscillations were more pronounced for weaker states of coordination. This suggests that df recruitment serves to enhance coordination and is not just a result of motor interference from an incompatible stimulus. Because coordinative stability in interpersonal tasks is similar to what occurs in intrapersonal tasks (e.g., Schmidt & Richardson, 2008), df recruitment should occur during incongruent intrapersonal bimanual rhythmic coordination tasks as well. The Present Research Question Although df recruitment has been shown to stabilize coordination, it is not clear under what conditions such stabilization occurs or when such stabilization is necessary. For example, if coordination is visually stable, but muscularly unstable, are additional df required to maintain the same degree of coordination stability? Mechsner et al. (2001) had 5

22 participants produce biomechanically asymmetric movements that were visually symmetric (Experiments 1 and 2). However, their experiment had fixed spatial df because participants used two-dimensional cranks to produce movement. By having participants create physically unconstrained oscillatory movements, the present research investigated the role of df recruitment in planar movement where visual information about coordination was also manipulated. Mechsner et al. (2001) showed that complex movements are stabilized with visual feedback, and suggest that coordinative stability is biased towards spatial, perceptual symmetry. If this is the case, visually symmetric conditions should be more stable than visually asymmetric conditions regardless of motor symmetry. Further, if df recruitment serves to stabilize coordination as suggested by Buchanan and Kelso (1999) and Richardson et al. (2009), increases in stability in biomechanically or visually asymmetric planar movement trials should be accompanied by greater excursion into the z-plane. Levin et al. s (2004) work, however, may suggest an alternate possibility. If heterologous joint combinations have higher stability in less familiar coordinative patterns, there would be no expected difference in stability during biomechanically asymmetric conditions regardless of the available visual information, as each effector would have different patterns of muscle activation which Levin et al. suggested may lead to increased flexibility of the system. The current study also allowed the apparent discrepancies between Mechsner et al. s (2001) and Levin et al. s (2004) hypotheses to be addressed by decoupling visual symmetry from biomechanical symmetry. A biomechanical asymmetry can also be introduced during visually symmetric conditions by using a translational gain that causes a transformation between limb movement and the visual feedback based on motion of a sensor attached to the limb. This 6

23 type of gain transformation is used in daily activities such as using a computer mouse, where movement of the cursor on the screen is greater than the physical movement of the mouse (i.e., a gain greater than one), or in driving, where movement of the steering wheel 180 does not cause the wheels of the car to rotate to the same degree (i.e., a gain less than one). To create a biomechanical asymmetry, a gain manipulation can be applied to only one hand, such that a control hand has a gain of 1 applied and the manipulated hand has a gain unequal to 1 applied. In the current study, for example, participants traced targets using a virtual marker with a translational gain applied. To trace circular targets that appeared symmetrical, translational gain was applied to one hand such that the control hand produced a circle while the manipulated hand produced an ellipse to trace the shape of a circle. This manipulation allowed visual symmetry and biomechanical symmetry to be decoupled. In a preliminary study I explored the proposed manipulations. The Pilot Study In a 3 (type of manipulation; e.g., movement compression, movement expansion, or control) 2 (hand; e.g., manipulated or control hand) 2 (axis of manipulation; e.g., compression/expansion along x-axis or y-axis) pilot study, participants sat in front of a screen that had two visual targets displayed, one control target that was always displayed as a circle and one target that was depicted either as a circle, an elongated ellipse ( expand ) or a compressed ellipse ( compress ). Each participant completed the experiment under two manipulations, a visual symmetry manipulation and a biomechanical symmetry manipulation. Manipulated hand was counterbalanced across participants, such that the control hand was alternated for each participant. Participants 7

24 held handles attached to motion sensors in each hand, and the participants motion was recorded and motion in the coronal plane was rendered on the screen in real time. An occluding curtain was placed below the chin to obstruct vision of the hands and arms while allowing freedom of movement of the hands. Participants were asked to create motion with the sensors by moving their hands in the transverse plane, such as if they were drawing on a table. This caused corresponding motion of a virtual marker in the coronal plane on the screen (see Figure 1 for experimental setup). The task was to trace the targets on the screen at a rate of 0.42 Hz, which was determined ahead of time to be a natural and comfortable pace for several participants. In visually asymmetric conditions, the manipulated hand s target was displayed as either elongated or compressed ellipses and the visual information about movement corresponded to actual (biomechanical) motion (i.e., the motion of the two hands corresponded to the visual information about the motion of the hands). In the gain manipulation, both the manipulated and control hands targets were displayed as circles, but during the compress and expand conditions, respectively, a gain was applied to the experimental hand such that participants had to produce a smaller amplitude (e.g., a horizontally compressed ellipse for a horizontal manipulation) in order to produce circular motion on the screen or a larger amplitude (e.g., a horizontally expanded ellipse for a horizontal manipulation) in order to produce circular motion on the screen. Thus, in the gain manipulation the visual information about movement did not match biomechanical movement in the compress and expand conditions. To summarize the manipulations, in the visual symmetry manipulation, visual information corresponded to biomechanical 8

25 information while biomechanical symmetry was manipulated such that producing visually symmetric movement patterns yielded biomechanically asymmetric movement patterns. Figure 1. Experimental setup. Movement in the transverse plane (depicted by dashed lines) causes corresponding motion in the coronal plane (i.e., on the screen). The amount of movement into the z-plane was calculated to determine df recruitment. Since the task goals were explicitly explained to participants as being twodimensional, excursion into the third dimension indexes the degree of recruitment of df (Buchanan & Kelso, 1999; Richardson et al, 2009), which may be a coordinative strategy to enhance coordination. Standard deviation of the relative phase angle (SDɸ), a measure of coordination stability, was calculated for motion in the x (lateral), y (anterior-posterior), and z (vertical) directions separately. Error of movement in the x-axis (actual movement subtracted from target movement) was also calculated to determine whether there was a relationship between movement error and df recruitment. During trials where participants traced a compressed ellipse with hands moving in anti-phase, the amount of movement into the z-plane was not different from the control 9

26 condition (see Figure 2); however, SDɸ increased, suggesting the condition was less stable than the control condition (see Figure 3). Further, during trials where participants traced a visually elongated ellipse, there was greater excursion into the z-plane (see Figure 2) and SDɸ was not different than in the control condition (see Figure 3). This suggests a possible tradeoff between df recruitment and stabilization in visually and biomechanically asymmetric tasks. Although there was no significant influence of the symmetry manipulations on error, there was a significant positive correlation between error of movement in the x-axis and amount of movement into the z-plane for the manipulated hand during anti-phase movements (r =.25, p <.0001). The nature of this correlation was that as participants became more accurate with the task, they also had greater excursion into the z dimension (i.e., greater df recruitment), suggesting a tradeoff between performance and df recruitment. This further suggests that df recruitment may be serving to stabilize interlimb coordination. This phenomenon was further explored in a series of experiments. Figure 2. Movement into the z-plane under visual manipulations of symmetry. 10

27 Figure 3. Standard deviation of the relative phase angle (SDɸ), a measure of stability for the x, y, and z axes under visual manipulations of symmetry. The Current Study The broad goal of the current set of experiments was to evaluate whether df recruitment serves to stabilize coordination, and if there is a tradeoff between df recruitment and coordination stability (and under what conditions). Also at issue in the present set of experiments was whether coordinative stability has a visual basis (e.g., Meschner et al., 2001) or a biomechanical basis (e.g., Levin et al., 2004). These goals were addressed using a set of experiments that manipulated motion symmetry by having one arm produce the movement of a circle while the other produced the motion of an elongated ellipse. These asymmetric conditions were predicted to be less stable (i.e., have greater df recruitment or lower values of SDɸ) than symmetric conditions. Visual and biomechanical influences on coordination were investigated by decoupling visual information from biomechanical information. These were decoupled by applying a translational gain to one limb such that visually symmetric conditions required biomechanically asymmetric movements to complete the task and visually asymmetric conditions required 11

28 biomechanically symmetric movements to complete the task (Experiment 1) and by reversing the marker mapping of one limb (Experiment 2). The role of feedback was also investigated by constraining movement along the x-y plane (Experiment 3a) and constraining movement along the z-plane (Experiment 3b). 12

29 CHAPTER 2: General Method The same general method was used for each experiment except as otherwise noted for each individual experiment. Participants Undergraduate students enrolled in psychology classes at the University of Cincinnati participated in each study on a voluntary basis in return for course credit. Participants had normal or corrected-to-normal vision, no injuries to either of their hands or arms, no musculoskeletal problems, and were right-handed according to self-report. Apparatus Participants were seated in a wooden chair facing a screen displaying two visual targets. Participants were seated approximately 200 cm from the screen. In each hand they held a wooden handle with motion sensors connected to a 6D motion capture unit (FasTrak II; Polhemus, Inc., Colchester, VT; sampling rate of 24 Hz). The motion sensors captured the participants motion and rendered a virtual marker in real time on the screen with the targets. Because previous research has demonstrated that images mirrored along the horizontal axis are more quickly discernable than images mirrored along the vertical axis (Quinlan, 2002), all symmetry manipulations for the current study were made along the horizontal axis. To further simplify the experimental design, all asymmetric ellipses were elongated along the horizontal axis, and the compressed ellipses used in the pilot study above were discarded from the current design. The visual target for the control hand 13

30 remained circular for the entirety of the experiment. The visual target for the experimental hand was either circular or an ellipse with a longer horizontal axis. Circular targets were displayed 16 cm in diameter with a thickness of 2 cm. Oval targets had a major diameter of 19.2 cm, a minor diameter of 16 cm, and were also 2 cm thick. Which hand held the control sensor was counterbalanced across participants and trial order was randomized. An occluding curtain was placed below the chin so that the only movement of the limbs visible to participants was that of the virtual marker on the screen. Procedure The participants task was to move the handles in the transverse plane such that their motion caused the virtual markers to trace targets on the screen. They were instructed that they should pretend they were drawing on a flat surface to produce motion on the screen, and that movement to the right or left caused motion to the right or left, respectively, on the screen, while motion away from their bodies and toward their bodies produced motion up and down, respectively, on the screen. Once participants were introduced to the task, they were given time to practice the experimental manipulations. They traced the ellipses to a metronome such that movement around the ellipse occurred at the rate of 0.42 Hz. After participants stated they were sufficiently comfortable with the task, the practice trials ended. The testing phase consisted of three trials in each condition presented in randomized order. Once a trial was presented on the screen, participants were verbally told to start movement around the ellipses. After they began moving, that motion was recorded for 30 seconds per trial, after which they were instructed to hold 14

31 their hands still while the next trial was presented. Sample movement for one participant can be seen in Figure 4a and 4b. Data Analyses Measures of Task Performance. To determine whether participants movement trajectories were, on average, the same dimensions as the target data, the average peak and average valley for the x- trajectory (see Figure 4c) and y-trajectory (see Figure 4d) were found using customized MATLAB code on MATLAB version (Mathworks, Natick, Massachusetts). Each column of data was analyzed individually by using the built-in PICKEXTR function to determine the positions of significant extrema. The absolute value of the difference between average peak position and average valley position was calculated and averaged across trials for each participant. Reported units are the default units from the motion capture unit; one unit is approximately equal to 2.6 cm of movement by the participant. To determine whether participants were moving at the same frequency as the metronome, the dominant frequency was calculated for each hand (i.e., manipulated and unmanipulated) along the x-axis and y-axis. Customized MATLAB code was used for these calculations. First, the total length of each time series was determined. To increase the speed of the Fast Fourier Transform (FFT) calculation when the time series was not a power of 2, the exponent for the smallest power of 2 that was greater than or equal to the length of the series was calculated. A FFT was then calculated on the time series using the built-in MATLAB function FFT. The FFT was used to find frequency components for each 15

32 time series. The dominant frequency used for analysis corresponded to the maximum value (i.e., the peak) of the FFT. As a measure of the synchronization of the two limbs, instantaneous relative phase (ɸ) was calculated separately for each axis of movement (i.e., x, y, and z). Customized MATLAB code was used for these calculations. The time series were not detrended because task performance was constrained to movement around targets, nor were they normalized, since all comparisons were made on the same scale. When participants movements were biomechanically anti-phase, the time series for x-axis in the unmanipulated hand was inverted since the hands were moving in opposite directions. This inversion was done by subtracting the difference between each value and the mean of the time series from the mean of the time series. Doing this resulted in a target ɸ = 0 for all conditions. Instantaneous phase was calculated using a Hilbert transform (Pikovsky, Rosemblum, & Kurths, 2001). Next, the phase angle of the manipulated hand was subtracted from the phase angle of the unmanipulated hand, which resulted in a time series of ɸ. The mean value of ɸ is reported in all sections. Measures of Stability. To measure df recruitment, movement in the z-plane was calculated by finding the positions of the average peak and average valley in the z-trajectory using the same customized MATLAB code used to determine peaks and valleys in the x- and y-trajectories. The absolute value of the difference was calculated and averaged across trials for each condition of each participant. This was done for each hand (i.e., the manipulated hand and 16

33 the unmanipulated hand). Reported units are the default units from the motion capture unit; one unit is approximately equal to 2.6 cm of movement by the participant. To measure coordination stability, the standard deviation of (ɸ), SDɸ was calculated separately for each axis of movement (i.e., x, y, and z). ɸ was calculated as above, and SDɸ was calculated by taking the standard deviation of the ɸ time series. Lower values of SDɸ indicate higher stability. Figure 4. Overhead view of participant movement (a)., side view of participant movement showing upward movement (b), and time series of movement displacement over time (with peaks and valleys denoted by asterisks) for the x-axis (c) and y-axis (d). 17

34 CHAPTER 3 Experiment 1: Visual and Biomechanical Asymmetry The first experiment was designed to replicate the pilot study while also properly controlling the biomechanical asymmetry resulting from the gain manipulation such that its biomechanical magnitude matched the visual asymmetry. Further, the present study was designed as a fully crossed 2 (visual symmetry) 2 (biomechanical asymmetry) design in order to properly investigate the respective influences of each factor on interlimb coordination. In further contrast to the pilot study, the gain manipulation was only applied along the x-axis (i.e., left/right on the screen) while the y-axis mapping (i.e., up/down on the screen) was not manipulated. Following Meschner et al. s (2001) predictions of visual stabilization of coordination, visually asymmetric conditions were predicted to be either less stable or have greater df recruitment than the visually symmetric conditions, where no significant influence of biomechanical asymmetry on coordination stability or df recruitment was predicted. If the present research aligns with Levin et al. s (2004) results, however, biomechanically asymmetric conditions should not be differently stable than biomechanically symmetric conditions, regardless of visual symmetry. Method Participants Twenty-seven undergraduate ranging in age from 18 to 22 (M = 19.33, SD = 1.30) participated in this study. 18

35 Apparatus The apparatus was the same as that described in the general experimental description. The display targets for the visually symmetric conditions were two circles, and the display targets for the visually asymmetric conditions were one circle for the unmanipulated hand and one elongated ellipse for the manipulated hand. In the visually symmetric-biomechanically symmetric (VS-BS) condition, the target for the experimental hand was a circle, and there was no gain manipulation such that participants produced circular motion to trace the test object. In the visually symmetric-biomechanically asymmetric (VS-BA) condition the target for the experimental hand was a circle, but a translational gain of 0.83 was applied to the experimental hand s motion sensor coordinate as displayed on the screen so that participants had to produce the motion of an elongated ellipse in order to successfully trace the circle on the screen. In the visually asymmetricbiomechanically asymmetric (VA-BA) condition, the target for the manipulated hand was elongated, and there was no gain manipulation such that participants had to produce elliptical motion in order to successfully trace the test object. In the visually asymmetricbiomechanically symmetric (VA-BS) condition, the target for the experimental hand was elongated, but there was a translational gain of 1.22 applied to the experimental hand s motion sensor coordinates as displayed on the screen so that the participant had to produce a circle (that matched that of the control hand) in order to successfully trace the elongated ellipse. 19

36 Procedure The procedure was the same as in the general experimental procedure. After participants were introduced to the basic task, they were allowed as much time as they needed to practice tracing both the circle and ellipse without a gain manipulation. Practice generally lasted less than five minutes. Participants were not informed of the gain manipulation. After completion of the experiment, participants were debriefed and asked whether they were aware of the gain manipulation; none indicated that they were aware of the manipulation. Results Task Performance Movement Amplitude. A series of paired t-tests compared values of xdiff to determine whether participants completed the task accurately. First, the manipulated hand was compared to the unmanipulated hand in all conditions (see Table 1). The only differences between hands were as expected; during asymmetric trials the manipulated hand had greater amplitude than the unmanipulated hand. Amplitude for the manipulated hand (see Table 2) and unmanipulated hand (see Table 3) were also compared across conditions to determine whether participants were moving consistently. For the manipulated hand, biomechanically symmetric and biomechanically asymmetric trials differed as expected, but there were unexpected differences when comparing the conditions with gain. Instead of matching the target amplitudes of VS-BS and VA-BA, participants traveled intermediary distances during the 20

37 VA-BS and VS-BA trials. During the VA-BS and VS-BA trials, the manipulated hand traveled further than VS-BS conditions, but less than VA-BA conditions. Though the unmanipulated hand had a lower amplitude than the manipulated hand in each condition, significant differences in the unmanipulated hand across conditions (Table 3) suggest that when the amplitude was greater in the manipulated hand (i.e., VA-BA and VS-BA), amplitude also increased in the unmanipulated hand compared to biomechanically symmetric trials (i.e., VS-BS and VA-BS). The amount of movement in the y-direction (ydiff) was also submitted to a series of paired t-tests in the manner above. If participants were doing the task as expected, there should be no significant differences between any conditions, since symmetry was only manipulated in the x-axis. When comparing the manipulated hand and unmanipulated hand for each condition (see Table 4), there was a significant difference in the VS-BA condition. The manipulated hand moved further than the unmanipulated hand. Comparisons of the manipulated hand across conditions (see Table 5) revealed varied participant performance. All comparisons were significantly different from each other except for the conditions without gain, VS-BS and VA-BA. This indicates that the gain manipulation in the x-axis also influenced performance in the y-axis. Comparisons of the manipulated hand across conditions (see Table 6) also revealed unexpected differences in amplitude during conditions with a gain manipulation, suggesting that during trials with an asymmetry or gain manipulation, performance was augmented in the y-axis for the unmanipulated hand as well. 21

38 Table 1. Mean and standard deviation for xdiff for each hand in each condition, and results of paired t-tests to determine whether each hand was moving differently. Bolded conditions were expected to be significantly different. All df = 26. Condition Manipulated hand Unmanipulated M(SD) hand M(SD) t VS-BS 3.41(0.25) 3.32(0.23) 1.21 VS-BA 3.77(0.30) 3.40(0.29) 4.76*** VA-BS 3.54(0.24) 3.29(0.22) 4.06*** VA-BA 3.93(0.25) 3.39(0.23) 8.61*** Notes: ***p <.001 Table 2. Table 3. T-values for paired t-tests comparing values of xdiff for the manipulated hand to determine task accuracy. Bolded entries were expected to be significantly different. All df = 26. T-values for paired t-tests comparing values of xdiff for the unmanipulated hand to determine task accuracy. There were no expected significant differences since all display targets were circles. All df = 26. VS-BS VS-BA VA-BS VA-BA VS-BS VS-BA VA-BS VA-BA VS-BS *** 5.37*** 11.24*** VS-BS * * VS-BA *** 3.49** VS-BA ** 0.44 VA-BS *** VA-BS ** VA-BA VA-BA Notes: **p <.01; ***p <.001 Notes: *p <.05; **p <.01 Table 4. Mean and standard deviation for ydiff for each hand in each condition, and results of paired t-tests to determine whether each hand was moving differently. No conditions were expected to be significantly different since all target asymmetries were in the x-axis. All df = 26. Condition Manipulated hand Unmanipulated M(SD) hand M(SD) t VS-BS 3.25(0.25) 3.21(0.29) 0.63 VS-BA 3.37(0.24) 3.20(0.28) 2.79** VA-BS 3.14(0.22) 3.10(0.24) VA-BA 3.28(0.20) 3.19(0.28) 1.82 Notes: **p <.01 22