Executive function (EF) refers to the higher-order cognitive processes that enable

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1 Executive function (EF) refers to the higher-order cognitive processes that enable flexible behavior when contextual demands change. Children in an elementary classroom, for example, are often required to adjust their behavior flexibly across contexts as they move from quiet reading time, to small group activities, to recess. The ability to modulate behavior in context-specific ways is a central developmental achievement that has broad and long-lasting impacts on specific forms of learning such as language development (Im-Bolter, Johnson, & Pascual-Leone, 2006) and mathematical abilities (Bull & Scerif, 2001), as well as on general cognitive functioning in childhood and adolescence (e.g., school performance, IQ, psychopathology; see Liss et al., 2001). Early theories of EF proposed that the emergence of cognitive flexibility reflected developmental changes in a central executive system a central resource that controls other aspects of cognition (Duncan, Johnson, Swales, & Freer, 1997). This view was anchored, in part, to evidence that core EF processes could be localized to lateral pre-frontal cortex (PFC), a large brain region anterior to the precentral sulcus. Lateral PFC is one of the slowest developing brain regions (Geidd, Blumenthal, & Jeffries, 1999) and evidence from patient populations (Baddeley, Sala, Papagno, & Spinnler, 1997) and single-unit neurophysiology (Assad, Rainer, & Miller, 2000) showed that impairments of PFC leads to behaviors that mimic the performance of young children (Dempster, 1992). Recent factor analytic models have suggested, however, that cognitive control and flexibility do not reflect the operation of a single resource. Rather EF has multiple distinct components, including inhibition (the ability to suppress inappropriate behaviors or actions), working memory (the ability to maintain an active representation of information or goals), and 1

2 task-switching (the ability to update behavior across different contexts; Miyake et al., 2000). Evidence from neuroimaging studies supports this, revealing an extensive network of regions within frontal and posterior brain regions (for review, see Fair et al., 2008). Cognitive control and flexibility are thought to emerge from interactions within this system-wide network. Here, I will focus on one new theoretical perspective Dynamic Field Theory (DFT) that has shown promise in tackling the different challenges facing an integrative theory of EF. DFT has been used to examine the early emergence of various aspects EF, but here I will focus on a case study in the component of task-switching. Specifically, I will focus on a canonical task used to probe the early emergence of flexible rule-use: the Dimensional Change Card Sort (DCCS) task. In this task children are asked to sort cards by shape or color and then switch and sort by the other dimension (see Figure 1). In this task, 3-year-olds robustly perseverate and continue the initial set of rules when instructed to switch. Four-year-olds, on the other hand, have little trouble switching between these two sorting dimensions. Critically, DFT has already been used to explore the early-emergence of task-switching within the context of an autonomous model of neural systems that can organize and change their own behaviors over time (Buss & Spencer, in press). This model was used to explain the behavior of 3- and 4-yearolds across numerous task-switching conditions using simulated neural populations. Rule-use in this model emerges from representations of labels corresponding to shapes and colors modulating posterior neural representations of these visual features. The developmental transition between 3- and 4-years-old emerged from stronger interactions between frontal and posterior systems as the labels for shapes and colors were learned. Moreover, recent work has demonstrated that DFT can effectively bridge between brain and behavior. I highlight this link, 2

3 presenting data that test specific neural predictions using a new neuroimaging technology near-infrared spectroscopy (NIRS). Task-switching Task switching taps the cognitive processes required to go from one mode of behavior or ruleset to another. The ability to flexibly switch between tasks is indexed by switch-costs: the increased errors or reaction times after a change in task rules. Switching tasks is a complex process that requires both WM to actively represent the rules and inhibition to suppress pre-switch responses (Monsell, 2003). Consequently, the details of the rules for different tasks have a major influence on performance. Univalent rule switches require changing from one set of rules with one stimulus set to a different set of rules with a different stimulus set. Few switch costs are seen by age 3 with univalent rules in which each stimulus is associated with a different response (Zelazo et al., 2003). Switching tasks becomes more difficult with bivalent rules where two different responses may be associated with a single stimulus (Crone, Donohue, Honomichl, Wendelken, Bunge, 2006). Such situations require the active selection of one rule among competitor rules for the same stimulus set. This adds an extra inhibitory component because the pre-switch rules are still afforded by the stimuli. By the age of 4, children are able to switch between bivalent sets of rules (Zelazo et al., 2003), but switch costs continue beyond 4 years (Crone et al., 2006). Neural evidence suggests that developmental changes in the frontal cortex are involved in the emergence of task switching between 3 and 5 years. Moriguchi and Hiraki (2009) reported an increase in oxygenated hemoglobin in the inferior PFC in children that switched successfully on the DCCS task. Beyond 5 years, fmri research suggests that different neural systems support the representations of rules and switching between rules. In particular, DLPFC has been shown to be involved in the execution of specific rules (Tanji & Hoshi, 2001), pre-sma/sma is critically involved in task switching, and VLPFC is sensitive to the demands on rule-representation (Crone et al., 2006). Further evidence shows that rule- 3

4 switching develops earlier than rule-representation: activation in pre-sma/sma shows adult-like patterns by 10 years, while activation in VLPFC does not show adult-like patterns until 16 years (Crone et al., 2006). Bridging the Gap between Brain and Behavior: Using DFT to Simulate Hemodynamics A central aspect of the emergence of EF over development is the complex pattern of behavioral and neural data. This highlights a central challenge for theories of EF to explain data at these different levels of analysis. As described previously, aspects of the DCCS model can be roughly localized to particular brain regions including cortical fields in parietal, temporal, and frontal cortex (see Figure 2). The question we explore here is whether we can move from the neural principles of DFT and this rough mapping to cortical regions to a more direct mapping between the neural dynamics of the model and the brain. The approach for mapping DFT to hemodynamics builds from research exploring the neural basis of the blood oxygen level dependent (BOLD) signal (the primary means of measure neural activity in humans in cognitive tasks is to measure the change in blood-oxygen usage by neural tissue using functional magnetic resonance imaging, fmri). For instance, Logothetis, Pauls, Augath, Trinath, and Oeltermann (2001) simultaneously recorded single-unit and multiunit activity, local field potentials, and the BOLD signal using fmri with non-human primates. Results showed that local field potentials were most strongly correlated with the BOLD signal. Local field potentials (LFPs) reflect synaptic activity over relatively large areas of cortex, providing a measure of the inputs to, and local processing within, an area. Logothetis and colleagues further showed that they could reproduce in quantitative detail the BOLD response by convolving the time-course of the LFP with a general impulse response function. 4

5 To examine whether this approach has potential merit, the neural field model of the DCCS task was used to simulate recent data from a study by Moriguchi and Hiraki (2009). These researchers used Near Infrared Spectroscopy (NIRS) to measure frontal activation in 3- and 5- year-olds while they performed the DCCS task. NIRS measures the relative absorption of nearinfrared light as it is passes through surface tissue and cortex. By recording from multiple wavelengths, one can reconstruct the relative concentrations of oxygenated or deoxygenated hemoglobin within a cortical volume between the source and detector (Strangman, Boas, & Sutton, 2002). Moriguchi and Hiraki (2009) reported a close association between rule-switching ability and frontal activation. Specifically, 5-year-olds (see blue lines in Figure 3A), all of whom switched rules, and some 3-year-olds who also switched rules (red lines in Figure 3A) showed stronger frontal activation during both the pre- and post-switch phases of the DCCS task than 3- year-olds who perseverated (green lines in Figure 3A). Strong frontal activation, then, is associated with correct rule-switching. To examine whether the DFT could capture these neuroimaging findings, batches of old and young models were executed while recording LFPs from the dimensional units, that is, the sum of the absolute value of excitatory and inhibitory contributions to the rate of change of activation of these units. This included local contributions to activation change such as selfexcitation as well as contributions from the posterior feature fields. We then convolved this time course of activity with a general impulse response function and normalized the signal in the same fashion as Moriguchi and Hiraki (2009), taking the z-score of the signal across the old and young models at each point in time. Figure 3B shows the model hemodynamic data. Models that perseverated showed weak frontal activation throughout, while models that 5

6 switched rules showed strong frontal activation throughout. This demonstrates that the model can simultaneously capture both behavioral and neural data, as well as changes at both levels of analysis over development. From Neural Principles to Neural Predictions: Testing the DFT using NIRS Although these initial results are compelling, a critical test of any theory is to generate novel predictions. The DFT has already been used to generate novel behavioral predictions (Buss & Spencer, in press). But can this theory also generate novel neural predictions? I examined this issue by using the DNF model to explore an apparent contradiction in the literature. In particular, data from Moriguchi and Hiraki (2009) suggest that frontal activation is necessary for correct rule-switching only children who showed robust frontal activation sorted correctly during the post-switch phase. If this is the case, then how are 3-year-olds who perseverate in the standard version of the DCCS task and show weak frontal activation able to switch rules in some circumstances? For example, how are 3-year-olds able to switch rules in a No-Conflict version where the test cards match the target cards along both dimensions during the pre-switch phase (e.g., sorting a red star to a red star and a blue circle to a blue circle)? To examine this issue in greater detail, a set of behavioral and neural simulations was used to simultaneously record the model s sorting behavior and predicted hemodynamics in a No Conflict version and a Standard version for comparison. As in previous simulations, the model sorted correctly in the No Conflict task and perseverated in the Standard task. Critically, the young model also showed stronger frontal hemodynamics when correctly switching in the No-Conflict version compare to the Standard version (in which it tends to perseverate). Figure 4A shows the predicted hemodynamic response in these two variants of the task. The plot 6

7 shows the event-related hemodynamic response from the model on post-switch trials from each condition. The larger hemodynamic response in the No-Conflict version is generated though the same mechanism which drives correct switching the overlap of Hebbian memories and the target card inputs. This creates stronger activation in the posterior neural system when a test card is presented and, consequently, a stronger input to the frontal dimensional attention system. To test this neural prediction, a continuous event-related version of the DCCS task was used in which children cycled through various switch conditions. The task was structured into blocks of 3 trials where the rule stayed the same. As children moved from block to block, the rules changed such that each block of 3 trials served as the pre-switch phase for the ensuing block of post-switch trials. Here, I focus on the Standard and No-Conflict conditions which were critical for the model s prediction. Further, the analyses below focused on the first trial of each block and only analyzed trials following blocks in which at least 2 out of 3 cards were sorted correctly. This ensured that children were either clearly switching rules or clearly perseverating. The data presented below is from a group of children between 3 years, 6 months and 4 years, 6 months who participated in a total of 4 runs through the experimental design across 2 visits to the laboratory. Figure 5 shows the NIRS probe design. Clusters of lights and detectors were placed near areas F7/F8 in the international EEG system. These are the same target regions measured by Moriguchi and Hiraki (2009). Children were initially sorted into two groups based on their behavioral performance in the Standard version. Children who were above 50% correct on post-switch trials were classified as Switchers, while children who performed below 50% correct were classified as 7

8 Perseverators. This resulted in 6 children within each group. Figure 6A shows the performance for these two groups of children in the Standard and No-Conflict versions. As can be seen, the task elicited the desired pattern of behavior. Perseverators performed significantly better on the No-Conflict version compared to the Standard version. Switchers, on the other hand, performed equally well in both conditions. For the analysis of the NIRS data, I focused on the two bilateral channels highlighted in Figure 5. We first examined the difference between Switchers and Perseverators to determine whether our NIRS data replicated the central finding of Moriguchi and Hiraki (2009). Figure 6B shows the hemodynamic response on the Standard condition when Perseverators sorted incorrectly compared to when Switchers sorted correctly. As in Moriguchi and Hiraki (2009), Switchers showed a significantly larger hemodynamic response than Perseverators (p<.05). Next, I looked at the key contrast needed to test the prediction of the DNF model. Figure 4B shows the hemodynamic response of Perseverators on (correct) No-Conflict trials compared to (incorrect) Standard trials. As predicted by the DFT, perseverators showed a significantly larger hemodynamic response on No-Conflict trials compared to Standard trials (p<.05). Although preliminary, these data are encouraging, and suggest that it is possible to test predictions of the DFT at both behavioral and neural levels. Further, this suggests that the dynamic field framework has the potential to integrate findings across levels and timescales one of the central challenges facing theories of EF. Conclusions Several challenges exist for any theory to address the emergence of EF. The first challenges were linked to the multi-component nature of EF that theories must explain how 8

9 these component emerge, differentiate, and co-evolve over development. Next, theories of EF must explain both behavioral and neural data, as well as how EF changes across multiple timescales. Finally, theories of EF must address the issue of autonomy how the neural system can organize its own behavior without a homunculus. In this paper, I emphasized the ways in which the DFT speaks to these different challenges. Using an existing model that is able to simulate the developmental transition in task-switching between 3- and 4-year-olds, I highlighted how a common developmental mechanism (enhanced selectivity and coupling of neural connections between fields) was able to capture behavioral and neural changes. Using this groundwork, I then turned to an innovative new aspect of our approach testing DNF models using neuroimaging techniques. Notably, the DNF model of task-switching in the DCCS task made a novel, specific neural prediction that is consistent with preliminary NIRS data. This is a positive sign, but clearly there is a long way to travel on this front. For instance, a localist view of our neural architecture (e.g., Figure 1) makes strong claims about changes in fronto-parietal connectivity as children develop the ability to switch rules. We next have yet to examine whether this is the case. In summary, DFT shows promise in its ability to integrate the multiple components shown to underlie EF. This theory was able to quantitatively capture empirical results from a canonical task used to examine the early development of EF the DCCS task. Moreover, the new approach to simulating hemodynamics with the model shows promise in bringing together behavioral and neural data. In this context, the DFT provides a robust starting point for an integrative theory of the development of executive function. 9

10 Figures Figure 1: Example of task structure in the Dimensional Change Card Sort (DCCS) task. Target cards are shown on the trays that indicate which features go where for the different games. The test cards that children sort (the blue-star and red circle) are shown at the bottom. Children would be instructed to sort by either shape or color during the pre-switch phase and then to switch and sort by the other dimension. Figure 2: The architecture and neural mapping of the dynamic field model. The general mapping to brain regions is shown in A, where the color of each circle matches the color of the parentheses that encompass each piece of the model architecture in the other panels. The object representation model is shown in panels B, C, and D. The dimensional attention system is shown in panel E. Figure 3: NIRS data from Moriguchi and Hiraki (2009) is plotted in A; DNF model simulations are plotted in B. The left columns show the hemodynamic response during the pre-switch phase, and the right column shows the hemodynamic response during the postswitch phase. Time goes along the x-axis, while the normalized z-score of the response is plotted along the y-axis. Older children showed a larger increase in the hemodynamic response than younger children, suggesting that older children engaged the frontal cortex more robustly. 10

11 Figure 4: Predicted hemodynamic data from the perseverative young model (left) and NIRS data from 3- and 4-year-olds (right) for No-Conflict (correct) trials and the Standard (incorrect) trials. Time goes along the x-axis, while the concentration of oxygenated hemoglobin is plotted along the x-axis. A larger hemodynamic response was observed in the No-Conflict condition suggesting that the frontal cortex was engaged more robustly in this condition. Figure 5: Layout of NIRS probe relative to the system. Red circles mark the locations of lights while blue circles mark the locations of detectors. Data channels used in our analysis are highlighted with a bold black line. Figure 6: Behavioral data from the NIRS experiment is shown at left. Percent correct is plotted along the y-axis. The replication of the basic effect reported in Moriguchi & Hiraki (2009) is plotted at right. 11

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