Decomposing Simon task BOLD activation using a drift-diffusion model framework

The Simon effect is observed in spatial conflict tasks where the response time of subjects is increased if stimuli are presented in a lateralized manner so that they are incongruous with the response information that they represent symbolically. Previous studies have used fMRI to investigate this phenomenon, and while some have been driven by considerations of an underlying model, none have attempted to directly tie model and BOLD response together. It is likely that this is due to Simon models having been predominantly descriptive of the phenomenon rather than capturing the full spectrum of behavior at the level of individual subjects. Sequential sampling models (SSM) which capture full response distributions for correct and incorrect responses have recently been extended to capture conflict tasks. In this study we use our freely available framework for fitting and comparing non-standard SSMs to fit the Simon effect SSM (SE-SSM) to behavioral data. This model extension includes specific estimates of automatic response bias and a conflict counteraction parameter to individual subject behavioral data. We apply this approach in order to investigate whether our task specific model parameters have a correlate in BOLD response. Under the assumption that the SE-SSM reflects aspects of neural processing in this task, we go on to examine the BOLD correlates with the within trial expected decision-variable. We find that the SE-SSM captures the behavioral data and that our two conflict specific model parameters have clear across subject BOLD correlates, while other model parameters, as well as more standard behavioral measures do not. We also find that examining BOLD in terms of the expected decision-variable leads to a specific pattern of activation that would not be otherwise possible to extract.

In previous work 1 we defined a model to capture the Simon task which we reproduce here with parameters consistent with the 6 present manuscript: Where the conflict c = 1−L·H 2 , and H and L are trial dependent variables with values of −1 or +1 corresponding to the 8 required handedness of the response (color), and visual hemifield of the stimulus respectively. All other parameters are defined 9 as presented in the main text, although we would also like to note that we refer to the parameter b as conflict counteraction as 10 opposed to attention.

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The model used in this manuscript removes the explicit dependence on L and H, and is instead written in terms of the 12 presence of conflict.

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Model fitting toolbox 14 In order to fit the SE-SSM, as well as the various nested models and extensions provided, we developed an Matlab toolbox 15 (https://github.com/jrmxn/malleable-ssm). For parameter initialization, this toolbox incorporates some core functions from the 16 HDDM toolbox 2 translated from Python to Matlab, as the speed of these methods 3 is unmatched for the SSM. However, in 17 order to generate density estimates with which to calculate likelihoods for our non-standard SSM candidates, we resorted to 18 encoding the probability distributions of the decision-variable given the value into a transition matrix. The toolbox allows for 19 rapid modification and testing of new models by inheriting from the base SSM class, and then redefining the density estimation. . We may at first consider trying to estimate p(x t |x t−1 ) iteratively in order to calculate 24 p(x > x th ;t), i.e. the probability of being above the decision threshold at any specific time point ( Figure S1a). From the 25 SE-SSM equation, we know that E(x t |x t−1 ) = x t−1 + v(1 + c · b · d)∆t and Var(x t |x t−1 ) = s 2 ∆t, we can therefore discretize the 26 decision variable, and structure a matrix of the form A i j = p(x j t |x i t−1 ), which given a starting condition x 0 , can be multiplied by  In the ideal case where the underlying behavioral data really comes from a process which is captured by our model, we sought 38 to confirm that our parameters could be recovered with sufficient confidence.

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In order to do this, we took our previously fitted parameter values and sampled from each subject the number of trials that 40 they performed. To replicate the procedure described in the manuscript, we repeated this fit with random starts five times. We 41 also repeated this procedure three times to gauge the variability induced by the limited number of samples available for each 42 subject. 43 We found that as shown in Figure 2, the parameters are well recovered, with correlations for the parameters between true 44 and recovered model being generally greater than 0.8. The parameter that is recovered least well is the conflict counteraction x 3 x 4 x 2 x 1 x 3 x 4 x 2 Decision variable Time x 1 x 3 x 4 x 2 x 1 x 3 x 4 x 2 -x th  Additional analyses 48 We pursued two additional analyses which we include here for completeness.

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Across trial BOLD estimates 50 We were interested in estimating model parameter fluctuations across trials, which we consider to be likely related to learning  Figure S2) represents a different sample from the original model, with each correlation value stemming from a comparison between the original model parameter and the recovered parameters initiated with a different random start.
The methods we have introduced thus far enable us to look at brain regions that appear related to our parameters across For this analysis, we considered several extensions to the base SE-SSM, for example the augmentation of the drift parameter in a trial dependent manner: consequently has to be computed for each trial as opposed to each condition. This is problematic as the time to calculate the 71 likelihood for a set of parameters then scales with the number of trials. Secondly, if a whole brain analysis is required, then this 72 model fit has to be performed at each voxel, which is also impractical. To address these two problems, we make the following compromise: we fix the model parameters at their final estimate (as described in the main text), and then introduce the scaling Small changes in drift and conflict counteraction both lead to similar changes in RT, and it is therefore not possible to say 87 whether one parameter is playing a role while the other is not. Additionally, conflict counteraction is associated with less data 88 (because its effect is zero on non-conflict trials) so a direct comparison is difficult to interpret. Having said this, we repeated 89 this analysis while optimizing drift and conflict counteraction simultaneously and found that no conflict counteraction clusters 90 remained significant. We take this as an indication that the trial-to-trial fluctuations are dominated by changes in drift. Particular or project to these regions. We were expecting pre-SMA activation as well as DLPFC activation, and potentially dACC. 96 We found that these were indeed activated, although other activation was also present. Other activated regions may simply 97 represent trial-to-trial differences in stimulus processing which are irrelevant to the Simon task. It is also worth noting that 98 on an individual trial, changes in drift and changes in conflict counteraction lead to similar changes in RT, making it hard to 99 attribute specific regions to particular processes. It is known that presence of conflict influences RT in subsequent trials 7, 8 . We therefore extended the SE-SSM with history terms: t e f f = t + ξ 2 s t (9) Where r i = c i − 0.5 represents the presence of conflict on the previous trial, and v h , b h and z h represent parameters to be fitted. 102 We initially fitted each candidate history parameter independent of the other, however to exclude the possibility that both z h and 103 b h are needed for the fit, we additionally ran this combination together.