2.7 Parameter optimization
In order to fit the model to the fMRI data, we need to find an optimal working point, which is a combination of parameters (i.e., A, G, F and M) within the search interval that maximizes the similarity between the simulated and empirical FC patterns and captures the intrinsic attractor dynamics of the brain. Therefore, the similarity between the empirical and simulated FC was measured to quantify the goodness of fitting. Accordingly, in the grid-search framework, we searched for parameter A from −0.2 to 0.2 with a step-size of 0.01, G from 0.005 to 0.05 with a step-size of 0.005, F from 0 to 1 with a step-size of 0.1, and M from 0.10 to 0.50 with a step-size of 0.03.Our search protocol resulted in 63,140 simulated sets of whole-brain signals. It is worth noting that the real part of state variable z was taken as the simulated regional BOLD signal. Next, simulated BOLD signals were band-pass filtered (0.008–0.1Hz), followed by computing and the Pearson correlation coefficients among all regions. Identical analysis was performed on the empirical data to achieve the empirical FC matrices. Of note, Fisher’s z-transformation was applied to both simulated and empirical FC measures with the aim of performing a subsequent correlation between the simulated and empirical FCs as an index of the goodness of fit of the model. The FC maps of a varying percentage of the patients (i.e., Monte Carlo thresholds) were randomly selected over 1500 Monte Carlo iterations to find the optimal parameter-sets within the search intervals for the whole-brain model. We sampled the FC maps for 500 iterations per threshold (i.e., 30%, 50% and 70%) to remove the dependency of our results on the percentage of patients randomly selected in Monte Carlo resampling procedure. We assessed the similarity between the simulated and empirical FC by taking the correlation between the upper triangles of the simulated and empirical FC matrices in each iteration of Monte Carlo resampling [Next, based on the similarity between each individual’s empirical FC and either of the two model-derived FC maps (i.e., simulated FC