Strength-dependent perturbation of whole-brain model working in different regimes reveals the role of fluctuations in brain dynamics
Fig 2
Model Schaefer1000 fitting of noise, fluctuations, and oscillatory for 1) Turbulence and 2) FC.
A-C) We explored the bi-dimensional parameter space defined by β and G for noise, fluctuating and oscillatory regime (bifurcation parameter a = -1.3, a = -0.02 and a = 1.3, respectively, indicated in upper row). We computed the level of amplitude turbulence error as the absolute difference between the empirical and simulated turbulence. Yellow stars indicate the (β, G) combination that reaches the lowest turbulence error in each regime. D) The upper subpanel shows the model fitting scheme in fine Schaefer1000 parcellation (the render on a flatmap of the hemisphere stands for a scheme of brain regions considered in this parcellation). The bottom subpanel displays the barplot that indicates the statistical distribution of the level of amplitude turbulence obtained by simulating 20 trials with 100 subjects for each model regime with the parameters set at the corresponding working point. We also display the results of two model-based surrogates created by increasing the shear parameter of each model regime. The red dashed line indicates the empirical level of amplitude turbulence averaged across participants. The subcritical, supercritical and empirical level of turbulence are not statistically different (Wilcoxon test, P = 0.33), the rest of the comparison are statistically significant (Wilcoxon test, P<0.001). E-G) We explored the bi-dimensional parameter space defined by β and G for noise, fluctuating and oscillatory regime computed the FC fitting as Euclidean distance between the empirical and simulated FC. Yellow stars indicate the (β, G) combination that reaches the lower turbulence error in each regime (the optimal working point obtained in panels A-C). H) The barplot indicates the statistical distribution of the FC fitting obtained by simulating 20 trials with 100 subjects for each model regime at the corresponding working point defined as the minimum turbulence error. We also display the results for the model-based surrogates. All comparisons are statistically significant (Wilcoxon, P<0.001). I) Visualization of the change of the local Kuramoto order parameter, R, in space and time reflecting amplitude turbulence in a single simulation at the optimal working point of each regime (noise, fluctuating and oscillatory cases) and one participant (empirical). This can be appreciated from continuous snapshots for segments separated in time rendered on a flatmap of the hemisphere.