Fig. 1: Overview of whole-brain modeling.
From: Recovery of neural dynamics criticality in personalized whole-brain models of stroke
a Average structural connectivity (SC) matrices (top) and their corresponding network architecture embedded in a glass dorsal view of the brain (bottom). SC matrices and brain networks are organized according to regions of interest (ROI) defined on the cortical parcellation of Gordon et al.59. b The probability distribution function of the structural connectivity weights in controls and patients after homeostatic normalization (see main text, Eq. (1)). For each group, the (non-zero) weights of all individual matrices were pooled together and then the histogram was computed leading to a representative pdf for the corresponding group. c Top. Illustration of the network dynamics with homeostatic plasticity following the transition probabilities between the three possible states: inactive (I), active (A) and refractory (R). The temporal evolution of the central inactive node (pink) is as follows: in t1, it is surrounded by three active nodes (green) and one refractory node (orange); in t2, the incoming excitation is propagated (\({\widetilde{W}}_{31}+{\widetilde{W}}_{32}+{\widetilde{W}}_{34} \, > \, T\)); and finally, in t3, it reaches the refractory state. Bottom. Procedure used to transform node's activity, si(t), in functional BOLD signals, xi(t). BOLD time-series are obtained by convolving instantaneous si(t) with a canonical hemodynamic response function (HRF). d Behavior of the neural variables, the largest (S1, continuous line), and the second largest (S2, dotted line) cluster size as a function of T (top). The peak in S2 (red dot) is identified as the critical phase transition62. Blue and green dots correspond to minimal and maximal values of T, and corresponding activity and BOLD time-series in the lower panels. Left panel: instantaneous network activity, A(t) = ∑isi(t), for different values of the activation threshold T; the super-critical phase T ≪ Tc (blue time-series), the critical phase T = Tc (red) and the sub-critical phase T ≫ Tc (green). Right panel: example of the simulated BOLD signals between two arbitrary ROIs and their corresponding Pearson correlation ρ. The highest correlation is achieved at the critical phase, where BOLD fluctuations are long-range correlated.
