Article Figures & Data
Figures
- Figure 1.
Simulation workflow in TVB. Graphic representation depicting the sequential steps of TVB modeling. A, Empirical inputs (structural connectome) are generated from DTI tractography based on T1-w brain parcellation. B, Subsequent parameter exploration at the global and local levels (w, Weights; cv, conduction velocity; c, global coupling). C, Once parameter values are obtained, the BOLD signal is simulated. D, The efficacy of the simulation is calculated by correlating it to the empirical signals.
- Figure 2.
Equations of the Stefanescu-Jirsa 3D model. A, Evolution equation implemented in TVB to simulate brain activity. The mean field potential xi (t) of a region i at time t is dependent on the local dynamics f(xi (t)) provided by the Stefanescu-Jirsa-3D model, the long-range structural connectivity
, which links regions i and j and is provided by the input of individual structural connectivity matrices (weights), and noise
. Time delays (
) are distance dependent and are provided by the structural connectivity matrices (lengths). All mathematical details of the model and its numerical implementation are provided by Sanz-Leon et al. (2015). B, Equations comprising Stefanescu-Jirsa 3D. The first three equations (ξ, η, τ) represent the excitatory subpopulation of neurons within a local region, whereas the last three equations (α, β, γ) represent the inhibitory subpopulation of neurons in that region. IE and II denote the input current to the excitatory and inhibitory populations of each node, respectively. The first of each of the two sets of equations accounts for neuron potentials. The second and third equations account for the transport of ions across the membrane through ion channels. Note that the dynamics of these populations are dependent on the interactions between inhibitory and excitatory influences (K12, K21, K11). - Figure 3.
Examples of global parameter space explorations in healthy controls and stroke. Two examples of heat graphs of global variance (mean variance of the time series across all regions) used to narrow down the range of parameter values more suitable for modeling in (A) a healthy control and (B) a stroke case. Global coupling is shown on the x-axis and conduction velocity (m/s) on the y-axis. Colors indicate degree of global variance with hotter colors indicating higher values. White arrows show the range of values considered for global coupling limited by bifurcation points (yellow). Black arrows point to the range in conduction velocity considered in each case. Note the higher range of values associated with global coupling and lower for conduction velocity in the stroke case.
- Figure 4.
Weights of structural connections in stroke and healthy controls. A, Structural connectivity matrices in a healthy control (left) and one individual with stroke (right). Dark blue denotes absence of connections while hotter colors indicate stronger weights. B, Frequency distribution of weight of connections in healthy controls (orange bars) and stroke (blue bars).
- Figure 5.
Comparison of simulated and empirical BOLD signals. A, Amplitude: example of a raw simulated (left) and empirical (right) time series (TS). Amplitudes are indicated by the maxima and minima of the time series. B, Frequency: frequency distribution graphs (FFT) of the simulated (left) and empirical (right) time series. Note that both empirical and simulated signals have the same range, profiles, and peaks. C, Phase: functional connectivity (FC) matrix based on simulated time series (left) and the empirical group matrix (right).
- Figure 6.
Correlation between modeling parameters and post-therapy motor outcomes. Scatterplots showing correlation between TVB modeling parameters (x-axis) and post-therapy motor outcomes (y-axis). Clear relationships were found between (A) K12 and Fugl–Meyer (Post-Therapy), (B) K12 and Fugl–Meyer (Maintenance), and (C) Global coupling and WMFT (Maintenance).
Tables
Subject Age Sex Handedness Affected hemisphere Affected hand Stroke location Stroke volume,mm3 1 41 F Right Right ND Cort 22495.0 2 54 F Right Left D Cort/subcort 49078.0 3 57 M Right Left D Cort/subcort 17411.0 4 57 M Right Left D Cort/subcort 38703.0 5 54 F Right Left D Subcort 27677.0 6 50 M Right Right ND Subcort 3570.0 7 23 M Right Left D Subcort 560.0 8 55 F Right Right ND Cort 6781.0 9 68 M Right Left D Subcort 1988.3 10 56 F Right Left D Subcort 6239.7 11 46 M Right Left D Subcort 325.0 12 56 F Left Right D Cort/subcort 60669.0 13 37 M Right Left D Cort/subcort 83406.2 14 62 M Right Left D Subcort 22154.8 15 57 M Right Right ND Cort/subcort 25392.0 16 66 M Right Left ND Cort/subcort 19927.0 17 61 M Right Left D Subcort 978.0 18 74 M Right Left D Cort/subcort 63642.0 19 67 F Right Right ND Subcort 588.0 20 74 F Right Left D Cort/subcort 44892.0 D, Dominant hemisphere; ND, non-dominant hemisphere; Cort, cortical, Subcort, subcortical.
- Table 2.
State variables and parameters of the Stefanescu-Jirsa 3D model and corresponding range of values used in the present study
Parameter Value Description a, b, c, d 1, 3, 1, 5 Constants affecting faster ion channels r 0.006 Constant affecting slower ion channels s 4 Bursting strength of model μ and σ 2.2, 0.3 Mean and dispersion of input current in each node X0 −1.6 Leftmost equilibrium point of X IE, II Derived from μ and σ Models excitability of each node and mode (IE for excitatory input, II for inhibitory input) Global Coupling 0.01–1.0 Coupling scaling factor for connections between nodes Conduction velocity 10–100 Scales delay for defined internode distances β, γ 4, 5 Corresponding values for IPs K12,K21,K11 0.01–1.0 Models coupling between excitatory and inhibitory populations within nodes Values used for the simulation included global coupling, conduction velocity, and K12, K21, and K11 optimized via parameter space explorations. Default values were used for all other variables.
- Table 3.
Summary of long-range and local parameters used in TVB to simulate BOLD time series in healthy controls and individuals with stroke
Group Variable Range Mean SD Wilcoxon
rank sum, pControl Global variables: Global coupling 0.044–0.047 0.053 0.009 Conduction velocity 45–90 61.9 9.9 Model variables: K12 0.12–0.55 0.49 0.338 K21 0.3–0.9 0.804 0.17 K11 0.6–0.95 0.833 0.142 Stroke Global variables: Global coupling 0.04–0.09 0.061 0.016 0.013 Conduction velocity 12–80 46 21 0.05 Model variables: K12 0.1–0.8 0.369 0.257 0.17 K21 0.1–0.9 0.674 0.302 0.01 K11 0.1–0.99 0.613 0.301 0.1 Comparison of interest Data structure Type of test p a Weights of connections: stroke vs control Normal >Kolmogorov–Smirnov test 0.42 b Pearson’s correlation coefficients: simulated vs empirical functional connectivity matrices Normal after
Z-transformationt test 0.9e-12 c TVB parameters: stroke vs control Control: non-normal
Stroke: normalWilcoxon rank sum test Conduction Velocity: 0.05 Global Coupling: 0.013 K12: 0.17 K21: 0.01 K11: 0.1 d Regression: TVB parameters with subject demographics, lesion characteristics and recovery Normal Multiple linear regression Post-therapy:
K12, Fugl–Meyer: 0.038Maintenance:
K12, Fugl–Meyer: 0.005
Global coupling, WMFT: 0.039p, Probability resulting from the Wilcoxon sum rank test comparing parameter values between the two groups.
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