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Research ArticleNew Research, Disorders of the Nervous System

Functional Mechanisms of Recovery after Chronic Stroke: Modeling with the Virtual Brain

Maria Inez Falcon, Jeffrey D. Riley, Viktor Jirsa, Anthony R. McIntosh, E. Elinor Chen and Ana Solodkin
eNeuro 23 March 2016, 3 (2) ENEURO.0158-15.2016; DOI: https://doi.org/10.1523/ENEURO.0158-15.2016
Maria Inez Falcon
1Department of Anatomy and Neurobiology, UC Irvine School of Medicine, Irvine, California 92697
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Jeffrey D. Riley
1Department of Anatomy and Neurobiology, UC Irvine School of Medicine, Irvine, California 92697
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Viktor Jirsa
2Institut de Neurosciences des Systèmes, Aix-Marseille Université, Faculté de Médecine, Marseille F-13000, France
3Inserm UMR1106, Marseille F-13000, France
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Anthony R. McIntosh
4Rotman Research Institute, Baycrest Health Sciences, M6A 2E1 University of Toronto, Toronto, Canada
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E. Elinor Chen
1Department of Anatomy and Neurobiology, UC Irvine School of Medicine, Irvine, California 92697
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Ana Solodkin
1Department of Anatomy and Neurobiology, UC Irvine School of Medicine, Irvine, California 92697
5Department of Neurology, UC Irvine School of Medicine, Irvine, California 92697
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  • Figure 1.
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    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.
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    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 Embedded Image , which links regions i and j and is provided by the input of individual structural connectivity matrices (weights), and noise Embedded Image . Time delays (Embedded Image ) 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.
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    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.
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    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.
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    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).

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    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

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    Table 1.

    Demographics and stroke characteristics of the stroke cohort

    SubjectAgeSexHandednessAffected hemisphereAffected handStroke locationStroke volume,mm3
    141FRightRightNDCort22495.0
    254FRightLeftDCort/subcort49078.0
    357MRightLeftDCort/subcort17411.0
    457MRightLeftDCort/subcort38703.0
    554FRightLeftDSubcort27677.0
    650MRightRightNDSubcort3570.0
    723MRightLeftDSubcort560.0
    855FRightRightNDCort6781.0
    968MRightLeftDSubcort1988.3
    1056FRightLeftDSubcort6239.7
    1146MRightLeftDSubcort325.0
    1256FLeftRightDCort/subcort60669.0
    1337MRightLeftDCort/subcort83406.2
    1462MRightLeftDSubcort22154.8
    1557MRightRightNDCort/subcort25392.0
    1666MRightLeftNDCort/subcort19927.0
    1761MRightLeftDSubcort978.0
    1874MRightLeftDCort/subcort63642.0
    1967FRightRightNDSubcort588.0
    2074FRightLeftDCort/subcort44892.0
    • D, Dominant hemisphere; ND, non-dominant hemisphere; Cort, cortical, Subcort, subcortical.

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    Table 2.

    State variables and parameters of the Stefanescu-Jirsa 3D model and corresponding range of values used in the present study

    ParameterValueDescription
    a, b, c, d1, 3, 1, 5Constants affecting faster ion channels
    r0.006Constant affecting slower ion channels
    s4Bursting strength of model
    μ and σ2.2, 0.3Mean and dispersion of input current in each node
    X0−1.6Leftmost equilibrium point of X
    IE, IIDerived from μ and σModels excitability of each node and mode (IE for excitatory input, II for inhibitory input)
    Global Coupling0.01–1.0Coupling scaling factor for connections between nodes
    Conduction velocity10–100Scales delay for defined internode distances
    β, γ4, 5Corresponding values for IPs
    K12,K21,K110.01–1.0Models 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.

    • View popup
    Table 3.

    Summary of long-range and local parameters used in TVB to simulate BOLD time series in healthy controls and individuals with stroke

    GroupVariableRangeMeanSDWilcoxon
    rank sum, p
    ControlGlobal variables:
    Global coupling0.044–0.0470.0530.009
    Conduction velocity45–9061.99.9
    Model variables:
    K120.12–0.550.490.338
    K210.3–0.90.8040.17
    K110.6–0.950.8330.142
    StrokeGlobal variables:
    Global coupling0.04–0.090.0610.0160.013
    Conduction velocity12–8046210.05
    Model variables:
    K120.1–0.80.3690.2570.17
    K210.1–0.90.6740.3020.01
    K110.1–0.990.6130.3010.1
    • View popup
    Table 4.

    Statistical table

    Comparison of interestData structureType of testp
    aWeights of connections: stroke vs controlNormal>Kolmogorov–Smirnov test0.42
    bPearson’s correlation coefficients: simulated vs empirical functional connectivity matricesNormal after
    Z-transformation
    t test0.9e-12
    cTVB parameters: stroke vs controlControl: non-normal
    Stroke: normal
    Wilcoxon rank sum testConduction Velocity: 0.05
    Global Coupling: 0.013
    K12: 0.17
    K21: 0.01
    K11: 0.1
    dRegression: TVB parameters with subject demographics, lesion characteristics and recoveryNormalMultiple linear regressionPost-therapy:
    K12, Fugl–Meyer: 0.038
    Maintenance:
    K12, Fugl–Meyer: 0.005
    Global coupling, WMFT: 0.039
    • p, Probability resulting from the Wilcoxon sum rank test comparing parameter values between the two groups.

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Functional Mechanisms of Recovery after Chronic Stroke: Modeling with the Virtual Brain
Maria Inez Falcon, Jeffrey D. Riley, Viktor Jirsa, Anthony R. McIntosh, E. Elinor Chen, Ana Solodkin
eNeuro 23 March 2016, 3 (2) ENEURO.0158-15.2016; DOI: 10.1523/ENEURO.0158-15.2016

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Functional Mechanisms of Recovery after Chronic Stroke: Modeling with the Virtual Brain
Maria Inez Falcon, Jeffrey D. Riley, Viktor Jirsa, Anthony R. McIntosh, E. Elinor Chen, Ana Solodkin
eNeuro 23 March 2016, 3 (2) ENEURO.0158-15.2016; DOI: 10.1523/ENEURO.0158-15.2016
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Keywords

  • brain dynamics
  • brain networks
  • computational biophysical modeling
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