Macroscale whole-brain computational models represent regional activity in terms of two key ingredients: (i) a biophysical model of each region's local dynamics; and (ii) inter-regional anatomical connectivity. Thus, such in silico models provide a well-suited tool to investigate how the structural connectivity of the brain shapes the corresponding macroscale neural dynamics (Cabral et al., 2017 (link); Cofré et al., 2020 (link); Deco and Kringelbach, 2014 (link); Demirtaş et al., 2019 (link); Kringelbach and Deco, 2020 (link); Shine et al., 2021 (link); Wang et al., 2019 (link)). In particular, the Dynamic Mean Field (DMF) model employed here simulates each region (defined via an anatomical parcellation scheme) as a macroscopic neural field comprising mutually coupled excitatory and inhibitory populations (80% excitatory and 20% inhibitory), providing a neurobiologically plausible account of regional neuronal firing rate. Regions are then connected according to empirical anatomical connectivity obtained e.g. from DWI data (Deco et al., 2014 (link); G. 2013 (link); Deco and Jirsa, 2012 (link)). The reader is referred to (Deco et al., 2018 (link); Herzog et al., 2022 (link); 2020 (link); Luppi et al., 2022b (link)) for details of the DMF model and its implementation. Due to its multi-platform compatibility, low memory usage, and high speed, we used the recently developed FastDMF library (Herzog et al., 2022 (link)), available online at https://www.gitlab.com/concog/fastdmf .
The structural connectivity (SC) for the DMF model used here was obtained by following the procedure described by Wang et al. (2019) (link) to derive a consensus structural connectivity matrix. A consensus matrix A was obtained separately for each group (healthy controls, MCS patients, UWS patients) as follows: for each pair of regions i and j, if more than half of subjects had non-zero connection i and j, Aij was set to the average across all subjects with non-zero connections between i and j. Otherwise, Aij was set to zero.
The DMF model has one free parameter, known as “global coupling” and denoted by G, which accounts for differences in transmission between brain regions, considering the effects of neurotransmission but also synaptic plasticity mechanisms. Thus, separately for each group, we used a model informed by that group's consensus connectome to generate 40 simulations for each value of G between 0.1 and 2.5, using increments of 0.1. Finally, we set the G parameter to the value just before the one at which the simulated firing of each model became unstable, reflecting a near-critical regime.
Subsequently, for each group, 40 further simulations were obtained from the corresponding DMF model with the optimal G parameter. A Balloon-Windkessel hemodynamic model (Friston et al., 2003 (link)) was then used to turn simulated regional neuronal activity into simulated regional BOLD signal. Finally, simulated regional BOLD signal was bandpass filtered in the same range as the empirical data (0.008–0.09 Hz, or 0.04–0.07 Hz for the intrinsic ignition analysis).
As an alternative way of finding the most suitable value of G for the simulation of each condition, we adopted the approach previously described (Deco et al., 2018 (link); Hansen et al., 2015 (link); Herzog et al., 2020 (link); Luppi et al., 2022b (link)) which aims to obtain the best match between empirical and simulated functional connectivity dynamics. First, we quantified empirical functional connectivity dynamics (FCD) in terms of Pearson correlation between regional BOLD timeseries, computed within a sliding window of 30 TRs with increments of 3 TRs (Deco et al., 2018 (link); Hansen et al., 2015 (link); Herzog et al., 2020 (link); Luppi et al., 2022b (link)). Subsequently, the resulting matrices of functional connectivity at times tx and ty were themselves correlated, for each pair of timepoints tx and ty, thereby obtaining an FCD matrix of time-versus-time correlations. Thus, each entry in the FCD matrix represents the similarity between functional connectivity patterns at different points in time. This procedure was repeated for each subject of each group (controls, MCS, and UWS). For each simulation at each value of G, we used the Kolmogorov-Smirnov distance to compare the histograms of empirical (group-wise) and simulated FCD values (obtained from the upper triangular FCD matrix). Finally, we set the model's G parameter to the value that was observed to minimize the mean KS distance - corresponding to the model that is best capable of simulating the temporal dynamics of resting-state brain functional connectivity observed in the corresponding group (Figure S8). After having found the value of G for each condition, simulated BOLD signals were obtained as described above. This same procedure was also used for fitting the DMF model based on each individual's structural connectome, simulating BOLD signals to fit their own empirical FCD.
The structural connectivity (SC) for the DMF model used here was obtained by following the procedure described by Wang et al. (2019) (link) to derive a consensus structural connectivity matrix. A consensus matrix A was obtained separately for each group (healthy controls, MCS patients, UWS patients) as follows: for each pair of regions i and j, if more than half of subjects had non-zero connection i and j, Aij was set to the average across all subjects with non-zero connections between i and j. Otherwise, Aij was set to zero.
The DMF model has one free parameter, known as “global coupling” and denoted by G, which accounts for differences in transmission between brain regions, considering the effects of neurotransmission but also synaptic plasticity mechanisms. Thus, separately for each group, we used a model informed by that group's consensus connectome to generate 40 simulations for each value of G between 0.1 and 2.5, using increments of 0.1. Finally, we set the G parameter to the value just before the one at which the simulated firing of each model became unstable, reflecting a near-critical regime.
Subsequently, for each group, 40 further simulations were obtained from the corresponding DMF model with the optimal G parameter. A Balloon-Windkessel hemodynamic model (Friston et al., 2003 (link)) was then used to turn simulated regional neuronal activity into simulated regional BOLD signal. Finally, simulated regional BOLD signal was bandpass filtered in the same range as the empirical data (0.008–0.09 Hz, or 0.04–0.07 Hz for the intrinsic ignition analysis).
As an alternative way of finding the most suitable value of G for the simulation of each condition, we adopted the approach previously described (Deco et al., 2018 (link); Hansen et al., 2015 (link); Herzog et al., 2020 (link); Luppi et al., 2022b (link)) which aims to obtain the best match between empirical and simulated functional connectivity dynamics. First, we quantified empirical functional connectivity dynamics (FCD) in terms of Pearson correlation between regional BOLD timeseries, computed within a sliding window of 30 TRs with increments of 3 TRs (Deco et al., 2018 (link); Hansen et al., 2015 (link); Herzog et al., 2020 (link); Luppi et al., 2022b (link)). Subsequently, the resulting matrices of functional connectivity at times tx and ty were themselves correlated, for each pair of timepoints tx and ty, thereby obtaining an FCD matrix of time-versus-time correlations. Thus, each entry in the FCD matrix represents the similarity between functional connectivity patterns at different points in time. This procedure was repeated for each subject of each group (controls, MCS, and UWS). For each simulation at each value of G, we used the Kolmogorov-Smirnov distance to compare the histograms of empirical (group-wise) and simulated FCD values (obtained from the upper triangular FCD matrix). Finally, we set the model's G parameter to the value that was observed to minimize the mean KS distance - corresponding to the model that is best capable of simulating the temporal dynamics of resting-state brain functional connectivity observed in the corresponding group (Figure S8). After having found the value of G for each condition, simulated BOLD signals were obtained as described above. This same procedure was also used for fitting the DMF model based on each individual's structural connectome, simulating BOLD signals to fit their own empirical FCD.
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