## 2 Materials and Methods
### Model Simulations
#### 2.1.2 Neural Mass Model  
To model the mesoscopic dynamics of cortical regions, we used the Larter and Breaks-pear model [49], a conductance-based neural mass model widely employed for simulating whole-brain dynamics in intact networks [50; 51; 52; 53; 54; 55; 56; 57; 58] and lesioned networks [39; 59]. According to the model, the dynamics of a node k are governed by the following ordinary differential equations (ODEs):  
\[ \begin{split}\frac{\mathrm{d}\mathrm{V}\mathrm{k}}{\mathrm{dt}}=- \Big{(}\mathrm{g}_{\mathrm{Ca}}+(1-\mathrm{C})\;\mathrm{r}_{\mathrm{NMDA}}\; \mathrm{a}_{\mathrm{ee}}\;\mathrm{Q}_{\mathrm{V}}+\mathrm{C}\;\mathrm{r}_{ \mathrm{NMDA}}\;\mathrm{a}_{\mathrm{ee}}\;\mathrm{Q}_{\mathrm{V}}^{\mathrm{ network}}\Big{)}\;\mathrm{m}_{\mathrm{Ca}}(\mathrm{V}-\mathrm{V}_{\mathrm{Ca}})\\ -\Big{(}\mathrm{g}_{\mathrm{Na}}\;\mathrm{m}_{\mathrm{Na}}+(1- \mathrm{C})\;\mathrm{a}_{\mathrm{ee}}\;\mathrm{Q}_{\mathrm{V}}+\mathrm{C}\; \mathrm{a}_{\mathrm{ee}}\;\mathrm{Q}_{\mathrm{V}}^{\mathrm{network}}\Big{)}( \mathrm{V}-\mathrm{V}_{\mathrm{Na}})\\ -\mathrm{g}_{\mathrm{K}}\mathrm{W}(\mathrm{V}-\mathrm{V}_{\mathrm{ K}})-\mathrm{g}_{\mathrm{L}}(\mathrm{V}-\mathrm{V}_{\mathrm{L}})-\mathrm{a}_{ \mathrm{ie}}\;\mathrm{Z}\;\mathrm{Q}_{\mathrm{Z}}+\mathrm{a}_{\mathrm{ne}} \mathrm{I}\end{split}  \tag{1}\]  
\[\frac{\mathrm{d}Z^{\mathrm{k}}}{\mathrm{dt}}=\;\mathrm{b}(\mathrm{a}_{\mathrm{ ni}}\mathrm{I}+\mathrm{a}_{\mathrm{ie}}\;\mathrm{V}\;\mathrm{Q}_{\mathrm{V}}) \tag{2}\]  
\[\frac{\mathrm{d}\mathrm{W}^{\mathrm{k}}}{\mathrm{dt}}=\frac{\Phi(\mathrm{m}_{ \mathrm{K}}-\mathrm{W})}{\tau_{\mathrm{K}}} \tag{3}\]  
where V is the mean membrane potential of the excitatory pyramidal neurons, Z is the mean membrane potential of the inhibitory interneurons, and W is the average number of open potassium ion channels. The term \(\mathrm{r}_{\mathrm{NMDA}}\) is the ratio of NMDA receptors to AMPA receptors, and \(\mathrm{a}_{\mathrm{xy}}\) is the synaptic strength originating from population x (e.g., e, i, n, where e refers to the excitatory population, i to the inhibitory one, and n denotes a nonspecific input) to population y (e.g., e, i). The rate terms b and \(\phi\) govern the time scales of Z and W, respectively. The term \(\mathrm{g}_{\mathrm{ion}}\) is the maximum conductance (i.e., when all channels are open) of the corresponding ion species. The voltage-dependent fractions of open channels for a given ion is determined by \(\mathrm{m}_{\mathrm{ion}}\) and is modeled by a sigmoidal shape function:  
\[\mathrm{m}_{\mathrm{ion}}=0.5\;\Big{(}1+\tanh\Big{(}\frac{\mathrm{V}-\mathrm{ T}_{\mathrm{ion}}}{\delta_{\mathrm{ion}}}\Big{)}\Big{)} \tag{4}\]  
where \(\mathrm{T}_{\mathrm{ion}}\) is the mean threshold membrane potential of a given ion channel population, and \(\delta_{\mathrm{ion}}\) is its standard deviation. The mean firing rates of the excitatory and inhibitory populations are determined by the voltage-dependent activation functions \(\mathrm{Q}_{\mathrm{V}}\) and \(\mathrm{Q}_{\mathrm{Z}}\), respectively, modeled as:  
\[\mathrm{Q}_{\mathrm{V}}=0.5\;\mathrm{Q}_{\mathrm{Vmax}}\;(1+\tanh\Big{(} \frac{\mathrm{V}-\mathrm{V}_{\mathrm{T}}}{\delta_{\mathrm{V}}}\Big{)}) \tag{5}\]\[Q_{Z}=0.5\,Q_{Z\max}\,(1+\tanh\left(\frac{V-Z_{T}}{\delta_{Z\mathrm{d}}}\right)) \tag{6}\]  
where \(QV_{\max}\) and \(QZ_{\max}\) are the maximum firing rates of the excitatory and inhibitory populations, respectively. Their corresponding thresholds for action potential generation are given by the terms \(V_{T}\) and \(Z_{T}\), with standard deviations \(\delta_{V}\) and \(\delta_{Z}\), respectively. The network input to node k is given by:  
\[Q_{V}^{\mathrm{network}}=\sum_{j}G\,u_{kj}Q_{V}\Big{(}V_{j}\left(t-\tau_{kj} \right)\Big{)} \tag{7}\]  
where \(u_{kj}\) is the connection weight from node j to node k, \(\tau\) is the input delay time, and G is the global coupling that scales the connection weights. The parameter C in Equation (1) ranges within \([0,1]\) and balances the strength of the self-connections against those of the rest of the network.