## 3 Results  
### Spontaneous Activity  
Impact of Local Node Silencing on Spontaneous Complexity Measures  
We first investigated the impact of local silencing on the model's spontaneous activity by quantifying the mean firing rate difference (\(\text{MFR}_{\Delta}\)) on the nodes within the manipulated hemisphere, the intact one, as well as in the entire model compared with the same nodes in the control condition (Figure 2a). This analysis revealed that the MFR decreased the most in the affected hemisphere (\(\text{MFR}_{\Delta}=-3.621\pm 1.629\) Hz, mean across all manipulations \(\pm\) SD) and to a lesser extent in the intact hemisphere (\(-1.431\pm 0.992\) Hz).  
We then quantified the impact of local node silencing on the complexity of spontaneous brain dynamics by computing Lempel-Ziv complexity (LZc) on the instantaneous firing rate (IFR) derived from the model time-series (Figure 2b). Notably, in 12 out of 20 local manipulations, LZc was not statistically different from control ([PERSON] post hoc test with Benjamin-Hochberg correction). As a consequence, even though LZc  
Figure 2: **Impact of local manipulations on whole-brain spontaneous activity.** (**a**) Mean firing rate difference (\(\text{MFR}_{\Delta}\), see Methods) for each silencing condition of the manipulated hemisphere (green), the intact one (yellow), and overall nodes (black). Note that the ranking (i.e., ranked local manipulations, see Table 2) is based on the black curve. (**b**) The Lempel–Ziv complexity (LZc) metric is reported versus the same ranked local manipulations. The red horizontal lines mark the average value of LZc in the control condition. Error bars represent one standard deviation and asterisks indicate a statistically significant difference from the control condition (\({}^{\bullet}p<0.05\), \({}^{\bullet\bullet}p<0.01\), \({}^{\bullet\bullet\bullet}p<0.001\); Kruskal-Wallis and Dunn post hoc test with Benjamin–Hochberg correction). (**c**) Linear regressions relating the mean firing rate of all nodes (MFR) to LZc (\(r=0.69\); \(p=0.0005\)). (**d**) Linear regression relating the averaged pairwise cross-correlation (\(\text{CC}_{\text{IFR}}\)) to LZc (\(r=-0.55\), \(p=0.009\)). (**e**) Multivariate regression of LZc with respect to the independent variables MFR and \(\text{CC}_{\text{IFR}}\) (\(\text{R}^{2}=0.98\), \(\text{R}^{2}{}_{\text{adjusted}}=0.98\), \(p=2\times 10^{-16}\)).  
positively correlated with MFR (LZc: r = 0.69; \(p\) = 0.0005, Figure 2c), it did not reflect the changes of network complexity with respect to control condition.  
Further exploring the network properties relevant for complexity, we computed the averaged pairwise cross-correlation (CC\({}_{\text{IFR}}\), see methods) between nodes as a measure of the synchrony of network interactions. CC\({}_{\text{IFR}}\) was lower across local manipulations when compared to control (control: 0.067, average across manipulations: 0.061 \(\pm\) 0.007; Figure 2d), which corresponds to a larger segregation of the network patterns. We found a negative correlation between LZc and CC\({}_{\text{IFR}}\) (r = \(-\)0.55, \(p\) = 0.009; Figure 2d).  
Considering the combined role of brain activity levels (MFR) and network interactions (CC\({}_{\text{IFR}}\)) in shaping brain complexity, we performed a multivariate regression between MFR and CC\({}_{\text{IFR}}\) in explaining LZc across all conditions (Figure 2e). This model effectively captured the variance of LZc (R\({}^{2}\) = 0.98, R\({}^{2}\)\({}_{\text{adjusted}}\) = 0.98, \(p\) = 2 \(\times\) 10\({}^{-16}\)). Confirming the results obtained with the univariate analyses, a positive relationship was found for LZc with respect to MFR (slope coefficient, \(\beta_{\text{MFR}}\) = 0.0072, 95% CI [0.0066, 0.0078]), while CC\({}_{\text{IFR}}\) was found to be negatively correlated with LZc (\(\beta_{\text{CC}}\) = \(-\)1.2, 95% CI [\(-\)1.3, \(-\)1.1]).