## 4 Discussion  
The present study employed whole-brain computer simulations, systematic local manipulations (i.e., node silencing), and perturbations (i.e., brief pulses applied to local nodes) to assess the circuit-level properties underlying estimates of brain complexity. Our model has proved to be particularly suitable for investigating the mechanisms underlying brain complexity using various metrics commonly employed in empirical studies. In the present implementation, we were able to obtain spontaneous network activity as well as complex and enduring cortical interactions upon exogenous perturbations (Figure 1b), reminiscent of empirical observations [17; 36]. Unlike in previous simulation works [33] and in line with experimental data, in the present model, brief local pulses were effective in evoking responses that propagated across distant nodes while spanning more prolonged time intervals. The presence of the non-linear NMDA current as implemented in the Larter  
Figure 5: Graph properties and complexity topographies. (**a**) The weighted degree (WD) of structural connectivity (SC) nodes correlated with the PCI-R\({}^{2}\)\(>\) topography (r = 0.34, \(p\) = 0.0026) but (**b**) not with the LZc-R\({}^{2}\) topography (\(p\) = 0.063). (**c**) The WD of the nodes of the functional connectivity (FC\({}_{\text{IFR}}\)) correlated with the PCI-R\({}^{2}\)\(>\) topography (r = 0.6, \(p\) = 10\({}^{-8}\)) but (**d**) not with the LZc-R\({}^{2}\) topography (\(p\) = 0.5). Each point is representative of an ROI/node in the network. The regression lines are reported in red. and Breakspear model [49] likely explains this important difference. Additionally, the same model has been shown to exhibit complex wave patterns, including traveling waves during spontaneous activity [56], thus arguably making it suitable for investigating complexity metrics that rely on activity propagation evoked by an external stimulus. Impact of Local Silencing on Complexity Measures: The Role of Global Activity Levels and Network Dynamics/Interactions  
All the local manipulations (i.e., node silencing) explored in this study showed an overall MFR decrease compared to the intact model (MFR\({}_{\Delta}\)), with a large variability depending on the manipulated nodes (Figure 2a). A similar trend was also observed for spontaneous complexity quantified with LZc, indicating a correlation between LZc and the global activity levels (MFR; Figure 2c). However, LZc often remained unchanged or even increased as compared to the control condition (Figure 2b), suggesting that the observed effects of local silencing on LZc were not merely explained by changes in global activity levels. Crucially, local manipulations resulting in a reduction of functional connectivity (i.e., segregation of network interactions) as captured by the correlation of activity across nodes (CC\({}_{\text{IFR}}\)) tended to exhibit higher LZc values (Figure 2d). Thus, we tested the interplay between global activity levels (MFR) and network interactions (CC\({}_{\text{IFR}}\)) in sustaining complex dynamics (LZc) through a 3D linear model (Figure 2e). This model, rooted in simple network activity variables, effectively described LZc, corroborating (1) the role of an optimal global activity level in shaping spontaneous complexity values and (2) the negative relationship of LZc with respect to network interactions. Importantly, this result underscores a significant limitation of various complexity metrics based on spontaneous activity, such as LZc, as they assume a priori network integration [6] and yield high values in systems composed of independent/segregated elements [41]. Here, we confirm, in a whole-brain connectome endowed with neural mass models, previous studies illustrating an imbalance of LZc towards network segregation [44]. A promising method to overcome this limitation and assess brain complexity, defined as the coexistence of integration and differentiation within a system, involves adopting a causal/perturbational approach [6].