## 3 Results
### Vast Parameter Space Exploration and Analysis
#### 3.2.4 The Effects of Stimulating External Excitatory and Inhibitory Populations  
As depicted in Figure 6, in the context of the model's dynamics, stimulating the excitatory population leads to a shift in mean activity levels, causing transitions both upward and downward, while concurrently reducing the correlation with the structural connectivity (SC). Conversely, stimulating the inhibitory population results in an increase in the mean excitatory firing rate and a decrease in the global spectral frequency. It is important to note that the excitation of both the excitatory and inhibitory neuronal populations collectively influences the maximum peak of variance within the excitatory population. Figure 5: Parameter exploration for global coupling and spike-frequency adaptation when modulating the subthreshold adaptation conductance, \(a_{e}\). The other parameters are as follows: _wNoise_: \(1.0\times 10^{-4}\), _speed_: \(3.0\), \(\tau_{\text{var}}\): \(417\), \(c_{F_{\text{var}}}\): \(0.5\times 10^{-3}\), \(c_{F_{\text{var}}}\): \(0.0\), \(c_{F_{\text{var}}}\): \(0.5\times 10^{-3}\), \(c_{F_{\text{var}}}\): \(0.0\). 2.5 Pathology and the Effect of Modulating the Propagation Speed of Action Potentials through the Connectome  
One intriguing aspect of mean-field models obtained through biophysical approaches is their potential utility in identifying abnormal patterns or irregularities associated with pathologies. The TVB-AdEx could potentially be used to investigate seizure activity related to epilepsy, for instance, due to the hyperactive or hypersynchronized states of the model [9] as the dynamical landscape of the model comprises a pathological fixed point around 190 Hz [10]. This is a point where neurons fire directly after their refractory period. The vast parameter sweep can be used to chart the landscape and find the conditions under which the mean-fields of the network settle at this pathological fixed point. The occurrence of reaching this fixed point can be localized by examining the conditions for a jump in the dynamics to high-frequency activity. Disconnected models and models with a lower global coupling have a higher probability of reaching this fixed point [10]. It is to be expected that the fixed point is less likely to be reached if the coupling is stronger. When examining the effects of modulating the speed of action potential propagation through the connectome, it becomes apparent that when the speed attains a value of 1.0 m/s, particular regions display varying probabilities to visit the paroxysmal fixed point and display a high-firing-rate activity exceeding 100 Hz. This observation is visually depicted in Figure 7. When quantifying the instances in which a high firing rate is observed  
Figure 6: Parameter exploration for global coupling and spike-frequency adaptation in the context of different external excitatory inputs. The other parameters are as follows: \(w\)_Noise_: \(1.0\times 10^{-4}\), _speed_: 3.0, \(\tau_{\text{ie}}\): 417, \(a_{\text{e}}\): 0.0.  
exclusively in single regions, we observe the following: The left parahippocampal region visits the paroxysmal fixed point for all 16,384 parameter combinations when the speed attains a value of 1.0 m/s. Furthermore, the subsequent four maximum counts are recorded: 6500 occurrences for the left entorhinal region, 3201 occurrences for the left inferior parietal region, 1866 occurrences for the right parahippocampal region, and 830 occurrences for the right entorhinal region. Intriguingly, the left parahippocampal region stands out with the highest input weights and has the strongest connection with the left entorhinal region. This observation may suggest that highly connected regions of the model are implicated in the generation of simulated epileptic seizures. This specific observation is only found when the speed property of the connectome, which globally influences the connections between regions, is low and affirms the assumption that less connected brains have a higher probability of reaching the pathological fixed point.