## 3 Results  
We start by showing the behavior of the mean-field model, then we show its integration in brain-wide models of mouse, monkey, and human cerebral cortexes. Figure 2 shows the spiking network model of AdEx neurons, comprising RS (blue) and FS (red) cells, as detailed in previous studies [6,8]. This network can generate asynchronous irregular (AI) activity states (Figure 2A, top), as well as slow synchronized activity in  
the form of up-down states (Figure 2A, bottom). The transition from these two states is obtained by the strengthening or weakening of the spike-frequency adaptation in RS cells (parameter \(b\) in the model). The mean rates of activity of these two states are shown in Figure 2B. The mean-field model of this AdEx network was derived in two previous publications [6; 8] and is shown for these two states in Figure 2C. As shown previously [13; 14], the AdEx mean-field model was implemented in The Virtual Brain (TVB) platform. This platform consists of a Python-based simulation environment [24] that allows the user to create a network of mean-field models (or, more generally, neural mass models) constrained by connectivity data extracted from a given connectome. The TVB environment can also generate a number of neural signals and be linked to neuro-imaging [26]. Integrating the AdEx mean-field model in TVB, leading to the \"TVB-AdEx\" model [13], has a double advantage. First, the mean-field model is biologically informed, so it has physically interpretable parameters (such as conductances and synaptic receptor kinetics) that can be changed and directly compared to experiments. Second, the AdEx mean-field model can generate states of activity that can be asynchronous or synchronized (see Figure 2), which is not the case with other neural mass models. This behavior is remarkably robust within the large parameter space of the model, as investigated in detail previously [27] and illustrated in Figure 3.  
The behavior of the TVB-AdEx model is illustrated in Figure 4 for mouse, monkey, and human brains. In all three species, the asynchronous activity of the mean-field model leads to global dynamics that are also asynchronous (Figure 4, middle panels). While there were some variations in the absolute amplitudes of the firing rates, the three models displayed consistent asynchronous dynamics. For higher levels of adaptation, the three models displayed slow-wave activity, as in the mean-field model. However, in this case, the individual nodes synchronized their slow oscillation, which generated globally synchronized slow-wave activity across large brain regions. In the case of the human brain, a  
Figure 3: Robustness of asynchronous and synchronized slow oscillatory states in the human TVB-AdEx model. The 3D graph represents the TVB model’s behavior in a space spanned by three parameters: the connection strength \(S\), the level of adaptation \(b\), and the time scale \(T\). The color indicates the duration of the up states \(D_{up}\) (large durations indicate that the dynamics are sustained and asynchronous). Adapted from [27]. grid scan of parameters showed that the level of synchrony depends on the parameters and, in particular, on the strength of the long-range connectivity [14]. A comparison of the two states across the models of the three species is further shown in Figure 5. The transition from asynchronous to slow-wave dynamics occurs at about the same value of adaptation parameter \(b\) (Figure 5A). Interestingly, the duration of the down states is predicted to be similar between species. One can also see that the down state duration increases with \(b\), and thus the slow-wave frequency also decreases proportionally to the level of adaptation. The level of synchrony of the activities is shown in Figure 5B,C, as measured by the phase-lag index (PLI), for excitatory and inhibitory population activities, respectively. The synchrony increases for excitatory cells as a function of adaptation parameter \(b\) (Figure 5B).