Linear-Threshold Dynamics for the Study of Epileptic Events

Optimal Network Interventions to Control the Spreading of Oscillations

“…An unbounded version of LTNs, termed rectified linear units (ReLU), is widely studied in the context of machine learning [28], [29]. In the context of neuroscience, it has been used to model diverse brain states, including goal-driven selective attention [30], [31] and epilepsy [32]. In particular, recent works [30], [31], [33] have studied structural conditions for oscillations in networks of EI pairs by directly linking the lack of stable equilibria to the presence of oscillations.…”

“…In particular, we model the excitatory and inhibitory activity of a small brain tissue (micro-domain) through a Wilson-Cowan model [20] characterized by a piece-wise activation function. We refer to this atomical unit as an Excitatory-Inhibitory (EI) pair, the structural properties of which have been well characterized, see e.g., [30]- [32]. We build networks of EI pairs in order to model the complex interactions among domains of the human brain.…”

“…We conclude the discussion with extensive numerical simulations on synthetically generated networks. Motivated by our previous work [32], in this paper we tie the discussion of oscillations in the brain to the the study of epilepsy; however our results can be also applied to other oscillation-related problems in network control.…”

“…While previous work [33] identifies structural conditions for the existence of oscillations in general LTN models, we focus here on oscillations that arise in LTN networks composed of coupled excitatory-inhibitory (EI) pairs, as motivated by [30], [32]. For a EI pair, the linear threshold model has the form…”

“…inhibitory) node. The fixed points and attractors of the EI pair have been fully characterized [30], [32], [33] for all possible parameter values. Here we pay attention to the following dynamical features of EI pairs: the origin as a stable fixed point (corresponding to healthy neurological behavior) and stable limit cycles (corresponding to a pathological oscillation characteristic of an epileptic seizure).…”