On the modelling of seizure dynamics

This scientific commentary refers to ‘On the nature of seizure dynamics’, by Jirsa et al. (doi:10.1093/brain/awu133) . In this issue of Brain , Jirsa and colleagues offer a masterful account of epilepsy that discloses the universal and invariant properties of seizure dynamics (Jirsa et al. , 2014). They derive a formal taxonomy of seizure activity from the basic principles of coupled dynamical systems. In brief, they show that a minimal model—comprising just five states or variables—is sufficient to describe the onset, time-course and offset of seizure activity. This may sound implausible; however, the repertoire of dynamics that coupled systems can generate may be much smaller than people imagine. In effect, Jirsa et al. use their understanding of dynamical systems to ‘diagnose’ the mathematical aetiology of the ‘signs and symptoms’ expressed in the statistics of seizure activity. Put simply, the existence of dissociable fast discharges and spike-wave events immediately tells them that the dynamics must be generated by two pairs of (hidden) coupled states generating fast and spike-wave oscillations, respectively. The fact that seizure activity waxes and wanes over a slower timescale then calls for a further slow permittivity variable that controls the expression of fast dynamics. Within this model, the onset and offset of seizure activity become well-defined mathematical objects: a saddle node and homoclinic bifurcation, respectively. The tell-tale signatures of these bifurcations were subsequently confirmed using in vitro experiments and focal seizures recorded in humans and zebrafish. So why is this important? Without recourse to Wikipedia, I confess that I could not explain the difference between a saddle node and homoclinic bifurcation. However, this is not important: the authors have done all the mathematical heavy lifting for us and bring three things to the table: first, the notion that seizure onset (and offset) can be cast in …