Neural diffusivity and pre-emptive epileptic seizure intervention

The propagation of epileptic seizure activity in the brain is a widespread pathophysiology that, in principle, should yield to intervention techniques guided by mathematical models of neuronal ensemble dynamics. During a seizure, neural activity will deviate from its current dynamical regime to one in which there are significant signal fluctuations. In silico treatments of neural activity are an important tool for the understanding of how the healthy brain can maintain stability, as well as of how pathology can lead to seizures. The hope is that, contained within the mathematical foundations of such treatments, there lie potential strategies for mitigating instabilities, e.g. via external stimulation. Here, we demonstrate that the dynamic causal modelling neuronal state equation generalises to a Fokker-Planck formalism if one extends the framework to model the ways in which activity propagates along the structural connections of neural systems. Using the Jacobian of this generalised state equation, we show that an initially unstable system can be rendered stable via a reduction in diffusivity–i.e., by lowering the rate at which neuronal fluctuations disperse to neighbouring regions. We show, for neural systems prone to epileptic seizures, that such a reduction in diffusivity can be achieved via external stimulation. Specifically, we show that this stimulation should be applied in such a way as to temporarily mirror the activity profile of a pathological region in its functionally connected areas. This counter-intuitive method is intended to be used pre-emptively–i.e., in order to mitigate the effects of the seizure, or ideally even prevent it from occurring in the first place. We offer proof of principle using simulations based on functional neuroimaging data collected from patients with idiopathic generalised epilepsy, in which we successfully suppress pathological activity in a distinct sub-network prior to seizure onset. Our hope is that this technique can form the basis for future real-time monitoring and intervention devices that are capable of treating epilepsy in a non-invasive manner.Author summary: Epilepsy is a disease that affects over 50 million people worldwide. Current treatments include dangerous surgical procedures in which brain connections are severed, or even in which entire problem brain regions are removed. Pharmaceutical options are available, but only about one third of patients are responsive. However, even in these cases the drugs can cause such severe side effects that the patients sometimes choose to suffer seizures. We are proposing an innovative treatment of epilepsy that could be achieved by using non-invasive electrical stimulation. Specifically, we show that stimulation should be applied in such a way as to mirror the activity in a problem brain region, by targeting its neighbouring areas. This counterintuitive approach is based on a mathematical model in which this mirroring strategy is applied pre-emptively, i.e. long before the seizure has a chance to set in. The hope is that future clinical trials will be able to use this model to lessen the effect of seizures, or even prevent them from occurring in the first place.