  Seizure activity is a ubiquitous and pernicious pathophysiology that, in
principle, should yield to mathematical treatments of (neuronal) ensemble
dynamics - and therefore interventions on stochastic chaos. A seizure can be
characterised as a deviation of neural activity from a stable dynamical regime,
i.e. one in which signals fluctuate only within a limited range. In silico
treatments of neural activity are an important tool for understanding how the
brain can achieve stability, as well as how pathology can lead to seizures and
potential strategies for mitigating instabilities, e.g. via external
stimulation. Here, we demonstrate that the (neuronal) state equation used in
Dynamic Causal Modelling generalises to a Fokker-Planck formalism when
propagation of neuronal activity along structural connections is considered.
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., connectivity that disperses neuronal fluctuations). We show, for neural
systems prone to epileptic seizures, that such a reduction can be achieved via
external stimulation. Specifically, we show that this stimulation should be
applied in such a way as to temporarily mirror epileptic activity in the areas
adjoining an affected brain region - thus 'fighting seizures with seizures'. 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. Our hope
is that this technique can form the basis for real-time monitoring and
intervention devices that are capable of suppressing or even preventing
seizures in a non-invasive manner.
