Data driven multiscale modelling of paroxysmal brain transitions using DC-coupled electrophysiological data.

We introduce a novel parameter estimation framework for a slow-fast neuronal model using DC-coupled electrophysiological data recorded from the WAG-Rij rat model of generalised seizures. In this animal model, fluctuations in extracellular potassium concentrations are hypothesised to drive infra-slow oscillations (ISO) that precede spike-wave discharges. We construct a biophysically motivated slow-fast dynamical system in which seizures are triggered by fluctuations in extracellular potassium concentrations to model the in vivo observations. Specifically, we interpret ISOs dynamics (mathematically) as the integral transform (or low-pass filter) of extracellular potassium concentrations, facilitating real time tracking of physiological states. Model parameters are estimated from empirical data, using an expectation-maximisation approach that optimises a regularised likelihood function, while biological states are inferred through the unscented Kalman filter. The inferred model allows tracking changes in latent proxy of extracellular potassium concentrations from DC-coupled electrophysiological recordings (exhibiting paroxysmal transitions) under the assumption that in our preclinical model extracellular potassium dynamics contribute to seizure generation. We validate the consistency of inferred hidden biological states across longer datasets containing multiple seizure events that were not utilised during parameter estimation. The results demonstrate that ISOs provide sufficient information to infer latent ionic dynamics and support the conceptualisation of seizure onset as bifurcation-driven transitions modulated by the ionic changes.