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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.
Chimera states---the coexistence of synchrony and asynchrony in a nonlocally-coupled network of identical oscillators---are often used as a model framework for epileptic seizures. Here, we explore the dynamics of chimera states in a network of modifi
We assess electrical brain dynamics before, during, and after one-hundred human epileptic seizures with different anatomical onset locations by statistical and spectral properties of functionally defined networks. We observe a concave-like temporal e
In this work we study how to apply topological data analysis to create a method suitable to classify EEGs of patients affected by epilepsy. The topological space constructed from the collection of EEGs signals is analyzed by Persistent Entropy acting
Objective: To identify if whole-brain structural network alterations in patients with temporal lobe epilepsy (TLE) and focal to bilateral tonic-clonic seizures (FBTCS) differ from alterations in patients without FBTCS. Methods: We dichotomized a co
Absence epilepsy is believed to be associated with the abnormal interactions between the cerebral cortex and thalamus. Besides the direct coupling, anatomical evidence indicates that the cerebral cortex and thalamus also communicate indirectly throug