Pathological pattern formation and cortical propagation of epileptic seizures

Abstract

The stochastic partial differential equations (SPDEs) stated by Steyn-Ross and co-workers constitute a model of mesoscopic electrical activity of the human cortex. A simplification in which spatial variation and stochastic input are neglected yields ordinary differential equations (ODEs), which are amenable to analysis by techniques of dynamical systems theory. Bifurcation diagrams are developed for the ODEs with increased subcortical excitation, showing that the model predicts oscillatory electrical activity in a large range of parameters. The full SPDEs with increased subcortical excitation produce travelling waves of electrical activity. These model results are compared with electrocortical data recorded at two subdural electrodes from a human subject undergoing a seizure. The model and observational results agree in two important respects during seizure: (i) the average frequency of maximum power, and (ii) the speed of spatial propagation of voltage peaks. This suggests that seizing activity on the human cortex may be understood as an example of pathological pattern formation. Included is a discussion of the applications and limitations of these results.

Human seizures self-terminate across spatial scales via a critical transition

“…Mean-field models have a long history in computational neuroscience (e.g., [26][27][28][29], including many important applications for seizure modeling. These include, for example, mean-field models of absence seizures (30)(31)(32), of depth and surface electrode recordings from patients with temporal lobe epilepsy (33,34), seizure generalization (35), and anesthetic-induced seizures (36).…”

Phase lagging model of brain response to external stimuli—modeling of single action potential

“…There is also ambiguity in the lead/lag relationships determined by the Windowed Cross Correlation that they used. They suggested that the seizing activity of the cortex may be understood as an example of pathological pattern formation [14]. Kulish This paper attempts to suggest a phase-lagged model of single action potential which is based on fundamental laws of physics.…”

A probabilistic method for determining cortical dynamics during seizures

“…There have been several studies in associating cortical states (including seizures) measured in patients with these types of meso-scale cortical models and neural mass models for both seizures (Kramer et al 2005(Kramer et al , 2007NevadoHolgado et al 2012;Wang et al 2012;Aarabi and He 2014) and sleep (Lopour et al 2011;Dadok et al 2013). In Kramer et al (2005Kramer et al ( , 2007, pathways to seizure regions identified with bifurcation analysis through the particular mesoscale model used in this work were explored qualitatively to determine potential directions through seizure and enumerate seizure regions.…”

“…If we engineer a way to take EEG or ECoG measurements of seizures and learn how the corresponding physiology is changing in a model of the cortex, there is great potential to gain understanding of seizures that among other implications may in the future lead to new treatment strategies for individual seizures or epilepsy as a condition, including such options as new drug development to target certain physiological changes, new implantable therapies, or new algorithms for existing devices (Kramer et al 2005(Kramer et al , 2007Wendling 2008;Bazhenov et al 2008).…”

“…In Kramer et al (2005Kramer et al ( , 2007, pathways to seizure regions identified with bifurcation analysis through the particular mesoscale model used in this work were explored qualitatively to determine potential directions through seizure and enumerate seizure regions. Using a different but related mathematical model, Nevado-Holgado et al (2012) explores a more quantitative approach to determining parameter pathways, concentrating on time domain waveforms and attempting to match specific waveforms in measured EEG to waveforms generated by a neural mass model.…”