Discussion of a simple model of spreading depressions
Abstract
This paper is devoted to the study of a model of spreading depression (SD) which is a profound and transient depolarization of neurons. SD have a great importance in stroke or migraine with aura for example. Contrary to the rodent brain, SD have never been observed in the human brain. An explanation of this difference is proposed here by studying the influence of the geometry and composition of the brain. The model is derived from experimental observations and leads to a reaction-diffusion system that governs the ionic exchanges in calcium and potassium between the various cells of the brain and the extracellular space. Parameters of the model are fixed using a random algorithm that is explained here. Then the influence of geometry and composition of the brain is numerically studied.
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