Traveling waves in a model for cortical spreading depolarization with slow–fast dynamics
نویسندگان
چکیده
Cortical spreading depression and depolarization (CSD) are waves of neuronal that spread across the cortex, leading to a temporary saturation brain activity. They associated with various disorders such as migraine ischemia. We consider reduced version biophysical model neuron–astrocyte network for initiation propagation CSD [Huguet et al., Biophys. J. 111(2), 452–462, 2016], consisting reaction-diffusion equations. The considers only dynamics astrocytic membrane potentials extracellular potassium concentration, capturing instigation process implicated in waves. present computational mathematical framework based on parameterization method singular perturbation theory provide semi-analytical results existence wave solution compute it jointly its velocity propagation. traveling can be seen heteroclinic connection an system ordinary differential equations slow–fast dynamics. presence distinct time scales within introduces numerical instabilities, which we successfully address through identification significant invariant manifolds implementation method. Our methodology allows identify efficiently accurately mechanisms responsible these velocity.
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ژورنال
عنوان ژورنال: Chaos
سال: 2023
ISSN: ['1527-2443', '1089-7682', '1054-1500']
DOI: https://doi.org/10.1063/5.0160509