Arachidonic acid metabolites and cortical depression: from local to spatial model

Background and Objectives: According to known experimental data, various metabolites of arachidonic acid have a vasoconstrictor or vasodilator effect, which in turn affects neuronal activity. The level of metabolite production can be influenced in several ways: by regulating oxygen levels or by glutamate-dependent increases in astrocytic calcium concentrations in response to neuronal activity. To analyze possible patterns of activity of nervous tissue in response to changes in the metabolic profile, a mathematical model was developed, within the framework of which computational experiments were carried out both in the local case and on spatial patterns. Materials and Methods: The work proposes a point model and its further extension for a spatially distributed system of connected neurogliovascular units. To test the performance of the model, we include an external influence leading to an increase in neuronal potassium and the occurrence of cortical depression, and an external influence on calcium activity, in order to analyze the influence of arachidonic acid metabolites on the process under study. Results: A new point model of the neurogliovascular unit has been developed that simulates the effect of arachidonic acid metabolites on cortical spreading depression, while expanding the point model to a spatially distributed case allowed us to determine the ways in which astrocytic activity influences the spatiotemporal characteristics of the wave of cortically spreading depression. Numerical studies of point and spatial models have confirmed the correspondence of the solutions to the observed experimental effects, including those associated with the peculiarities of the influence of arachidonic acid metabolites on the speed, area and lifetime of depression waves. It is assumed that in the future the results of the theoretical study can be used to find ways to return nervous tissue to the normal state from pathological conditions that occur with epilepsy, migraines and other neurodegenerative conditions associated with the occurrence of cortical depression waves.