Mathematical and numerical modeling of focal cerebral ischemia

Cerebral focal ischemia is a local degeneration of brain tissue induced by a reduction of blood supply. We introduce a mathematical model that includes the blood dynamics, represented by a flow in a porous medium and ion dynamics (calcium and potassium), together with other variables (energy stores, tissue integrity, oxygen and glucose) representing the biochemical events consequent to the vessel occlusion. The accurate description of the coupling between fluid dynamics and Biochemics is one of the distinctive features of the present work. We present both 2D and 3D simulations. Occurrence of peculiar ion dynamics, called spreading depression waves, formerly pointed out in the literature, is observed in 2D results. The role of some parameters of the problem in suppressing these waves is discussed. We moreover simulate in 3D the effects of a forced reperfusion of the occluded vessel (fibrinolysis) and the consequent blood leakage (hemorrhagic infarct).