A Mathematical Model of Cellular Metabolism During Ischemic Stroke and Hypothermia

Stroke is a major cause of death and disability worldwide. Therapeutic hypothermia is a potentially useful neuroprotective treatment. A mathematical model of brain metabolism during stroke is extended here to simulate the effect of hypothermia on cell survival. Temperature decreases were set to reduce chemical reaction rates and slow diffusion through ion channels according to the Q
₁₀
rule. Heat delivery to tissues was set to depend on metabolic heat generation rate and perfusion. Two cooling methods, scalp and vascular, were simulated to approximate temperature variation in the brain during treatment. Cell death was assumed to occur at continued cell membrane depolarization. Simulations showed that hypothermia to 34.5 °C induced within 1-1.5 h of stroke onset could extend cell survival time by at least 5 h in tissue with perfusion reduced by 80% of normal. There was good agreement between simulated metabolite dynamics and those reported in rat model studies.