Spreading depression in focal ischemia: a computational study.

When a cerebral infarction occurs, surrounding the core of dying tissue there usually is an ischemic penumbra of nonfunctional but still viable tissue. One current but controversial hypothesis is that this penumbra tissue often eventually dies because of the metabolic stress imposed by multiple cortical spreading depression (CSD) waves, that is, by ischemic depolarizations. We describe here a computational model of CSD developed to study the implications of this hypothesis. After simulated infarction, the model displays the linear relation between final infarct size and the number of CSD waves traversing the penumbra that has been reported experimentally, although damage with each individual wave progresses nonlinearly with time. It successfully reproduces the experimental dependency of final infarct size on midpenumbra cerebral blood flow and potassium reuptake rates, and predicts a critical penumbra blood flow rate beyond which damage does not occur. The model reproduces the dependency of CSD wave propagation on N-methyl-D-aspartate activation. It also makes testable predictions about the number, velocity, and duration of ischemic CSD waves and predicts a positive correlation between the duration of elevated potassium in the infarct core and the number of CSD waves. These findings support the hypothesis that CSD waves play an important causal role in the death of ischemic penumbra tissue.