Spreading Depression in Focal Ischemia: A Computational Study

Abstract

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.

Local uptake of 14C‐labeled acetate and butyrate in rat brain in vivo during spreading cortical depression

“…A focal brain injury can induce spreading depression, i.e., wide-spread depolarization of neurons and glia, severe disruption of ion and neurotransmitter homeostasis, and behavioral changes; spreading depression is linked to the pathophysiology of stroke and migraine (Lauritzen, 1994;Revett et al, 1998). Glucose utilization (CMR glc ) rises heterogeneously in cerebral cortex during spreading depression (Shinohara et al, 1979), and there is a shift in labeling of metabolites by [6-14 C]glucose, with increased labeling and rapid export of large quantities of both labeled and unlabeled lactate from cerebral cortex (Adachi et al, 1995;Cruz et al, 1999).…”

Modélisation des dépressions corticales envahissantes et existence de fronts progressifs

“…D'autres modèles utilisant des équations de réaction-diffusion ont été développés dans [14,22,26,27,34]. Ces modèles plus simples biologiquement sont en revanche centrés sur le problème de la propagation des DCE et ne sont que sommairement rattachés aux observations physico-biologiques au niveau membranaire.…”

Modeling Brain Energy Metabolism and Function: A Multiparametric Monitoring Approach

“…This simplification enables us to utilize the so-called integral-or point-model approach, when the physiological variables are regarded as functions of time only (their interdependence apart), rather than as space-distributed variables. Hence, the "diffusion" terms and the spatial derivatives that appear in the space-distributed models (Revett et al, 1998;Ruppin et al, 1999) are omitted, and we arrive at a classical dynamic system, whose states are described by ordinary differential equations of the kinetic type. Furthermore, using this approach, we can tune the model, maximizing the fit to the actual clinical and experimental data with little risk of overfitting.…”

“…In a series of reports, mathematical models were applied to study the processes underlying the pathogenesis of tissue damage (Reggia et al, 1997;Revett et al, 1998;Ruppin et al, 1999). Aiming at the investigation of the lengthwise propagation of the tissue damage and taking into account the spatial heterogeneity of the tissue, the authors of the above-referenced works had to consider both the temporal and spatial variability of several key metabolic variables characterizing the tissue state.…”