First-Order Mathematical Modeling of Brain Swelling in Focal Cerebral Ischemia

Abstract

Edema is an important part of the pathophysiology of stroke. However, it remains unclear how brain swelling may influence the progression and measurement of infarction after cerebral ischemia. Initial studies in a mouse model of transient middle cerebral artery occlusion demonstrated that infarction grew from 24 to 72 h after stroke onset. Comparison of 24-h versus 72-h brains suggested that tissue swelling developed in both infarcted and non-infarcted ipsilateral regions. Volumes of infarction differed, depending on the method of calculation: direct, indirect, or normalized. A simple first-order model was constructed dividing total brain into three subsets, comprising normal contralateral tissue, non-infarcted ipsilateral tissue, and infarcted ipsilateral tissue. Each subset was then defined as a ratio of original volumes plus additional swollen volumes. By changing the relative portion of swelling assigned to infarct versus non-infarct, our model demonstrated that direct, indirect, and normalized calculations led to different thresholds for matching absolute infarct volumes. In this proof-of-principle study, we described a mathematical model to simulate the distribution of brain swelling and infarct development over time. Our findings suggest that accurate quantitation of infarct volumes depends on relative distributions of edema that may occur in both infarcted as well as non-infarcted brain.