A mathematical model for vasogenic brain edema

Abstract

A hydraulic model of the intracranial compartments is used to analyze the quantitative contribution of various factors to vasogenic brain edema. These factors include osmotic and hydrostatic pressures, tissue compliance, and capillary and tissue hydraulic conductivities. The brain is assumed to be composed of a vascular cortical Region a (corresponding to gray matter) and an avascular periventricular Region b (corresponding to white matter). The model predicts that edema will develop if there is an elevated driving force for filtration across the normal capillary bed, or if capillary permeability and hydraulic conductivity are increased. In the former case, filtrate does not contain salt, and therefore dilutes perivascular osmolality and reduces the driving force for further filtration. If the capillary is permeable to salt, on the other hand, dilutional protection is absent, brain swelling is greater and proportional in Regions a and b to the product of interstitial hydrostatic pressure and regional compliance k. As brain hydraulic conductivity is low, the model predicts that a transient increase in cerebrovascular permeability results in swelling only of Region a, but that increased permeability lasting for days results as well in swelling of Region b and attainment of a steady state. Vasogenic edema might be treated by reducing elevated capillary permeability and hydraulic conductivity, by reducing brain compliance or, if brain hydraulic conductivity is also elevated, by reducing cerebrospinal fluid pressure.