Spring 2020 – General Algebraic Formulas Predicting Cerebral Flow and Intracranial Pressure After Hemorrhagic Stroke

The damage from hemorrhagic strokes, especially arising from rupture of cerebral aneurysms, arteriovenous and cavernous malformations, can occur within minutes. Cerebral blood flow and intracranial pressure are critical variables that impact clinical outcomes. These variables emerge from the complex interaction of the mechanical properties of the cerebral vasculature, cerebrospinal fluid, brain tissue, and hematoma. Conventional animal models used to study hemorrhagic strokes are inherently limited because hematoma volume is too difficult to control experimentally and results do not readily translate to humans. Although complex computational models can provide key insights absent from animal models, results depend on specific parameter values assumed and cannot be easily extrapolated to different cases. Therefore, the purpose of the present work is to develop a general algebraic formula that predicts cerebral flow and intracranial pressure from critical parameters. First, a multi-compartment model was assumed, with filtration across the blood-brain barrier characterized by the Starling-Landis equation, and fluid flow between the other compartments as simple resistances. Each compartment pressure-volume relationship was assumed to be linear and was characterized by a constant compliance and unstressed volume. Cerebral blood flow and intracranial pressure were solved analytically, yielding general algebraic formulas for cerebral blood flow and intracranial pressure in terms of parameters characterizing the cerebral vasculature, cerebrospinal fluid, brain tissue, and hematoma. The present work therefore provides a universal framework with which to interpret data from diverse animal models and data from human clinical studies