Abstract

Variations in cerebral blood flow, vascular pressure, oxygen supply, and cellular metabolism interact to cause ischemic stroke, which cannot be explained by a single physiological factor alone. To represent these changes as an interconnected dynamic system at both the vascular and tissue levels, this study presents a novel, multi-scale mathematical model. A unified state-space model incorporates compartmental hemodynamics, anisotropic transport in porous media, pressure-driven transport, spatial oxygen advection-diffusion, and nonlinear, oxygen-dependent metabolism. The transport and reaction mechanisms are defined using non-dimensional metrics derived from Damköhler and Péclet types. Numerical study reveals that as the degree of ischemia increases, pressure and perfusion gradually deteriorate, coupled with a heterogeneous loss of oxygen in space. Sensitivity analysis helps determine which parameters most affect tissue behavior, while nonlinear metabolic function saturates at higher oxygen levels. Combining these elements into a single framework is the study’s primary breakthrough. A quantitative approach to comprehending how small modifications in the vascular system impact the process at larger scales and alter oxygen dynamics in the tissues under ischemia would be provided by such an analysis. This approach provides a foundation for estimating additional parameters. It enables interpretation of oxygen-related inadequacies arising from the phenomena without relying solely on correlation.