# Modeling Pressure‐Dependent Wave and Vessel Compliance in the Brain Following Middle Cerebral Artery Occlusion

## TL;DR

This study uses mathematical modeling to show how changes in pressure and vessel compliance affect brain perfusion after a stroke caused by MCA occlusion.

## Contribution

The study introduces a model that incorporates vessel compliance and pulsatility to better understand cerebrovascular responses to stroke.

## Key findings

- Increased distensibility reduces pressure oscillations, while decreased distensibility increases them.
- Occlusion significantly alters flow changes when incoming pressure varies.
- Elevated arterial pressure boundary conditions are linked to lower ischemia and improved autoregulation.

## Abstract

This study demonstrates the impact of alterations in pressure, vascular compliance, arterial pulsatility, and autoregulation on tissue perfusion following middle cerebral artery (MCA) occlusion using mathematical modeling.

Our previous mathematical model of the cerebral circulation is expanded to include vessel compliance and pulsatility of blood flow. An experimentally‐obtained pressure waveform is used as an incoming boundary condition to simulate the effects of vascular compliance and pulsatility of flow on perfusion following MCA occlusion. The waveform is adjusted to model the effects of elevated mean arterial pressure.

Increased distensibility reduces the amplitude of oscillations in the time‐dependent pressure solutions, whereas decreased distensibility produces more variation in these pressures. Occlusion significantly alters the magnitude of flow changes when incoming pressure is varied. The addition of the pulsatile pressure boundary condition and capacitances in the arteries and veins shifts the autoregulation plateau to higher pressures.

This study reveals how changes in incoming pressure affect compensatory responses to ischemic stroke caused by MCA occlusion. Boundary conditions corresponding to elevated mean arterial pressures are associated with lower degrees of ischemia, an improvement that is supported by changes in autoregulation patterns following occlusion. The results also demonstrate how increases in arterial stiffness associated with aging can inhibit the ability of the vasculature to accommodate pulsatile flow by analyzing resulting patterns such as larger amplitudes of pressure and flow oscillations in the microcirculation. The study provides a foundation for modeling the relationships among vessel compliance, arterial blood pressure, and cerebrovascular conditions.