A Model of Cerebrovascular Reactivity Including the Circle of Willis and Cortical Anastomoses

Cerebrovascular pathologies are extremely complex, due to the multitude of factors acting simultaneously on cerebral hemodynamics. In this work, a mathematical model of cerebral hemodynamics and intracranial pressure (ICP) dynamics, developed in previous years, is extended to account for heterogeneity in cerebral blood flow. The model includes the Circle of Willis, six regional districts independently regulated by autoregulation and CO₂ reactivity, distal cortical anastomoses, venous circulation, the cerebrospinal fluid circulation, and the ICP–volume relationship. Results agree with data in the literature and highlight the existence of a monotonic relationship between transient hyperemic response and the autoregulation gain. During unilateral internal carotid artery stenosis, local blood flow regulation is progressively lost in the ipsilateral territory with the presence of a steal phenomenon, while the anterior communicating artery plays the major role to redistribute the available blood flow. Conversely, distal collateral circulation plays a major role during unilateral occlusion of the middle cerebral artery. In conclusion, the model is able to reproduce several different pathological conditions characterized by heterogeneity in cerebrovascular hemodynamics and cannot only explain generalized results in terms of physiological mechanisms involved, but also, by individualizing parameters, may represent a valuable tool to help with difficult clinical decisions.