Influence of hydrodynamic and functional nonlinearities of blood flow in the cerebral vasculature on cerebral perfusion and autoregulation pressure reserve

Ensuring the transport of oxygenated blood to the brain is one of the priorities of the human body. In the literature, there are many models of cerebral circulation with different levels of complexity used to assess pathological conditions, support clinical decisions, and learn about the relationships governing cerebral circulation. This paper presents a zero-dimensional cerebral circulation model that considers hydrodynamic nonlinearities and autoregulation mechanisms. The model has been verified using a computational fluid dynamics (CFD) model of the Circle of Willis (CoW) and its supplying and outgoing branches. Despite the considerable simplicity, the presented model captured the dominant features of cerebral circulation and provides good agreement with the CFD model. The errors in relation to the CFD model did not exceed 2.6% and 9.9% for the symmetrical and highly asymmetrical CoW configurations, respectively. The practical application of the model was demonstrated for predicting the autoregulation pressure reserve for different diameters of natural anastomoses: Posterior and Anterior Communicating Arteries. The advantages and limitations of the model were discussed.