The Circle of Willis as a Pressure-Dissipative System

Abstract

Cerebrovascular diseases, including stroke and dementia, rank among the top 10 causes of death globally. Where the Circle of Willis is an anatomical structure at the base of the brain that redistributes blood flow. Vrselja et al. challenged the traditional view that the primary function of the Circle of Willis is to provide collateral circulation, suggesting instead that it dissipates high pressures in the cerebrovasculature.

One-dimensional (1D) modeling, based on the simplified Navier-Stokes equations, offers a way to accurately predict blood flow with only a fraction of the computational expense of a three-dimensional (3D) model. SimVascular, a computational modeling software tailored for representing blood flow, recently added a 1D modeling feature. This study assessess the suitability of the 1D model in SimVascular for representing the cerebrovasculature, by testing it on the Circle of Willis. Additionally, preliminary research investigates whether the Circle of Willis functions as a pressure dissipative system, particularly through its communicating arteries.

The modeling pipeline included centerline extraction, mesh generation, boundary conditions, material model and solver parameters. Challenges were identified during centerline extraction, as SimVascular is inherently unable to handle loops, and inlet boundary conditions, where it could not manage multiple inlets. Considering these limitations, a series of 1D linear elastic models were created from the 3D geometry of the Circle of Willis to test whether it serves as a pressure dissipative system.

While SimVascular was unable to handle closed-loop geometries and multiple inlets, results indicated that the absence of a communicating artery induced relatively minor pressure oscillations. This suggests first, that SimVascular, in its current form, is not well-suited for 1D modeling of the cerebrovascular system's complexities, including loops and multiple inlets. Second, that the hypothesis of the Circle of Willis functioning primarily as a pressure dissipative system holds promise but requires further validation.