Refinement of a Poroelastic Model for Zero Porosity: Finite Element Implementation and Investigation of Fluid Mechanics in the Perivascular Space

TL;DR

This paper presents a reformulated poroelastic model capable of handling zero porosity scenarios, verified through numerical methods, and applied to study fluid mechanics in brain perivascular spaces, revealing critical parameter sensitivities.

Contribution

We developed a poroelastic model based on mixture theory that remains valid at zero porosity and applied it to brain fluid flow, addressing limitations of traditional models.

Findings

Model successfully handles zero porosity conditions.

Extreme parameter values can cause non-physiological predictions.

Tissue deformation mitigates some extreme conditions.

Abstract

In conventional formulations of poroelasticity, when the porosity approaches zero or vanishes in some parts of the poroelastic domain, if only temporarily, the governing equations degenerate to those for the solid phase thereby inhibiting a suitable determination of the fluid velocity field. To address this challenge, we reformulated a poroelastic model based on mixture theory to accommodate scenarios with zero porosity. We verified our model using the method of manufactured solutions and demonstrated its ability to handle extreme conditions in a sample test problem. As an application of our framework, we investigated peristaltic flow in the perivascular space of a penetrating arteriole in brain. Our analysis revealed that some literature-suggested parameters can drive the model to predict extreme non-physiological conditions. We further demonstrated that these extreme conditions can be somewhat mitigated by accounting for the deformation of the surrounding brain tissue.