A mid-fidelity numerical method for blood flow in deformable vessels

Abstract

In this work, a novel fluid–structure interaction algorithm for the simulation of blood flow in three-dimensional deformable vessels is addressed. The method extends the mid-fidelity strategy named as Transversally Enriched Pipe Element Method, extensively tested as an efficient approach to simulate the blood flow under rigid wall hypothesis, by taking into account the distensibility of the lumen boundary by means of an independent ring structural model. The Navier–Stokes equations, in Arbitrary Lagrangian–Eulerian framework, are used as the governing equations for the blood flow dynamics, the vessel wall mechanics is represented through an elastic constitutive law, and the fluid domain deformation problem is explicitly solved by exploiting the layered structure of the geometry discretization associated to the mid-fidelity model. The result is an approximation strategy able to take into account the wall deformation at nearly zero added cost when compared with a rigid wall model. An extensive numerical validation and verification of the proposed methodology is reported employing simple domains and complex patient-specific geometries to highlight the potential for real applications.