A voxelized immersed boundary (VIB) finite element method for accurate and efficient blood flow simulation

TL;DR

This paper introduces a voxelized immersed boundary finite element method that accurately and efficiently simulates blood flow in complex geometries, improving upon existing IB methods in terms of accuracy and applicability.

Contribution

The paper presents a novel voxelized IB finite element approach combining IPCS and BCE-IB methods for precise blood flow simulation in complex vascular geometries.

Findings

High accuracy verified with analytical and experimental data

Effective simulation of blood flow in aneurysmal vessels and aorta

Computational efficiency comparable to traditional FE methods

Abstract

We present an efficient and accurate immersed boundary (IB) finite element (FE) method for internal flow problems with complex geometries (e.g., blood flow in the vascular system). In this study, we use a voxelized flow domain (discretized with hexahedral and tetrahedral elements) instead of a box domain, which is frequently used in IB methods. The proposed method utilizes the well-established incremental pressure correction scheme (IPCS) FE solver, and the boundary condition-enforced IB (BCE-IB) method to numerically solve the transient, incompressible Navier--Stokes flow equations. We verify the accuracy of our numerical method using the analytical solution for the Poiseuille flow in a cylinder, and the available experimental data (laser Doppler velocimetry) for the flow in a three-dimensional 90{\deg} angle tube bend. We further examine the accuracy and applicability of the proposed method by considering flow within complex geometries, such as blood flow in aneurysmal vessels and the aorta, flow configurations that would otherwise be difficult to solve by most IB methods. Our method offers high accuracy, as demonstrated by the verification examples, and high applicability, as demonstrated through the solution of blood flow within complex geometry. The proposed method is efficient, since it is as fast as the traditional finite element method used to solve the Navier--Stokes flow equations, with a small overhead (not more than 5$\%$) due to the numerical solution of a linear system formulated for the IB method.