Direct 0D-3D coupling of a lattice Boltzmann methodology for fluid-structure hemodynamics simulations

TL;DR

This paper presents a novel numerical method for directly coupling complex 0D boundary models, like heart and vascular systems, with 3D lattice Boltzmann fluid simulations to improve physiological hemodynamics modeling.

Contribution

It introduces a direct coupling approach for complex 0D boundary conditions with 3D lattice Boltzmann fluid-structure simulations, enabling realistic cardiovascular hemodynamics analysis.

Findings

Successfully simulates physiological pressure and flow waveforms.

Demonstrates convergence and stability of the coupled solver.

Applicable to various boundary conditions and fluid problems.

Abstract

This work introduces a numerical approach and implementation for the direct coupling of arbitrary complex ordinary differential equation- (ODE-)governed zero-dimensional (0D) boundary conditions to three-dimensional (3D) lattice Boltzmann-based fluid-structure systems for hemodynamics studies. In particular, a most complex configuration is treated by considering a dynamic left ventricle- (LV-)elastance heart model which is governed by (and applied as) a nonlinear, non-stationary hybrid ODE-Dirichlet system. Other ODE-based boundary conditions, such as lumped parameter Windkessel models for truncated vasculature, are also considered. Performance studies of the complete 0D-3D solver, including its treatment of the lattice Boltzmann fluid equations and elastodynamics equations as well as their interactions, is conducted through a variety of benchmark and convergence studies that demonstrate the ability of the coupled 0D-3D methodology in generating physiological pressure and flow waveforms -- ultimately enabling the exploration of various physical and physiological parameters for hemodynamics studies of the coupled LV-arterial system. The methods proposed in this paper can be easily applied to other ODE-based boundary conditions as well as to other fluid problems that are modeled by 3D lattice Boltzmann equations and that require direct coupling of dynamic 0D boundary conditions.