Direct 0D‐3D coupling of a lattice Boltzmann methodology for fluid–structure aortic flow simulations

• Published in: International journal for numerical methods in biomedical engineering 2023-05, Vol.39 (5), p.e3683-n/a
• Main Authors: Wei, Heng, Amlani, Faisal, Pahlevan, Niema M.
• Format: Article
• Language: English
• Subjects: 0D‐3D coupling; 3D blood flow; Aorta; Aorta - physiology; Biomechanics; Boundary conditions; Computer Science; Computer Simulation; Coupling; Differential equations; Dirichlet problem; Elastodynamics; Flow simulation; Fluid Dynamics; Fluid flow; fluid–structure interactions; Heart - physiology; Heart Ventricles; Hemodynamics; Hemodynamics - physiology; Hybrid systems; lattice Boltzmann equations; LV‐arterial hemodynamics; Mathematical models; mathematical physiology; Mathematics; Mechanics; Modeling and Simulation; Numerical Analysis; Ordinary differential equations; Parameters; Physics; Physiology; Solid mechanics; Three dimensional models; Ventricle; Waveforms
• ISSN: 2040-7939; 2040-7947
• DOI: 10.1002/cnm.3683

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. This work presents a numerical approach and implementation for the direct coupling of arbitrary complex ODE‐governed 0D boundary conditions to 3D lattice Boltzmann based fluid‐structure systems for hemodynamics studies. Specifically, a nonlinear, nonstationary hybrid ODE‐Dirichlet system is applied to a scenario with a dynamic LV‐elastance heart model. Using our methods, one can easily apply ODE‐based boundary conditions to other fluid problems modeled by 3D LBM that require direct coupling with dynamic 0D boundary conditions.