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

This work introduces a numerical approach for the implementation and direct coupling of arbitrary complex ordinary differential equation- (ODE-)governed boundary conditions to three-dimensional (3D) lattice Boltzmann-based fluid equations for fluid-structure hemodynamics simulations. 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. The complete 0D-3D solver, including its treatment of the fluid and solid equations as well as their interactions, is validated 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 (such as those based on Windkessel lumped parameter models) as well as to other fluid problems that are modeled by 3D lattice Boltzmann equations and that require direct coupling of dynamic 0D conditions.