Left Heart Hemodynamics Simulations With Fluid-Structure Interaction and Reduced Valve Modeling

The combination of reduced models of cardiac valve dynamics with a one-way kinematic uncoupling of blood flow and electromechanics is a widespread approach for reducing the complexity of cardiac hemodynamics simulations. This comes, however, with a number of shortcomings: artificial pressure oscillations, missing isovolumetric phases, and valve laws without precise continuous formulation. This paper is aimed at overcoming these three difficulties while still mitigating computational cost. A novel reduced model of valve dynamics is proposed in which unidirectional flow is enforced in a mathematically sound fashion. Artificial pressure oscillations are overcome by considering a fluid-structure interaction model, which couples bi-ventricular electromechanics and blood flow in the left cavities. The interface coupling is solved in a partitioned fashion via an unconditionally stable loosely coupled scheme. A priori energy estimates are derived for both the continuous coupled problem and its numerical approximation. The benefits and limitations of the proposed approaches are illustrated in a comprehensive numerical study.