A Novel Solid Mechanics Approach to Modelling the Interaction of the Left Ventricle and Blood Cavity

Abstract

This paper presents a novel computationally-efficient physical-based solid/fluid constitutive framework for modelling the cardiac cycle using the finite element method. Previous models of the left ventricle simulate the cardiac cycle by applying pressure or nodal displacements as boundary conditions, which in reality are both ouptuts that are generated due to the interaction between the active contractility of the ventricular myocardium and the temporally varying fluid domain which it encloses. By modelling the blood cavity using C3D8 solid continuum elements, a Windkessel-type volumetric stress formulation governs the pressure-volume relationship during ejection using a central-difference scheme within the user-defined material subroutine. We have developed a patient-specific model of the left ventricle directly from CINE Echocardiography scan data and the model can accurately capture the key trends of Inferior Vena Cava Occlusion (IVCO) experiments, demonstrating the Frank-Starling mechanism as an output. For the first time, the effect of including nonlinear aortic compliance on ventricular pressure-volume loops is studied, and it is demonstrated its inclusion is critical to accurately capture key features of IVCO and endovascular aortic repair (EVAR) experiments. This model acts as an alternative to computationally expensive fluid-structure interaction simulations, and overcomes multiple limitations of current finite element models, and can run full cardiac cycles of a patient-specific left ventricle in 5 minutes, rendering it feasible for clinical integration and real time analysis of patient ventricle dynamics.