Abstract:

We investigate the properties of static mechanical and dynamic electro-mechanical models for the deformation of the human heart. Numerically this is realized by a staggered scheme for the coupled partial/ordinary differential equation (PDE-ODE) system. First, we consider a static and purely mechanical benchmark configuration on a realistic geometry of the human ventricles. Using a penalty term for quasi-incompressibility, we test different parameters and mesh sizes and observe that this approach is not sufficient for lowest order conforming finite elements. Then, we compare the approaches of active stress and active strain for cardiac muscle contraction. Finally, we compare in a coupled anatomically realistic electro-mechanical model numerical Newmark damping with a visco-elastic model using Rayleigh damping. Nonphysiological oscillations can be better mitigated using viscosity.

Abstract:

The restraining effect of the pericardium and surrounding tissues on the human heart is essential to reproduce physiological valve plane movement in simulations and can be modeled in different ways. In this study, we investigate five different approaches used in recent publications and apply them to the same whole heart geometry. Some approaches use Robin boundary conditions, others use a volumetric representation of the pericardium and solve a contact problem. These two strategies are combined with a smooth spatially varying scaling or a region-wise partitioning of the epicardial surface. In general, all simulations follow the same morphology regarding mitral valve displacement, tricuspid valve displacement and left ventricular twist. We show that – with the parameters used in the original papers – Robin boundary conditions are computationally more expensive and lead to smaller stroke volumes and less ventricular twist. Unrelated to this, simulations with a penalty scaling result in a less pronounced displacement of the tricuspid valve. In one of the investigated scenarios adipose tissue is modeled using a volumetric mesh and the Robin boundary conditions are applied on its outside surface. We conclude that this approach leads to similar results as a partitioning of the epicardial surface into two regions with different penalty parameters and therefore a volumetric representation of the adipose tissue is neither necessary nor practical.

Abstract:

Lumped parameter models of the human circulatory sys-tem are able to reproduce major features and phases of human circulation. However, they often lack physiological detail regarding pressure and flow across the valves. To alleviate these shortcomings, we implement a model of heart valve dynamics based on Bernoulli's principle to account for the transvalvular pressure drop and extend it by smooth opening and closing of the valves. We evaluate the new model based on a simulation with healthy valves and explore the possibility of simulating heart valve diseases by considering a case of severe aortic stenosis. The model more faithfully reproduces pressure, volume, and flow in all four chambers and in particular across the valves. Most of the changes are related to the consideration of blood inertia. However, only by opening and closing the valves more slowly, it is possible to reproduce features connected to backflow. When reducing the maximum area ratio of the aortic valve to 10%, a pressure gradient of 77.2 mmHg during systole and a 20% reduction in stroke volume was observed in accordance with the AHA guidelines of severe aortic stenosis. To conclude, we were able to improve our existing OD circulation model in terms of physiological accuracy by replacing the diode-like valves with an easy to implement model of heart valve dynamics that is capable of simulating both healthy and pathological scenarios.