The importance of the pericardium for cardiac biomechanics: from physiology to computational modeling.

The human heart is enclosed in the pericardial cavity. The pericardium consists of a layered thin sac and is separated from the myocardium by a thin film of fluid. It provides a fixture in space and frictionless sliding of the myocardium. The influence of the pericardium is essential for predictive mechanical simulations of the heart. However, there is no consensus on physiologically correct and computationally tractable pericardial boundary conditions. Here, we propose to model the pericardial influence as a parallel spring and dashpot acting in normal direction to the epicardium. Using a four-chamber geometry, we compare a model with pericardial boundary conditions to a model with fixated apex. The influence of pericardial stiffness is demonstrated in a parametric study. Comparing simulation results to measurements from cine magnetic resonance imaging reveals that adding pericardial boundary conditions yields a better approximation with respect to atrioventricular plane displacement, atrial filling, and overall spatial approximation error. We demonstrate that this simple model of pericardial-myocardial interaction can correctly predict the pumping mechanisms of the heart as previously assessed in clinical studies. Utilizing a pericardial model not only can provide much more realistic cardiac mechanics simulations but also allows new insights into pericardial-myocardial interaction which cannot be assessed in clinical measurements yet.

Multiphysics Modeling of the Atrial Systole under Standard Ablation Strategies.

The aim of this study was to develop a computational framework to compare the impact of standard ablation concepts on the mechanical performance of the atria, since different line combinations cannot be applied in practice to the same patient. For this purpuse, we coupled electro-mechano-hemodynamic mathematical models based on biophysical principles and simulate the contractile performance of the atria. We computed systolic pressures and volumes in two patient-specific atrial geometries (one of normal size and one hypertrophied) with various ablation concepts. We found that our computational model is able to detect the differences in the left atrial contractility and ejection fraction for various electrical activation sequences resulting from different ablation line combinations. We show that multiphysics modeling has the potential to quantify the hemodynamic performance of left atria for different ablation lines, which could be used as additional pre-operative clinical information for the choice of the ablation concept in the future.

Maximum likelihood estimation of cardiac fiber bundle orientation from arbitrarily spaced diffusion weighted images.

We propose an estimation scheme for local fiber bundle direction in the left ventricle directly from gray values of arbitrarily spaced cardiac diffusion weighted images (DWI). The approach is based on a parametric and space-dependent mathematical representation of the myocardial fiber bundle orientation and hence the diffusion tensor (DT) for the ventricular geometry. By solving a nonlinear inverse problem derived from a maximum likelihood estimator, the degrees of freedom of the fiber and DT model can be estimated from the measured gray values of the DWIs. The continuity of the DT model allows to relax the restriction to the individual DWIs to match spatially like for voxelwise DT calculation. Hence, the spatial misalignment between image slices with different diffusion encoding directions, that is encountered in-vivo cardiac imaging practice can be integrated into the estimation scheme. This feature results then in a negligible impact of the spatial misalignment on the reconstructed solution. We illustrate the methodology using synthetic data and compare it against a previously reported fiber bundle reconstruction technique. To show the potential for real data, we also present results for multi-slice data constructed from ex-vivo cardiac diffusion weighted measurements in both mono- and bi-ventricular configurations.

Material modeling of cardiac valve tissue: Experiments, constitutive analysis and numerical investigation.

A key element of the cardiac cycle of the human heart is the opening and closing of the four valves. However, the material properties of the leaflet tissues, which fundamentally contribute to determine the mechanical response of the valves, are still an open field of research. The main contribution of the present study is to provide a complete experimental data set for porcine heart valve samples spanning all valve and leaflet types under tensile loading. The tests show a fair degree of reproducibility and are clearly indicative of a number of fundamental tissue properties, including a progressively stiffening response with increasing elongation. We then propose a simple anisotropic constitutive model, which is fitted to the experimental data set, showing a reasonable interspecimen variability. Furthermore, we present a dynamic finite element analysis of the aortic valve to show the direct usability of the obtained material parameters in computational simulations.