Models of cardiac mechanics are increasingly used to investigate cardiac physiology. These models are characterized by a high level of complexity, including the particular anisotropic material properties of biological tissue and the actively contracting material. A large number of independent simulation codes have been developed, but a consistent way of verifying the accuracy and replicability of simulations is lacking. To aid in the verification of current and future cardiac mechanics solvers, this study provides three benchmark problems for cardiac mechanics. These benchmark problems test the ability to accurately simulate pressure-type forces that depend on the deformed objects geometry, anisotropic and spatially varying material properties similar to those seen in the left ventricle and active contractile forces. The benchmark was solved by 11 different groups to generate consensus solutions, with typical differences in higher-resolution solutions at approximately 0.5%, and consistent results between linear, quadratic and cubic finite elements as well as different approaches to simulating incompressible materials. Online tools and solutions are made available to allow these tests to be effectively used in verification of future cardiac mechanics software.
Orientations of myocytes impact electric excitation propagation and mechanical contraction in the human heart. Measured fiber angles in experiments are obtained from different species (e. g. rat, canine, dog, human heart) and vary by various reasons. It is unclear to what ex- tent non-exact fiber angles impact the quality of computa- tional simulations. In this paper, mechanical simulations with different ventricular angles were performed and com- pared. The simulations covered the complete heart with both ventricles, both atria and the pericardium and were performed using finite element method. Helix angles were varied between 20\0 and 70\0 on endocardium and \070\0 and \020\0 on epicardium. Results showed that fiber ori- entations had only a minor contribution to the difference between endsystolic and enddiastolic pressure of < 8.3 %. The influence on stroke volume as well as AVPD is sig- nificant (changes by 34 % for SV and 241 % for APVD) , but it could not be observed that a higher AVPD yields a higher stroke volume. Concludingly, fiber orientations are important for reliable computational simulations of human hearts and should be incorporated with great care.
L. Baron, A. Loewe, and O. Dössel. From clinics to the virtual beating heart a general modeling workflow for patient-specific electromechanical heart simulations. In BMTMedPhys 2017, vol. 62(S1) , pp. S70, 2017
Generating meshes of complex structures in the human body like the heart organ is a prerequisite for computational simulations of of organ function. The quality of the conclusions derived from these simulations greatly depends on the quality and accuracy of the mesh they are based on. Volumetric computation domain can be represented by an equally-spaced voxel grid, or – in case of more sophisticated partial differential equation discretization methods (finite elements, finite volumes) – first, second or even higher order tetrahedral meshes. Here, we present a workflow that is capable of creating high quality meshes for such simulations. The workflow contains segmentation, surface mesh generation, volume mesh generation, and patient-specific parameter fitting to produce the desired results. While segmentation itself is a more or less unique mapping from a grayscale DICOM data set to a labeled, three-dimensional voxel mesh, different approaches exist for their transformation to a surface mesh. Our process involves a two-level approach for obtaining triangular or mixed rectangular surface meshes of desired quality and resolution. Both are crucial for the next step: obtaining a volumetric tetrahedral grid with the desired degrees of freedom. In the last step, a derivative-free parameter estimation approach is used to calibrate the dynamic behavior and tailor the model patient-specifically. All software used in the workflow is published under open source licenses and freely available. Its capability is demonstrated by means of an elastomechanical simulation of a human heart and yields measurable validation quantities in physiological ranges. We want to stress that the presented approach is generic and can easily be used for the model generation of other organs like liver, lungs or the aortic arch as well. The resulting meshes can be used for various types of simulations (electrical excitation propagation, blood flow) and use cases (clinical diagnostics, therapy planning etc.).
The human heart is an organ of high complexity and hence, very challenging to simulate. To calculate the force developed by the human heart and therefore the tension of the muscle fibers, accurate models are necessary. The force generated by the cardiac muscle has physiologically imposed limits and depends on various characteristics such as the length, strain and the contraction velocity of the cardiomyocytes. Another characteristic is the activation time of each cardiomyocyte, which is a wave and not a static value for all cardiomyocytes. To simulate a physiologically correct excitation, the functionality of the cardiac simulation framework CardioMechanics was extended to incorporate inhomogeneous activation times. The functionality was then used to evaluate the effects of local activation times with two different tension models. The active stress generated by the cardiomyocytes was calculated by (i) an explicit function and (ii) an ode-based model. The results of the simulations showed that the maximum pressure in the left ventricle dropped by 2.3% for the DoubleHill model and by 5.3% for the Lumens model. In the right ventricle the simulations showed similar results. The maximum pressure in both the left and the right atrium increased using both models. Given that the simulation of the inhomogeneously activated cardiomyocytes increases the simulation time when used with the more precise Lumens model, the small drop in maximum pressure seems to be negligible in favor of a simpler simulation model.
S. Schuler, L. Baron, A. Loewe, and O. Dössel. Developing and coupling a lumped element model of the closed loop human vascular system to a model of cardiac mechanics. In BMTMedPhys 2017, vol. 62(S1) , pp. S69, 2017
Modelling the interaction of the heart and the vascular system allows to study the pumping efficiency of the heart in a controlled environment under various cardiac and vascular conditions such as arrhythmias, dyssynchronies, regions of stiffened myocardium, valvular stenoses or decreased vascular compliances. To pose realistic hemodynamic boundary conditions to a four-chambered elastomechanical heart model, we developed a lumped element model of the closed loop human vascular system. Systemic and pulmonary circulations were each represented by a three-element Windkessel model emptying into a venous compliance. Both circulations were coupled by connecting the venous compliances to the corresponding atrium via venous resistances. Cardiac valves were represented by ideal diodes and resistances. Strong coupling between the heart and the vascular system model was accomplished by estimating the cardiac pressures that lead to continuous flows across the model interfaces. Active regulatory mechanisms were not considered. Pressures, flows and volumes throughout the circulatory system were simulated until a steady state was reached and the effects of model parameters on these hemodynamic parameters were evaluated in a sensitivity analysis. Increasing the systemic peripheral resistance by 50% caused an 8% decrease in stroke volume (SV) and a 33% increase in mean arterial pressure. Increased venous resistance descreased the E/A wave ratio of the atrioventricular flow and led to a reduced SV by impeding passive cardiac filling. Increasing the arterial compliance decreased mean cardiac pressures, while only slightly reducing the SV. Larger arterial resistances mainly caused higher peak systolic pressures. Furthermore, we show that embedding the heart model into surrounding elastic tissue by forcing permanent contact at the pericardial surface leads to more realistic time courses of atrial volumes and atrial pressure-volume curves composed of an A and a V loop as found in measurements. In conclusion, this work enables simulations of diseases that involve significant cardiovascular interaction.