A framework for multi-physics simulations using four-chamber cardiac models
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Computational cardiac models have been extensively used to study different cardiac biomechanics; specifically, finite-element analysis has been one of the tools used to study the cardiac wall's internal stresses and strains during the cardiac cycle. Cubic-Hermite finite element meshes have been used for simulating cardiac biomechanics due to their convergence characteristics and their ability to capture smooth geometries compactly- fewer elements are needed to build the cardiac geometry-compared to linear tetrahedral meshes. Such meshes have previously been used only with simple ventricular geometries with non-physiological boundary conditions due to challenges associated with creating cubic-Hermite meshes of the complex heart geometry. However, it is critical to accurately capture the different geometric characteristics of the heart and apply physiologically equivalent boundary conditions to replicate the in vivo heart motion. In this work, we created a four-chamber cardiac model utilizing cubic-Hermite elements and simulated a full cardiac cycle by coupling the 3D finite element model with a lumped circulation model. The myocardial fiber-orientations were interpolated within the mesh using the Log-Euclidean method to overcome the singularity associated with the interpolation of orthogonal matrices. Physiologically equivalent rigid body constraints were applied to the nodes along the valve plane. The accuracy of the resulting simulations was validated using open source clinical data. Based on this validated four-chamber model, we studied different disease states and complex interactions of the different boundary conditions on the cardiac function. We simulated a complete cardiac cycle of a heart with the acute myocardial infarction. We also assessed the effect of the Myocardial Infarction and Pericardium sac on the ventricular pumping ability and cardiac motion, respectively.A fluid-structure interaction (FSI) simulation on the left cardiovascular system (including the left ventricle, atria, and the aorta) was also performed using a hybrid ALE/IMGA framework. The Arbitrary Lagrangian-Eulerian method models the left chambers' moving walls. The immersogeometric analysis couples the bioprosthetic heart valves with the intraventricular and interatrial flow. The simulation results show two openings for the Mitral valve, one major and one minor, during the cardiac cycle due to the atrial kick. The reproduction of these detailed hemodynamics and structural features of the cardiac cycle demonstrates the ability of our framework to replicate the in-vivo hemodynamics of the left cardiovascular system.