A primarily Eulerian means of applying left ventricle boundary conditions for the purpose of patient-specific heart valve modeling

Patient-specific multi-physics simulations have the potential to improve the diagnosis, treatment, and scientific inquiry of heart valve dynamics. It has been shown that the flow characteristics within the left ventricle are important to correctly capture the aortic and mitral valve motion and corresponding fluid dynamics, motivating the use of patient-specific imaging to describe the aortic and mitral valve geometries as well as the motion of the left ventricle (LV). The LV position can be captured at several time points in the cardiac cycle, such that its motion can be prescribed a priori as a Dirichlet boundary condition during a simulation. Valve leaflet motion, however, should be computed from soft-tissue models and incorporated using fully-coupled Fluid Structure Interaction (FSI) algorithms. While FSI simulations have in part or wholly been achieved by multiple groups, to date, no high-throughput models have been developed, which are needed for use in a clinical environment. This project seeks to enable patient-derived moving LV boundary conditions, and has been developed for use with a previously developed immersed boundary, fixed Cartesian grid FSI framework. One challenge in specifying LV motion from medical images stems from the low temporal resolution available. Typical imaging modalities contain only tens of images during the cardiac cycle to describe the change in position of the left ventricle. This temporal resolution is significantly lower than the time resolution needed to capture fluid dynamics of a highly deforming heart valve, and thus an approach to describe intermediate positions of the LV is necessary. Here, we propose a primarily Eulerian means of representing LV displacement. This is a natural extension, since an Eulerian framework is employed in the CFD model to describe the large displacement of the heart valve leaflets. This approach to using Eulerian interface representation is accomplished by applying “morphing” techniques commonly used in the field of computer graphics. For the approach developed in the current work, morphing is adapted to the unique characteristics of a Cartesian grid flow solver which presents challenges of adaptive mesh refinement, narrow band approach, parallel domain decomposition, and the need to supply a local surface velocity to the flow solver that describes both normal and tangential motion. This is accomplished by first generating a skeleton from the Eulerian interface representation, and deforming the skeleton between image frames to determine bulk displacement. After supplying bulk displacement, local displacement is determined using the Eulerian fields. The skeletons are also utilized to automate the simulation setup to track the locations upstream and downstream where the system inflow/outflow boundary conditions are to be applied, which in the current approach, are not limited to Cartesian domain boundaries.