Fluid-structure interaction simulations of the human heart
Date:
Mathematical and computational modeling is ever-present in the physical sciences and in engineering. The development of models for physiological processes that are credible and predictive is considered a great challenge. Their variability and complexity make accurate modeling and simulation an ambitious goal. However, a reliable physiological model that would provide detailed information could possibly be utilized for clinical decision making and patient treatment. Cardiac models have long been a domain of high interest for investigation, generating and testing hypotheses, and experimental design. There are hundreds of publications involving models attempting to simulate the behavior of the cardiac activity.
This talk is concerned with the simulation of the dilation of the left ventricle during the diastolic phase. To this aim the two goals that have to be addressed are: 1) the reconstruction of patient-specific cardiac mesh models from CT scan data, and 2) the numerical simulation of the interaction between blood and the surrounding wall tissue. In this work a fictitious domain method is adopted whose main idea is to model the solid structure as immersed in a background fluid grid. The coupling between the fluid and the solid problems is achieved by means of an overlapping domain decomposition method in conjunction with an L2-projection approach, thus using a Lagrange multiplier field to weakly enforce a velocity vector constraint along the interface-boundary between the solid and the fluid. The FSI framework is first validated by means of a benchmark configuration describing the self induced oscillating deformations of two elastic beams in a flow channel and then utilized to simulate the interaction between the blood and the wall of the left ventricle.