A. Daub, A. Loewe, and B. Frohnapfel. Haemodynamics in an elasto-mechanic model of the human heart. In Annual Scientific Conference of the International Association of Applied Mathematics and Mechanics, 2018
Numerical modelling enables a quantitative evaluation of physiological and patho-physiological relationships within the human heart and the circulatory system. Surgical planning and optimisation of medical equipment using a virtual heart become possible by merging of empirical studies with physical and mathematical knowl- edge. These goals motivate a multi-physical coupling between electro-physiology, elasto-mechanics, blood flow and the circulatory system. In a first step a one-way coupling of all four relevant physical domains is considered. Simulation of electro- physiological excitation spread in conjunction with excitation contraction coupling yields the spatio-temporal distribution of cardiac active tension. This, as well as a closed loop model of the circulatory system, drive the continuum mechanics simulation of cardiac deformation and pressure, which in turn serve as a boundary condition for blood flow simulation. Physiological blood flow dynamics are dominated by the formation of a ring vortex that washes out the ven- tricles and thereby reduces the risk of thrombogenesis and flow stasis. This process is strongly affected by the heart valves. However, including the three dimensional leaflets and their interaction with the blood flow is computationally expensive. Further, the effort for construction is not negligible. Therefore, a simpler model is implemented as a first step. It comprises of three layers of porous cells that move with the valve plane and time dependently block or open the plane respectively. First results illustrate a high potential of the model to reliably reproduce the physiological vortex formation in the ventricles.