Implicit Partitioned Cardiovascular Fluid-Structure Interaction of the Heart Cycle Using Non-newtonian Fluid Properties and Orthotropic Material Behavior

Although image-based methods like MRI are well-developed, numerical simulation can help to understand human heart function. This function results from a complex interplay of biochemistry, structural mechanics, and blood flow. The complexity of the entire system often causes one of the three parts to be neglected, which limits the truth to reality of the reduced model. This paper focuses on the interaction of myocardial stress distribution and ventricular blood flow during diastole and systole in comparison to a simulation of the same patient-specific geometry with a given wall movement (Spiegel, Stromungsmechanischer Beitrag zur Planung von Herzoperationen, 2009). The orthotropic constitutive law proposed by Holzapfel et al. (Philos. Trans. R. Soc. Lond. Ser. A, 367: 3445-3475, 2009) was implemented in a finite element package to model the passive behavior of the myocardium. Then, this law was modified for contraction. Via the ALE method, the structural model was coupled to a flow model which incorporates blood rheology and the circulatory system (Oertel, Prandtl-Essentials of Fluid Mechanics, 3rd edn, Springer Science + Business Media, 2010; Oertel et al., Modelling the Human Cardiac Fluid Mechanics, 3rd edn, Universitatsverlag Karlsruhe, 2009). Comparison reveals a good quantitative and qualitative agreement with respect to fluid flow. The motion of the myocardium is consistent with physiological observations. The calculated stresses and the distribution are within the physiological range and appear to be reasonable. The coupled model presented contains many features essential to cardiac function. It is possible to calculate wall stresses as well as the characteristic ventricular fluid flow. Based on the simulations we derive two characteristics to assess the health state quantitatively including solid and fluid mechanical aspects.