Modelling poroelastic fluid-structure interaction in the heart using a hybrid immersed boundary/finite element framework

Correspondence *Xiaoyu Luo, School of Mathematics and Statistics, University of Glasgow, UK. Email: xiaoyu.luo@glasgow.ac.uk Abstract Cardiac function relies on the continuous flow of blood through the coronary arteries to perfuse the heart muscle. The use of porous media and poroelasticity is now widely regarded as the standard approach to model cardiac perfusion. Cardiac tissue as a saturated porous medium mainly contains the pore fluid (blood) and the “skeleton”, such as myocytes and collagen scaffold. Fluid-structure interaction in the heart has been studied by a number of groups, but in many cases, the myocardium is assumed to be a hyperelastic fibre-reinforced material. On the other hand, studies that treat the myocardium as a poroelastic material typically neglect the interaction between the myocardium and ventricular blood flow. In this work, we present an immersed-boundary/finite-element framework to model the dynamic left ventricle in a three-phase poroelastic system, namely, pore blood fluid, skeleton, and chamber blood fluid.We demonstrate there although it is possible to track velocity of either the skeleton or the mixture in the IB/FE framework, the latter allows us to couple with the Darcy systemmore straightforwardly. We benchmark our approach by examining a pair of prototypical poroelastic formations using a simple cubic geometry, as introduced in the work by Chapelle et al1. This cubic case also enable us to compare the differences between system behaviour when using isotropic and anisotropic skeletons. Finally wemodel the poroelastic dynamics for a three-dimensional left ventricle geometry, in which the skeleton of myocardium obeys the Holzapfel–Ogden model2. The results are compared with that of a corresponding hyperelastic left ventricle model studied previously.