M.Sc. Jonathan Krauß

B.Eng. Lars Dominik Ehrenfeuchter

Motivation:
Computational modeling and simulation is a promising approach to tackle cardiovascular diseases, which remain a major reason for morbidity and mortality around the world. The pumping of blood is driven by the mechanical contraction of the heart. Both processes can be modeled (continuum solid mechanics and fluid mechanics, Brenneisen et al. 2021) but their interplay is complex. Taking also comprehensive patient-specific measurements into account for the simulations is a great challenge. For example, solving parameter identification through inverse problem solutions (Kovacheva et al. 2021) incurs high computational costs in classic Finite Element Method (FEM) settings. Lattice Boltzmann Methods (LBM) are computationally more efficient and were successfully used to identify static fluid domain boundaries (Klemens et al. 2018). Their further development and application are the overall goals of this project.
Task:
The main goal of this work is the realization of a one-way-coupled fluid-structure interaction simulation of the blood flow in one half of the human heart by using Lattice Boltzmann Methods for the fluid part. To achieve this, it is first necessary to identify the relevant aspects of fluid mechanics, Lattice Boltzmann Methods and the physiology of the heart for this task. The research group on Computational Models of the Heart of the Institute of Biomedical Engineering at KIT runs simulations of the electrophysiology and the resulting mechanical deformation of the heart muscle. The resulting geometries of the heart at discrete time steps will serve as boundary conditions for the flow simulation. Therefore, it is necessary to familiarize with the format of this geometric data and convert it in a format which can be used for solving the problem with Lattice Boltzmann Methods. Since Lattice Boltzmann Methods use smaller discrete time steps, interpolation between the geometric data at its time steps is required. Thus, appropriate interpolation methods need to be researched and implemented
to interpolate between the geometric data. The chosen interpolation methods must be evaluated, requiring a suitable evaluation approach. The OpenLB framework will be used to calculate the blood flow. Thus, it is important to familiarize with homogenized Lattice Boltzmann Methods for fluid-structure interaction within this framework. Solving fluid-structure interaction problems also requires defining proper boundary conditions for the flow. Therefore, research is necessary to find suitable boundary conditions for the blood flow in the heart.
On the way to the simulation of one half of the heart, various stages of fluid-structure interaction problems should be implemented. First, a pipe with a varying diameter should be examined. Then a static sphere with an inlet and an outlet that open alternately. In a next step this sphere is deforming to simulate the movement of the heart muscle. Those cases can be either self-constructed or from literature. At last the geometries of a heart should be used for the calculations of the blood flow. First the geometry should be static and two cases should be modeled. One without valves and the other with valves. After this a deforming heart should be examined. Analogous to the static case once without the valves and once with the valves.