Uncertainty Quantification for Fluid-Structure Interaction: Application to Aortic Biomechanics

Abstract

Diseases of the cardiovascular system count to the most common causes of death in the developed countries. There are many open research questions with respect to a better understanding for example of the physiology of the heart and the main arteries or to the determination of the factors for aneurysm or stenosis development of the aorta. Furthermore, on a daily basis, a heart surgeon has to estimate the probability of success for different treatment scenarios as opposed to no intervention. In recent decades, methods of investigation with living probands (in vivo) and artificial experiments (in vitro) have been complemented more and more by computational methods and simulation (in silico). In particular, numerical simulations have the capability to enhance medical imaging modalities with additional information. However, to date, the biomechanical simulation of aortic blood flow given an uncertain data situation represents a major challenge. So far, mostly deterministic models have been used, Yet, measurement data for the configuration of a simulation is subject to measurement inaccuracies. For the choice of model parameters, which are non-measurable in a living body, often imprecise information is available only. In this work, novel development steps for a numerical framework are presented aiming for the simulation and evaluation of aortic biomechanics using methods of Uncertainty Quantification (UQ). The work includes the modelling of the aortic biomechanics as a fluid-structure interaction (FSI) problem with uncertain parameters. By means of a subject-specific workflow, the simulation of different probands, phantoms and, ultimately, patients is enabled. For the solution of the complex partial differential system of equations, they are discretised with the finite element method (FEM) and a novel, parallelly efficient and problem-specific solver is developed. To verify the numerical framework implemented in the course of this work, a novel analytically solvable benchmark for UQ-FSI problems is proposed. Furthermore, the numerical framework is validated by means of a prototypical aortic phantom experiment. Finally, the UQ-FSI simulation enables the evaluation of a stress overload probability. This novel parameter is exemplarily evaluated by means of the simulation of a human aortic bow. Therewith, this work represents a new contribution to aspects of the development of simulation methods for the investigation of aortic biomechanics.