Robin Willems

The integration of patient-specific computational models into clinical practice is a viable step forward in enhancing clinical treatment and improving the fundamental understanding of diseases. Clinically integrated models should be robust, provide meaningful, accurate, and timely feedback, and reduce the costs associated with (a.o.) the time spent by the clinician in diagnosis and/or treatment. One potential clinical application of such models involves the treatment of ventricular tachycardia (VT), a life-threatening heart rhythm disorder caused by an erratic electrophysiological response. To study potential mechanisms involved in VTs, new methods are required that enable high-fidelity analyses in a computationally efficient and accurate manner. Additionally, incorporating these methods into the clinical workflow should allow for the rapid output of indicators that support clinical decision-making.

The goal of this dissertation is twofold: (i) To develop a computationally robust, efficient, and accurate framework that provides a basis to investigate potential mechanisms of VTs, subject to varying input, particularly regarding geometric data. It should be assessed whether this cardiac analysis framework, based on the Isogeometric Analysis (IGA) paradigm, offers significant benefits compared to the traditional finite element (FE) approach. (ii) To move toward a clinically integrated model, a reduced-order model should be developed that limits computation costs, while providing quantitative indicators of the cardiac behavior accompanied by a measure of uncertainty.

To accomplish the first objective, the developed model considers an IGA-based workflow, which is the integration of spline-based geometry parametrization into higher-order numerical analyses. In this dissertation, the development of three innovative modules is discussed: A template-geometry module, a geometry-fit module, and a cardiac-analysis module. The template-geometry module parametrizes an idealized left- or bi-ventricle using Non-Uniform Rational B-Splines (NURBS). This module relies on a multi-patch representation of the ventricle(s), allowing for an analysis-suitable geometry. The geometry-fit module deforms an arbitrary spline-based template geometry, given data of any structure and/or density. Within the context of the IGA workflow, this module is applied to the left ventricle template, subject to sparse echocardiogram data obtained from the clinic. The cardiac-analysis module solves the cardiac mechanics and circulatory-system dynamics in a monolithic manner. The code is set up such that additional sub-models, i.e., fiber-field definitions, constitutive laws, and circulatory models, can be easily implemented. The analysis module also supports the options of myocardial infarction analysis and treatment analyses, such as ablation therapy.

The second objective is addressed using a reduced-order modeling framework. This framework leverages the IGA-based full-order model results to train and enrich the parameters of an established semi-analytical model using Bayesian inference. It interpolates new parameter values using Gaussian Processes. Once properly trained, the reduced-order model provides a cardiac response within specified uncertainty bounds in a fraction of the time required for the full-order simulations.

The developed workflow was benchmarked against cardiac mechanics results of a healthy and diseased or infarcted idealized patient, which were obtained from an established FE cardiac analysis. Global pump and local fiber strain results were virtually indiscernible for both cases in the limit of mesh convergence. However, the IGA-based workflow exhibited superior mesh convergence properties. The workflow has been thoroughly used to investigate a strain-based mechanism of VT by coupling it to a dedicated electrophysiological solver. The proposed reduced-order modeling framework has been shown to be an effective tool to provide rapidly evaluated indicators of the cardiac response, including uncertainty bounds.

The developed methods enhance the ability to test new hypotheses in cardiac mechanics, particularly those that require multiple computations or the incorporation of additional physics. This accelerates computational research of various disease treatments, ultimately benefiting clinical research. Furthermore, the developed framework can be extended to more advanced cardiac models and, in principle, is also applicable to other engineering fields.