A PDF version of the full thesis is available online, but you can also read the full contents on this website at the links below.

Dissertation presented in partial fulfillment of the requirements for the degrees of:

• Doctor of Science (PhD): Mathematics
• Doctor of Philosophy (PhD): Medicine

Institutions:

• KU Leuven, Arenberg Doctoral School, Faculty of Science
• Leiden University Medical Center (LUMC), LUMC Graduate School, Faculty of Medicine

Supervisors:

• Dr. Hans Dierckx (LUMC)
• Prof. Dr. Daniël A. Pijnappels (LUMC)
• Dr. Antoine A.F. de Vries (LUMC)
• Prof. Dr. Tom Van Doorsselaere (KU Leuven)

Members of the examination committee:

• Prof. Dr. Stefan Van Aelst (chair) (KU Leuven)
• Prof. Dr. Piet Claus (KU Leuven)
• Prof. Dr. Jasmina Magdalenić Zhukov (KU Leuven)
• Prof. Dr. Roeland Merks (Leiden University)
• Dr. Vincent Portero (LUMC)
• Prof. Dr. Maxime Sermesant (Inria, IHU Liryc, 3IA Côte d’Azur)

Abstract

Heart rhythm disorders like atrial and ventricular tachycardia and fibrillation can be treated in various ways. These arrhythmias are characterised by abnormal electrical activity in the heart such as re-entrant circuits—for instance spiral waves. Clinicians can choose from methods ranging from medication to surgical interventions like ablation or implantation of a pacemaker or defibrillator. These choices depend on a large variety of factors that, in the end, all come down to tweaking the electrical patterns to restore a healthy heart rhythm.

It is not always clear which treatment is the best for a particular patient and what outcome can be expected. The diagnosis and treatment of the cause of an arrhythmia, for instance by localisation of re-entrant circuits, is a complex process as it should also take into account the patient’s unique anatomy and physiology. This is why personalised computational models of the heart—so-called cardiac digital twins—hold great promise for the future of cardiology.

Zooming in to the level of individual heart muscle cells, creating a computational model of their electrical activity remains challenging: The response of individual cells to stimuli must be measured and combined into a model that should then be able to predict behaviour on the tissue and organ level—which can be a big leap requiring a lot of validation.

In this dissertation, we explore computational methods for personalised modelling of cardiac electrophysiology. We create software packages to numerically simulate the reaction-diffusion equations for the electrical activity of the heart. We also develop methods to detect and study re-entrant circuits in the heart as phase defects. We describe arrhythmia formation via quasiparticles in Feynman-like diagrams. Lastly, we create data-driven models for cardiac electrophysiology directly from optical voltage mapping data on monolayers—videos of the excitation waves in two-dimensional tissue samples.

While the reaction-diffusion based software package can be used for highly detailed simulations of the electrical patterns in the heart, the novel data-driven approach allows streamlined creation of models specific to individual tissue samples at much lower computational cost. Spiral wave dynamics can be predicted from just focal wave data. The phase defect approach offers a new way to study re-entrant circuits in the heart: With the quasiparticle view, we uncovered deeper insights into the mechanisms of arrhythmia formation.

The presented methods are a few steps towards the creation of fully personalised cardiac digital twins. In the future, the data-driven model creation pipeline could be used to refine a general model of the cardiac excitation waves to a patient-specific one. In conjunction with the phase defect approach, this could lead to improved diagnosis and treatment strategies for heart rhythm disorders that are truly personal.

Chapters

1. Introduction to computational modelling of cardiac excitation waves
2. The Ithildin library for efficient numerical solution of anisotropic reaction-diffusion problems in excitable media
3. Numerical methods for the detection of phase defect structures in excitable media
4. Analysis of complex excitation patterns using Feynman-like diagrams
5. Fast creation of data-driven low-order predictive cardiac tissue excitation models from recorded activation patterns
6. Steps towards true cardiac digital twins
7. Acknowledgements