| dc.description.abstracteng | With three million people worldwide (three hundred thousand people in the United States alone) experiencing sudden cardiac arrest per year, it is one of the most common causes of death in developed countries. Ventricular fibrillation, a dysfunction of the heart characterized by a highly chaotic spatio-temporal wave dynamics, is the main cause for sudden cardiac arrest. The application of a high-energy defibrillation shock, as the current medical treatment to restore the sinus rhythm, comes along with severe side-effects, among others additional damage of the heart. Furthermore, patients with an ICD (implantable cardioverter-defibrillator) in particular suffer from posttraumatic stress symptoms.
The goal of this thesis is to investigate the dynamics of the heart (and in particular the nature of cardiac arrhythmias (specifically ventricular fibrillation)) using concepts and perceptions from the dynamical systems theory. On the basis of the interdisciplinary interplay between mathematical approaches and interaction with experimental and clinical knowledge and results, two general scientific objectives are addressed:
Derive an enhanced understanding of the dynamics during episodes of ventricular fibrillation, including the development of concepts for the improvement of current defibrillation techniques and suggestions for completely new strategies which may find their way into the clinical application. Obtain novel insights into the fundamental dynamics of complex, nonlinear systems (thus excitable systems and beyond).
These objectives are addressed using numerical simulations, which constitute the main tool to investigate specific research questions. The results of this thesis are organized in four chapters, each focusing on one specific question:
The first results chapter is dealing with the mechanism of spontaneous termination of ventricular fibrillation. We investigate the transient behavior of spiral and scroll wave dynamics using different cell models. The observed transients can be classified into the group of so called type-II supertransients. We find, that in 3D simulations, a critical thickness of the medium plays an essential role. Basic features of the simulations agree with general observations of clinicians, e.g. that larger heart muscle volumes increase the risk of cardiac arrhythmias.
In the second results chapter, we address the question whether a self-termination of a chaotic episode can be predicted. By applying small but finite perturbations to specific trajectories of chaotic spiral wave dynamics we find that the state space structure close to the “exits” of the chaotic regime changes significantly. We could verify this effect also in low-dimensional maps. This analysis shows, that although the upcoming self-termination is not visible in conventional variables, it should in principle be possible to derive such a quantity.
In the third results chapter, we investigate complexity fluctuations of the chaotic spatio-temporal dynamics in simulations using realistic heart geometries. We show, that the level of organization of the spatio-temporal dynamics can be estimated by analyzing the time series of a multi-electrode setup.
In the last results chapter, we discuss whether a successful termination of chaotic spiral wave dynamics is possible using a minimal interaction with the system. We show, that since the underlying topological object which determines the chaotic dynamics is a chaotic saddle, one can terminate the dynamics (as a proof of concept) by the application of a specific but very small perturbation.
We hope that the insights provided by this thesis contribute to the general understanding of cardiac arrhythmias and the nonlinear dynamics of complex systems. The results suggest that an improved medical treatment of cardiac arrhythmias can benefit from:
A more detailed state analysis of the dynamics during spatio-temporal chaos, incorporating diverse measure techniques (e.g. multiple-ECG measurements, CT scans, MRI scans).
An intervention strategy which should adapt to individual patients and the respective dynamical state of the heart.
A variety of new experimental approaches will be available which may help to achieve these goals and to improve the understanding of the phenomena investigated in this thesis:
Filament identification in the bulk tissue during experiments using sophisticated ultra sound techniques, inverse ECG measurements for the reconstruction of spatio-temporal wave dynamics or using techniques from optogenetics for the stimulation of cardiac tissue via light pulses are promising candidates which can have a significant impact on the field of cardiac dynamics. This technological progress in combination with novel data analysis techniques from the fields of machine learning or data assimilation and sophisticated simulations of the complex dynamics has great potential to develop advanced and efficient strategies for a patient specific medical treatment. | de |