- Nominated as an outstanding Ph.D. thesis by the University of Göttingen, Germany
- Investigates cardiac dynamics and its control from an entirely new perspective
- Reveals new mechanisms of arrhythmia development and control
- Demonstrates first systematic application of nonlinear dynamics tool (Lyapunov stability analysis) to excitable media
- Results facilitate the development and optimization of low-energy defibrillation therapies, potentially improving quality of life and as preventive measure
This award-winning thesis investigates the mechanisms underlying cardiac arrhythmia development and termination from an entirely new perspective. By viewing the heart as a complex system, the author uses theoretical tools from nonlinear dynamics combined with numerical simulations and experiments to achieve insights into the relationship between its structure and dynamics, thereby paving the way towards innovative low-energy defibrillation strategies. The work tackles, among other things: the effect of substrate heterogeneity on the spatial-temporal dynamics of cardiac arrhythmias and ways in which weak pulsed electric fields can be used to control these dynamics in heterogeneous cardiac tissue.
The long-term vision of this research is to replace the current strategy of applying painful and sometimes tissue damaging electric shock – currently the only reliable way to terminate life-threatening fibrillation – by a more subtle but equally effective intervention. The book maps out a number of promising research directions for biophysicists and medical researchers working on the origins and treatment of cardiac arrhythmias.
Table of Contents1 Introduction
- 1. Anatomyof the Heart
- 1.2 Physiology of the Heart
- 1.2.1 Cardiomyocytes
- 1.2.2 Cell-to-Cell Coupling
- 1.3 Structural Heterogeneity
- 1.4 Arrhythmias
- 1.5 Antiarrhythmic Therapies
1.6 Complexityin Structureand Dynamics - 1.7 This Thesis
References
2 Methods
- 2.1 Mathematical Background
- 2.1.1 Single Cell Dynamics
- 2.1.2 Bi-domain Description of Cardiac Tissue
- 2.1.3 Mono-domain Descriptions of Cardiac Tissue
- 2.1.4 Anisotropy
- 2.1.5 The Phase-Field Method
- 2.1.6 Models
- 2.1.7 Spiral Tips and Phase Singularities
- 2.1.8 Lyapunov Stability Analysis
- 2.2 Numerical Implementation
- 2.2.1 Time Stepping Scheme
- 2.2.2 Diffusion Term
- 2.2.3 Boundary Conditions
- 2.2.4 Stability Considerations
- 2.2.5 Spiral Tip Detection
- 2.2.6 Lyapunov Exponents and Vectors
- 2.2.7 Hardware,Software,Parallelization
- 2.3 Experimental Methods
- 2.3.1 Set up and Tissue Preparation
- 2.3.2 Optical Imaging
- 2.3.3 Electric-Field Stimulation Experiments
- 2.3.4 Signal Processing:Activation Maps
- References
3 Results
3.1 Quantification of Dynamical Complexityin Heterogeneous
Excitable Media- 3.1.1 Plane Waves
- 3.1.2 Rigidly Rotating Spiral Waves
- 3.1.3 Multiple Spiral Waves
- 3.1.4 Transition to Meandering
- 3.1.5 Circular Heterogeneities
- 3.1.6 Random Heterogeneities
- 3.1.7 Heterogeneitiesin Spatio-Temporal Chaos
- 3.1.8 Brief Summary
- 3.2 Sensitivity of Curved Tissue Boundaries to Electric-Field Stimulation
- 3.2.1 Theoretical Framework
- 3.2.2 Set up of Numerical Simulations
- 3.2.3 Generic Propertiesof Induced Membrane Potential Changes
- 3.2.4 Tissue Domains of Different Dimension
- 3.2.5 Curvature Dependencein Cell Culture Experiments
- 3.2.6
- Definition of Boundary Curvature
- 3.2.7 Flat Boundaries
- 3.2.8 Circular Boundaries
- 3.2.9 Semi-circular Protuberances
- 3.2.10 Parabolic Boundaries
- 3.2.11 Inherently Three-Dimensional Boundaries
- 3.2.12 Boundary Effects in Full Numerical Simulations
- 3.2.13 Influence of Finite Pulse Duration
- 3.2.14 Brief Summary
- 3.3 Heterogeneity-Induced Wave Sources in Low-Energy Defibrillation
- 3.3.1 Hypothesis
- 3.3.2 Theoretical Framework
- 3.3.3 Blood Vessel Size Distributions
- 3.3.4 Activation Times
- 3.3.5 Linking Structure and Function
- 3.3.6 Universality of Activation Time Scaling
- 3.3.7 Brief Summary
- References
4 Conclusion
- 4.1 Summary
- 4.2 Discussion and Outlook
- 4.3 Concluding Remarks
- References
Appendix A: Modeling Details
Appendix B: Supplementary Data
Appendix C: Media Sim— An Open Framework for Simulating Extended Systems
Curriculum Vitae
Index
