UCLA

Cardiac arrhythmias are a leading cause of death worldwide. Notably, the electrophysiologiy and microstructural requirements for a fatal ventricular arrhythmia remain incompletely understood, thereby the treatment remains largely empirical. Standard antiarrhythmic drug therapy has failed to reduce, and in some instances has increased, the incidence of Sudden Cardiac Death (SCD). Hence, a more complete understanding of the mechanisms that foment a fatal arrhythmia is needed and computational models offer an excellent way to test hypotheses about various changes to cellular electrophysiology and myocardial microstructure in a manner not easily achieved in experiments. The understanding of associated deformation is also a longstanding research field; to some extent it provides the paradigm of a complex system, as it incorporates several mathematical issues such as geometric and material nonlinearity, complex geometrical and material data, fluid-structure interaction, that are already challenging by themselves without even mentioning the social relevance of the problem.

This thesis is concerned with the development of a unified formulation of cardiac electromechanics. The computational requirements for physiologically and numerically accurate computational analysis of the coupled equations of cardiac electrophysiology and finite-deformation contractile mechanics are carefully examined. The validation criterion which needs to be satisfied by any generic model are laid out.

The voltage evolution in the heart is obtained by solving the reaction diffusion monodomain equations. The convergence properties of finite-element procedures, employing various combinations of different shape functions, quadrature methods, and operator splitting strategies are studied which place the most stringent limitations on mesh resolution. Computational speedup is achieved preferential by row-sum lumping of the capacitance and mass matrices. However, selective lumping of these matrices can have noticeable effects on the convergence.

Finite element model of a rabbit ventricle is developed using Diffusion Tensor(DT) - MRI images. His-Bundle is included in the model to provide the correct activation sequence. Different geometries of the conduction system are analyzed comparing the obtained activation pattern and six lead electrocardiogram (ECG). The ventricular model is further validated by reproducing scroll wave break up.

Cardiac excitation coupling is modeled using an active deformation formulation based on Calcium dynamics. Analysis of the formulation of the active part of the deformation gradient and its dependence on Calcium concentration is studied. Effects of material models and inclusion of fiber anisotropy are also studied. Using a simplified ellipsoid model with assumed fiber orientation consistent with commonly used values in literature we successfully reproduce the twisting action and 60% volume reduction which is typically observed in experiments.