Noise and complexity of transmembrane potential in three-dimensional cardiac tissue using cellular excitable and bidomain continuous models

This dissertation investigates the propagation of transmembrane potential in three-dimensional cardiac tissue using excitable cellular automata and a continuous bidomain model. Different coupling regimes are found in cellular automata for the stability of scroll waves. The role of noise is discussed and autonomous stochastic resonance is discovered not only in the sub-threshold regime but in the suprathreshold regime. Virtual ECGs are developed to reveal the signature of stochastic resonance. In the continuous model, a new computational formula is developed to solve the bidomain equations efficiently. A semi-implicit method for the finite difference equations is adopted in the three-dimensional bidomain model with rotational anisotropy and realistic boundary conditions with blood layer. An O(n) iterative linear solver is embedded and the performance is measured. The three-dimensional potential fields are visualized by extracting equipotential surfaces and two-dimensional cross sections along different axes. Finally, it is suggested that the computational tool developed in this dissertation has pushed cardiac bidomain simulations to the limit where the observation and study of fibrillation and defibrillation become possible. The tremendous speed-up will allow full three-dimensional simulations of cardiac tissue for seconds after an electric defibrillation attempt, giving us important clues about what stimuli can achieve the best possible results.