Action potential of a cardiac cell membrane and its conduction in the cardiac tissue provide a basis of the electrophysiological function of the heart through the cardiac excitation-contraction coupling mechanism. Towards a better and a quantitative understanding of electrophysiological mechanisms of the reentrant cardiac arrhythmias at cellular, tissue, and organ levels, mathematical models of cardiac cells, tissues, and the heart have been developed and analyzed by simulating conduction of action potentials in a variety of conditions. However it is inevitable for those models to become large scale in the number of dynamical variables, requiring immense amount of computational time for their dynamic simulations. In this study, an analog-digital hybrid circuit model of electrical excitation of a cardiac cell based on Luo-Rudy phase I (LR-I) model, a typical mathematical model of a cardiac cell was developed. Through its hardware implementation, real-time simulations of the cellular excitations as well as their propagation in a cardiac tissue model have been performed with the hybrid circuit model. This thesis is organized as follows. It is started with a general introduction in Chapter 1. The research background is discussed in Chapter 2, where physiology of the heart and the mechanism of electrical system which controls the cardiac contraction are elaborated. These are then followed by explaining the basis of knowledge on electrical potentials that exist across cell membranes and describing how they are modeled. Computational techniques of mathematical modeling and hardware-implemented circuits that have been developed over past few decades in understanding the dynamics of cells and excitationconduction are also reviewed especially in cardiac cell modeling. Chapter 3 is focusing on the work presented in a single cell model, where a design method of the analog-digital hybrid circuit cell is overviewed, followed by details of the analog-digital hybrid active circuit. The design method of current-voltage (I-V ) relationships between ion currents and the membrane potential reproduced by analog and digital circuits is also explained. Furthermore, action potential of the hybrid circuit model is initiated by an external stimulus and the result is compared to the result of the LR-I model. Action potential generation of the hybrid circuit model in response to periodic current impulse trains with different interval (period) T are carried out and comparisons to the result from the LR-I model are presented. Classification of excitation response patterns on the parameter plane spanned by the period T and the intensity A of the impulse trains 1 in the hybrid model and LR-I model are analyzed, and the results between the two models are also compared. According to the simulations results, the action potential characteristics of the hybrid cell model and the LR-I cell model are comparable as the hybrid cell model generally well reproduces the I-V relationships of ion currents described in the LR-I model, as well as the action potential waveform, and the excitation dynamics in response to periodic current impulse trains with various intervals and intensity levels. In Chapter 4, the work on investigating the spatio-temporal dynamics and control of reentrant action potential conduction in active cable models is being reviewed. Manner and underlying mechanisms in the initiation of the reentrant action potential conduction in a one dimensional ring-topology-network of the hybrid active circuit cable model are constructed as a model of anatomical reentrant tachycardia. Dynamics of the hybrid active circuit cable model are then compared with those in the numerical simulation of the LR-I cable model. Resetting and annihilation of the reentrant wave under the influence of single and sequence of stimulations are investigated by using the hybrid cable model and comparisons to the result from the LR-I cable model are carried out. Resetting and annihilation of the reentrant wave are of crucial importance in clinical situations where the reentrant cardiac arrhythmias are often controlled and terminated by delivering electrical stimulations to the heart through catheters. Phase resetting curves (PRCs) of both models are presented to show the relationship between the phase reset of the reentry and the phase of single stimulation. According to the PRCs, sequential phase resetting by periodic stimulation that leads to annihilations of the reentry are predicted and illustrated with onedimensional discrete Poincare mappings. As the results in the simulations of the reentrant action potential conduction, quantitative correspondence between the hybrid cable model and the LR-I cable model was demonstrated using a one dimensional active cable as a model of the anatomical reentry in a cardiac tissue with various conditions. Those include (1) unidirectional block to initiate reentry, (2) phase resetting by single impulsive stimulations, (3) annihilations of the reentry by appropriately timed single stimulations, (4) phase resetting curves (PRCs) that can characterize the reentry dynamics in response to single stimulations at various timings, and (5) sequential phase resetting that leads to annihilation of the reentry as predicted by the one dimensional discrete Poincare mappings. Finally, general discussion and conclusions are being reviewed in Chapter 5. The overall results of the hybrid circuit model are satisfied with those of the LR-I model, corresponding to the subjects examined in the study. Therefore, by taking into account the satisfactory results and the real-time simulation capability of the hybrid model, these can be concluded that the hybrid model might be a useful tool for large scale simulations of cardiac tissue dynamics, as an alternative to numerical simulations, toward further understanding of the reentrant mechanisms. As a matter of fact, minimizing power consumption and physical size of the circuits need to put into consideration regarding to large-scale development of the hybrid model
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