Conventional electrocardiography (ECG) is an essential tool for investigating cardiac disorders such as arrhythmias or myocardial infarction. It consists of interpretation of potentials recorded at the body surface that occur due to the electrical activity of the heart. However, electrical signals originated at the heart suffer from attenuation and smoothing within the thorax, therefore ECG signal measured on the body surface lacks some important details. The goal of forward and inverse ECG problems is to recover these lost details by estimating the heart&amp / #8217 / s electrical activity non-invasively from body surface potential measurements. In the forward problem, one calculates the body surface potential distribution (i.e. torso potentials) using an appropriate source model for the equivalent cardiac sources. In the inverse problem of ECG, one estimates cardiac electrical activity based on measured torso potentials and a geometric model of the torso. Due to attenuation and spatial smoothing that occur within the thorax, inverse ECG problem is ill-posed and the forward model matrix is badly conditioned. Thus, small disturbances in the measurements lead to amplified errors in inverse solutions. It is difficult to solve this problem for effective cardiac imaging due to the ill-posed nature and high dimensionality of the problem. Tikhonov regularization, Truncated Singular Value Decomposition (TSVD) and Bayesian MAP estimation are some of the methods proposed in literature to cope with the ill-posedness of the problem. The most common approach in these methods is to ignore temporal relations of epicardial potentials and to solve the inverse problem at every time instant independently (column sequential approach). This is the fastest and the easiest approach / however, it does not include temporal correlations. The goal of this thesis is to include temporal constraints as well as spatial constraints in solving the inverse ECG problem. For this purpose, two methods are used. In the first method, we solved the augmented problem directly. Alternatively, we solve the problem with column sequential approach after applying temporal whitening. The performance of each method is evaluated.

The heart is a muscular organ which acts as a biomechanical pump. Electrical impulses are generated in specialized cells and flow through the heart myocardium by the ion changes on the cell membrane which is the beginning of both the electrical and the mechanical activity. Both the electrical and the mechanical states of the organ will directly affect the pumping activity. The main motivation of this thesis is to better understand physiological and pathological properties of the heart muscle via studying the electro-mechanics of the heart. This model could be used to gain better solutions of the ill-posed inverse problem of ECG and Body Surface Potential Maps (BSPM) or to estimate the electrical propagation and mechanical response on patient specific heart geometry models which can be obtained by using MRI technique. Cellular automaton technique will be used to simulate the physiological function of the left ventricle to estimate the cardiac functions. To model the heart tissue firstly the anatomical knowledge of the heart will be used such as properties of the myocardium, fiber orientations, etc. to simulate the three dimensional electrical propagation. Then the mechanical activity consisting of contraction and relaxation will be simulated according to the material properties of the heart. Using this simulation, the effects of the cardiac arrhythmias such as reentry will be generated. In this study, electrical and mechanical properties of the heart tissue are modeled for normal heart beat and heart beat in case of ischemic heart tissue. Contraction of the tissue via electrical activation has also been considered in terms of time synchronization. &ldquo / Cellular automaton&rdquo / method is used for modeling the electromechanical interactions in the heart tissue. A simplified left ventricle model is used to observe the electrical and the mechanical behavior. Using this method, both the normal heart beat&rsquo / s electrical activation and the arrhythmia excitation could be taken on, without using complex differential equations. To consider the anisotropy of the heart tissue, fiber orientations have also been added to the model. In this thesis work, electro-mechanic models at cellular, macroscopic and heart left ventricle level are presented. The electro-mechanical adaptation is performed by cellular electrophysiology and cellular force development due to intercellular excitation propagation. Varying densities of transmembrane proteins, changes on concentration of calcium, metabolic and hormonal effects are neglected. Also in simplified ventricular model the fluid mechanics and mechanoelectrical feed-back is not taken into-account.