The electrical activities in living tissues are caused by ionic movements along cell membranes, particularly in excitable tissues like neurons, cardiac cells, and skeletal muscles. The heart muscles produce currents that flow through the tissue in the body's volume conductor. These currents generate potentials and magnetic field that are measurable at and beyond the thorax surface using detectors. Researchers have been studying these electrical activities by modeling their electrophysiology. This research work discusses the different approaches to model electrical activities of the heart. One challenge in this area is developing algorithms to visualize or localize cardiac anomalies non-invasively. This requires a prior forward model that represents the spatial relationship between the heart and the detectors. Traditional forward models assume the locations and strengths of the current sources but not their orientations, leading to potential inaccuracies or misinterpretations in inverse calculations. Further, this work introduces a novel method for constructing the forward matrix by constraining prior heart vectors scaled with time varying information of activation sequences. The resulting spatial matrix is used to locate hidden abnormal sources in the myocardium through solving the inverse problem. The inverse problem is extended to identify ventricular anomalies by modeling ruptured nodes in specific heart regions.