In this Master thesis we aim at studying some physiological and computational aspects of the excitation-contraction mechanisms in the heart muscle. This phenomenon exhibits many complexities at different spatio-temporal scales. The relevance and applicability of several recent phenomenological and physiologically detailed ionic models will be assessed. The choice of the treated models is based on an equilibrium between results that manage to reproduce correctly the complexity of the cardiac electrophysiology and a weak computational cost in order to solve the large set of ODEs which describe the dynamics of that ionic model. The preferred models include a large part of the more recent electrophysiological discoveries and understandings (e.g. L-type calcium and ryanodine channels) in order to reproduce at best the electrical conduction in the human cardiac tissue based on different experimental or computational measurements. According to these previous remarks, we will perform a thorough testing and quantitative comparison of these models and mechanical activation mechanisms in the framework of the LifeV finite element library. In a second step, a recent model for the description of crossbridge dynamics will be implemented. The importance of using good ionic models makes sense to identify correctly the possible influence on the muscle mechanics activation, which enable the heart to pump blood throughout the entire circulatory system.