In this paper, we adapt a previously developed poromechanical formulation to model the perfusion of myocardium during a cardiac cycle. First, a complete model is derived in 3D. Then, we perform a dimensional reduction under the assumption of spherical symmetry and propose a numerical algorithm that enables us to perform simulations of the myocardial perfusion throughout the cardiac cycle. These simulations illustrate the use of the proposed model to represent various physiological and pathological scenarios, specifically the vasodilation in the coronary network (to reproduce the standard clinical assessment of myocardial perfusion and perfusion reserve), the stenosis of a large coronary artery, an increased vascular resistance in the microcirculation (microvascular disease) and the consequences of inotropic activation (increased myocardial contractility) particularly at the level of the systolic flow impediment. Our results show that the model gives promising qualitative reproductions of complex physiological phenomena. This paves the way for future quantitative studies using clinical or experimental data.