Within this work, we investigate how physiologically observed microstructural changes induced by myocardial infarction impact the elastic parameters of the heart. We use the LMRP model for poroelastic composites (Miller and Penta in Contin Mech Thermodyn 32:1533–1557, 2020) to describe the microstructure of the myocardium and investigate microstructural changes such as loss of myocyte volume and increased matrix fibrosis as well as increased myocyte volume fraction in the areas surrounding the infarct. We also consider a 3D framework to model the myocardium microstructure with the addition of the intercalated disks, which provide the connections between adjacent myocytes. The results of our simulations agree with the physiological observations that can be made post-infarction. That is, the infarcted heart is much stiffer than the healthy heart but with reperfusion of the tissue it begins to soften. We also observe that with the increase in myocyte volume of the non-damaged myocytes the myocardium also begins to soften. With a measurable stiffness parameter the results of our model simulations could predict the range of porosity (reperfusion) that could help return the heart to the healthy stiffness. It would also be possible to predict the volume of the myocytes in the area surrounding the infarct from the overall stiffness measurements.