We propose a method for the analysis of cardiac images with the goal of reconstructing the motion of the ventricular walls. The main feature of our method is that the inversion parameter field is the active contraction of the myocardial fibers. This is accomplished with a biophysically-constrained, four-dimensional (space plus time) formulation that aims to complement information that can be gathered from the images by a priori knowledge of cardiac mechanics. Our main hypothesis is that by incorporating biophysical information, we can generate more informative priors and thus, more accurate predictions of the ventricular wall motion. In this paper, we outline the formulation, discuss the computational methodology for solving the inverse motion estimation, and present preliminary validation using synthetic and tagged MR images. The overall method uses patient-specific imaging and fiber information to reconstruct the motion. In these preliminary tests, we verify the implementation and conduct a parametric study to test the sensitivity of the model to material properties perturbations, model errors, and incomplete and noisy observations.