We propose a method for the analysis of Magnetic Resonance (MR) 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 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 and electrophysiology. 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 results using synthetic data. We integrate an in-house spatially non-uniform octree meshing scheme with an adjoint-based inversion solver. The overall method uses pat...