A theoretical model of the cross-linking topology of ventricular muscle tissue is developed. Using parameter estimation the terms of the theoretical model are estimated for normal and pathological conditions. The model represents the anisotropic structure of the tissue, reproduces published experimental data and characterizes the role of different tissue components in the observed macroscopic behavior. Changes in the material parameters are consistent with expected structural changes and the model is extended to reproduce force-Calcium relationships. Model results are invoked to argue that semisoft behavior and the material axis anisotropy arise from the constraints on the extracellular matrix cross-linking topology.