Development of constitutive models that connect tissue function and local tissue structure require local quantitative structural data. Ideally, we are interested in methods for full 3D tissues that can also be potentially used for in vivo studies. Diffusion tensor magnetic resonance imaging (DT-MRI) is a particularly attractive non-invasive method for in vivo tissue structure; based on the observation that the apparent diffusivity of water is greatest along the dominant structural feature orientations (e.g. fibers). DT-MRI permits determination of the dominant orientation of structured tissue within a single image voxel, and thus provides local structural information at the high spatial resolution. With respect to developing mathematical formulations of material models, DTMRI is particularly attractive in that it produces a symmetric second rank tensor diffusion tensor D that represents the local tissue anisotropic structure in a compact form. In the present study we developed a universal approach for ex vivo tested 3D myocardium tissue modeling based on use of the full form of D, that is all six independent components, and not just the eigendirections as in past studies. he approach included separate extensional/compression and shear-like interactions terms. To develop the necessary mathematical forms we utilized a neural network approach trained using pure-shear loading paths. This approach allowed us to utilize an overall hyperelastic form that included separate contributions from directional extension/compression and more complex shear-normal interaction terms. From the NN results, a final analytical model form was formulated and model parameters determined using the same data sets. The approach was tested on two full triaxial mechanical datasets for myocardium and human breast tissue. The resultant constitutive model was able to simulate the unique anisotropic tension/compression behaviors, including directionally dependent non-linearities. The constitutive model was validated in two steps. First, we used the model to predict D and compared it measured DTMRI, which compared very well. Secondly, validation of the predictive capabilities of the model were demonstrated by accurate predictions of tissue in simple compression, also showing good agreement. The present modeling approach was able to predict 3D mechanical behavior accurately, as well as shed insight into connections to the underlying tissue microstructure.