Characterizing the behavior of water diffusion within a volume element (voxel) provides a means for describing inner microstructure at a cellular scale, taking into account experimental diffusion times and apparent diffusion coefficients measured in muscle. The mean square displacement of water molecules is close to the dimensions of cells of the order of microns. As muscle, and meat, is highly organized in a fibrillar structure, the diffusion of water is facilitated in the fiber direction. We therefore modeled this anisotropic diffusion voxelwise using ellipsoid by means of a first order tensor, according to Diffusion Tensor Imaging (DTI). We also applied this modeling at different degrees of diffusion sensitization (given by the b-value). New diffusion parametric maps were obtained on tissue that have been registered with high-resolution anatomical images obtained by MRI and histology to put in obvious relationships between meat microstucture and diffusion parameter observed at a meso-scale. Diffusion decays were measured at a mesoscopic scale. From these data, first order tensor fitting at each b-value, and subsequent diagonalisation revealed a diffusion reference frame in an anisotropic medium. Maps of diffusion parameters (e.g. eigenvalues or trace of the diffusion tensor, diffusion anisotropy, difference between mono and multi-exponential fits) were superimposed on anatomical images, i.e. histological and high-resolution susceptibility-weighted MR images (SWI), revealing structural details which do not appear in SWI.