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A diffusion tensor imaging (DTI) -based statistical micromechanical model was developed to study the effect of axonal fiber architecture on the inter- and intra-regional mechanical heterogeneity of the white matter. Three characteristic regions within the white matter, i.e., corpus callosum, brain stem, and corona radiata, were studied considering the previous observations of locations of diffuse axonal injury. The embedded element technique was used to create a fiber-reinforced model, where the fiber was characterized by a Holzapfel hyperelastic material model with variable dispersion of axonal orientations. A relationship between the fractional anisotropy and the dispersion parameter of the hyperelastic model was used to introduce the statistical DTI data into the representative volume element. The FA-informed statistical micromechanical models of three characteristic regions of white matter were developed by deriving the corresponding probabilistic measures of FA variations. Comparison of the model predictions and experimental data indicated a good agreement, suggesting that the model could reasonably capture the inter-regional heterogeneity of white matter. Moreover, the standard deviations of experimental results correlated well with the model predictions, suggesting that the model could capture the intra-regional mechanical heterogeneity for different regions of white matter.

This study presents a novel statistical volume element (SVE) for micromechanical modeling of the white matter structures, with histology-informed randomized distribution of axonal tracts within the extracellular matrix. The model was constructed based on the probability distribution functions obtained from the results of diffusion tensor imaging as well as the histological observations of scanning electron micrograph, at two structures of white matter susceptible to traumatic brain injury, i.e. corpus callosum and corona radiata. A simplistic representative volume element (RVE) with symmetrical arrangement of fully alligned axonal fibers was also created as a reference for comparison. A parametric study was conducted to find the optimum grid and edge size which ensured the periodicity and ergodicity of the SVE and RVE models. A multi-objective evolutionary optimization procedure was used to find the hyperelastic and viscoelastic material constants of the constituents, based on the experimentally reported responses of corpus callosum to axonal and transverse loadings. The optimal material properties were then used to predict the homogenized and localized responses of corpus callosum and corona radiata. The results indicated similar homogenized responses of the SVE and RVE under quasi-static extension, which were in good agreement with the experimental data. Under shear strain, however, the models exhibited different behaviors, with the SVE model showing much closer response to the experimental observations. Moreover, the SVE model displayed a significantly better agreement with the reports of the experiments at high strain rates. The results suggest that the randomized fiber architecture has a great influence on the validity of the micromechanical models of white matter, with a distinguished impact on the model's response to shear deformation and high strain rates. Moreover, it can provide a more detailed presentation of the localized responses of the tissue substructures, including the stress concentrations around the low caliber axonal tracts, which is critical for studying the axonal injury mechanisms.