Directional hyperelasticity of transversely isotropic white matter tissue under tension-compression

Mechanical structure of fibrous tissues is well recognized as key player in modulating their functionality. Regional and directional mechanical properties of brain white matter mainly originate from anisotropic arrangement of its axonal fibers. Mechanics-driven computational models provide powerful means in studying the tissue mechanics. However, appropriate constitutive modeling and dependable material identification are critical for a reliable simulation. Because of the complex structure and properties of the white matter, material models have mostly been calibrated under certain loadings. This paper presents a systematic study on directional characterization of the corpus callosum in the axial (axonal) and transverse directions under tensile-compressive loading. In either direction analytical formulations for the Cauchy stresses are derived for nine hyperelastic models, and verified using a previously validated micromechanical finite element model. Material characterization is conducted using two one-way regressions (i.e. tension-only and compression-only regressions) and a full-range tension-compression regression to examine which approach is more appropriate for directional characterization. Results of tension-only regression indicated that all models fail to predict the tissue responses under axial compression. With the compression-only regression, however, the generalized Ogden can well predict the tissue response under axial tension. Nevertheless, neither of the one-way approaches was successful in full-range transverse stress prediction. Interestingly, with the full-range regression in the axial direction, the generalized Ogden and polynomial models could well capture the stress responses in both tension and compression, although they are rather less fitted in transverse direction. Generally, the goodness of fits was better in full-range regression in both directions.