Measurements of mechanical anisotropy in brain tissue and implications for transversely isotropic material models of white matter

White matter in the brain is structurally anisotropic, consisting largely of bundles of aligned, myelin-sheathed axonal fibers. White matter is believed to be mechanically anisotropic as well. Specifically, transverse isotropy is expected locally, with the plane of isotropy normal to the local mean fiber direction. Suitable material models involve strain energy density functions that depend on the I-4 and I-5 pseudo-invariants of the Cauchy-Green strain tensor to account for the effects of relatively stiff fibers. The pseudo-invariant I-4 is the square of the stretch ratio in the fiber direction; I-5 contains contributions of shear strain in planes parallel to the fiber axis. Most, if not all, published models of white matter depend on I-4 but not on I-5. Here, we explore the small strain limits of these models in the context of experimental measurements that probe these dependencies. Models in which strain energy depends on I-4 but not I-5 can capture differences in Young's (tensile) moduli, but will not exhibit differences in shear moduli for loading parallel and normal to the mean direction of axons. We show experimentally, using a combination of shear and asymmetric indentation tests, that white matter does exhibit such differences in both tensile and shear moduli. Indentation tests were interpreted through inverse fitting of finite element models in the limit of small strains. Results highlight that: (1) hyperelastic models of transversely isotropic tissues such as white matter should include contributions of both the I-4 and I-5 strain pseudo-invariants; and (2) behavior in the small strain regime can usefully guide the choice and initial parameterization of more general material models of white matter. (c) 2013 Elsevier Ltd. All rights reserved.