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

Abstract

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 I4 and I5 pseudo-invariants of the Cauchy–Green strain tensor to account for the effects of relatively stiff fibers. The pseudo-invariant I4 is the square of the stretch ratio in the fiber direction; I5 contains contributions of shear strain in planes parallel to the fiber axis. Most, if not all, published models of white matter depend on I4 but not on I5. 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 I4 but not I5 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 I4 and I5 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.

The Mechanics of Traumatic Brain Injury: A Review of What We Know and What We Need to Know for Reducing Its Societal Burden

“…In selected studies, the regional and local anisotropic variation in brain material properties was examined [76][77][78][79][80][81]. At small strains, the relative stiffness of highly oriented brain stem samples showed modest anisotropy [81].…”

“…In some cases, existing material models gleaned from the composite materials community can help assist in interpreting anisotropic material behavior [79,80]. Some models of the white matter already suggest how different cell types may couple to each other and propose how structural elements of the tissue interact in complex manner to expose a subpopulation of axons to high mechanical loading [86][87][88][89][90].…”

RETRACTED: Experimental and numerical study on the mechanical behavior of rat brain tissue

“…Indeed, soft biological tissue is proven to be represented well by the Ogden formulation and most of the mechanical test data available for brain tissue in the literature fits with an Ogden hyperelastic function. 5,10,16,35,36 Finally, the Ogden hyperelastic constants have been implemented into our FE model to indicate a very good consistency of constitutive modeling which originates from a fairly suitable assumption in the behavior of brain tissue with FE modeling outcomes ( Figure 3). The FE results for longitudinal ( Figure 3a) and circumferential ( Figure 3b) loading directions, interestingly, depicted fairly good agreement with the experimental results as there are 18.21% and 35.96% variation, respectively.…”

Fitted hyperelastic parameters for Human brain tissue from reported tension, compression, and shear tests

“…In experimental studies, brain tissue has shown a nonlinear, viscoelastic, and anisotropic, mechanical behavior (Feng et al, 2013;Miller and Chinzei, 1997;Prevost et al, 2011). In addition, it is a highly compliant material, which makes its mechanical characterization a challenging task.…”