Anisotropic Behavior of White Matter in Shear and Implications for Transversely Isotropic Models

Abstract

Experimental studies [1] have shown that white matter (WM) in the brain is mechanically anisotropic. Based on its fibrous structure, transversely isotropic (TI) material models have been suggested to capture WM behavior. TI hyperelastic 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 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 WM depend on I4 but not on I5.