Experimental studies  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.
- Bioengineering Division
Anisotropic Behavior of White Matter in Shear and Implications for Transversely Isotropic Models
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Okamoto, RJ, Feng, Y, Genin, GM, & Bayly, PV. "Anisotropic Behavior of White Matter in Shear and Implications for Transversely Isotropic Models." Proceedings of the ASME 2013 Summer Bioengineering Conference. Volume 1A: Abdominal Aortic Aneurysms; Active and Reactive Soft Matter; Atherosclerosis; BioFluid Mechanics; Education; Biotransport Phenomena; Bone, Joint and Spine Mechanics; Brain Injury; Cardiac Mechanics; Cardiovascular Devices, Fluids and Imaging; Cartilage and Disc Mechanics; Cell and Tissue Engineering; Cerebral Aneurysms; Computational Biofluid Dynamics; Device Design, Human Dynamics, and Rehabilitation; Drug Delivery and Disease Treatment; Engineered Cellular Environments. Sunriver, Oregon, USA. June 26–29, 2013. V01AT10A002. ASME. https://doi.org/10.1115/SBC2013-14039
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