A computational study of invariant I5 in a nearly incompressible transversely isotropic model for white matter |
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| Institution: | 1. Center for Molecular Imaging and Nuclear Medicine, School of Radiological and Interdisciplinary Sciences (RAD-X), Soochow University, Collaborative Innovation Center of Radiation Medicine of Jiangsu Higher Education Institutions, Suzhou, Jiangsu 215123, China;2. School of Mechanical and Electronic Engineering, Soochow University, Suzhou, Jiangsu 215021, China;3. School of Electronic and Information Engineering, Soochow University, Suzhou, Jiangsu 215021, China;4. Thayer School of Engineering, Dartmouth College, Hanover, NH 03755, USA;5. School of Aerospace and Mechanical Engineering, The University of Oklahoma, Norman, OK 73019, USA;6. Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, TX 78712, USA;1. School of Mathematics, Cardiff University, Senghennydd Road, Cardiff CF24 4AG, UK;2. Chair for Nonlinear Analysis and Modelling, Fakultät für Mathematik, Universität Duisburg-Essen, Thea-Leymann Sraß e 9, 45141 Essen, Germany;1. Center for Cardiovascular Simulation, Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, Texas;2. Department of Agricultural and Biological Engineering, Mississippi State University, Mississippi State, Starkville, Mississippi;3. Medtronic, Minneapolis, Minnesota;1. Center for Cardiovascular Simulation, Institute for Computational Engineering and Sciences (ICES), Department of Biomedical Engineering, The University of Texas at Austin, 201 East 24th Street, POB 5.236, 1 University Station C0200, Austin, TX 78712, USA;2. Cardiac Rhythm Disease Management (CRDM) Clinical Specialist, Medtronic, Minneapolis, MN 55432, USA;3. Gorman Cardiovascular Research Group, University of Pennsylvania, 3400 Civic Center Blvd, Philadelphia, PA 19104, USA;1. School of Mathematics, Cardiff University, Senghennydd Road, Cardiff CF24 4AG, UK;2. Mathematical Institute, University of Oxford, Woodstock Road, Oxford OX2 6GG, UK |
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| Abstract: | The aligned axonal fiber bundles in white matter make it suitable to be modeled as a transversely isotropic material. Recent experimental studies have shown that a minimal form, nearly incompressible transversely isotropic (MITI) material model, is capable of describing mechanical anisotropy of white matter. Here, we used a finite element (FE) computational approach to demonstrate the significance of the fifth invariant (I5) when modeling the anisotropic behavior of white matter in the large-strain regime. We first implemented and validated the MITI model in an FE simulation framework for large deformations. Next, we applied the model to a plate-hole structural problem to highlight the significance of the invariant I5 by comparing with the standard fiber reinforcement (SFR) model. We also compared the two models by fitting the experiment data of asymmetric indentation, shear test, and uniaxial stretch of white matter. Our results demonstrated the significance of I5 in describing shear deformation/anisotropy, and illustrated the potential of the MITI model to characterize transversely isotropic white matter tissues in the large-strain regime. |
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| Keywords: | White matter Biomechanics Constitutive modeling of biomaterials Finite element methods Tissue mechanics |
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