Simulation of the Mechanical Behavior of White Matter Using a Micromechanics Finite Element Method
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Simulation of the Mechanical Behavior of White Matter Using a Micromechanics Finite Element Method Yi Pan, Assimina A. Pelegri Department of Mechanical and Aerospace Engineering, Rutgers, the State University of New Jersey, 98 Brett Rd., Piscataway, NJ 08854, U.S.A. David I. Shreiber Department of Biomedical Engineering, Rutgers, the State University of New Jersey, 599 Taylor Rd., Piscataway, NJ 08854, U.S.A. ABSTRACT The atypical mechanical behavior of white matter and its influence on the mechanical properties of brain tissue necessitate adoption of a mutli-scale model of white matter for accurate computational analysis. Herein, we present a micromechanical analysis coupled with finite elements into a biomechanical interacting model of white matter. A representation of the white matter of central nervous system is identified and its microstructure is generated. The geometric descriptions of the axon and the surrounding matrix are obtained from neurofilament immunohistochemistry images. Consecutively, linear elastic material constitutive models are applied to describe the behavior of axons and their surrounding matrix subjected to small deformations. This model facilitates determination of the tissue’s stress and strain fields, and enables an understanding of the effects of axon undulation on local fields. The fundamental nature of the model enables future scale-up for structural tissue analysis and predictions of axon damage at the microscale. INTRODUCTION Finite element analysis has become increasingly utilized to study traumatic brain injury (TBI) and spinal cord injury (SCI), particularly to identify the spatial-temporal evolution of stress and strain and relate the profiles to the location and severity of injury. Specifically, axonal injury represents a critical target for TBI and SCI prevention and treatment. Mechanical strain has been identified as the proximal cause of axonal injury [1], while secondary ischaemic and excitotoxic insults associated with the primary trauma potentially exacerbate the structural and functional damage. Many studies have attempted to identify the states of stress and strain in white matter using animal and finite element models [2-10]. These material models and finite element simulations of the central nervous system (CNS) soft tissues heavily depend on phenomenological representations. Accuracy of the above simulations depends not only on the correct determination of the material properties but also on the precise depiction of the tissues’ microstructure. Given the fibrous nature of axon bundles in white matter, a microstructural finite element model is necessary for an accurate representation of axon mechanics. Myelinated axons, myelinated glia, and astrocytes are the primary structural constituents in white matter that provide the tissue with mechanical integrity to prevent deformation during trauma when macroscopic loading conditions are transferred to the microscopic, cellular components. Accordingly, white matter may be treated as a “composite material”, in which the undula
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