Relationship between structural modeling and hyperelastic material behavior: application to CNS white matter

Abstract

Recent measurements of the material properties of brain tissue allow an examination of the underlying microstructural basis in both physiological and pathophysiological conditions. The purpose of this study is to develop a mathematical relationship between microstructurally based models of the central nervous system (CNS) white matter and equivalent hyperelastic material models. For simplicity, time dependent material behavior is not included in this formulation. The microstructural representation is used to formulate structural property relationships for highly oriented white matter, and is mathematically compared to one isotropic and two anisotropic hyperelastic formulations. For the anisotropic characterizations, the population of axons in the white matter is assumed to align along one preferred direction of the material, yielding a transversely isotropic formulation. Relatively simple strain-energy functions incorporating material anisotropy provide sufficient flexibility to model the nonlinear behavior predicted from structurally based models, although the tangential stiffness of the hyperelastic approaches does not follow completely the behavior of the structurally based formulations. This analysis is an initial step towards linking microstructural aspects of the tissue to material models commonly used for large deformations, and may be an important step in relating predicted tissue deformation to the deformation and stress of cellular and subcellular structures.

Altered collagen fiber kinematics define the onset of localized ligament damage during loading

“…Strain is a common metric used to localize injury and define tissue tolerances (1,5,9,14,24,25,31) and is often used as a criterion in finite-element (11,12,26) and computational (7,22,28,47) models to predict injury. However, the use of strain for these purposes may not always be appropriate for biological tissues in which macroscale measurements do not translate to similar microscale strain values.…”

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

“…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]. Continuum-based nonlinear material descriptions are also available to correlate with these structurallybased material models [87,89]. With their continuum formulation, the integration of these models into existing finite element software packages is possible.…”

“…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]. Continuum-based nonlinear material descriptions are also available to correlate with these structurallybased material models [87,89].…”

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“…Proposed models include the hyperelastic white matter constitutive model of Meaney [16] or the nonlinear transversely isotropic viscoelastic model of Ning et al [17]. In hyperelastic models of a transversely isotropic material, the strain energy is a function of the invariants (I 1 , I 2 , I 3 ) of a finite deformation strain tensor, and also of the "pseudoinvariants" (I 4 , I 5 ) that are invariant to rotation about the normal to the plane of isotropy [18].…”