A micromechanical procedure for modelling the anisotropic mechanical properties of brain white matter

Abstract

This paper proposes a micromechanics algorithm utilising the finite element method (FEM) for the analysis of heterogeneous matter. The characterisation procedure takes the material properties of the constituents, axons and extracellular matrix (ECM) as input data. The material properties of both the axons and the matrix are assumed to have linear viscoelastic behaviour with a perfect bonding between them. The results of the modelling have been validated with experimental data with material white input from brainstem by considering the morphology of brainstem in which most axons are oriented in longitudinal direction in the form of a uniaxial fibrous composite material. The method is then employed to examine the undulations of axons within different subregions of white matter and to study the impact due to axon/matrix volume fractions. For such purposes, different unit cells composed of wavy geometries and with various volume factions have been exposed to the six possible loading scenarios. The results will clearly demonstrate the undulation and axon volume fraction impacts. In this respect, undulation affects the material stiffness heavily in the axon longitudinal direction, whereas the axons' volume fraction has a much greater impact on the mechanical properties of the white matter in general. Also the results show that the created stresses and strains in the axons and matrix under loading will be impacted by undulation change. With increase in undulation the matrix suffers higher stresses when subjected to tension, whereas axons suffer higher stresses in shear. The axons always exhibit higher stresses whereas the matrix exhibits higher strains. The evaluated time-dependent local stress and strain concentrations within a repeating unit cell of the material model are indicative of the mechanical behaviour of the white tissue under different loading scenarios.

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

“…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].…”

Blast and the Consequences on Traumatic Brain Injury-Multiscale Mechanical Modeling of Brain

“…Publication #s: [6], [7], [12], [22], [23] In Figure 16 (a), a histology slide is shown which represents the axonal distribution inside the brainstem. The conventional hexagonal packing of the axons within the composite tissue is used to represent the repetitive distribution of axons inside the extracellular matrix.…”

“…Publication #s: [6], [7], [12], [22], [23] The response of the tissue composed of ECM and axon subject to stretch has been examined. In Figure 17, the composite with different values of axonal concentration (V f ) due to a uniaxial stretch in the axon direction.…”

“…Publication #s: [6], [7], [12], [22], [23] Diffuse axonal injury (DAI) is a devastating type of brain injury. DAI is characterized by microscopic damage to axons throughout the white matter of the brain and focal lesions in the corpus callosum and rostral brainstem.…”

Micromechanics of diffuse axonal injury: influence of axonal orientation and anisotropy

“…Computational mechanical modeling of the brain at the cellular level has been done to some extent (Arbogast and Margulies 1999; Khoshgoftar et al 2007;Abolfathi et al 2009;Karami et al 2009). These studies were mainly focused on the relation between the tissue-level mechanical behavior and the cellular-level structures.…”