A micromechanical hyperelastic modeling of brain white matter under large deformation.

A finite element based micromechanical model has been developed for analyzing and characterizing the microstructural as well as homogenized mechanical response of brain tissue under large deformation. The model takes well-organized soft tissue as a fiber-reinforced composite with nonlinear and anisotropic behavior assumption for the fiber as well as the matrix of composite matter. The procedure provides a link between the macroscopic scale and microscopic scale as brain tissue undergoes deformation. It can be used to better understand how macroscopic stresses are transferred to the microstructure or cellular structure of the brain. A repeating unit cell (RUC) is created to stand as a representative volume element (RVE) of the hyperelastic material with known properties of the constituents. The model imposes periodicity constraints on the RUC. The RUC is loaded kinematically by imposing displacements on it to create the appropriate normal and shear stresses. The homogenized response of the composite, the average stresses carried within each of the constituents, and the maximum local stresses are all obtained. For each of the normal and shear loading scenarios, the impact of geometrical variables such as the axonal fiber volume fraction and undulation of the axons are evaluated. It was found that axon undulation has significant impact on the stiffness and on how stresses were distributed between the axon and the matrix. As axon undulation increased, the maximum stress and stress in the matrix increased while the stress in the axons decreased. The axon volume fraction was found to have an impact on the tissue stiffness as higher axon volume fractions lead to higher stresses both in the composite and in the constituents. The direction of loading clearly has a large impact on how stresses are distributed amongst the constituents. This micromechanics tool provides the detailed micromechanics stresses and deformations, as well as the average homogenized behavior of the RUC, which can be efficiently used in mechanical characterization of brain tissue.

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

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.