Revealing the nonlinear mechanical behavior of white matter brain tissue by analyzing the asynchronous deformation and damage of matrix and axonal fibers

Abstract

The mechanical behavior of the brain plays a vital role in regulating brain morphology and brain function. The experimental results show that the brain tissue behaves with strong nonlinearity, heterogeneity, loading rate and direction dependence, and complicated damage behavior. However, the underlying mechanism attributed to the interlacement of extremely soft matrix and complex axonal fibers network in white matter brain tissue is still not well understood. In this work, the nonlinear mechanical behavior of white matter brain tissue is analyzed by developing a mesoscale visco-hyperelastic constitutive model that considers isotropic matrix and anisotropic axonal fibers separately. Based on the diffusion tensor imaging data, the generalized structure tensor is introduced to reflect axonal fiber's orientation and distribution characteristics in different parts of white matter. Furthermore, the damage models of matrix and axonal fibers are established to characterize their damage evolution differences. In particular, a damage initiation criterion based on the equivalent strain of axonal fibers stretch is proposed by analogy with the Tsai-Hill criterion, according to the distribution characteristics of axonal fibers. Then the mesoscale constitutive model is applied to reveal the effects of matrix and axonal fibers on the deformation and damage of white matter. On the one hand, it is found that the “S-shaped” nonlinear stress curve of white matter in uniaxial tension is the superposition of the convex stress curve of matrix and the “J-shaped” stress curve of axonal fibers, and the nonlinearity is stronger with the increase of strain rate. On the other hand, with the change of the distribution of axonal fibers from uniaxially oriented to dispersed, the anisotropy of white matter caused by the stress reinforcement of axonal fibers gradually evolves from transverse isotropy to isotropy. With the increase of strain rate, the reinforcement effect of axonal fibers tends to be more isotropic, and the proportion of isotropic matrix stress is increased, resulting in the isotropic tendency of white matter. Moreover, the asynchrony of matrix and axonal fibers damage also results in the complex transition of white matter deformation behavior. Along with the increase of deformation, the anisotropic mechanical behavior of white matter rapidly degenerates to isotropy with the damage of axonal fibers. Overall, the strong coupling of nonlinear, anisotropic, and strain rate-dependent mechanical behaviors of white matter is well explained by combining the asynchronous deformation and damage of matrix and axonal fibers in this study. It will help understand brain injury, brain growth and development, physiological brain diseases, and other relevant problems.