Optimized Load-Independent Hyperelastic Microcharacterization of Human Brain White Matter

Abstract

A micromechanical methodology combined with genetic algorithm (GA) as a global optimization method is used to find the material properties of axons and extracellular matrix (ECM) in corpus callosum which is a part of human brain white matter. Studies have shown that axons are highly oriented in the ECM which enables us to approximate brain white matter as a unidirectional fibrous composite model. Using the one-term Ogden hyperelastic constitutive equations for the constituents and knowing the mechanical response of corpus callosum, GA optimization procedure is used in conjunction with finite element (FE) micromechanical analysis to find optimal material parameters for axon and ECM in three uniaxial loading scenarios of tension, compression, and simple shear. Moreover, by simultaneous fitting to the three loading modes' responses and applying Nelder–Mead simplex optimization method, best-fit parameters are found. The best-fit parameters can be used to approximate the behavior of axons and ECM in different uniaxial loading conditions with the minimum error and hence, can be interpreted as load-independent parameters. Micromechanical simulations by best-fit parameters show maximum stress increase of 2% and 29% for tension and shear and less than 1% reduction for compression mode compared to the case where optimal parameters are used. The findings and the methodology of this study can be employed for constitutive modeling of axonal fibers and its implementation in human head FE model where load-independent parameters are needed for simulating different loading scenarios.