In this study, we propose a computational characterization technique for obtaining the material properties of axons and extracellular matrix (ECM) in human brain white matter. To account for the dynamic behavior of the brain tissue, data from time-dependent relaxation tests of human brain white matter in different strain rates are extracted and formulated by a visco-hyperelastic constitutive model consisting of the Ogden hyperelastic model and the Prony series expansion. Through micromechanical finite element simulation, a derivative-free optimization framework designed to minimize the difference between the numerical and experimental data is used to identify the material properties of the axons and ECM. The Prony series expansion parameters of axons and ECM are found to be highly affected by the Prony series expansion coefficients of the brain white matter. The optimal parameters of axons and ECM are verified through micromechanical simulation by comparing the averaged numerical response with that of the experimental data. Moreover, the initial shear modulus and the reduced shear modulus of the axons are found for different strain rates of 0.0001, 0.01, and 1 s⁻¹. Consequently, first- and second-order regressions are used to find relations for the prediction of the shear modulus at the intermediate strain rates.

The applied procedure for characterization of brain white matter micro-level constituents. The macro-level experimental data in different strain rates are used in the context of simulation-based optimization to obtain the properties of axons and extracellular matrix material.

在这项研究中，我们提出了一种计算表征技术，用于获得人脑白质中轴突和细胞外基质（ECM）的材料特性。为了说明脑组织的动态行为，使用由Ogden超弹性模型和Prony级数展开组成的粘-超弹性本构模型，提取并制定了不同应变速率下人脑白质的时间依赖性松弛测试的数据。通过微机械有限元模拟，设计用于最小化数值数据与实验数据之间差异的无导数优化框架来识别轴突和ECM的材料特性。发现轴突和ECM的Prony级数膨胀参数受脑白质的Prony级数膨胀系数的很大影响。通过比较平均数值响应与实验数据的平均数值响应，通过微机械仿真验证了轴突和ECM的最佳参数。此外，轴突的初始剪切模量和减小的剪切模量在0.0001、0.01和1 s的不同应变速率下被发现^-1。因此，使用一阶和二阶回归来找到用于预测中等应变速率下的剪切模量的关系。

表征脑白质微量成分的应用程序。在基于模拟的优化中使用了不同应变率下的宏观实验数据，以获得轴突和细胞外基质材料的特性。