Relationship between structural modeling and hyperelastic material behavior: application to CNS white matter
Relationship between structural modeling and hyperelastic material behavior: application to CNS white matter
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DOI：
10.1007/s10237-002-0020-1
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发表时间：
2003-04-01
影响因子：
3.5
通讯作者：
Meaney, D. F.
中科院分区：
文献类型：
--
作者：
Meaney, D. F.
最近对脑组织材料特性的测量可以检查生理和病理生理条件下的潜在微观结构基础。本研究的目的是建立中枢神经系统 (CNS) 白质微观结构模型与等效超弹性材料模型之间的数学关系。为简单起见，此公式中不包括时间相关的材料行为。微观结构表示用于制定高度定向白质的结构特性关系，并在数学上与一种各向同性和两种各向异性超弹性公式进行比较。对于各向异性特征，假设白质中的轴突群体沿着材料的一个优选方向排列，从而产生横向各向同性的公式。尽管超弹性方法的切向刚度并不完全遵循基于结构的公式的行为，但结合材料各向异性的相对简单的应变能函数提供了足够的灵活性来对基于结构的模型预测的非线性行为进行建模。该分析是将组织的微观结构方面与通常用于大变形的材料模型联系起来的第一步，并且可能是将预测的组织变形与细胞和亚细胞结构的变形和应力联系起来的重要步骤。
Recent measurements of the material properties of brain tissue allow an examination of the underlying microstructural basis in both physiological and pathophysiological conditions. The purpose of this study is to develop a mathematical relationship between microstructurally based models of the central nervous system (CNS) white matter and equivalent hyperelastic material models. For simplicity, time dependent material behavior is not included in this formulation. The microstructural representation is used to formulate structural property relationships for highly oriented white matter, and is mathematically compared to one isotropic and two anisotropic hyperelastic formulations. For the anisotropic characterizations, the population of axons in the white matter is assumed to align along one preferred direction of the material, yielding a transversely isotropic formulation. Relatively simple strain-energy functions incorporating material anisotropy provide sufficient flexibility to model the nonlinear behavior predicted from structurally based models, although the tangential stiffness of the hyperelastic approaches does not follow completely the behavior of the structurally based formulations. This analysis is an initial step towards linking microstructural aspects of the tissue to material models commonly used for large deformations, and may be an important step in relating predicted tissue deformation to the deformation and stress of cellular and subcellular structures.