Zhang Wei, Kassab Ghassan S
Department of Biomedical Engineering, IUPUI, Indianapolis, IN 46202, USA.
Biomaterials. 2007 Feb;28(6):1307-15. doi: 10.1016/j.biomaterials.2006.10.022. Epub 2006 Nov 16.
A comprehensive understanding of the mechanical properties of blood vessels is essential for vascular physiology, pathophysiology and tissue engineering. A well-known approach to study the elasticity of blood vessels is to postulate a strain energy function such as the exponential or polynomial forms. It is typically difficult to fit experimental data to derive material parameters for blood vessels, however, due to the highly nonlinear nature of the stress-strain relation. In this work, we generalize the strain definition to absorb the elastic nonlinearity and then propose a two-dimensional bilinear stress-strain relation between second Piola-Kirchhoff stress and the new strain measure. The model is found to represent the Fung's exponential model very well. The novel linearized constitutive relation simplifies the determination of material constants by reducing the nonlinearity and provides a clearer physical interpretation of the model parameters. The limitations of the constitutive model and its implications for vascular mechanics are discussed.
全面了解血管的力学特性对于血管生理学、病理生理学和组织工程至关重要。一种研究血管弹性的著名方法是假设一个应变能函数，如指数形式或多项式形式。然而，由于应力 - 应变关系的高度非线性性质，通常很难将实验数据拟合以得出血管的材料参数。在这项工作中，我们推广了应变定义以吸收弹性非线性，然后提出了第二皮奥拉 - 基尔霍夫应力与新应变度量之间的二维双线性应力 - 应变关系。结果发现该模型能很好地代表冯氏指数模型。这种新颖的线性化本构关系通过减少非线性简化了材料常数的确定，并为模型参数提供了更清晰的物理解释。讨论了本构模型的局限性及其对血管力学的影响。
