Yin F C, Chew P H, Zeger S L
J Biomech. 1986;19(1):27-37. doi: 10.1016/0021-9290(86)90106-5.
Delineation of the mechanical properties of biologic tissues is one of the cornerstones of biomechanics. Abundant data from uniaxial tests exist but these cannot be extrapolated to describe three-dimensional properties of tissue. Biaxial stress-strain studies have been performed using skin, blood vessels and pericardium. Quantitative description of tissue properties in these studies has employed either polynomial or exponential strain-energy functions. Interpretation of these data, however, is difficult because of wide variability of the estimated coefficients of these functions. This variability has been attributed to experimental noise, numerical instabilities in the algorithms, or to strain-history dependence. No systematic method has been proposed to evaluate the variability. This paper describes a statistically based approach to assessing the sources of and accounting for variability of coefficients in describing biaxial stress-strain data. Our data are from canine pericardium subjected to various combinations of simultaneous biaxial stretching. We first determine a suitable strain-energy function with the least number of free parameters that will fit the data reasonably. We then perform residual analysis to see if standard statistical methods can be used to assess the variability. If not, we use a nonparametric method called bootstrapping that is suitable for assessing the uncertainty in the coefficients. Using a five-parameter exponential strain-energy function, pericardial tissue is found to be strain-history dependent and anisotropic. These findings cannot be attributed to either experimental noise or instability in the numerical algorithms.
描述生物组织的力学特性是生物力学的基石之一。单轴试验已有大量数据，但这些数据无法外推以描述组织的三维特性。已经使用皮肤、血管和心包进行了双轴应力 - 应变研究。在这些研究中，对组织特性的定量描述采用了多项式或指数应变能函数。然而，由于这些函数估计系数的广泛变异性，对这些数据的解释很困难。这种变异性归因于实验噪声、算法中的数值不稳定性或应变历史依赖性。尚未提出系统的方法来评估变异性。本文描述了一种基于统计的方法，用于评估描述双轴应力 - 应变数据时系数变异性的来源并对其进行解释。我们的数据来自犬心包，其经受了同时双轴拉伸的各种组合。我们首先确定一个具有最少自由参数且能合理拟合数据的合适应变能函数。然后进行残差分析，看看是否可以使用标准统计方法来评估变异性。如果不行，我们使用一种称为自助法的非参数方法，该方法适用于评估系数的不确定性。使用五参数指数应变能函数，发现心包组织具有应变历史依赖性和各向异性。这些发现既不能归因于实验噪声，也不能归因于数值算法中的不稳定性。
