An approach to quantification of biaxial tissue stress-strain data.
An approach to quantification of biaxial tissue stress-strain data.
复制标题
双轴组织应力应变数据的量化方法。
DOI：
10.1016/0021-9290(86)90106-5
复制
发表时间：
1986
影响因子：
2.4
通讯作者：
Zeger,SL
中科院分区：
文献类型：
--
作者：
Yin,FC;Chew,PH;Zeger,SL
生物组织力学性质的描述是生物力学的基石之一。来自单轴试验的大量数据是存在的，但这些数据不能外推来描述组织的三维特性。使用皮肤、血管和心包进行了双向应力-应变研究。在这些研究中，组织属性的定量描述采用了多项式或指数应变能函数。然而，这些数据的解释是困难的，因为这些函数的估计系数具有很大的可变性。这种可变性被归因于实验噪声、算法中的数值不稳定性或应变历史相关性。目前还没有提出系统的方法来评估这种可变性。本文描述了一种基于统计学的方法来评估在描述双向应力-应变数据时系数的来源和变异性。我们的数据来自于同时双轴拉伸的不同组合的犬心包。我们首先确定了一个合适的应变能函数，其中自由参数的个数最少，可以合理地拟合数据。然后，我们进行残差分析，看看是否可以使用标准的统计方法来评估变异性。如果没有，我们使用一种称为Bootstrapping的非参数方法，该方法适用于评估系数中的不确定性。使用五参数指数应变能函数，心包组织被发现是应变历史相关和各向异性的。这些发现既不能归因于实验噪声，也不能归因于数值算法的不稳定性。
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.