Vorp D A, Rajagopal K R, Smolinski P J, Borovetz H S
University of Pittsburgh, Department of Surgery, PA 15261, USA.
J Biomech. 1995 May;28(5):501-12. doi: 10.1016/0021-9290(94)00012-s.
Characterization of the constitutive behavior of normal and pathological blood vessel segments could provide the clinician with a means to predict the onset and assess the severity of certain vascular maladies. Many of the constitutive models that have been proposed to date either fail to properly consider certain features of the anatomic structure and function of vascular tissue or are so mathematically complex that their utilization is intractable. We have developed a material identification technique that first required the adaptation and validation of a constitutive law describing the nonlinear, three-dimensional behavior of orthotropic, compressible, hyperelastic vascular segments. By coupling a nonlinear finite element program and experimental data with a robust nonlinear least-squares regression algorithm, a set of elastic parameters (moduli) is obtained. Regressions on data for a canine carotid artery and rabbit infrarenal aorta yielded coefficients of variation of 0.21 and 0.08, respectively. The estimated moduli demonstrated certain trends found by other investigators: both the canine carotid artery and rabbit aorta were found to be stiffer radially than circumferentially, and the former was found to be stiffer circumferentially than longitudinally. Using these material constants and measured arterial pressures, the stress distribution was computed for each specimen. The predicted radial stress was consistent with a transmural variation of approximately--p (applied luminal pressure) to approximately zero in both specimens, while the circumferential stresses ranged from 2.2p to 0.7p for the canine carotid, and from 6.4p to 3.7p for the rabbit aorta. The stress distributions qualitatively agreed with those reported in previous investigations, as well as with certain physiologic observations. Based on the results of our two sample cases, we believe that our technique could be beneficial to the assessment of the three-dimensional, anisotropic behavior of vascular tissue.
对正常和病变血管段本构行为的表征可为临床医生提供一种手段，用以预测某些血管疾病的发作并评估其严重程度。迄今为止提出的许多本构模型要么未能恰当考虑血管组织解剖结构和功能的某些特征，要么在数学上过于复杂以至于难以应用。我们开发了一种材料识别技术，该技术首先需要对描述正交各向异性、可压缩、超弹性血管段非线性三维行为的本构定律进行调整和验证。通过将非线性有限元程序和实验数据与强大的非线性最小二乘回归算法相结合，获得了一组弹性参数（模量）。对犬颈动脉和兔肾下腹主动脉数据的回归分析分别得出变异系数为0.21和0.08。估计的模量显示出其他研究人员发现的某些趋势：犬颈动脉和兔主动脉在径向都比周向更硬，并且前者在周向比纵向更硬。使用这些材料常数和测量的动脉压力，计算了每个标本的应力分布。在两个标本中，预测的径向应力与从大约 -p（施加的腔内压力）到大约零的跨壁变化一致，而犬颈动脉的周向应力范围为2.2p至0.7p，兔主动脉的周向应力范围为6.4p至3.7p。应力分布在定性上与先前研究报告的结果以及某些生理观察结果一致。基于我们两个样本案例的结果，我们认为我们的技术可能有助于评估血管组织的三维各向异性行为。
