Teng Zhongzhao, Yuan Jianmin, Feng Jiaxuan, Zhang Yongxue, Brown Adam J, Wang Shuo, Lu Qingsheng, Gillard Jonathan H
Department of Radiology, University of Cambridge, UK; Department of Engineering, University of Cambridge, UK.
Department of Radiology, University of Cambridge, UK.
J Biomech. 2015 Nov 5;48(14):3912-21. doi: 10.1016/j.jbiomech.2015.09.023. Epub 2015 Oct 21.
Calculating high stress concentration within carotid atherosclerotic plaques has been shown to be complementary to anatomical features in assessing vulnerability. Reliability of stress calculation may depend on the constitutive laws/strain energy density functions (SEDFs) used to characterize tissue material properties. Different SEDFs, including neo-Hookean, one-/two-term Ogden, Yeoh, 5-parameter Mooney-Rivlin, Demiray and modified Mooney-Rivlin, have been used to describe atherosclerotic tissue behavior. However, the capacity of SEDFs to fit experimental data and the difference in the stress calculation remains unexplored. In this study, seven SEDFs were used to fit the stress-stretch data points of media, fibrous cap, lipid and intraplaque hemorrhage/thrombus obtained from 21 human carotid plaques. Semi-analytic solution, 2D structure-only and 3D fully coupled fluid-structure interaction (FSI) analyses were used to quantify stress using different SEDFs and the related material stability examined. Results show that, except for neo-Hookean, all other six SEDFs fitted the experimental points well, with vessel stress distribution in the circumferential and radial directions being similar. 2D structural-only analysis was successful for all seven SEDFs, but 3D FSI were only possible with neo-Hookean, Demiray and modified Mooney-Rivlin models. Stresses calculated using Demiray and modified Mooney-Rivlin models were nearly identical. Further analyses indicated that the energy contours of one-/two-term Ogden and 5-parameter Mooney-Rivlin models were not strictly convex and the material stability indictors under homogeneous deformations were not always positive. In conclusion, considering the capacity in characterizing material properties and stabilities, Demiray and modified Mooney-Rivlin SEDF appear practical choices for mechanical analyses to predict the critical mechanical conditions within carotid atherosclerotic plaques.
计算颈动脉粥样硬化斑块内的高应力集中已被证明在评估易损性方面与解剖特征具有互补性。应力计算的可靠性可能取决于用于表征组织材料特性的本构定律/应变能密度函数（SEDFs）。不同的SEDFs，包括新胡克模型、一/二项奥格登模型、杨模型、五参数穆尼-里夫林模型、德米拉伊模型和修正穆尼-里夫林模型，已被用于描述动脉粥样硬化组织的行为。然而，SEDFs拟合实验数据的能力以及应力计算的差异仍未得到探索。在本研究中，使用七种SEDFs来拟合从21个人类颈动脉斑块获得的中膜、纤维帽、脂质和斑块内出血/血栓的应力-拉伸数据点。采用半解析解、二维仅结构分析和三维全耦合流固相互作用（FSI）分析，使用不同的SEDFs量化应力，并检查相关的材料稳定性。结果表明，除新胡克模型外，其他六种SEDFs均能很好地拟合实验点，血管在周向和径向的应力分布相似。二维仅结构分析对所有七种SEDFs均成功，但三维FSI仅适用于新胡克模型、德米拉伊模型和修正穆尼-里夫林模型。使用德米拉伊模型和修正穆尼-里夫林模型计算的应力几乎相同。进一步分析表明，一/二项奥格登模型和五参数穆尼-里夫林模型的能量等值线并非严格凸形，均匀变形下的材料稳定性指标并非总是正值。总之，考虑到在表征材料特性和稳定性方面的能力，德米拉伊模型和修正穆尼-里夫林SEDF似乎是预测颈动脉粥样硬化斑块内临界力学条件的力学分析的实际选择。
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