肌腱变形微观结构超弹性模型的贝叶斯推断
Bayesian inference on a microstructural, hyperelastic model of tendon deformation
摘要：
软组织变形的微观结构模型在包括人造组织设计和手术规划的应用中是重要的。这些模型的基础，以及它们相对于现象学模型的优势在于，它们结合了与组织的微观结构和本构行为直接相关的参数，因此可以用于预测组织结构变化的影响。虽然研究试图确定这些参数使用不同的，国家的最先进的，实验技术，值范围超过几个数量级的报告，导致不确定性的真实参数值，并创建一个需要的模型，可以处理这种不确定性。我们推导出一个横观各向同性软组织的微观结构，超弹性模型，并用它来模拟肌腱的力学行为。考虑到参数的不确定性，我们采用贝叶斯方法，并应用自适应马尔可夫链蒙特卡罗算法来确定模型参数的后验概率分布。所获得的后验分布与先前报道的参数测量结果一致，并使我们能够量化每个肌腱样本的建模值的不确定性。这种方法可以作为一个原型量化参数的不确定性在其他软组织。
英文摘要：
Microstructural models of soft tissue deformation are important in applications including artificial tissue design and surgical planning. The basis of these models, and their advantage over their phenomenological counterparts, is that they incorporate parameters that are directly linked to the tissue's microscale structure and constitutive behaviour and can therefore be used to predict the effects of structural changes to the tissue. Although studies have attempted to determine such parameters using diverse, state-of-the-art, experimental techniques, values ranging over several orders of magnitude have been reported, leading to uncertainty in the true parameter values and creating a need for models that can handle such uncertainty. We derive a microstructural, hyperelastic model for transversely isotropic soft tissues and use it to model the mechanical behaviour of tendons. To account for parameter uncertainty, we employ a Bayesian approach and apply an adaptive Markov chain Monte Carlo algorithm to determine posterior probability distributions for the model parameters. The obtained posterior distributions are consistent with parameter measurements previously reported and enable us to quantify the uncertainty in their values for each tendon sample that was modelled. This approach could serve as a prototype for quantifying parameter uncertainty in other soft tissues.
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