The results of a study comparing model calibration techniques for Ogden's constitutive model that describes the hyperelastic behavior of brain tissue are presented. One and two-term Ogden models are fit to two different sets of stress-strain experimental data for brain tissue using both least squares optimization and Bayesian estimation. For the Bayesian estimation, the joint posterior distribution of the constitutive parameters is calculated by employing Hamiltonian Monte Carlo (HMC) sampling, a type of Markov Chain Monte Carlo method. The HMC method is enriched in this work to intrinsically enforce the Drucker stability criterion by formulating a nonlinear parameter constraint function, which ensures the constitutive model produces physically meaningful results. Through application of the nested sampling technique, 95% confidence bounds on the constitutive model parameters are identified, and these bounds are then propagated through the constitutive model to produce the resultant bounds on the stress-strain response. The behavior of the model calibration procedures and the effect of the characteristics of the experimental data are extensively evaluated. It is demonstrated that increasing model complexity (i.e., adding an additional term in the Ogden model) improves the accuracy of the best-fit set of parameters while also increasing the uncertainty via the widening of the confidence bounds of the calibrated parameters. Despite some similarity between the two data sets, the resulting distributions are noticeably different, highlighting the sensitivity of the calibration procedures to the characteristics of the data. For example, the amount of uncertainty reported on the experimental data plays an essential role in how data points are weighted during the calibration, and this significantly affects how the parameters are calibrated when combining experimental data sets from disparate sources.

提出了一项研究结果，该研究比较了描述脑组织超弹性行为的Ogden本构模型的模型校准技术。使用最小二乘优化和贝叶斯估计，将一期和两期Ogden模型拟合到两组不同的脑组织应力应变实验数据。对于贝叶斯估计，本构参数的联合后验分布是通过使用哈密顿量蒙特卡罗（HMC）采样（一种马尔可夫链蒙特卡罗方法）来计算的。HMC方法在这项工作中得到了丰富，通过制定非线性参数约束函数来本质上执行Drucker稳定性准则，从而确保本构模型产生有意义的物理结果。通过嵌套采样技术的应用，确定本构模型参数的95％置信界，然后将这些界传播通过本构模型，以生成应力应变响应上的合成界。广泛评估了模型校准程序的行为以及实验数据特征的影响。结果表明，增加模型的复杂性（即在Ogden模型中添加一个附加项）可以提高最佳拟合参数集的准确性，同时还可以通过扩大校准参数的置信范围来增加不确定性。尽管两个数据集之间存在一些相似之处，但所得分布却明显不同，突出了校准程序对数据特征的敏感性。例如，