Division of Biomedical Engineering and Imaging Sciences, Department of Biomedical Engineering, King's College London, UK; Departments of Biomedical Engineering and Cardiac Surgery, University of Michigan, North Campus Research Center, Building 20, 2800 Plymouth Rd, Ann Arbor 48109, MI, USA.
Division of Biomedical Engineering and Imaging Sciences, Department of Biomedical Engineering, King's College London, UK.
Acta Biomater. 2021 Nov;135:441-457. doi: 10.1016/j.actbio.2021.08.036. Epub 2021 Sep 4.
Understanding the biomechanics of the heart in health and disease plays an important role in the diagnosis and treatment of heart failure. The use of computational biomechanical models for therapy assessment is paving the way for personalized treatment, and relies on accurate constitutive equations mapping strain to stress. Current state-of-the art constitutive equations account for the nonlinear anisotropic stress-strain response of cardiac muscle using hyperelasticity theory. While providing a solid foundation for understanding the biomechanics of heart tissue, most current laws neglect viscoelastic phenomena observed experimentally. Utilizing experimental data from human myocardium and knowledge of the hierarchical structure of heart muscle, we present a fractional nonlinear anisotropic viscoelastic constitutive model. The model is shown to replicate biaxial stretch, triaxial cyclic shear and triaxial stress relaxation experiments (mean error ∼7.68%), showing improvements compared to its hyperelastic (mean error ∼24%) counterparts. Model sensitivity, fidelity and parameter uniqueness are demonstrated. The model is also compared to rate-dependent biaxial stretch as well as different modes of biaxial stretch, illustrating extensibility of the model to a range of loading phenomena. STATEMENT OF SIGNIFICANCE: The viscoelastic response of human heart tissues has yet to be integrated into common constitutive models describing cardiac mechanics. In this work, a fractional viscoelastic modeling approach is introduced based on the hierarchical structure of heart tissue. From these foundations, the current state-of-the-art biomechanical models of the heart muscle are transformed using fractional viscoelasticity, replicating passive muscle function across multiple experimental tests. Comparisons are drawn with current models to highlight the improvements of this approach and predictive responses show strong qualitative agreement with experimental data. The proposed model presents the first constitutive model aimed at capturing viscoelastic nonlinear response across multiple testing regimes, providing a platform for better understanding the biomechanics of myocardial tissue in health and disease.
了解健康和疾病中心脏的生物力学在心力衰竭的诊断和治疗中起着重要作用。使用计算生物力学模型进行治疗评估为个性化治疗铺平了道路，并且依赖于将应变映射到应力的精确本构方程。当前最先进的本构方程使用超弹性理论来描述心肌的非线性各向异性应力-应变响应。虽然为理解心脏组织的生物力学提供了坚实的基础，但大多数当前的定律忽略了实验中观察到的粘弹性现象。利用人类心肌的实验数据和心脏肌肉的层次结构知识，我们提出了一种分数非线性各向异性粘弹性本构模型。该模型被证明可以复制双轴拉伸、三轴循环剪切和三轴应力松弛实验（平均误差约为 7.68%），与超弹性模型（平均误差约为 24%）相比有所改进。展示了模型的灵敏度、保真度和参数唯一性。还将模型与率相关的双轴拉伸以及不同模式的双轴拉伸进行了比较，说明了模型对一系列加载现象的可扩展性。
描述心脏力学的常见本构模型尚未将人类心脏组织的粘弹性响应纳入其中。在这项工作中，基于心脏组织的层次结构，引入了一种分数粘弹性建模方法。在此基础上，使用分数粘弹性将当前最先进的心肌生物力学模型进行转换，复制了多个实验测试中的被动肌肉功能。与当前模型进行比较，突出了这种方法的改进，预测响应与实验数据具有很强的定性一致性。所提出的模型提出了第一个旨在捕获多个测试范围内粘弹性非线性响应的本构模型，为更好地理解健康和疾病中心肌组织的生物力学提供了一个平台。
