PDF(Pubmed)
Abstract：
OBJECTIVE: Through their contractile and synthetic capacity, vascular smooth muscle cells (VSMCs) can regulate the stiffness and resistance of the circulation. To model the contraction of blood vessels, an active stress component can be added to the (passive) Cauchy stress tensor. Different constitutive formulations have been proposed to describe this active stress component. Notably, however, measuring biomechanical behaviour of contracted blood vessels ex vivo presents several experimental challenges, which complicate the acquisition of comprehensive datasets to inform complex active stress models. In this work, we examine formulations for use with limited experimental contraction data as well as those developed to capture more comprehensive datasets.
METHODS: First, we prove analytically that a subset of constitutive active stress formulations exhibits unstable behaviours (i.e., a non-unique diameter solution for a given pressure) in certain parameter ranges, particularly for large contractile deformations. Second, using experimental literature data, we present two case studies where these formulations are used to capture the contractile response of VSMCs in the presence of (1) limited and (2) extensive contraction data.
RESULTS: We show how limited contraction data complicates selecting an appropriate active stress model for vascular applications, potentially resulting in unrealistic modelled behaviours.
CONCLUSIONS: Our data provide a useful reference for selecting an active stress model which balances the trade-off between accuracy and available biomechanical information. Whilst complex physiologically motivated models\' superior accuracy is recommended whenever active biomechanics can be extensively characterised experimentally, a constant 2nd Piola-Kirchhoff active stress model balances well accuracy and applicability with sparse contractile data.
METHODS: First, we prove analytically that a subset of constitutive active stress formulations exhibits unstable behaviours (i.e., a non-unique diameter solution for a given pressure) in certain parameter ranges, particularly for large contractile deformations. Second, using experimental literature data, we present two case studies where these formulations are used to capture the contractile response of VSMCs in the presence of (1) limited and (2) extensive contraction data.
RESULTS: We show how limited contraction data complicates selecting an appropriate active stress model for vascular applications, potentially resulting in unrealistic modelled behaviours.
CONCLUSIONS: Our data provide a useful reference for selecting an active stress model which balances the trade-off between accuracy and available biomechanical information. Whilst complex physiologically motivated models\' superior accuracy is recommended whenever active biomechanics can be extensively characterised experimentally, a constant 2nd Piola-Kirchhoff active stress model balances well accuracy and applicability with sparse contractile data.
摘要：
目的：通过它们的收缩和合成能力，血管平滑肌细胞（VSMC）可以调节循环的硬度和阻力。为了模拟血管的收缩，可以将主动应力分量添加到（被动）柯西应力张量。已经提出了不同的本构配方来描述这种活性应力成分。值得注意的是,然而,测量离体收缩血管的生物力学行为提出了几个实验挑战，这使得全面数据集的获取复杂化，以告知复杂的主动应力模型。在这项工作中,我们检查了用于有限的实验收缩数据的配方以及用于捕获更全面数据集的配方。
方法：首先，我们通过分析证明了一部分本构主动应力公式表现出不稳定的行为(即，给定压力的非唯一直径解)在某些参数范围内，特别是对于大的收缩变形。第二,利用实验文献数据，我们提供了两个案例研究,在存在(1)有限收缩数据和(2)广泛收缩数据的情况下,这些制剂用于捕获VSMC的收缩反应.
结果：我们展示了有限的收缩数据如何使选择适合血管应用的主动应力模型变得复杂，可能导致不切实际的建模行为。
结论：我们的数据为选择主动应力模型提供了有用的参考，该模型可以平衡准确性和可用的生物力学信息之间的权衡。尽管只要可以通过实验广泛表征主动生物力学，就建议使用复杂的生理动机模型\'更高的准确性，恒定的第二个Piola-Kirchhoff主动应力模型在稀疏收缩数据下平衡了准确性和适用性。
方法：首先，我们通过分析证明了一部分本构主动应力公式表现出不稳定的行为(即，给定压力的非唯一直径解)在某些参数范围内，特别是对于大的收缩变形。第二,利用实验文献数据，我们提供了两个案例研究,在存在(1)有限收缩数据和(2)广泛收缩数据的情况下,这些制剂用于捕获VSMC的收缩反应.
结果：我们展示了有限的收缩数据如何使选择适合血管应用的主动应力模型变得复杂，可能导致不切实际的建模行为。
结论：我们的数据为选择主动应力模型提供了有用的参考，该模型可以平衡准确性和可用的生物力学信息之间的权衡。尽管只要可以通过实验广泛表征主动生物力学，就建议使用复杂的生理动机模型\'更高的准确性，恒定的第二个Piola-Kirchhoff主动应力模型在稀疏收缩数据下平衡了准确性和适用性。
