AGH University of Science and Technology, Faculty of Mechanical Engineering and Robotics, Mickiewicza 30 Av., Krakow 30-059, Poland.
Andrzej Frycz Modrzewski Krakow University, Faculty of Medicine and Health Sciences, Gustawa Herlinga-Grudzinskiego 1, Krakow 30-705, Poland.
Acta Biomater. 2021 Apr 15;125:138-153. doi: 10.1016/j.actbio.2021.02.041. Epub 2021 Mar 4.
The human Achilles tendon (AT) is a hierarchical structure macroscopically composed of three subtendons originating from the soleus (SOL) and gastrocnemius (GL, GM) muscles. According to recent reports, the divisible structure of the AT together with diverse material properties of its subtendons are suspected as a probable cause of non-homogeneous stress and strain distribution occurring in loaded AT. Despite numerous investigations on human AT, there is still relatively little knowledge regarding mechanical properties of subtendon-level hierarchy, which is crucial in fully understanding the multiscale relationship which governs tendon mechanics. In this paper we present the first ex vivo study conducted on SOL, GL, and GM subtendons of human AT. We investigate differences in viscoelastic properties of SOL, GM, and GL subtendons in terms of tensile modulus, mechanical hysteresis as well as stress relaxation observed at two different values of strain. Our results show that the most significant differences in mechanical properties exist between subtendon attached to the soleus muscle (SOL) and subtendons originating from the two heads of the gastrocnemius muscle (GM and GL). We used our experimental results to calibrate three different constitutive models: the hyperelastic Yeoh model with power-law flow, the microstructurally motivated Holzapfel-Gasser-Ogden model enhanced with strain-dependent Berström-Boyce flow and the phenomenological elasto-viscoplastic Arruda-Boyce-based model with strain-dependent Berström-Boyce flow supplemented with component representing matrix response. All calibrated models may be applied to commercial FEA software as a sufficient solution for rapid mechanical response modeling of human AT subtendons or for the purpose of future development of comprehensive patient-specific models of human lower limbs. STATEMENT OF SIGNIFICANCE: The divisible structure of the Achilles tendon together with diverse material properties of its subtendons are suspected as a probable cause of non-homogeneous stress and strain distribution occurring in loaded Achilles tendon. Despite numerous investigations on mechanical properties of Achilles tendon, there is still relatively little knowledge regarding mechanical properties of subtendon-level hierarchy, which is crucial in fully understanding the multiscale relationship which governs tendon mechanics. This study is the first reported ex vivo investigation conducted on SOL, GL, and GM human Achilles subtendons. We investigate differences in the viscoelastic properties of individual subtendons and demonstrate that the observed differences should be considered as muscle-dependent. Our experimental research is supported with a modeling study in which we calibrate three different constitutive models.
人类跟腱（AT）是一种具有层次结构的组织，宏观上由起源于比目鱼肌（SOL）和腓肠肌（GL、GM）的三个次级腱组成。根据最近的报告，跟腱的可分结构以及次级腱的不同材料特性被怀疑是导致加载跟腱中出现非均匀应力和应变分布的可能原因。尽管对人类跟腱进行了大量研究，但对于次级腱层次结构的力学性能仍然知之甚少，这对于充分理解控制肌腱力学的多尺度关系至关重要。在本文中，我们首次对人类跟腱的 SOL、GL 和 GM 次级腱进行了离体研究。我们研究了在两种不同应变值下，拉伸模量、力学滞后以及应力松弛方面，SOL、GM 和 GL 次级腱的粘弹性性能差异。我们的研究结果表明，附着于比目鱼肌的次级腱（SOL）和起源于腓肠肌两个头的次级腱（GM 和 GL）之间的力学性能差异最为显著。我们使用实验结果对三种不同的本构模型进行了校准：带幂律流的超弹性 Yeoh 模型、用应变相关的 Berström-Boyce 流增强的基于微观结构的 Holzapfel-Gasser-Ogden 模型以及用应变相关的 Berström-Boyce 流补充基质响应分量的基于 phenomenological elasto-viscoplastic Arruda-Boyce 模型。所有校准的模型都可以应用于商业有限元分析软件，作为快速模拟人类跟腱次级腱力学响应的充分解决方案，或者用于未来开发全面的人类下肢患者特异性模型。
跟腱的可分结构以及次级腱的不同材料特性被怀疑是导致加载跟腱中出现非均匀应力和应变分布的可能原因。尽管对跟腱的机械性能进行了大量研究，但对于次级腱层次结构的机械性能仍然知之甚少，这对于充分理解控制肌腱力学的多尺度关系至关重要。这项研究是首次对 SOL、GL 和 GM 人类跟腱次级腱进行的离体研究。我们研究了各个次级腱的粘弹性特性差异，并证明观察到的差异应被视为与肌肉相关。我们的实验研究得到了建模研究的支持，我们在建模研究中对三种不同的本构模型进行了校准。
