The differences in viscoelastic properties of subtendons result from the anatomical tripartite structure of human Achilles tendon - ex vivo experimental study and modeling

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.