Influence of altered geometry and material properties on tissue stress distribution under load in tendinopathic Achilles tendons – A subject-specific finite element analysis

Abstract

Achilles tendon material properties and geometry are altered in Achilles tendinopathy. The purpose of this study was to determine the relative contributions of altered material properties and geometry to free Achilles tendon stress distribution during a sub-maximal contraction in tendinopathic relative to healthy tendons. Tendinopathic (n=8) and healthy tendons (n=8) were imaged at rest and during a sub-maximal voluntary isometric contraction using threedimensional freehand ultrasound. Images were manually segmented and used to create subject-specific finite element models. The resting cross-sectional area of the free tendon was on average 31% greater for the tendinopathic compared to healthy tendons. Material properties for each tendon were determined using a numerical parameter optimisation approach that minimised the difference in experimentally measured longitudinal strain and the strain predicted by the finite element model under submaximal loading conditions for each tendon. The mean Young's modulus for tendinopathic tendons was 53% lower than the corresponding control value. Finite element analyses revealed that tendinopathic tendons experience 24% less stress under the same submaximal external loading conditions compared to healthy tendons. The lower tendon stress in tendinopathy was due to a greater influence of tendon cross-sectional area, which alone reduced tendon stress by 30%, compared to a lower Young's modulus, which alone increased tendon stress by 8%. These findings suggest that the greater tendon cross-sectional area observed in tendinopathy compensates for the substantially lower Young's modulus, thereby protecting pathological tendon against excessive stress.Achilles tendinopathy is a common tendon injury which is prevalent in, but not exclusive to, athletic populations (Kongsgaard et al., 2005;Rolf and Movin, 1997). Up to 25% of affected patients will eventually require operative treatment and 20% of those undergo further surgery (Alfredson, 2003). Achilles tendinopathy is most commonly located in the mid-portion of the free tendon, 2-6 cm from the calcaneal insertion (Astrom and Rausing, 1995;Maffulli et al., 2004;Rolf and Movin, 1997) and is characterised by collagen bundle disruption, hyper-cellularity, hyper-vascularity and altered collagen, glycosaminoglycan and fluid content (Khan et al., 1999). Tendinopathy has also been reported to cause a reduction in tendon mechanical and material properties (Arya and Kulig, 2010;Helland et al., 2013). For the Achilles tendon, stiffness was reduced by 20% and Young's modulus by 50% relative to healthy tendons (Arya and Kulig, 2010). For a tendon of a given length, a lower stiffness would result in greater tendon strain under the same external load. A further adaptation in Achilles tendinopathy is tendon thickening, which increases the tendon cross-sectional area (CSA) by 20-66% (Arya and Kulig, 2010;Helland et al., 2013;Leung and Griffith, 2008;Nuri et al., 2017bNuri et al., , 2018Obst et al., 2018). Tendon thickening may therefore be an adaptation...

Targeted Achilles Tendon Training and Rehabilitation Using Personalized and Real-Time Multiscale Models of the Neuromusculoskeletal System

“…Single leg hop exercises resulted in the highest free Achilles tendon global strains, which is likely related to some combination of higher muscle activation and more favorable force-length-velocity behavior (i.e., longer triceps surae muscle lengths and faster lengthening speeds) than for walking and eccentric heel drops. It is however, important to consider that we presented data from a single subject and the results are likely to differ when analyzing Achilles tendon strain distribution in multiple individuals and pathological tendons (Hansen et al, 2017;Shim et al, 2019).…”

“…Prior to FE analysis, a generic tendon mesh is morphed to match the resting 3D geometry of tendon measured using freehand 3D ultrasound via free form deformation ( Fernandez et al, 2004 ). The constitutive mechanical behavior of the free Achilles tendon can be modeled using a transversely isotropic hyperelastic formulation, which has been successfully applied to both cadaveric ( Shim et al, 2014 ) and in vivo analyses ( Hansen et al, 2017 ; Shim et al, 2018 , 2019 ). Material properties of the Achilles tendon can be estimated using an inverse FE approach, wherein an optimization procedure identifies the subject-specific material properties parameters that produce the best match between the geometry of the loaded subject-specific FE mesh and the geometry of the free Achilles tendon measured under submaximal loading conditions using freehand 3D ultrasound ( Hansen et al, 2017 ).…”

“…As both tendon geometry and material properties ( Arya and Kulig, 2010 ; Obst et al, 2018 ) are altered in Achilles tendinopathy, it is also important to determine how these alterations affect Achilles tendon stress distributions in tendinopathic Achilles tendons. Shim et al (2019) reported that tendinopathic tendons have a 30% larger cross-sectional area and 50% lower modulus compared to healthy tendons, but that the lower modulus resulted in only an 8% increase in average tendon stress during a 70% submaximal isometric contraction, compared to a 30% decrease in average tendon stress due to the larger cross-sectional area. It was therefore suggested that the larger cross-sectional area reported in tendinopathic Achilles tendons ( Arya and Kulig, 2010 ) could be protective against higher tendon stresses, but could also result in regions of underloading/stress shielding with associated catabolic effects on the tendon.…”

“…A FE model of the free Achilles tendon was modeled using CMISS 1 as an incompressible, transversely isotropic hyperelastic material with 30° twisted fibers, and geometry personalized via freehand 3D ultrasound, as well as material properties parameters calculated via inverse FE approaches ( Shim et al, 2014 , 2019 ; Hansen et al, 2017 ). To enable calculation of longitudinal principal component strains (i.e., localized), the reference FE material coordinate system was rotated to align with the fiber orientation of the tendon, which run in the proximal-distal direction ( Shim et al, 2018 ).…”

Neuromusculoskeletal Modeling-Based Prostheses for Recovery After Spinal Cord Injury

“…The FE method is a computational method that can be used to predict tissue damage or rupture by modeling the internal mechanics of tissue (i.e., localized stress and strain), as demonstrated by ex vivo studies (Shim et al, 2014, 2018). The geometry of FE models can be personalized to the individual via medical imaging (e.g., magnetic resonance imaging, x-ray computed tomography, or ultrasound) (Devaprakash et al, 2019), while material properties are typically applied from literature data or estimated experimentally (Hansen et al, 2017; Shim et al, 2019). Individual-specific boundary conditions calculated from NMS models (i.e., model pose and applied external forces) are supplied to FE models to estimate the internal stresses and strains of selected musculoskeletal tissues.…”