Tissue-scale anisotropy and compressibility of tendon in semi-confined compression tests
Introduction
Mammalian tendons are specialised tissues that usually connect muscles and bones, and provide two main mechanical functions: force transmission and energy storage. The former, i.e. transmission of the high forces caused by muscular contraction to the bones, is vital for joint movement (Roberts, 2002, Benjamin et al., 2008, Magnusson et al., 2008). Although tension seems to be the primary state of deformation in this case, tendon may additionally experience lateral compressive loads if wrapped around a bony process (Vogel and Koob, 1989), e.g. the deep digital flexor tendon of diverse species. The function of energy storage and release occurs during motion. An example is ordinary gait, where tendons are stretched (Alexander, 1984) and thus gain elastic energy which is finally converted into kinetic energy by elastic recoil (Alexander and Bennet-Clark, 1977, Alexander, 1991, Astley and Roberts, 2012).
Tendons are composed of an extracellular matrix (ECM) that mainly consists of highly organised collagen fibrils hierarchically embedded into a distinctly smaller amount of non-collagenous matrix (NCM) (Silver et al., 2003, James et al., 2008). It is known that under continuous compressive conditions the amount of proteoglycans (PGs) in the tendon NCM increases drastically (Vogel, 1996, Feitosa et al., 2002, Feitosa et al., 2005, Matuszewski et al., 2012). PGs play a direct role in inter-fibril load sharing (Scott, 1990, Scott, 2003, Cribb and Scott, 1995), which has also been verified by theoretical considerations (Vesentini et al., 2005, Fessel and Snedeker, 2011). This indicates that the compressive response of tendon tissue is physiologically relevant and suggests that PGs are potentially involved in the load bearing mechanisms.
Only few compression experiments on tendons have been reported (Koob et al., 1992, Lee et al., 2000, Williams et al., 2008, Fang et al., 2014) in contrast to tensile testing, which has been applied on various length scales, reaching from single collagen molecules (Sun et al., 2002, Sun et al., 2004, Bozec and Horton, 2005) and fibrils (Graham et al., 2004, Shen et al., 2008, Svensson et al., 2010, Svensson et al., 2012) over fascicles (Screen et al., 2004, Screen et al., 2013, Clemmer et al., 2010, Thorpe et al., 2012) to whole tendons and tendon segments (Wren et al., 2003, Lake et al., 2010, Rigozzi et al., 2009, Kahn et al., 2010, Kahn et al., 2013).
Many of the aforementioned studies were used to identify the material parameters of constitutive models establishing relations between tissue stress and strain. Since the arrangement of fibres and fascicles is approximately unidirectional, tendon is widely considered as a transversely isotropic material. Although direction dependent experiments are indispensable to characterise the anisotropic properties (Sacks, 2000, Holzapfel and Ogden, 2008), only a limited number of studies have focussed on this issue (Lynch et al., 2003, Williams et al., 2008, Lake et al., 2010, Szczesny et al., 2012).
Apart from few exceptions (Pioletti et al., 1998, Spyrou and Aravas, 2011, Tang et al., 2011), many specific constitutive models for tendon tissue distinguish between collagen fibrils and NCM, and describe the tissue as an anisotropic elastic or viscoelastic material (Natali et al., 2005, Ciarletta et al., 2006, Tang et al., 2009, Maceri et al., 2010, Kahn et al., 2013). Moreover, a larger number of general fibre-reinforced models for biological tissues, distinguishing between collagenous fibres and matrix material, have been applied to model tendons and ligaments (Limbert and Taylor, 2002, Limbert and Middleton, 2006, de Vita and Slaughter, 2006, Federico and Gasser, 2010, Vassoler et al., 2012). Both, specific tendon and more general fibre-reinforced models assume that fibre and non-fibre constituents are responsible for load transmission in tension but the compressive resistance is often solely attributed to the non-fibre part and the fibre contribution is set to zero (Limbert and Middleton, 2004, Limbert and Middleton, 2006, Ciarletta et al., 2006, Vassoler et al., 2012). The underlying assumption that collagen fibres buckle under compressive loads and have therefore only negligible contribution to the compressive tissue stress is well-accepted in the field of constitutive modelling of soft biological tissues. Although this is probably a meaningful assumption for many tissues, in particular those that are subject to tensile conditions in vivo, the general applicability seems questionable. As a counterexample, we have shown by a dedicated test that for skeletal muscle tissue, the fibre direction remains an axis of transverse isotropy in compression suggesting that muscle fibres and the surrounding hierarchical structures bear compressive loads (Böl et al., 2014). In the present work, the testing technique is applied to investigate the anisotropic response of porcine flexor digitorum longus tendon samples under semi-confined compression.
Section snippets
Material and methods
Based on similar experiments on skeletal muscle tissue recently accomplished in our group (Böl et al., 2012, Böl et al., 2014), fascicle orientation dependent, semi-confined compression tests were performed. A detailed description of the experimental set-up is given in Böl et al. (2014). Shortly, cubic tissue samples were placed between two parallel plates and compressed along the vertical direction , cf. Fig. 1. While the plates pose constraints preventing extension in the -direction, the
Direction-dependent stress response
The mean stress responses are provided in Fig. 3 as black curves together with the standard deviations (s.d.) presented as grey shaded areas. The maximal standard deviations consistently occurred at the maximal stress value. Expressed in percent of the corresponding mean value, i.e. s.d./mean × 100, they were 63%, 33%, and 75%, given in the order I, II, III, respectively. Mode III, in which the fascicles are kept at constant length yielded the softest response. The stiffest tissue response was
Semi-confined compressive response of tendon tissue
To the best of the authors׳ knowledge, semi-confined compression tests that preserve the specimen dimension in one preferred direction and induce a state of biaxial stress have not been used before to characterise the mechanical response of tendon tissue. Multiaxial states of stress, however, may occur in vivo, particularly in situations where tendons are wrapped around bones and are exposed to bending and transverse compressive loads during locomotion (Vogel and Koob, 1989, Vogel, 1996, Vogel
Conflict of interest statement
All authors have no conflicts of interest.
Acknowledgements
Partial support for this research was provided by the Deutsche Forschungsgemeinschaft (DFG) under Grants BO 3091/4-1 and BO 3091/4-2. The second author gratefully acknowledges the support within the ETH Zurich Postdoctoral Fellowship Program and the Marie Curie Actions for People COFUND Program. Furthermore, the authors thank Dr. Roland Kruse for his support during this study.
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