Mechanical properties of tendons

The mechanical properties of tendons can be assessed by means of loading tests. In vitro, single tendinous fibres are constantly elongated and the corresponding tensile force is recorded (Butler et al., 1978). The most common procedure for human in vivo measurements includes a maximum voluntary muscle contraction on a dynamometer and the corresponding tendon elongation is visualized using ultrasonography (more detailed in chapter 1.4) (Fukashiro et al., 1995; Kubo et al., 1999). The loading test paradigm allows to determine the relationship of tendon force to tendon elongation (fig. 1.2) and therewith the tendon mechanical properties.

The tendon structure and composition described in the previous chapter directly affects the force-elongation relationship (Silver et al., 2003). At rest, a crimp pattern of the collagen fibres and fascicles can be observed, which disappears following the application of tensile forces in correspondence to the straightening of the fibres (Elliott, 1965; Hess et al., 1989; Józsa and Kannus, 1997). Since the initial forces are accompanied by a pronounced tendon elongation, the primary part of the force-elongation relationship is concave-shaped and was termed toe region (fig. 1.2) (Butler et al., 1978; Elliott, 1965). Increasing the tendon force further, the elongation shows a relatively linear response (fig. 1.2) (Butler et al., 1978; Elliott, 1965). The slope of this linear region of the force-elongation relationship was defined as tendon stiffness (Butler et al., 1978; Heinemeier and Kjaer, 2011). Up to the end of this region the tendon elongation is fully recovered to rest length when the load is removed (i.e. reversible strain) (Józsa and Kannus, 1997). At the terminal part of the linear region, micro failure of single collagen fibres may occur, indicating the so-called yield region as the third part of the force-elongation relationship.

Relatively low force increments are now accompanied by massive elongation (Nigg and Herzog, 1999). Consequently, additional fibres fail and fibre cross-links are detached until macroscopic failure takes place and the load-supporting ability of the tendon is lost (fig. 1.2) (Butler et al., 1978; O’Brien, 1992).

6 Fig. 1.2 Schematic stress-strain and force-elongation relationship.

(Modified from Wang 2006, J. Biomech., 39:1563-1582, p.1567; with permission by Elsevier)

The tendon force-tendon elongation relationship is directly affected by the morphological tendon properties, i.e. cross-sectional area and rest length (Butler et al., 1978). Accordingly, a thicker and/or shorter tendon accounts for a steeper slope of the force-elongation relationship, indicating less tendon elongation at a given tendon force and, thus, a higher stiffness of the tendon (Butler et al., 1978; Thompson and Czernuszka, 1995). To account for the effect of cross-sectional area and length, the tendon force can be normalized to the tendon cross-cross-sectional area (i.e. tendon stress) and the tendon elongation to the tendon rest length (i.e. tendon strain) (Butler et al., 1978; Heinemeier and Kjaer, 2011). The resulting tendon stress-tendon strain relationship is quite similar in shape to the force-elongation curve, but independent of the individual tendon morphology (fig. 1.2) (Butler et al., 1978). Therefore, the stress-strain relationship displays the actual material characteristics of the tendon. The linear slope of the stress-strain relationship is referred to as Young's modulus (or elastic modulus) and is a common parameter to describe the material properties of a tendon (Arampatzis et al., 2009;

Butler et al., 1978; Heinemeier and Kjaer, 2011). Accordingly, a high Young's modulus indicates a relatively stiff tendon tissue (Heinemeier and Kjaer, 2011). For the stress to strain relationship the toe-region lies typically below 3% and the linear region extends to about 4-5% of tendon strain (Nigg and Herzog, 1999; Wang, 2006). Macroscopic tendon failure was reported at strain-levels of 8-10% as investigated by in vitro tests (O’Brien, 1992; Wang, 2006). However, tests on whole tendons also indicated that higher levels of strain might be tolerable (Józsa and Kannus, 1997), most likely due to the three-dimensional organization of collagen fibre bundles throughout the tendon (Butler et al., 1978). Whereas the ultimate strain (i.e. strain at tendon

Force (N) or stress (N/mm²)

Elongation (mm) or strain (%)

7 failure) is more or less constant (Abrahams, 1967; LaCroix et al., 2013; Loitz et al., 1989;

Nakagawa et al., 1996), the ultimate stress (i.e. stress to tendon failure) is dependent on the material properties (Józsa and Kannus, 1997; Nigg and Herzog, 1999; Thompson and Czernuszka, 1995).

Furthermore, due to the content of collagen, elastin, water and the interactions between collagenous and non-collagenous proteins (e.g. proteoglycans), tendons feature viscous and elastic properties (Wang, 2006). The elastic component allows for a recovery of the rest length following loading-induced elongation and is a time-independent phenomenon, whereas the viscous component is responsible if recovery was not complete and, by contrast, strongly depends on time (Józsa and Kannus, 1997). Viscoelasticity accounts for several specific characteristics of tendons, like force-relaxation, creep and hysteresis (Butler et al., 1978; Józsa and Kannus, 1997; Nigg and Herzog, 1999). Force-relaxation indicates that the load, which is required to maintain a certain strain-level decreases over time. Creep, on the other hand, means that tendon length increases over time during a constant load application (Butler et al., 1978;

Józsa and Kannus, 1997). Viscosity is also responsible for the sensitivity of tendons to different strain rates. During lower strain rates the deformation of the tendon is higher. Thus, the tendon absorbs more strain energy but is less effective in transferring loads. With higher rates, the tendon elongates less (higher stiffness) and the load transfer becomes more efficient (Józsa and Kannus, 1997; McNeill Alexander, 2002; Noyes et al., 1974; Wren et al., 2001). During a loading cycle, characterized by a stretch and recoil of the tendon, the resulting force-elongation curve forms a loop, indicating that a proportion of strain energy expended during elongation is not completely recovered when the load is removed (Butler et al., 1978; Nigg and Herzog, 1999).

This phenomenon is called hysteresis and the area between the two curves refers to the energy that is dissipated (e.g. as heat). However, the loss of the exerted energy was reported to be low (i.e. 6-11%), indicating that most energy is recovered when the applied force is removed (Bennett et al., 1986; Ker, 1981). Several in vivo measurements on human tendons reported higher hysteresis values but these discrepancies might be explained by the challenging and different methodological approaches used for tendon elongation measurement in vivo (Finni et al., 2013; Lichtwark et al., 2013). Hysteresis, force-relaxation and creep are particular examples for the viscous component of tendon properties (Finni et al., 2013; Nigg and Herzog, 1999).

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