2 Mechanical Properties of Tendons

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The primary role of tendons is to transmit contractile forces to the skeleton to generate joint movement. In doing so, however, tendons do not behave as rigid bodies.

In this chapter, the mechanical behavior of tendons and its major determinants and implications are reviewed.

In Vitro Measurements

Most of our knowledge of the mechanical properties of tendons comes from isolated material testing. Two methods have traditionally been used in biomechanics investigations: 1) The free-vibration method, which is based on quantifying the decay in oscillation amplitude that takes place after a transient load is applied to a specimen [1–3]; and 2) tensile testing methodologies, in which the specimen is stretched by an external force while both the specimen deformation and the applied force are recorded [2,4–6]. The latter methodology seems to be preferable, mostly because it is considered to mimic ade- quately the way that loading is imposed on tendons in real life [7–14].

A tensile testing machine is composed of an oscillating actuator and a load cell (see Figure 2-1). The tendon specimen studied is gripped by two clamps, a static one mounted on the load cell and a moving one mounted on the actuator. The actuator is then set to motion while the load cell records the tension associated with the stretching applied. The tensile deformation of the specimen is taken from the displacement of the actuator, in which case the deformation of the whole specimen is quantiﬁed, or by means of an extensometer, in which case deformation measurements are taken over a restricted region of the whole specimen.

A typical force-deformation plot of an isolated tendon is shown in Figure 2-2. Generally, in force-deformation curves, slopes relate to stiffness (N/mm), and areas to energy (J). In elongation-to-failure conditions, 4 different regions can be identiﬁed in the tendon force-deformation

curve. Region I is the initial concave portion of the curve, in which stiffness gradually increases; it is referred to as the tendon “toe” region. Loads within the toe region elongate the tendon by reducing the crimp angle of the collagen fibers at rest, but they do not cause further fiber stretching. Hence, loading within the toe region does not exceed the tendon elastic limit, and subsequent unloading restores the tendon to its initial length. Further elongation brings the tendon into the “linear” Region II, in which stiffness remains constant as a function of elongation. In this region, elongation is the result of stretching imposed in the already aligned fibers by the load imposed in the preceding toe region. At the end point of this region, some fibers start to fail. Thus, A) the tendon stiffness begins to drop; and B) unloading from this point does not restore the tendon’s initial length. Elongation beyond the linear region brings the tendon into Region III, where additional fiber failure occurs in an unpre- dictable fashion. Further elongation brings the tendon into Region IV, where complete failure occurs [4,5,15–18].

Although Regions I, II, III, and IV are apparent in tendon force-deformation curves during elongation-to- failure conditions, the shape of the curves obtained differs between specimens. These differences can be accounted for to a great extent by interspecimen dimensional differences. For example, tendons of equal lengths but different cross-sectional areas exhibit different force-deformation properties, and thicker tendons are stiffer. Similarly, different force-deformation curves are obtained from tendons of equal cross-sectional areas but different initial lengths, in which case shorter tendons are stiffer [5].

To account for interspecimen dimensional differences, tendon force is reduced to stress (MPa) by normalization to the tendon cross-sectional area, and tendon deformation is reduced to strain (%) by normalization to the tendon original length. The tendon stress-strain curve is similar in shape to the force-deformation curve, but it

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2

Mechanical Properties of Tendons

Constantinos N. Maganaris and Marco V. Narici

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reﬂects the intrinsic material properties rather than the structural properties of the specimen.

The most common material variables taken from a stress-strain curve under elongation-to-failure conditions are Young’s modulus (GPa), ultimate stress (MPa), ultimate strain (%), and toughness (J/kg). Young’s modulus is the product of stiffness multiplied by the original length-to-cross-sectional area ratio of the specimen.

Experiments on several tendons indicate that the Young’s modulus reaches the level of 1 to 2 GPa at stresses exceeding 30 MPa [5,11,12,19]. Ultimate tendon stress (i.e., stress at failure) values in the range of 50 to 100 MPa are generally reported [5,11,12,17]. Ultimate tendon strain (i.e., strain at failure) values of 4% to 10% have been reported [5,16,17]. The tendon toughness (i.e., work done on the tendon until failure) values reported are in the range of 1000 to 4500 J/kg [12].

If a tendon is subjected to a tensile load, the tendon does not behave perfectly elastically, even if the load applied is less than that required to cause failure. This is because the tendon collagen ﬁbers and interﬁber matrix possess viscous properties [20,21]. Due to the presence of viscosity, the entire tendon exhibits force-relaxation, creep, and mechanical hysteresis [2,4,5,8,15,16,22].

Force-relaxation means that the force required to cause a given elongation decreases over time. The decrease in force follows a predictable curvilinear pattern until a steady-state value is achieved (see Figure 2-3). Creep is the analogous phenomenon under constant-force conditions. In this case, deformation increases over time curvi- linearly until a steady state value is reached. In both force-relaxation and creep, the decrease in magnitude of

load cell

clamp

tendon specimen

clamp displacement

Figure 2-1. Diagram of an apparatus for tendon tensile testing.

Force

Deformation

I II III IV

Figure 2-2. Typical force-elongation curve of a tendon pulled by a load exceeding the tendon elastic limit. I, toe region; II, linear region; III and IV, failure regions.

A

B

C Force

Force

force application

Time

Deformation

Deformation force application

Time

hysteresis

Figure 2-3. (A) Typical force-relaxation curve in a tendon. The force required to cause a given deformation decreases over time. (B) Typical creep curve in a tendon. The deformation caused by a given force increases over time. (C) Typical mechanical hysteresis in a tendon. The arrows indicate loading and unloading directions during a test with a tensile load within the elastic limit of the tendon. The area of the loop between the loading and unloading curves relative to that underneath the loading curve represents the fraction of strain energy lost as heat by the tendon viscous damping.

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the variable studied reﬂects the viscous component of the tendon, and the steady-state values reﬂect the elastic component of the tendon. The presence of mechanical hysteresis is retrieved in load-deformation plots during loading and subsequent unloading of the specimen [2,6,8,12]. Larger tendon deformations are taken during recoil than stretch at given loads, yielding a loop (the hysteresis loop) between the curves in the loading and unloading directions (see Figure 2-3).The area of the loop represents the amount of strain energy lost as heat upon recoil due to the viscous component, and it is usually expressed in relative terms (%) with respect to the total work performed on the tendon during stretching.

Mechanical hysteresis values in the range of 5% to 25%

have been reported, with most values concentrated around the value of 10% [7,8,11,12,19]. The proportion of strain energy input recovered by elastic recoil is the con- verse of mechanical hysteresis, and is known as rebound resilience.This variable is, therefore, an index of the material potential for elastic energy recovery.

Several factors may account for differences in the material properties of tendons. Some differences can be attributed to interstudy methodological differences in A) tendon gripping (conventional clamps, Cryo Jaw clamps, or use of cyanoacrylate adhesive [2,6,8,11,12,23]; B) tendon deformation measurement (actuator-based measurements, extensometer-based measurements, or noncontact optical methodologies [2,6,9,11,24]; and C) tendon cross-sectional area measurement (gravimetry- based measurements, micrometry-based measurements, or mass- and density-based estimations [9,11,25]. Some studies have shown that the status of the specimen studied (e.g., preserved or fresh) and the environmental conditions during testing may also affect the mechanical response of collagenous tissue [5,26–28], thus accounting for the above variations.

Studies on the effect of several other factors on the mechanical properties of tendinous tissue have been performed. The major of these factors are discussed below.

Disuse

To determine the effects of disuse on tendinous tissue properties, 3 limb immobilization models have traditionally been employed. In most experiments, the joint is ﬁxed at a certain position for a prolonged period of time.

Using the specimens of the contralateral, nonimmobi- lized limb as controls, postintervention comparisons are then made [5,10,29,30]. Limb suspension and denervation models have also been used [29,31]. Most studies show that immobilization results in decreased stiffness, ultimate strength and energy-to-failure. These changes are attributed to specimen atrophy and changes in the specimen material properties. Disuse-induced changes in intrinsic material properties are associated with increased

collagen turnover and reducible cross-linking, decreased glycosaminoglycan and water content, and increased nonuniform orientation of collagen ﬁbrils [5,10,17,18, 31–33].

Physical Activity

Most of the studies report that long-term physical activity improves the tensile mechanical properties of tendons and yields opposite effects compared with disuse [5,9,10,30,34]. Increases in stiffness, ultimate strength, and energy-to-failure in response to exercise training have been reported. Dimensional changes (i.e., hypertrophy) may partly account for these changes. Increases in ultimate stress and strain, however, indicate that the improvement of mechanical properties is also associated with training-induced changes in the tendon intrinsic material properties. Such biochemical and structural changes include increased glycosaminoglycan content, decreased collagen, reducible cross-linking, and increased alignment of collagen ﬁbers [5,10,17,18,31–33].

Anatomical Site

Since chronic physical activity enhances the mechanical properties of tendons, it would be reasonable to suggest that tendons located at anatomical sites that allow high- level and frequent loading may have enhanced properties as compared with tendons loaded by low-level forces.

Examples of tendons that are frequently loaded by high- tensile loads are the tendons of the ankle plantarﬂexor and digital ﬂexor muscles. These tendons are loaded by the ground impact forces during terrestrial locomotion.

At the other end of the spectrum are the tendons of the ankle dorsiﬂexor and digital extensor muscles. These tendons are physiologically loaded primarily by the in- series muscles that contract to enable joint displacement.

Some experimental results indicate that the location and functional role of a tendon may be associated with the tendon mechanical response [12,35], but more recent studies stand in opposition with the above notion [19,36].

Aging

Several studies have shown that aging affects the properties of tendinous tissue [4,5,12,15,18,37,38]. However, some studies have shown that aging may result in intrin- sically stiffer, stronger, and more resilient tendons [12,13], while other studies have challenged these results [37–40].

This inconsistency may be partly accounted for by differences in the initial age examined. In some studies, specimens from very young subjects have been used [12,35,41]. On such occasions, changes in tissue properties reﬂect changes occurring as a function of maturation, which may mask an actual aging effect.

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Steroids

Corticosteroids have frequently been used for the treat- ment of articular inﬂammations. Intra-articular and intra- collagenous injections of corticosteroid may reduce the stiffness, ultimate stress, and energy-to-failure of collagenous tissue, even after short-term administration [42–44].

These results indicate that steroids may predispose the user to tendon injuries. Furthermore, using steroids may also impair the tendon healing process after an injury [45].

In Situ and In Vivo Protocols

In vitro–based studies have made it clear that tendons do not behave as rigid elements. Reference, however, to mechanical properties of in vitro material when inter- preting in vivo function should be treated with caution.

Although frequencies met in physiological locomotion have often been used in in vitro tensile tests, three impor- tant facts raise doubts as to whether such tests can mimic or predict accurately the tendon mechanical behavior under in vivo loading conditions: 1) Fixing a fibrous struc- ture with clamps is inevitably associated with A) slippage of the outer fibers; and B) stress concentration that may result in premature fracture. 2) Many experiments have been performed using preserved tendons, which may have altered properties [26,27]. 3) Tendon loads within the physiological region have traditionally been pre- dicted from the muscle maximal stress potential, which has been treated as a constant [12,25,46]. There is experimental evidence, however, that maximal muscle stress is muscle-specific, with fiber composition being the major determinant factor [47–49].

Some of these problems have been circumvented by testing animal tendons in situ after the animal has been killed or anesthetized [50–53]. This has been achieved by surgically releasing the tendon from its surrounding tissues, maintaining the proximal end of the tendon attached to the in-series muscle, and having the distal bone of the muscle-tendon unit gripped by a clamp inter- faced to a load cell. The in situ muscle contracts artiﬁcially by electrical stimulation and pulls the tendon, which lengthens as a function of the contractile force applied to its proximal end in a similar fashion to that obtained when the actuator of a tensile machine pulls an isolated specimen (see Figure 2-4). The advantage of such experimental protocols is that they allow assessment of the tendon and aponeurosis (i.e., intramuscular tendon) mechanical properties A) separately, and B) under physiological loading levels. Notwithstanding these advan- tages, the above in situ protocols are not applicable to humans. However, adapting similar principles to those used under in situ material testing has recently allowed

the development of a noninvasive method for assessing the mechanical properties of human tendons in vivo.

The method is based on real-time, sagittal-plane ultrasound scanning of a reference point along the tendon during static contraction of the in-series muscle. The limb is ﬁxed on the load cell of a dynamometer to record changes in muscle torque during isometric contraction (see Figure 2-5). The tensile forces generated by contrac-

distal bone

tendon

markers

load cell

muscle

proximal bone

stimulation

Figure 2-4. Experimental set-up to measure the mechanical properties of a tendon in situ. The muscle-tendon complex is intact. The proximal and distal bones are clamped. Loading is imposed by stimulation-induced muscle contraction. The resultant forces are measured by a load cell placed in series with the muscle-tendon complex. The resultant deformation in the tendon is obtained from off-line analysis of the displacement of markers attached on the tendon.

b

a

e c g

h

f

d i j

Figure 2-5. Experimental set-up to measure the mechanical properties of the human tibialis anterior tendon in vivo. The limb is ﬁxed on the footplate of a dynamometer. Isometric muscle contractions are generated by stimulation, while the resultant displacement of the myotendinous junction is recorded in real time using ultrasonography. The load imposed is taken from the dynamometer reading. a, dynamometer footplate; b, velcro straps; c, ankle joint; d, tibialis anterior muscle; e, tibialis anterior tendon; f, myotendinous junction; g, ultrasound probe, h; percutaneous stimulating electrodes; i, knee joint; j, knee mechanical stop. (Reprinted with permission from Maganaris and Paul.)

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tion pull the tendon proximally and cause a deformation, which is measured by the recorded displacement of the reference landmark in the tendon (see Figure 2-6). The load-elongation plot obtained by this method resembles in form that taken using in vitro and in situ methodolo- gies for muscle [36,54–56].

Particular attention should be paid at several stages in the measurements taken with the above in vivo method:

1) A reference marker visible in all scans recorded throughout the entire contraction must be selected. We found that the tendon proximal end in the myotendinous junction is a reliable landmark. Since the tendon is echoreﬂective and the muscle echoabsorptive, the myotendinous junction can be seen clearly. Repro- ducibility measurements of the displacement of the tendon distal end in the myotendinous junction as assessed by ultrasonography have yielded intra- and interobserver coefﬁcients of variation of less than 10%

[54–57]. Other authors have used as reference markers the intersection points of fascicles in the aponeurosis of the muscle [58–62]. This approach has the disadvantage that it yields displacements not only in the tendon, but also in a part of the aponeurosis, which may have different mechanical properties than the tendon itself [52,53].

Moreover, it is practically impossible to retrieve the location of a given fascicle (and therefore a given reference landmark) once the scanning probe has been removed from the scanned limb.

2) The scanning probe must be ﬁxed on the skin over the scanned limb [54,60–62], or an external constant point [36]. Adhesive tape has been shown to be effective in ﬁxing the probe securely on the skin.

3) The method necessitates that the contraction of the muscle is truly isometric, i.e., no joint movement occurs.

However, this is virtually impossible because A) structures surrounding the joint deform by the loading induced by contracting the muscle, e.g. ligaments, surrounding muscles and fat pads, and A) the dynamometer itself has an inherent compliance. Therefore, additional measurements need to be taken to correct for un- wanted shifts in the tendon “fixed” end when the scanning probe is externally fixed [36]. Kinematic measurements of the joint angle studied during contraction can give an estimate of the shift in the tendon “fixed” end [61,62].

4) The contractile forces elicited must be transmitted entirely to the tendon. If other muscles co-contract, then the forces recorded by the dynamometer load cell do not represent the tensile load applied to the tendon. Several authors, however, have neglected this important effect [58–62]. Isolating the mechanical action of a muscle can be achieved through percutaneous electrical stimulation over the muscle’s motor points or main nerve branch [54–56].

5) To reduce force to stress and elongation to strain, the tendon initial dimensions are required. These can also be taken using ultrasonography [54,55,58]. To obtain the mechanical hysteresis of the tendon, the contracting muscle must relax to allow the tendon to recoil [56].

By following the above steps, we estimated the mechanical properties of the human tibialis anterior and

Tibialis anterior tendon Tibialis anterior muscle

Rest

Stimulation with 75V

Stimulation with 150V

1 cm

Proximal end Distal end

Figure 2-6. Ultrasound-based assessment of tendon elongation. The sonographs shown were taken over the tibialis anterior myotendinous junction of a subject at rest (top), and electrical stimulation of the tibialis anterior muscle at 75 V (middle) and 150 V (bottom). The white arrow in each scan points to the tibialis anterior tendon end in the myotendinous junction. Notice the displacement of this reference landmark in the transition from rest to 75 V contraction and from 75 to 150 V contraction. The displacements shown were digitized and combined with the respective estimated force applied in the tendon to calculate the tendon force-elongation relation [54].

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gastrocnemius tendons. The tendon Young’s modulus and mechanical hysteresis values obtained were ~1.2 GPa and 18%, respectively [36,54–56]. Notwithstanding the good agreement of these estimates with in vitro tendon exper- imental results, the in vivo experiments failed to show the tendon linear region. Instead, the tendon tensile response was curvilinear over the loads examined. This ﬁnding indicates that isometric contractions of the tibialis anterior and gastrocnemius tendons generate tendon loads within the toe region, and are therefore unlikely to tear the tendon in a single pull. Further tensile measurements with reference landmarks chosen along the aponeurotic part of the tibialis anterior tendon showed that A) the entire aponeurosis strains almost 3 times as much as the tendon and B) the aponeurosis’s strain is not homoge- neous along its entire length [55,57]. Moreover, morpho- metric analysis of scans taken in the axial plane of the muscle showed that contraction increases the resting- state aponeurosis’s width and entire area [63]. These in vivo ﬁndings are in line with in situ–based reports [52,53,64].

The general consistency between the above in vivo ﬁndings and in situ-based results, as well as results from measurements on in vitro material subjected to tensile loads much smaller than that required to cause failure, adds credibility to the in vivo method. However, further studies are required to eliminate potential measurement errors. Although anatomical measurements on cadaveric muscle-tendon units have indicated that ultrasonography accurately locates connective tissue at rest [65,66], systematic research is needed to assess the accuracy of ultrasound-based measurements of connective tissue dimensions during movement upon muscle contraction and subsequent relaxation. Clearly, however, future research with respect to in vivo protocols should also be focused on quantifying the errors made in the measurement/calculation of tendon load.

Functional Consequences of the Mechanical Behavior of Tendons

The elasticity exhibited by a tendon on application of a tensile load has several important implications for the function of the in-series muscle.

First, having a muscle attached to a compliant tendon makes it more difﬁcult to control the position of the joint spanned by the tendon [67]. Consider, for example, an external oscillating force applied to a joint at a certain angle. Trying to maintain the joint still would require generating a constant contractile force in the muscle.

If the tendon of the muscle is very compliant, its length will change by the external oscillating load, even if the muscle is held at a constant length. This will result in failure to maintain the joint at the angle desired.

Second, the elongation of a tendon during a static muscle contraction is accompanied by an equivalent shortening in the muscle. For a given contractile force, a more extensible tendon will allow greater shortening of the muscle. This extra shortening induces shortening in the sarcomeres of the muscle. According to the cross- bridge mechanism of contraction [68], the result of this sarcomeric shortening on the contractile force elicited would depend on the region over which the average sar- comere of the muscle operates. If the sarcomeres operate in the ascending limb of the force-length relation, a more extensible tendon will result in less contractile force. In contrast, if the sarcomeres operate in the descending limb of the force-length relation, having a more extensible tendon will result in greater contractile force [51,69].

Third, stretching a tendon results in elastic energy storage. Since tendons exhibit low mechanical hysteresis, most of the elastic energy stored during stretching is returned once the tensile load is removed. This passive mechanism of energy provision operates in tendons in the feet of legged mammals during terrestrial locomotion, thus saving metabolic energy that would otherwise be needed to displace the body ahead [36,70,71].

The interplay between the mechanical properties of tendons and muscle function necessitates full apprecia- tion of the mechanical properties of a healthy tendon when aiming at restoring normal muscle function and joint performance. Consider, for example, surgical proce- dures involving limb and muscle-tendon lengthening.

Any change in the resting-state length of the tendon without taking into account that this will change the extensibility of the tendon itself will clearly affect the function of the in-series muscle. Therefore, protocols for the assessment of the mechanical properties of tendons in vivo could provide crucial help for optimizing the outcome of a corrective surgery. For example, they could be used for measurements in the tendon of the contralateral healthy limb of the patient, thus providing reference values that could then be used for guiding the decision making.

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