, David B. Burr2, Neil A. Sharkey3 and David P. Fyhrie4
Orthopaedic Surgery, UC Davis Medical Center, Olga, WA, USA
Department of Anatomy and Cell Biology, Indiana University School of Medicine, Indianapolis, IN, USA
Kinesiology, Orthopedics and Rehabilitation, Pennsylvania State University, University Park, PA, USA
Orthopaedic Surgery, Biomedical Engineering, UC Davis Medical Center, Sacramento, CA, USA
In Chap. 2 we explored the architecture and composition of ligaments and tendons, non-calcified but nonetheless extremely tough skeletal tissues responsible for binding bones together, transmitting forces from muscles and constraining motion within normal limits. To briefly review, ligaments and tendons are composed of linearly arranged collagen molecules assembled in a hierarchal fashion into subfibrils, fibrils and fibers. Collagen fibers within ligaments are architecturally orientated to effectively control and constrain joint motion; in tendon they are grouped into distinct but parallel fascicles.
KeywordsElastic modulusResidual strainAponeurosisViscoelastic
The movement of animals is like that of automatic puppets…For they have functioning parts that are of the same kind: the sinews and bones. The latter are like the pegs and the iron in our example, the sinews like the cables.
Aristotle (384–322 B.C.), De Motu Animalium
Get Clinical Tree app for offline access
4.1 Quasi-static Tensile Properties
In Chap. 2 we explored the architecture and composition of ligaments and tendons, non-calcified but nonetheless extremely tough skeletal tissues responsible for binding bones together, transmitting forces from muscles and constraining motion within normal limits. To briefly review, ligaments and tendons are composed of linearly arranged collagen molecules assembled in a hierarchal fashion into subfibrils, fibrils and fibers. Collagen fibers within ligaments are architecturally orientated to effectively control and constrain joint motion; in tendon they are grouped into distinct but parallel fascicles (Figs. 2.24 and 2.25). In this chapter we will take an in-depth look at the mechanical behavior of these skeletal soft tissues and some of the specialized laboratory and in-vivo approaches used to determine their behaviors. We will also briefly examine some common sites of injury, repair and assessment.
When loaded in the laboratory, ligaments and tendons produce characteristic load-deformation patterns that reflect their structural architecture. Materials such as steel and aluminum display linear stress-strain characteristics because of their crystalline nature. In these materials, the modulus of elasticity is constant throughout the elastic region and is representative of the atomic forces at work within their crystalline architecture. If the elastic limit is exceeded, crystalline materials will yield and eventually fail. In contrast, noncrystalline materials display what is termed rubbery elasticity. Tensile tests of these materials produce continuous upwardly concave load-displacement and stress-strain curves. In the noncrystalline materials, the elastic modulus is dependent on load magnitude because of intra- and intermolecular forces and molecular cross-linking. Failure of these materials is often abrupt and can occur without a well-defined yield point. Tensile tests of tendon and ligament produce curves that display both crystalline and rubbery characteristics, reflecting their complex structural hierarchy and molecular interactions.
A typical load-deformation (or stress-strain) curve for tendon or ligament (Fig. 4.1) can be divided into three regions. In the toe region, collagen crimps are removed by elongation. Initially minimal force is required for this elongation, but as the collagen fibers straighten, more and more force is required and the curve swings upward. The toe region typically ends at about 1.5–3.0 % strain. It is a matter of some controversy whether the toe region is physiologically or functionally important in vivo. It may actually be artifactual and the result of assuming that the normal resting length of the tendon or ligament in vivo occurs at zero load. Gillis et al. (1995) showed that in the forelimb of the standing horse the superficial flexor tendon has a strain of about 1.5 % compared to the extracted tendon under zero load (Fig. 4.2). Therefore during standing, a resting position for the horse, the structure is pre-strained beyond the toe region seen in laboratory tests of extracted tendons.
Typical load-deformation curve from a tendon or ligament showing the toe, linear, and yield and failure regions. The stress-strain curve would have a similar shape. Reprinted with permission from Simon SR (ed): Orthopaedic Basic Science. Rosemont, IL, American Academy of Orthopaedic Surgeons, 1994 (Woo et al. 1994).
Different stress-strain curves for equine superficial flexor tendon are obtained when measured in vivo (dashed line) and on specimens removed from the animal and loaded in the laboratory (solid line). Previously published as Fig. 3 from Gillis, C., Sharkey, N.A., Stover, S.M., Pool, R.R., and Meagher, D.M. The effect of maturation and aging on the material and ultrasonographic properties of equine superficial digital flexor tendon. American Journal of Veterinary Research 1995; 56:1345–1350 (Gillis et al. 1995).
Further loading produces a linear region in which the molecular crosslinks of the collagen are stressed (see Fig. 4.1). As for bone, the slope of this region of the load-deformation curve represents the stiffness of the tendon or ligament, and the slope of the stress-strain curve is a measure of the tissue’s modulus of elasticity (see Fig. 4.6). In practice, the slopes of these curves are usually determined at a standardized load or stress, close to the limits of the most linear portion of these curves. Elastic modulus values reported for tendon and ligament range between 1.0 and 2.0 GPa; the modulus of highly specialized tissues (such as the ligamentum nuchae, described further in Sect. 4.6) can be substantially less.
In the final region of the curve, a reduction in slope marks the yield point or onset of cross-link or fiber damage. If loading is continued, the tendon or ligament will eventually fail. Tendons and ligaments can be strained to between 5 and 7 % without damage. The maximum strain that a ligament or tendon can endure before failure is generally in the neighborhood of 12–15 %; however, substantial damage to the collagen network can occur well before complete rupture. Ligaments with unusually high elastin content can be strained to 30 % or more without damage. Ultimate tensile strengths for tendons and ligaments range from 50 to 150 MPa (for comparison, recall that the tensile strength of bone is about 150 MPa).
4.2 Viscoelastic Properties
The mechanical behavior of ligament and tendon is viscoelastic; thus, their load-displacement and stress-strain relationships are rate and history dependent. Testing parameters must always be carefully considered when establishing or comparing material properties such as ultimate strength, ultimate strain, and modulus of elasticity. Two representative stress strain curves for rat tail tendon are plotted in Fig. 4.3. The longer and shorter curves were produced using strain rates of 720 % per second and 3.6 % per second, respectively. As can be seen, the higher strain rate resulted in higher stress and strain at both failure and yield, and a slightly increased elastic modulus. Compare this behavior with that of bone in Fig. 7.13. Note that the ductility (energy absorption) of bone is decreased at higher strain rates, but that of tendon is increased.
Effect of strain rate on stress-strain curve for rat tail tendon. At high strain rates the linear portion of the curve is extended. Previously published as Fig. 3 from Haut, R.C. Age-dependent influence of strain rate on the tensile failure of rat-tail tendon. Journal of Biomechanical Engineering 1983; 110:296–299 (Haut 1983).
Tendon and ligament display hysteresis, another behavior caused, at least in part, by viscoelasticity. Hysteresis refers to loss of energy during a load-deformation cycle (Fig. 4.4). If a purely elastic material is loaded in its elastic range and then immediately unloaded, the load-deformation curve for the loading phase is identical to the load-deformation curve for the unloading phase. The energy absorbed during loading and returned to the system during unloading will be the same, and the system will be 100 % efficient. The loading-unloading profiles of ligaments and tendons are not identical, however. The area under the loading curve is greater than the area under the unloading curve, and the difference between the two represents the energy lost during the load cycle, which is referred to as hysteresis. The amount of hysteresis observed depends on the particular ligament or tendon and on the testing conditions. Tendons involved in gait tend to be efficient stores of elastic energy (i.e., have minimal hysteresis). For example, the digital flexor tendons of horses studied by Gillis et al. (1995) lost only about 5 % of their strain energy during a loading-unloading cycle.
Energy is lost each time a tendon is repeatedly loaded and unloaded, a process called hysteresis. The consequence of this over time is reduced stiffness and greater deformation for a given load or stress. Generally, a steady state develops after 10–20 cycles.
Where the lost energy goes is difficult to determine. Frictional forces at work within the sample cause some energy to be converted to heat, some of which flows to the surroundings while the remainder remains within the sample, raising its temperature and altering its mechanical properties. When the load is removed, the accumulated thermal energy slowly dissipates and the tendon or ligament may shorten further with time. However, residual strain may remain in the tissue for some time or indefinitely. Some of the lost strain energy has probably been used to break molecular cross-links or otherwise disrupt the molecular structure of the tissue.
Figure 4.4 demonstrates the effect of loading history. The mechanical behavior in cycle four is clearly different than that in cycle one. The shift to the right reflects a decrease in tendon or ligament stiffness and may be accompanied by a decrease in ultimate strength. For most tendons and ligaments a steady state is achieved after 10–20 cycles of loading. However, if the peak load is increased on a subsequent cycle, the steady state is disrupted and additional cycles of loading will be required to reestablish stability. Conditioning effects have been measured in-vivo and are an inherent time-dependent property reflective of actual physiologic behavior and not just an artifact of laboratory testing (Maganaris 2003). Tendons and ligaments are also subjected to constant loads or deformations, and, like bone and cartilage, they exhibit creep under constant load and stress relaxation under constant deformation (Fig. 4.5).
(a) When a constant load is applied to a tendon or ligament, its deformation gradually “creeps” to a stable value. (b) When a constant deformation is applied, the load (material stress) “relaxes” to a stable value. The times required for these processes are of the order of minutes or hours.
4.3 Mathematical Modeling
When modeling musculotendon dynamics, many investigators have chosen to simulate tendon as a purely elastic component for simplicity’s sake. Zajac (1989) assumed pure tendon elasticity in developing a generic musculotendon force-strain curve using two parameters, the tendon slack length, L S, and the peak isometric muscle force, F 0M. L S is the length at which the tendon just begins to exhibit some resistance to lengthening. Tendon strain is defined as ε = (L − L S)/L S. Suppose that the force-strain curve for a tendon has the shape shown in Fig. 4.6. The peak isometric force is measured for the tendon’s muscle and used to normalize the tendon force values (as shown on the right-hand axis). By dividing the force values by tendon cross-sectional area, the normalized force-strain curve, can be turned into a stress-strain curve which defines the response of a generic tendon. This relationship can then be scaled to obtain the force-length response of a musculotendon unit having a different area, F 0M, and L S.
The stress-strain curve for tendon may be normalized by the peak isometric muscle force, F 0M (expressed per unit cross-sectional area of the muscle), to obtain a generic tendon response shown by the scale on the right side of the graph (Zajac 1989).
Actually, of course, tendon tissue is viscoelastic and nonlinear. Lieber and associates (1992) developed an empirical model for muscle–tendon units by isolating and measuring the individual mechanical behavior of the frog semitendinosis muscle and its tendon and aponeurosis (the connection between the two; see following). They obtained the following regression equations for tendon and aponeurosis material behavior:
where ε is percent tendon or aponeurosis strain and F T and F A are the corresponding tensions in the tendon or aponeurosis, respectively, expressed as percent of the maximum tetanic muscle tension.
The viscoelastic properties of tendon or ligament are often represented using rheological models composed of two basic components: springs and dashpots (Fig. 4.7). The elastic component of their behavior is represented by the spring element, in which strain is linearly proportional to the applied stress. The dashpot represents the viscous behavior, in which the strain rate is linearly proportional to the applied stress. (The dashpot is a “leaky” piston in a cylinder; under load the fluid slowly flows past the piston, allowing it to move at a velocity proportional to the load.) In practice, combinations of elements are connected to simulate various behaviors. Two common models are the Kelvin solid and the three-parameter solid (Fig. 4.8). It is interesting to compare the behaviors of these models to those seen in Fig. 4.5. For the Kelvin solid, the strain, ε, is the same in each element, and the total stress supported by the combination is
Symbols used for the two basic rheological model components: a spring [A] and a dashpot [B].
Two rheological models: a Kelvin solid [A] and a three-parameter solid [B].
where is strain rate, E is the elastic modulus of the spring, and η is the viscosity of the dashpot. In a creep test, one has a constant load, σ 0, and Eq. (4.3) can be integrated to obtain
As t becomes very large, the strain asymptotically approaches σ 0/E. Initially, however, t = 0 and ε = 0; contrary to Fig. 4.5, there is no instantaneous elastic response in a creep test. When a constant strain, ε 0, is applied, the second term in Eq. (4.3) is zero, and the stress is constant at E ε 0. Thus, there is no relaxation effect for this model, either.
For the three-parameter model, a single spring is in series with a Kelvin solid. The equation for the series spring is σ = E′ε′ and that for the Kelvin element is σ = E″ε″ + ″. Using the LaPlace transform method (Flugge 1967), these equations may be combined to obtain
Using the LaPlace method, one may obtain for the creep solution
where E * = (E′ + E″)/E″ and λ = E″/η. In this case, at t = 0 there is an instantaneously produced strain σ 0/E′, and the strain subsequently approaches σ 0 E */E′. For the relaxation solution, one obtains
where ε 0 is the applied strain and γ = (E′ + E″)/η. Again, there is a stress E′ε 0 at t = 0, and this subsequently relaxes asymptotically to E′ε 0/E *. Thus, this model exhibits the general behavior observed in tendon and ligament. By fitting its equations to experimental data, values for E′, E″, and η can be obtained. These results may be useful for predictive purposes, but the model is still phenomenological rather than mechanistic. That is, we have not learned much about how the viscoelastic behavior is caused by the tissue structure. What parts of the tendon have the attributes associated with E′ and E″? Presumably η is associated with a flow of water, but where, exactly? These questions remain open.
A more elaborate and popular nonlinear viscoelastic theory was described by Fung (1972). This quasi-linear viscoelastic (QVL) model mathematically describes the stress relaxation of collagenous tissues as the product of independent functions of time and strain:
where σ e is the elastic response, a function of strain (ε) only, and G is the reduced relaxation function, which is dependent on time (t) only. Versions of this theory have been successfully applied by other investigators as well (Haut and Little 1972; Jenkins and Little 1974; Woo 1982). However, the form of this model assumes time and strain to be separable functions, i.e. time dependent relaxation behavior (G(t)) is the same at any given strain (ε). Experimental evidence demonstrates that this is not the case (Hingorani et al. 2004; Duenwald et al. 2010) indicating that even more elaborate nonlinear models are required to accurately describe the strain dependent relaxation behavior of collagenous tissue. A specialized transversely isotropic viscoelastic constitutive model developed by Davis and De Vita (2012) considers finite strain, tissue anisotropy and the strain dependent nature of stress relaxation. The model was able to represent the increase in stress relaxation with strain for rat tail tendon fascicles strained to 0.98, 2.00, and 3.28 %. Their phenomenological model remains in development, but is an improvement for tendon over the QLV model where the relaxation kernel is a function of strain.
4.4 Measuring Structural and Material Properties
A load-deformation curve, such as that shown in Fig. 4.1, is obtained by securely mounting each end of a sample in a material testing apparatus and then elongating the sample until it ruptures. Stress and strain behavior can then be generated by normalizing load to cross-sectional area and elongation to original length. However, unlike metals, plastics, or even bone, tendons and ligaments cannot easily be machined into standardized testing specimens. To further compound matters, they are difficult to grip, perhaps even more sensitive to moisture and temperature than bone, and have complex internal structures that make data interpretation difficult. For these reasons and others accurate and reproducible laboratory measurement of tendon and ligament tensile properties is notoriously difficult.
4.4.1 Storage and Testing Environments
The treatment and storage of ligament and tendon specimens and the environment in which testing is actually conducted are important practical considerations. Because it is not always possible to test tissue immediately after death, the issue of storage by freezing is particularly crucial. Investigations as early as 1847 reported the effects of various storage methods on the mechanical properties of tendons and ligaments, and although the data are somewhat conflicting, it would appear that freezing at −20 °C or below has little effect on their mechanical behavior (Wertheim 1847; Barad et al. 1982; Noyes and Grood 1976). Later, Woo et al. (1986) evaluated the effects of freezing rabbit medial collateral ligaments for up to 3 months. The only parameter significantly changed by freezing was the area of hysteresis in the first few cycles; by cycle 10 this difference became insignificant. Cyclic stress relaxation, load-deformation characteristics, and energy-absorbing capacity were unchanged. Jung et al. (2011) subsequently examined the consequences of up to eight freeze (−20 °C)-thaw (22 °C) cycles on human bone-patellar tendon-bone preparations and found little measurable effect on structural properties of these constructs.
Carefully controlled studies have shown that storage of specimens at room temperature has time-dependent effects that appear to be amplified in small specimens. Davison (1989) noted that the breaking strength of rat tail tendon decreased with time. Because this could be prevented by immediately washing the harvested rat tail tendon with enzyme inhibitors and keeping them on ice, Davison concluded that the collagen molecules were being subjected to gradual enzymatic degradation. An acidic environment (pH below 6) can also induce changes in the collagen molecule and lead to decreased material strength. Figure 4.9 shows the breaking strengths of rat tail tendon after being soaked in buffers of varying pH for 30 min at 0 °C.
Rat tail tendon strength declines with diminishing pH. Previously published as Fig. 4 in Davison, P.F. The contribution of labile crosslinks to the tensile behavior of tendons. Connective Tissue Research 1989; 18:293–305 (Davison 1989).
As we have learned, biologic tissues are viscoelastic with mechanical behavior dependent on fluid pressures and flow. Not surprisingly, numerous studies have shown the mechanical behavior of these tissues to vary as a function of hydration (Chimich et al. 1992; Haut and Haut 1997; Thornton et al. 2001; Hoffman et al. 2005). It is therefore important to keep test specimens immersed, or at least saturated, in physiologic testing fluids throughout experimentation. The fluids most frequently used are physiologic saline, phosphate buffered saline and Ringer’s solution. The former is a 0.9 % (g of solute/ml of solvent) solution of sodium chloride. This ionic concentration of salt is termed isotonic because its osmotic pressure is the same as that within the intracellular fluid of most cells. Cells remain intact and normally shaped when bathed in this fluid. Cells bathed in hypotonic solutions of lower ionic concentration take on water, swell, and eventually burst, releasing hydrolases and other potentially harmful enzymes into the extracellular matrix. Ringer’s is a more elaborate isotonic electrolyte solution that closely matches the electrolyte concentration of the blood. It contains small amounts of potassium and calcium in addition to sodium and chloride.
Because the viscoelastic behavior of the tendon and ligament is temperature dependent, good experimental technique dictates careful control of temperature as well as hydration during laboratory testing. Body temperature best simulates the in-vivo situation. Substantial heat can be generated in cyclically loaded tendon. In the laboratory situation, the amount of energy stored as strain energy or released to the environment as heat is dependent on the heat conduction characteristics and temperature of the test system. It is interesting to note that Wilson and Goodship (1994) measured temperatures in the superficial flexor tendons of racehorses greater than 44 °C and postulated heat-induced cell death as a possible cause of tendon degeneration, a frequent problem in the equine athlete.
In should be clear from the foregoing discussion that testing conditions are important and should be closely examined when reviewing previous work. Discrepancies between experimental results can often be explained by the different conditions under which the materials were evaluated. Obviously, conditions closely matched to the biologic environment are best able to reproduce the normal behavior of these tissues within the living body.
4.4.2 Measuring Cross-Sectional Area
Derivation of stress-strain behavior from load-elongation data requires knowledge of specimen cross-sectional area (CSA) and resting length (L o). In testing rigid materials these parameters are easily determined and controlled, but the viscoelastic nature of tendon and ligament makes accurate measurement of CSA and L o difficult. A variety of techniques have been developed to establish the cross-sectional area of ligaments or tendons, including measurement of specimen weight or volume per unit length, physical measurement using a micrometer, shadow amplitude contour reconstruction, laser reflectance, ultrasonographic measurement, and computer digitization of cross sections, photomicrographs, or inkblots. Significant systematic differences between these methodologies have been demonstrated (Ellis 1969; Woo et al. 1990; Moon et al. 2006). These systematic differences are often responsible for the considerable variation in absolute tissue stress and modulus values reported across studies.
If the density of the tissue is known, one can estimate the specimen’s mean CSA by dividing its weight by its length and density. Alternatively, the specimen’s volume can be determined by water displacement and divided by length to obtain mean cross-sectional area. These gravitational methods can be very reproducible but are generally useful only with long specimens of uniform dimensions. If a circular or elliptical cross section can be assumed, an alternative approach is to simply measure its diameter(s) with calipers at the site of interest and calculate the area. As might be expected, this technique produces more variable results. A more reproducible approach deforms the cross-sectional shape of the sample into a rectangle by pushing the segment of interest into a slot of known width and closing the slot with a plunger conforming to the dimensions of the slot. A standardized force is applied through the plunger and over time the specimen conforms to the rectangular geometry of the slot, after which height is measured and the area calculated as height × slot width. This method of deriving the cross-sectional area of a specimen yields reproducible values but may introduce substantial systematic error. Clearly, the result will depend on the force used to deform the ligament or tendon into a rectangular cross-section, the tissue’s normal architecture, and the time between force application and height measurement. If these variables are carefully controlled, the method is convenient and can produce excellent results.
Shadowing amplitude contour reconstruction, a fairly involved technique that requires a collimated light source, a detector, and a mechanical apparatus to rotate the sample, may give a more precise measure of specimen CSA; however, it is less reproducible than other techniques, and the apparatus is expensive to fabricate. Laser micrometer systems (Woo et al. 1990) and newer laser reflectance systems (Moon et al. 2006; Pokhai et al. 2009) offer the advantage of nondestructive measurement on intact specimens, and can also be used to measure CSA while the structure is loaded. Ultrasonography should be included in the list of reliable cross-sectional area measurement techniques and can be used for both in-vitro and in-vivo measurement (Gillis et al. 1995; Gellhorn and Carlson 2013). And finally, computer digitization of histologic cross sections taken from the test specimen after testing is accurate and reproducible but labor intensive and incompatible with destructive testing.
4.4.3 Gripping Slippery Viscoelastic Tissues
The mechanical testing of tendons or ligaments requires that they be grasped at the ends for mounting in the testing apparatus; this is particularly difficult because these tissues are so slippery. In addition, the viscoelastic nature of these tissues causes the specimen to deform over time and loosen within clamps, leading to slippage at the interface when loads are applied. Adhesive compounds, cyanoacrylates, have been found to work well for small slips of rat tendon but do not work for larger samples. A variety of methods have been employed for tensile testing larger tendons and ligaments. These include: looping the specimen around a post with or without suture augmentation, use of grips with roughened or serrated surfaces, use of bone–muscle–tendon–bone preparations, and freezing the tendon into the clamps. We have found the latter two methods work best.
Bone–muscle–tendon–bone (or bone–ligament–bone) preparations are an excellent choice if sub-failure characteristics are to be determined. The bone affords a reliable grip site that can accommodate high loads. Much has been learned about ligamentous behavior using the rabbit medial collateral ligament (MCL) and methods developed by Woo et al. (1983); see upper panel of Fig. 4.10. However, the method is obviously limited to bone-ligament-bone preparations and failures often occur near the insertions rather than in the mid-substance of ligament. When testing muscle–tendon–bone preparations, the muscle fibers will fail at tendon strains greater than 4 % or 5 %, which precludes complete recordings of the tendon stress-strain relationship. In either case, appropriate orientation of the bony ends of the specimen is critical to achieve a physiologic application of stress.
Riemersma and Schamhardt (1982) were the first to use cryogenic clamps to grip these tissues during testing. In our modification of this method (Sharkey et al. 1995) (lower panel of Fig. 4.10), liquid nitrogen flows through hollow chambers in the clamp, causing the specimen to freeze thereby forming a rigid interlock with the serrations of the clamp. Because the mechanical properties of tendon and ligament are sensitive to temperature, it is important to have a long specimen so that the test region is well away from the clamps. We have been able to apply supra-physiological loads to a variety of human tendons using this approach. Other investigators have employed other versions of this technique with good success (Matthews et al. 1996; Bowser et al. 2011).
4.4.4 Determining Resting Length
When you read in a research paper that a tendon or ligament was stretched 5 %, it is important to also know how the unstretched length was designated. Extracted collagenous tissues such as ligament and tendon do not have an obvious gauge length, i.e. resting length prior to loading that is subsequently used to determine strain. The reason is that their length depends not only on current loads but also on past loading history. Several conventions are used to handle this problem. One is to apply a small load to the structure for a fixed period of time and to arbitrarily call the resulting length the gauge length. An alternative method is to extrapolate from the linear portion of the load-deformation curve to the point at which the load goes to zero and refer to the length intercept at that point as the gauge length.
A closely related problem is the determination of tendon or ligament lengths in vivo and in situ. For both ligaments and tendons, this depends on body position, joint angles, and muscle activity. For example, strains in the ulnar collateral ligament of the elbow joint are diminished when the joint is near full extension if the flexor muscles are active. In tendons, the relationships between body position, muscle activity, tendon compliance, and the architecture of the muscle–tendon construct are extremely complex. This is particularly true for tendons that traverse two or more joints. In addition, because of the viscoelastic features of these structures, cyclic loading alters resting length. Finally, we must keep in mind that there is considerable individual variability in the innate tightness of ligaments; some individuals have very lax ligaments and hypermobile joints, whereas others have very tight ligaments. Women generally have more compliant tendons and ligaments than men, and this difference can be further increased during pregnancy. The viscoelastic properties of the cervix and other tissues in the birth canal are greatly altered by hormonal factors when mammals give birth (see pp. 97–99 in Alexander 1968), and this effect “spills over” into other connective tissues as well.
4.4.5 Measuring Specimen Elongation
Methodologies to measure sample elongation can be grouped into two broad categories: measuring the displacement of the testing machine crosshead and measuring changes in a defined gauge length on the test specimen itself. The latter can be done mechanically or by using optical, radiographic or other imaging techniques.
Using crosshead displacement as a measure of sample elongation is the least preferred. Such experiments usually yield erroneously high strain values because of extraneous displacement (i.e., slipping) at the grips. Bone–ligament–bone preparations can reduce but not always eliminate this testing artifact. Because the error is systematic, methods that use machine displacement may be adequate for comparative experiments, but the error may increase non-linearly with strain.
Measurement of elongation within the central region of the specimen, far from the grip sites, is much more likely to reflect the actual material properties of the tendon or ligament. Mechanical techniques for local measurement of elongation use extensometers supplied by the testing apparatus manufacturer or more generic linear displacement transducers. In either case the instrument is coupled to the sample directly, which can present problems. Many tendons and ligaments have complex fiber geometry or a helical fiber arrangement; pins inserted through the body of these structures for instrument attachment often rotate and produce out-of-plane motions that hamper axial elongation measurement. Using suture for attachment can reduce this problem but may produce results that reflect the behavior of the collagen fibers in the direct vicinity of the suture and not the tendon or ligament as a whole.
Preferred methods for elongation measurement employ imaging techniques. Cinematography or sequential still frame photographs were used in the past (Holmes et al. 1991), but digitized imaging is now the more common approach. An early schematic of this technique as presented by Woo et al. (1983) is provided in Fig. 4.11. An alternative method used for in-situ measurement employs radiography and radiopaque spheres placed within the substance of the tendon or ligament (Bay et al. 1997). Newer methods employ speckle tracking and digital image correlation to measure local strain and strain fields (Davis and De Vita 2012; Andarawis-Puri et al. 2010). One shortcoming of optical techniques is that they only measure surface strain; internal behavior may be different. Another is that stain or dye markings tend to disperse under load, which makes distance measurements difficult. Recorded behavior may also be influenced by surrounding fascia. Newer texture correlation techniques make it possible to avoid markers altogether and measure strain by tracking the displacements of natural features within the structure (Bey et al. 2002; Doehring et al. 2009). Texture correlation can also be applied to ultrasound images, which allows for in-vivo strain measurements at different depths within structures of interest (Kim et al. 2011; van Doesburg et al. 2012).
22.214.171.124 Architectural Implications
Although the collagen fibers in tendons typically are parallel, those in ligaments often are not. The pathways from origin to insertion of particular fibers are such that at any given angle of joint rotation certain fibers are stressed more than others. In testing a bone–ligament–bone preparation, orientation of the bones or the bone plugs to which the ligament is attached becomes critical. If only one particular joint angle is simulated, the characteristic behavior of the ligament at other angles of the joint will not be seen. Moreover, introduction of any extraneous twist or malalignment of the tissue may alter the measured mechanical properties. For testing to failure of either ligament or tendon, failure at the bony insertion always raises the concern that slight malpositioning of the bony block in the apparatus has resulted in nonphysiologic stresses at the bone-tendon or bone–ligament junction.
Because of ligament nonuniformity in relation to joint angles, elongation in loaded ligaments is best measured in two or even three dimensions using speckle techniques or image correlation so that local variations in strain can be appreciated.
126.96.36.199 In-Vivo Approaches
As indicated above, it is now possible to determine the displacements and strains present within the collagenous soft-tissues of live human subjects performing various activities. Ultrasound, the safest and most common technique, has been successfully used to track tendon displacements (van Doesburg et al. 2012) and measure strain at various depths within tissues (Kim et al. 2011). These studies are indeed informative but without simultaneous force measurement structural and material behaviors cannot be determined. Maganaris overcame this limitation by measuring strain from sonographic images of the tendons (and aponeuroses) of the tibialis posterior and gastrocnemius muscles taken while maximally stimulating the respective muscle and simultaneously measuring ankle joint moments with a dynamometer. Force was then indirectly derived by dividing the measured joint moments through by the tendon moment arms measured on magnetic resonance images. Sonography was used to measure tendon cross-sectional area. Force-displacement and stress-strain relationships were thus derived (Maganaris 2002; Maganaris and Paul 2002). The in-vivo results calculated by Maganaris and colleagues are in close agreement with data obtained in bench top experiments, with functional strains for tendon in the 3–5 % range, Youngs modulus values in the neighborhood of 0.9–1.4 GPa, and hysteresis values of 14–22 %.
Several different in-vivo transducer designs have been employed to measure the forces transmitted by the skeletal soft-tissues during normal activities. All designs work on a similar principal in that they deform as axial load is applied to the tendon or ligament to which they are attached. Buckle transducers, implantable force transducers and fiberoptic cables have all been used to measure tendon and ligament forces in humans. Of course all of these devices require surgical implantation with attendant risk to subjects. And once implanted the transducers require calibration, which is usually achieved indirectly by measuring joint moments and calibrating the transducer to the theoretic forces derived by dividing the moments obtained by the moment arm through which the tendon works. Once calibrated, forces within the structure during normal activities can be measured.
Forces in the anterior cruciate ligament (Roberts et al. 1994; Howe et al. 1990) and patellar tendon (Finni et al. 2000) have been successfully measured within implanted transducers, but functional forces in the Achilles tendon have been the primary focus of in-vivo work because of its important functional role in locomotion and relatively easy accessibility (Gregor et al. 1987; Komi et al. 1992, 1996; Fukashiro et al. 1995). Although not without technical challenges, the fiberoptic transducers have been used in several such studies with good success; they are minimally invasive, easy to place, and inexpensive. Finni and colleagues (1998) used fiberoptics to study eight normal subjects and reported peak Achilles tendon forces during walking of 750–2360 N.
4.5 Functions at Junctions
Suppose that you were given the daunting task of designing the interfaces between muscles and tendons and between tendons and bones. How would you design an interface between two soft tissues of very different tensile stiffnesses so that it could resist forces of hundreds of Newtons? Or one between flexible and rigid tissues where the angle of pull would vary considerably? We now examine the solutions found in the skeleton.
4.5.1 The Myotendinous Junction
The transition from muscle to tendon occurs at the aponeurosis, a flat thin sheet of collagenous material that gradually narrows and thickens to form tendon. Individual muscle fibers attach to these tendinous extensions both proximally and distally. At each junction the force developed by the intracellular contractile apparatus of the fiber is transferred to the extracellular matrix of the tendon. The junction site is characterized by extensive membrane folding, which increases the surface area available for force transmission and thus decreases the junctional stress. The inter-digitation also enables more effective load transmission because the interface is subjected primarily to shear stress rather than tensile stress. In fact, the angles at the junctions between muscle fibers and tendon collagen are usually close to zero, which greatly enhances junctional strength. Increases in the junctional angle may be associated with disuse atrophy and junction failure (Tidball 1983).
Binding of the muscle fiber to the tendon collagen apparently occurs at discrete sites along the interface (Trotter et al. 1981; Tidball and Daniel 1986). Subsarcolemmal “densities” have been identified within skeletal muscle cells at these sites. The cytoskeletal proteins alpha-actinin, vinculin, and talin and the adhesive proteins integrin and vitronectin have all been implicated in the load transmission process, but our understanding of myotendinous junctions is far from complete.
Several studies of musculotendinous preparations have shown that muscle strain injuries usually occur at or near the junction of muscle and its tendon of origin. Lieber and associates (1991), using frog semitendinosis muscle–tendon–bone preparations, demonstrated that during passive stretch the aponeurosis was significantly more compliant than both the tendon and the bone–tendon junction (Fig. 4.12, Left) Maganaris (2002) measured very similar behavior in the tibialis anterior aponeurosis of live human subjects (Fig. 4.12, Right).
Left: Variations in compliance of the three junctional components of frog semitendinosis muscle-tendon-bone preparations. Previously published as Fig. 3D in Lieber, R.L., Leonard, M.E., Brown, C.G., and Trestik, C.L. Frog semitendinosus tendon load-strain and stress-strain properties during passive loading. American Journal of Physiology 1991; 261:C86–C92 (Lieber et al. 1991). Right: Compliance of the tibialis anterior (TA) tendon and aponeurosis measured in live human subjects (Maganaris and Paul 2002).
In another study using frog semitendinosis units, Tidball et al. (1993) reported large increases in failure load (30 %) and energy absorption (112 %) in stimulated (actively contracting) preparations as compared to nonstimulated controls. If the muscle–tendon unit is strained to failure with the muscle stimulated, most fibers fail at the myotendinous junction, whereas failure in nonstimulated muscle–tendon preparations occurs within the inactive fibers a short distance from the junction.
Most studies of aponeurosis mechanics, whether under passive, active, in-vivo or in-vitro conditions, have only characterized strains in the longitudinal direction, i.e. along the trajectory of its emanating tendon. But it has been shown that the aponeurosis also expands in the transverse directions, which makes sense given that muscle fibers surround and attach on opposite sides of these tendinous sheets and muscles bulge upon contraction (Scott and Loeb 1995; Donkelaar et al. 1999; Maganaris et al. 2001). Azizi and Roberts (2009) used high-speed fluoroscopy to measure biaxial strains within the aponeuroses of actively contracting gastrocnemius muscles extracted from turkeys. Transverse strain within the aponeurosis was found to be 4X greater than longitudinal strains. More important in terms of functional significance was the fact that longitudinal stiffness varied as a function of transverse strain, thereby providing a mechanism to modulate overall stiffness of the muscle–tendon unit, which in turn modulates energy storage and recovery capacity, factors we briefly explore in forthcoming sections.
4.5.2 Ligament and Tendon Insertions to Bone
Tendons and ligaments attach to bone at insertions or entheses. Insertions are generally classified as direct or indirect, but they are anatomically and functionally diverse, constituting a continuum of morphology with each site uniquely suited to its location and function. Direct insertions, also referred to as fibrocartilagenous entheses (Benjamin et al. 2006), often meet the adjoining bone at right angles, and have four microscopic transitional zones of varying thicknesses. Zone 1 is represented by the normal collagen and fibroblasts of tendon or ligament; zone 2 is made of fibrocartilage and contains cells with morphology similar to chondrocytes; zone 3 is mineralized fibrocartilage; and zone 4 is bone. Between zones 2 and 3 is a mineralization tidemark (Fig. 4.13). The transition from tendon or ligament to bone is 300–700 μm across.