Elastic energy storage in tendons: mechanical differences related to function and age ROBERT Department
SHADWICK,
mechanical
ROBERT
differences
E. SHADWICK of Biology, University of Calgary, Calgary, Alberta T2N lN4, Canada
E. Elastic energy storage in tendons: related to function and age. J. Appl.
Physiol. 68(3): 1033-1040, 1990.-We investigated the possibility that tendons that normally experience relatively high stressesand function as springs during locomotion, such as digital flexors, might develop different mechanical properties from those that experienceonly relatively low stresses,such as digital extensors.At birth the digital flexor and extensor tendons of pigs have identical mechanical properties, exhibiting higher extensibility and mechanicalhysteresisand lower elastic modulus,tensile strength, and elastic energy storagecapability than adult tendons. With growth and aging these tendons becomemuch stronger, stiffer, lessextensible, and more resilient than at birth. Furthermore, these alterations in elastic properties occur to a significantly greater degreein the highload-bearing flexors than in the low-stressextensors. At maturity the pig digital flexor tendons have twice the tensile strength and elastic modulusbut only half the strain energy dissipation of the correspondingextensor tendons. A morphometric analysis of the digital musclesprovides an estimate of maximal in vivo tendon stressesand suggeststhat the muscletendon unit of the digital flexor is designedto function as an elastic energy storageelement whereasthat of the digital extensor is not. Thus the differences in material properties between mature flexor and extensor tendons are correlated with their physiological functions, i.e., the flexor is much better suited to act as an effective biological spring than is the extensor. digital tendon; flexor; extensor; mechanicalproperties; modulus of elasticity; strain energy; hysteresis OF TENDONS in the legs and feet of many terrestrial animals provides an important mechanism for saving substantial quantities of muscular energy during locomotion (2, 3, 12). The body is decelerated as the foot lands on the ground, causing kinetic and potential energy to be stored transiently as strain energy in tendons and muscles that are stretched by the impact forces. Elastic recoil, primarily by the tendons, converts most of the stored energy back to kinetic and potential energy as the foot leaves the ground (1). Metabolic energy savings provided by tendon elasticity during fast locomotion of large animals may be as high as 50% (2,3,12). Tendons have mechanical properties which generally make them well suited to act as biological springs. They are relatively stiff (i.e., have a high elastic modulus), can sustain high tensile stress (force per cross-sectional area), can stretch elastically up to -5% strain (length increment relative to initial length), and are very resilient (9, 20, 42). This means that large amounts of strain THE ELASTICITY
0161-7567/90
$1.50 Copyright
energy will be stored in tendons that are subjected to high tensile stresses, as occurs in fast locomotion (2, 32) and that most of this energy will be recovered in an elastic recoil when the load is removed. The impressive mechanical properties of tendons are provided by their major constituent, parallel fibrils of covalently crosslinked collagen molecules. It is well known that the density and structure of cross-links and the fibril morphology in collagenous tissues change as a function of age, in a way that can be correlated with age-related changes in mechanical properties (25, 26, 28-30, 38). Evidence from long-term exercise and limb immobilization studies (23, 33, 35, 36, 39, 43) suggests that ground reaction forces may have an important influence on the growth and structure of tendons as well as other skeletal elements. It seems possible, therefore, that tendons that normally experience relatively high stresses in locomotion, such as digital flexors, may develop different mechanical properties than those that experience only relatively low stresses, such as digital extensors. This premise forms the basis of the present investigation. There is no agreement in the literature as to whether the mechanical properties of tendons may vary in different species or with anatomic location and function. In a recent study of “high stress” tendons from a variety of mammals, Bennett et al. (9) found that the elastic modulus could vary by twofold, from -1-2 GPa, at stresses >30 MPa. Several studies have compared the properties of mammalian flexor and extensor tendons, but the results are not consistent (8, 11, 21,41,43). These discrepancies may be partly the result of the difficulties of clamping and making accurate strain measurements on such very stiff structures and the different techniques used by various investigators. Woo et al. (41, 43) measured strain with a video dimension analyzer and showed that the tensile strength and stiffness of digital flexor tendons in miniature swine were about twice as high as those of the corresponding extensor tendons. We have made similar measurements on pig tendons at birth and maturity. The results presented here show that the mechanical properties of digital tendons change dramatically with age and that important differences in the elastic energy storage capabilities exist between the flexors, which function as springs in locomotion, and the extensors, which do not. METHODS
Mechanical tests. Front feet of domestic pigs (Sus scrofa) were obtained from local slaughterhouses. The
0 1990 the American
Physiological
Society
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ELASTIC
PROPERTIES
digital extensor tendons and the deep digital flexor tendons were excised from nine mature pigs (age 4-5 mo, 80-100 kg) and two newborns, wrapped in plastic film, and stored at 4°C until tested. During the mechanical tests at room temperature the tendons were kept moist with saline, but not immersed, because this is known to cause appreciable swelling (9). Tensile tests were performed by clamping the specimen in either steel vice or pneumatic-type grips and stretching it in a mechanical testing machine. Two different testing systems were used, and results were combined. In one, an Instron 1102 machine was used to perform slow extensions at constant rates of 5 mm/min. Force was measured continuously by a strain gauge load cell. Length changes were determined by a noncontact optical method that measured the displacement of two surface markers (black brush bristles) glued onto the central region of the tendon sample, with the use of a video dimension analyzing system as described by Woo et al. (43). Analog force and displacement data were recorded on a flatbed X-Y recorder. Dynamic tests were performed with an Instron 8031 servo-hydraulic machine, as described by Ker et al. (22). In these tests tendons were stretched sinusoidally by the actuator of the machine at frequencies of 0.055 or 2.2 Hz. Length changes were determined on the central portion of the tendon by an electronic extensometer, kindly loaned by Dr. Robert Ker. The design and performance of this instrument has been described previously (20). The extensometer attached to the tendon by clamps containing small steel pins. We put cyanoacrylate glue on the tips of these pins to ensure that no slipping occurred when the tendon was stretched. This was particularly helpful with the relatively thin and flat extensor tendons. Force and extension signals were recorded simultaneously with a pair of synchronized digital transient recorders, and selected cycles were then plotted on an X-Y recorder. In cyclic tests the data were recorded only after several successive cycles of extension had been completed and the response of the tendon was stable and reproducible. Some tendons were tested to failure after being preconditioned by cyclic loading. For this purpose pneumatic grips were used for the newborn tendons, while cryojaws (31) were employed to clamp the adult tendons. The pneumatic grips provided a self-tightening effect that prevented slippage in the relatively thin newborn tendons. The cryojaws were well suited to grip the adult tendons securely against the large forces required for fracture. In all tests the tensile stress was calculated as the tensile force (in Newtons) + specimen cross-sectional area (in m2) and expressed in megapascals (1 MPa = lo6 N/m2). Strain was calculated as the change in length + initial length, as measured between the two surface markers in tests with the video system or between the attachment clamps of the extensometer. Tendon crosssectional areas were calculated by dividing the wet weight of a tendon sample by its length and density (9). We determined the water content from wet and dry weights (Table 1) and calculated the density of hydrated tendon, assuming the density of dry tendon to be 1,400 kg/m3
OF
DIGITAL
TENDONS
(24) and that of water to be 1,000 kg/m3. This method yielded a density of 1,120 kg/m3 for adult tendons, which is similar to that measured gravimetrically by Ker (20). The higher water content of the newborn tendons gave a lower wet density value of 1,060 kg/m3. The modulus of elasticity, a measure of the elastic stiffness of the tendon, was calculated as the gradient of the stress-strain curve and expressed in gigapascals. The mechanical hysteresis is the proportion of strain energy that is dissipated by internal viscous damping in each extension cycle. It is calculated as the ratio of the area within the stress-strain loop (strain energy dissipated) to the area beneath the load portion of the curve (strain energy input). Resilience is the converse of hysteresis, i.e, the proportion of strain energy input which is recovered by elastic recoil. The material toughness is defined as the total strain energy absorbed (joules/kg) when the specimen is stretched to failure. It is calculated from the area under the stress-strain curve up to the failure strain. Reliability of measurement techniques. Much of the variation in the literature values of tendon mechanical properties undoubtedly arises from inaccuracies in the measurement of tensile strain and cross-sectional area of the test samples. The problems associated with the use of the actual displacement of the tendon grips to calculated strain are well recognized (9, 20, 41, 43, 44). Reliable measurements of length changes can be made in the central body of the tendon, well away from the clamps where slipping, tissue distortion, and stress concentrations may occur. These effects are much more significant in thick tendons, such as the digital flexors, and less problematic in small flat tendons (9, 31). In our cyclic tests we determined strain by two different techniques that we believe are reliable. The video system has the advantage of requiring no direct contact with the sample but was used only for quasi-static tests because of its relatively low frequency response. The extensometer, on the other hand, requires attachment to the specimen but performs very well in dynamic tests up to frequencies of at least 11 Hz (20). We found good agreement between the results from these two methods. Muscle properties. The mass of the muscle inserting on each digital tendon in the mature animal was measured in four fresh front limbs. The muscles were then fixed in 20% Formalin, and fiber lengths were measured on sections cut in the plane of the fibers. Without establishing the sarcomere length of each fiber, this method has a possible uncertainty of ~25% in values of fiber length and subsequently cross-sectional area (21). From the muscle mass and fiber length, and with the use of a density of 1,060 kg/ m3, we calculated the cross-sectional area of muscle fibers and the corresponding maximum stress that could be imposed on each tendon by its muscle, by the method of Ker et al. (21). This method assumes that the maximum isometric stress that can be produced by striated muscle is 0.3 MPa and that pennation angles are less than ~30’. Because tendons are in series with muscles, the maximum tension in a tendon cannot exceed the tension developed by its muscle. Therefore, the maximal tendon stress (at) is proportional
ELASTIC
0
1
2 Strain
3 (%I
4
5
0
1
PROPERTIES
2 Strain
3 1%)
OF
4
5
FIG. 1. Examples of stress-strain curves for a digital extensor tendon (A) and a digital flexor tendon (B) from a newborn pig, obtained by cycling the specimens between 0 and 5% strain. Hysteresis is 24% in A and 28% in B. Elastic modulus for the linear portion of loading cycle is 0.12 and 0.13 GPa, respectively.
to the ratio of the muscle and tendon cross-sectional areas, A, and At, respectively, and the maximal muscle stress (21) ot = 0.3(A,/At)MPa
(I)
Higher muscle stresses (and proportionately higher tendon stresses) may occur when active muscles are stretched rapidly (see DISCUSSION). The mechanical safety factor is defined as the ratio of tensile strength of a tendon to the maximum in vivo stress it will experience. A dimensionless fiber length factor, L, has been defined as the ratio of muscle fiber length to the extension of its tendon that occurs when the muscle is producing maximum force (21). Tendon extension at ct was calculated by applying the corresponding strain of 2.5-3% (see Figs. 4 and 7, and below) to the actual tendon length. L is useful in the context of the present study because it is an expression of the relative importance of muscle vs. tendon length changes, and therefore strain energy storage capability, under maximal loads (21). According to a recent theory for the optimization of tendon thickness (21), the parameter L should indicate whether the dimensions of a muscle-tendon unit have been optimized for effective elastic energy storage (L < 2) or, alternatively, control of joint displacement and minimal total mass (L > 4) (21). The digital extensor tendons arise from individual muscle heads that together form the extensor digitorum communis and extensor digitorum lateralis muscles. The TABLE
Values
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TENDONS
flexor digitorum profundus has three heads that insert on a common tendon; this then divides into two deep digital flexor tendons that end on the distal phalanges of the principal digits and two minor tendons that end on the accessory digits. Within each muscle head the fiber length was relatively constant. The humeral head was the largest of the three, representing -85% of the total muscle mass. The humeral, radial, and ulnar heads of the flexor digitorum profundus were weighed and measured separately, and individual values of A, were summed to give the total muscle cross section. RESULTS
lMechanicaL properties. In the newborn animal, digital flexor and extensor tendons were indistinguishable in their mechanical properties but very different from those of mature pigs. Figure 1 shows typical stress-strain data for newborn extensor and flexor tendons, cyclically loaded to 5% strain. The initial “toe” region, associated with the straightening of the crimped collagen fibrils (37), extends to a strain of -4%, at which point the linear region of the stress-strain curve begins. The elastic modulus for this linear region averaged only 0.16 GPa in the newborn tendons, whereas the strain energy dissipated per cycle was -25% (Table 1). Figure 2 shows examples of failure tests on flexor and extensor tendons from a newborn animal, again demonstrating the similarity in mechanical behavior of these tendons at birth. Mechanical failure occurred at relatively high strains and low stresses compared with the mature tendons (Figs. 2 and 7). These results demonstrate that, at birth, the pig digital tendons are relatively poor biological springs; their capacity to store and release elastic strain energy is far below that of mature tendons (Table 1). We tested the mature digital tendons at low strain rates (5 mm/min or 0.055 Hz) to simulate in vivo loading rates that would occur during slow movement and at a high frequency (2.2 Hz) to mimic stress application that might occur during fast locomotion. After initial periods of conditioning we found no appreciable variation in the mechanical behavior of any tendon within this range of strain rates (examples in Fig. 3). Repeated extension of flexor and extensor tendons produced highly stable responses (Fig. 3). This indicates that strains up to 5% did not exceed elastic limits or cause appreciable mechanical
1. Summary of mechanical properties of digital tendons from newborn and mature pigs Strain Energy Recovered Elastically from 3% Strain,
Maximum Energy
Strain at cf,
Elastic Modulus, GPa
Hysteresis, %
18.9kO.56
0.16t0.02
24.5k3.5
7
35.3t1.1
0.76t0.12
17.5k5.2
164
1,400 (tf = 7%)
36.8k1.6
1.66t0.16
9.2s.4
415
4,500
%Dry Weight
Newborn Digital Mature Digital Digital
DIGITAL
J/k
J/k
900 (Ef = 15%)
tendons extensor tendon flexor tendon
(Ef = 9%)
are means t SD. Flexor and extensor tendons have identical elastic properties in the newborn. Elastic modulus and hysteresis differ significantly (P < 0.01) between newborn and mature tendons and between flexor and extensor of mature animals (means are for values taken at stresses >30 MPa in the mature flexors, ~10 MPa in the mature extensors, and >3 MPa in the newborn tendons). Based on average mechanical properties of each type of tendon, strain energy that would be released by elastic recoil from an extension of 3% is calculated, as well as maximum strain energy absorbed in each if extended to its failure strain Ef (i.e., toughness). For the latter calculation we used failure strain values averaged from our observations and those of Woo et al. (41,43).
1036
ELASTIC
PROPERTIES
OF DIGITAL
TENDONS
50-
402 a I - 302 Q) L
_
3j 20-
20 Strain
(%I
2. Examples of tests on newborn digital extensor (E) and flexor (F) tendons stretched to the breaking point. Failure began at -17% strain, corresponding to ultimate stresses of 17-18 MPa, whereas final rupture occurred at much higher strains. Elastic modulus for linear portion of these curves is 0.16 GPa. FIG.
2 Strain
(%)
4. Examples of stress-strain curves obtained from digital flexor (F) and extensor (E) tendons of adult pigs while cycled sinusoidally at 2.2 Hz to -3.6% strain. Arrows, loading and unloading directions. Elastic modulus values at peak stress are 1.8 and 0.7 GPa, and hysteresis values are 7 and 19%) respectively. FIG.
2.Or
a
cl
a
0 0
0
0
2
.-z0
,Q 0.5
1.0 Extension
1.5 (mm)
3. Plot of force vs. extension for a mature digital flexor (F) cycled to 4.6% strain at 0.055 and 2.2 Hz successively, showing that resilience and stiffness have virtually no frequency dependence, and for a mature digital extensor (E) cycled to 4.7% strain, showing that no fatigue occurred in successive cycles. These 2 curves represent 14th and 150th cycle. FIG.
fatigue. These observations are in accord with previous studies on mature tendons (20, 31). Typical cyclic stress-strain curves for digital flexor and extensor tendons of mature pigs are compared in Fig. 4. There is a remarkable difference between the material properties of the two types of tendon, the flexor exhibiting about twice the stress at each strain and only half the hysteresis of the extensor. The elastic modulus increases, in each tendon, as the slope of the stress-strain curve. We calculated the modulus at different levels of extension from all tests of up to 5% strain; the mature flexor, extensor, and newborn tendons are compared in Fig. 5. The modulus rises with strain, reach ing a plateau level in the mature tendons >2.5% strain. In this region the fl .exor tendons are twice as stiff as the extensors and an order of magnitude stiffer than those of the newborn animal. When the elastic modulus values are plotted as a function of tensile stress (Fig. 6), plateau levels are reached above -30 MPa in the mature flexors, 10 MPa in the mature extensors, and 3 MPa in the newborn tendons. Mean values of elastic modulus, computed from
00
0
1.0
O
O
0.5
0
AA
0 OA
A
AtA
A;j
44
AA
t
2.5% strain. Data were pooled from tests at different strain rates and from the 2 strain measurement systems.
the data in these plateau regions, are 1.66,0.76, and 0.16 GPa, respectively, whereas the corresponding hysteresis means (i.e., percent energy dissipated), determined from cyclic tests, are 9.2, 17.5, and 24.5% (Table 1). Both modulus and hysteresis were determined to be significantly different for each tendon group (P < 0.01). The percent tissue dry weight, an approximate indication of tendon collagen content (13), was 35.3-36.8% in mature tendons but only 18.9% in those of the newborn. We conducted a small number of fracture tests on the digital tendons to determine the ultimate strains that could be reached. Usually the tendon broke at one grip, where stress concentrations likely caused the breaking strain to be an underestimate of the true value for the tendon. In some tests the break occurred in the central region of the tendon, and two examples are shown in Fig. 7. The failure strains for these particular flexor and extensor tendons were 8.5% and 6.8%, respectively. The breaking stress is equivalent to the tensile strength: for
ELASTIC
PROPERTIES
OF
A f
20
40
WPa)
Stress
FIG. 6. Plot of elastic modulus as a function of tensile stress for adult digital flexor tendons (o), adult digital extensor tendons (A), and newborn digital tendons (0). Linear regression lines have been fit through data points at stresses ~30 MPa for adult flexors and X0 MPa for adult extensors.
DIGITAL
TENDONS
1037
Muscle properties in mature animals. Muscle fiber length averaged 34 t 7 mm (n = 12) in the extensor digitorum communis and 20 t 3 mm (n = 8) in the extensor digitorum lateralis. In the major (humeral) head of the flexor digitorum profundus the fiber length averaged 14 t 1 mm (n = 4), compared with 58 t 3 and 13 t 5 mm in the ulnar and radial heads, respectively. In the mature pig the total cross-sectional area of the paired deep digital flexor tendons was generally about twice the combined area of the five digital extensor tendons. However, the flexor digitorum profundus had by far the greatest mass and fiber cross section of all forefoot muscles, so that the area ratio (A,/AJ averaged 100 for the flexors and only 50 for the extensors (Table 2). From Eq. 1 these values predict an in vivo ct of -30 MPa in the deep digital flexor tendons and -15 MPa in the digital extensors, yielding safety factors of -3 in each case. The corresponding strain for these maximal stress levels is ~2.5-3% for both tendons (Figs. 4, 7). L was relatively low for the major humeral head of the deep digital flexor compared with the digital extensors (Table 2), an indication that the former is designed to function in elastic energy storage, whereas the latter is not (21). DISCUSSION
4 0
2
6
4 strain
8
(%I
7. Examples of tensile tes ts to failure and flexor (F) tendons, by the use of cryojaws.
of mature
FIG.
extensor
(E)
2. Functional properties of mature digital tendons and musculature TABLE
An/At
Extensor Deep flexor
50 100
* Extensor
lateralis;
Tendon Tensile Strength, MPa
;;a
15 30 t extensor
40-50 80-90 communis;
Safety Factor
3 3
Muscle Fiber Length, mm
20*,34t 14$
$ humeral
L 3",5? 1.5$
head.
mature tendons we recorded strengths in the range of 80-90 MPa for the flexors but only 40-50 MPa for the extensors (Table 2). When the break occurred away from the grips in mature tendons, there was a sudden and catastrophic rupture across the whole specimen (Fig. 7). The newborn tendons were much more ductile and broke in a different manner. Failure was initiated at -12-E% strain, where the stress reached a maximum value and thereafter dec reased as the tendon gradually pulled apart with further extension (see Fig. 2). The tensile strength of the newborn tendons was generally ~20 MPa.
Mechanical properties and age-related changes. The major findings of this study are that the mechanical properties of digital tendons in the pig change dramatically from birth to maturity and that these changes are significantly greater in the deep flexors than in the extensors. This is, to our knowledge, the first study to show differential age-related mechanical changes in anatomically distinct tendons of the same limb. As structural materials, the digital flexor and extensor tendons of the mature pig are clearly different from each other and from those of the newborn animal. At birth the digital flexor and extensor tendons have identical mechanical properties, exhibiting much higher extensibility and mechanical hysteresis and much lower elastic modulus and tensile strength than are typical of adult tendons (9, 17, 20). With growth and aging these properties all change, such that the mature tendons are much stronger, stiffer, less extensible, and more resilient than at birth. Furthermore, these alterations in elastic properties occur to a significantly greater degree in the major load-bearing flexors than in the less stressed extensors (Table 1). By 4-5 mo of age the digital flexor tendons exhibit approximately two times the tensile strength and elastic modulus but only half the internal damping of the corresponding extensor tendons. The mechanical properties of the mature pig digital flexor tendon are very close to those of other mature mammalian tendons, such as the superficial and deep digital flexor of the horse (31), deer, and donkey (9) and the plantaris and gastrocnemius of the sheep (20), camel (5), wallaby, and deer (9). These studies showed that adult tendons that experience high stresses during locomotion generally have an elastic modulus between -1.2 and 1.8 GPa, a tensile strength ranging from 70 to 120 MPa, and elastic strain energy recovery of 90-96%/cycle, at physiologically relevant strain rates. On the other
1038
ELASTIC
PROPERTIES
hand, the mechanical properties of the digital extensor tendons of the mature pig fall well below these ranges. This discrepancy is in accord with the observations of Woo et al. (41, 42), who found that the tensile strength and stiffness of digital flexor tendons of adult miniature swine were about twice those of the corresponding digital extensor tendons. The same authors reported average failure strains of -9% for these tendons but did not investigate their hysteresis behavior. No clear pattern has emerged with respect to differences between digital flexor and extensor tendons of mammals in general. In a study of amputated human lower limbs, Blanton and Biggs (11) reported that the digital flexor tendons were 18% stronger than the digital extensors, whereas Benedict et al. (8) found opposing results. Kent et al. (19) and our own laboratory (unpublished observations) have found differences in mechanical stability and collagen cross-linking between flexor and extensor tendons of the rabbit forefoot. Recently, Ker et al. (21) demonstrated that the digital extensor tendon of an adult cow forelimb had a tensile strength (80 MPa) and an elastic modulus (1.5 GPa) that were indistinguishable from those of adult digital flexor tendons. Differences in species, age, and exercise level probably contribute to the overall disparity of these observations. Viidik (36) and others since (see Ref. 33 for a review) have shown that long-term exercise can increase the tensile mechanical properties of locomotory tendons. Of particular interest are the studies by Woo et al. (4143) that showed that a 12-mo exercise program improved the strength and stiffness of pig digital extensors such that the differences between flexors and extensors, seen in controls, were greatly diminished. More recent studies have demonstrated that induced physical loading of rodent tendons in vivo can cause an increase in the number, diameter, and degree of alignment of the constituent collagen fibrils (27, 39) and in the collagen content of the loaded muscles (23). In a prolonged hindlimb suspension experiment, Vailas et al. (35) found that the collagen and proteoglycan content of rat patellar tendons decreased, and they concluded that ground reaction forces were necessary to maintain homeostasis of tendons as well as muscle and bone. There is also evidence that tendons are stronger in wild rats than in laboratory strains (6), suggesting the involvement of exercise or age factors. In addition to our observations on pig digital tendons, age-dependent alterations in the mechanical properties of other mammalian tendons have been documented. For example, major changes in the tensile strength and elastic modulus of rat tail tendon occur during the first 4 mo of life, increasing, respectively, from -30 MPa and 0.33 GPa at 1 mo to 100 MPa and 1.3 GPa at 4 mo (38). Less dramatic increases in these parameters occur with further aging (13, 38). Walker et al. (40) found increased strength and stiffness with age in canine leg tendons, as did Woo et al. (42) for the digital tendons of miniature swine from 15 to 24 mo. The tensile strength of human tendons increases from -30 MPa in infants to 100 MPa in adults (17). Similarly, the strength and stiffness of collagenous ligaments and skin generally increase from
OF
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TENDONS
birth to maturity, as well as during wound repair (18, 26, 38). Reduced extensibility and a change in failure behavior with aging, from a relatively low stress ductile mode to a high stress brittle one (cf. Figs. 2 and 7) are also typical of rat tail tendons (34,38). The changes in tensile mechanical properties of tendons and other collagenous connective tissues that occur with aging or new growth seem to be correlated with morphological and biochemical changes. These include increases in the collagen content, fibril diameter (28, 29, 35), covalent cross-link stabilization (7,25,30,38), a reduction in the fibril crimp angle in the unstressed state (14, 34), and a decreased water content (13, 17, 18). Inspection of Figs. 1 and 4 shows that the toe region , which is associated with the straightening of co llagen fibril crimps, is reduced with age from -4% strain at birth to -1.5% strain in mature tendons, suggesting a concomitant decrease in the unstressed crimp angle. The water content of the pig digital tendons decreased significantly from birth to maturity but did not differ between the mature flexors and extensors (Table 1). Because the dry weight fraction of a tendon is a good indicator of its collagen content (l3), and this content is expected to increase with maturation (17), the mechanical changes from birth to maturity in the pig tendons probably result partly from increased collagen content, as well as increased cross-linking within fibrils. However, it is unli .kely that the significant met hanica 1 differences between flexor and ex .tensor tendons in the mature animal could be the result of quantitative differences in collagen alone. There must be other morphological or biochemical factors that differ between the mature flexor and extensor tendons. One hypothesis is that the increase in cross-link stabilization that normally occurs in collagen during growth and aging may take place faster in the flexor tendon than in the extensor, thus providing the superior mechanical properties of the former at maturity. Furthermore,, these changes may be influenced by the level of stress experienced in vivo. In a parallel study we have found some evidence to support this hypothesis, and a full report of these findings is now in preparation. Tendons as elastic energy storage elements. The physiological relevance of the mechanical differences between the mature flexor and extensor tendons of the pig forefoot becomes apparent when we consider their elastic energy storage capabilities and respective functions in locomotion. For a strain of 3% (i.e., the maximum in vivo level), the strain energy recovered by elastic recoil from the mature digital flexor tendon would average 415 J/kg, whereas the digital extensor tendon would yield only 165 J/kg (Table 1). This substantial discrepancy arises because for equal strains the flexor tendon absorbs more energy per unit volume than does the extensor (i.e., it is stiffer) and releases a greater proportion of that stored energy by elastic recoil (i.e, it has lower hysteresis). At birth, however, the digital flexor and extensor tendons both have a very low capacity to store and release elastic energy as a result of their relatively low modulus and high internal damping. Differences in the material properties of these te ndons are also i llustrated by their toughness, defined as the total strain energy required to
ELASTIC
PROPERTIES
extend each to its failure strain (Table 1). The high failure energy of the mature digital flexor indicates that this tendon is three times tougher than the mature extensor and five times tougher than either tendon at birth. Thus, with age, the capacity to withstand high stresses and to store and release elastic strain energy is increased far more in the deep flexor than in the extensor, i.e., the deep flexor tendon becomes much better suited to act as a biological spring. These differences in mechanical properties appear to be consistent with the different physiological roles of the digital tendons. As in other mammals, the deep digital flexors of the pig forefoot, along with the superficial flexors, must support large gravitational loads when standing and substantial dynamic loads during walking and running, i.e., when the foot strikes the ground and the digital flexor muscles are active (3). In contrast, the digital extensor tendons will be loaded only by the weight of the foot as it is lifted by the extensor muscles and will be unloaded when the foot is in contact with the ground. Thus, the flexor tendons may function as springs, converting external kinetic and potential energy to elastic strain energy during each stride cycle, whereas the extensor tendons may not. Studies on other mammals show that ground reaction forces can produce large stresses in toe flexor tendons, resulting in significant extension and elastic energy storage. For example, Alexander and Dimery (4) calculated that the forefoot deep digital flexor tendon of a trotting donkey would experience a peak stress of 44 MPa at a strain of 3.7%. In the horse, Dimery et al. (15) estimated peak strains in the forelimb deep digital flexor tendon of 3% and 4% during walking and galloping, respectively. For the same tendon in a galloping fallow deer a peak stress of 65 MPa and a peak strain of 4% were calculated (16). We have no data for peak stresses during locomotion in the pig but, from our calculations of muscle fiber cross section, we estimate that ct would be -30 MPa in the digital flexor but only 15 MPa in the digital extensor (Table 2). Ker et al. (21) pointed out that high-stress tendons may operate at low mechanical safety factors (notable examples whose safety factor approaches 1 are the hindlimb deep digital flexor in the horse and the Achilles tendon in the dog and human), but the majority of tendons, such as digital extensors, are never subjected to high stresses and thus have safety factors of -8. This conclusion is based on the tensile strength being identical in all tendons. In the pig digital tendons, the lower strength of the mature extensor compared with the flexor results in a safety factor of 3 in each. If the digital flexor muscles are active and rapidly stretched as the foot contacts the ground, then the stress generated could potentially rise by nearly twofold (10) and the safety factor of the flexor tendon would be reduced to nearly 1.5.
Ker et al. (21) showed that a small fiber length factor (L c 2) is characteristic of tendons that are relatively long and thin and whose corresponding muscles can impose high stresses. Such tendons are ideally suited to act as locomotory springs. On the other hand, a large fiber length factor (L > 4) is typical of tendons that are
OF
DIGITAL
1039
TENDONS
relatively short and thick and attached to muscles that produce large shortening at low stress. Furthermore, they proposed that tendons that are designed to function as springs during locomotion should have the following features: attachment to muscles with relatively short fibers, Am/At ~75, in vivo ct > 25 MPa, and L < 2. Table 2 shows that the pig digital flexor tendons clearly fall into this group, whereas the digital extensor tendons do not. Indeed, the digital extensor muscle-tendon units of quadrupedal and bipedal mammals in general have relatively long muscle fibers, Am/At ~50, ct ~15 MPa, and L greater than -4 (21). According to these authors, digital extensor tendons, and others not involved in elastic energy storage, are optimized in thickness to provide a relatively inextensible link between muscle and bone while at the same time minimizing the combined muscletendon mass. Our data are consistent with these generalizations and, furthermore, show that in the pig there are differences in the material properties of the digital tendons that make the flexor more suited to act as an effective biological spring than the extensor. In a parallel study we are attempting to elucidate the underlying structural and biochemical bases of the mechanical differences between these tendons. I am grateful to Dr. Allen J. Bailey (AFRC Food Research Institute, Bristol) and Professor R. McNeil1 Alexander (University of Leeds) for the use of their laboratory facilities to carry out portions of this work and to R. F. Lauff for technical help. Dr. Robert Ker kindly loaned the extensometer. Drs. M. B. Bennett, M. E. DeMont, and R. F. Ker provided assistance with the dynamic testing system and helpful discussion. Financial support came from the Natural Sciences and Engineering Research Council of Canada. Address for reprint requests: R. E. Shadwick, Marine Biology Research Div., Scripps Institution of Oceanography, A-004, La Jolla, CA 92093. Received
30 May
1989; accepted
in final
form
9 October
1989.
REFERENCES
5.
6. 7.
8.
9.
10.
ALEXANDER, R. M. Animal Mechanics (2nd ed.). Oxford, UK: Blackwell Scientific, 1983. ALEXANDER, R. M. Elastic energy stores in running vertebrates. Am. Zool. 24: 85-94, 1984. ALEXANDER, R. M. Elastic Mechanisms in Animal Movement. Cambridge, UK: Cambridge Univ. Press, 1988. ALEXANDER, R. M., AND N. J. DIMERY. Elastic properties of the forefoot of the donkey, Equus asinus. J. Zool. Lond. 205: 511-524, 1985. ALEXANDER, R. M., G. M. 0. MALOIY, R. F. KER, A. S. JAYES, AND C. N. WARUI. The role of tendon elasticity in the locomotion of the camel (Camelus dromedarius). J. Zool. Lond. 198: 293-313, 1982. BARFRED, T. Experimental rupture of the Achilles tendon. Acta Orthop. Stand. 42: 406-428, 1971. BARNARD, K., N. D. LIGHT, T. J. SIMS, AND A. J. BAILEY. Chemistry of the collagen cross-links. Origin and partial characterization of a putative mature cross-link of collagen. Biochem. J. 244: 303309,1987. BENEDICT, J. V., L. B. WALKER, AND E. H. HARRIS. Stress-strain characteristics and tensile strength of unembalmed human tendon. J. Biomech. 1: 53-63, 1968. BENNETT, M. B., R. F. KER, N. 3. DIMERY, AND R. M. ALEXANDER. Mechanical properties of various mammalian tendons. J. Zool. Lond. 209: 537-548,1986. BIEWENER, A. A., R. BLICKHAN, A. K. PERRY, N. C. HEGLUND, AND C. R. TAYLOR. Muscle forces during locomotion in kangaroo rats: force platform and tendon buckle measurements compared.
1040
ELASTIC
PROPERTIES
J. Exp. Biol. 137: 191-205, 1988. 11. BLANTON, P. L., AND N. L. BIGGS. Ultimate tensile strength of fetal and adult human tendons. J. Biomech. 3: 181-189, 1970. 12. CAVAGNA, G. A., N. C. HEGLUND, AND C. R. TAYLOR. Mechanical work in terrestrial locomotion: two basic mechanisms for minimizing energy expenditure. Am. J. Physiol. 233 (Regulatory Integrative Comp. Physiol. 2): R243-R261, 1977. 13. DANIELSEN, C. C., AND T. T. ANDREASSEN. Mechanical properties of rat tail tendon in relation to proximal-distal sampling position and age. J. Biomech. 21: 207-212. 14. DIAMANT, J., A. KELLER, E. BAER, M. LITT, AND R. G. C. ARRIDGE. Collagen; ultrastructure and its relation to mechanical properties as a function of aging. Proc. R. Sot. Lond. B Biol. Sci. 180: 293315. 15. DIMERY, N. J., R. M. ALEXANDER, AND R. F. KER. Elastic extension of leg tendons in the locomotion of horses (Equus caballus). J. Zool. Lond. 210: 415-425,1986. 16. DIMERY, N. J., R. F. KER, AND R. M. ALEXANDER. Elastic properties of the feet of deer (Cervidae). J. 2002. Lond. 208: 161-169, 1986. 17. ELLIOT, D. H. Structure and function of mammalian tendon. Biol. Rev. 40: 392-421,1965. 18. FRANK, C. S. L-Y. Woo, D. AMIEL, F. HARWOOD, M. GOMEZ, AND W. AKESON. Medial collateral ligament healing. A multidisciplinary assessment in rabbits. Am. J. Sports Med. 11: 379-389, 1983. 19. KENT, M. J. C., N. D. LIGHT, AND A. J. BAILEY. Evidence for glucose-mediated covalent cross-linking of collagen after glycosylation in vitro. Biochem. J. 225: 745-752, 1985. 20. KER, R. F. Dynamic tensile properties of the plantaris tendon of sheep (&is aries). J. Exp. Biol. 93: 283-302, 1981. 21. KER, R. F., R. M. ALEXANDER, AND M. B. BENNETT. Why are mammalian tendons so thick? J. Zool. Lond. 216: 309-324,1988. 22. KER, R. F., N. J. DIMERY, AND R. M. ALEXANDER. The role of tendon elasticity in hopping in a wallaby (Macropus rufogriseus). J. Zool. Lond. 208: 417-428,1986. 23. KOVANEN, V., H. SUOMINEN, AND L. PELTONEN. Effects of aging and life-long physical training on collagen in slow and fast skeletal muscle in rats. Cell Tissue Res. 248: 247-255, 1987. 24. LEES, S. Water content in type I collagen tissues calculated from the generalized packing model. Int. J. Biol. Macromol. 8: 66-72, 1986. 25. LIGHT, N. D., AND A. J. BAILEY. Molecular structure and stabilization of the collagen fibre. In: Biology of Collagen, edited by A. Viidik and J. Vuust. London: Academic, 1980, p. 15-38. 26. NOYES, F. R., AND E. S. GROOD. The strength of the anterior cruciate ligament in humans and rhesus monkeys: age-related and species-related changes. J. Bone Joint Surg. 58A: 1074-1082, 1976. 27. MICHNA, H. Morphometric analysis of loading-induced changes in collagen-fibril populations in young tendons. Cell Tissue Res. 236: 465-470,1984. 28. PARRY, D. A. D., G. R. G. BARNES, AND A. S. CRAIG. A comparison of the size distribution of collagen fibrils in connective tissues as a function of age and a possible relation between fibril size and distribution and mechanical properties. Proc. R. Sot. Lond. B Biol. Sci. 203: 305-321,1978. 29. PARRY, D. A. D., A. S CRAIG, AND G. R. G BARNES. Tendon and
OF
30.
31.
32.
33.
34.
35.
36. 37.
38.
39.
40.
41.
42.
43.
44.
DIGITAL
TENDONS
ligament from the horse: a ultrastructural study of collagen fibrils and elastic fibres as a function of age. Proc. R. Sot. Lond. B Biol. Sci. 203: 293-303,1978. REISER, K. M., S. M. HENNESSY, AND J. A. LAST. Analysis of ageassociated changes in collagen crosslinking in the skin and lung of monkeys and rats. Biochim. Biophys. Acta 926: 339-348,1987. RIEMERSMA, D. J., AND H. C. SCHAMHARDT. In vitro mechanical properties of equine tendons in relation to cross-sectional area and collagen content. Res. Vet. Sci. 39: 263-270, 1985. RIEMERSMA, D. J., H. C SCHAMHARDT, W. HARTMAN, AND J. L. M. A. LAMMERTINK. Kinetics and kinematics of the equine hind limb: in vivo tendon loads and force plate measurements-in ponies. Am. J. Vet. Res. 49: 1344-1352, 1988. TIPTON, C. M., A. C. VAILAS, AND R. D. MATTHES. Experimental studies on the influence of physical activity on ligaments, tendons and joints: a brief review. Acta Med. Stand. Suppl. 71: 157-168, 1986. TORP, S., R. G. C. ARRIDGE, C. D. ARMENIADES, AND E. BAER. Structure-property relationship in tendons as a function of age. In: Structure of Fibrous Biopolymers, edited by E. D. T. Atkins and A. Keller. London: Butterworths, 1975, p. 197-221. VAILAS, A. C., D. M. DELUNA, L. L. LEWIS, S. L. CURWIN, R. R. ROY, AND E. K. ALFORD. Adaptation of bone and tendon to prolonged hindlimb suspension in rats. J. Appt. Physiol. 65: 373376,1988. VIIDIK, A. The effect of training on the tensile strength of isolated rabbit tendons. Stand. J. Plast. Reconstr. Surg. 1: 141-147, 1967. VIIDIK, A. Interdependence between structure and function in collagenous tissues. In: Biology of Collagen, edited by A. Viidik and J. Vuust. New York: Academic, 1980, p. 257-280. VIIDIK, A. Age-related changes in connective tissues. In: Lectures on Gerontology, edited by A. Viidik. London: Academic, 1982, p. 173-211. VILARTA, R., AND B. C. VIDAL. Anisotropic and biomechanical properties of tendons modified by exercise and denervation: Aggregation and macromolecular order in collagen bundles. Matrix 9: 55-61,1989. WALKER, P., H. C. AMSTUTZ, AND M. RUBENFELD. Canine tendon studies II. Biomechanical evaluation of normal and regrown canine tendons. J. Biomed. Mater. Res. 10: 61-76, 1976. Woo, S. L-Y., M. A. GOMEZ, M. A. RITTER, R. H. GELBERMAN, AND W. H. AKESON. The effects of exercise on the biomechanical and biochemical properties of swine digital flexor tendons. J. Biomech. Eng. 103: 51-56, 1981. Woo, S. L-Y., M. A. GOMEZ, Y. K. Woo, AND W. H. AKESON. Mechanical properties of tendons and ligaments. II. The relationships of immobilization and exercise on tissue remodelling. Biorheology 19: 397-408,1982. Woo, S. L-Y., M. A. RITTER, T. M. SANDERS, M. A. GOMEZ, S. C. KEUL, S. R. GARFIN, AND W. H. AKESON. The biomechanical and biochemical properties of swine tendons-long term effects of exercise on the digital extensors. Connect. Tissue Res. 7: 177-183, 1980. ZERNICKE, R. F., D. L. BUTLER, E. S. GROOD, AND M. S. HEFZY. Strain topography of human tendons and fascia. J. Biomech. Eng. 106: 177-180,1984
