C. M. Pollock and R. E. Shadwick Am J Physiol Regulatory Integrative Comp Physiol 266:1016-1021, 1994. You might find this additional information useful... This article has been cited by 8 other HighWire hosted articles, the first 5 are: Motor unit composition has little effect on the short-range stiffness of feline medial gastrocnemius muscle L. Cui, E. J. Perreault and T. G. Sandercock J Appl Physiol, September 1, 2007; 103 (3): 796-802. [Abstract] [Full Text] [PDF] Unloaded rat Achilles tendons continue to grow, but lose viscoelasticity P. Eliasson, A. Fahlgren, B. Pasternak and P. Aspenberg J Appl Physiol, August 1, 2007; 103 (2): 459-463. [Abstract] [Full Text] [PDF]
Variations in apparent mass of mammalian fast-type myosin light chains correlate with species body size, from shrew to elephant S. Bicer and P. J. Reiser Am J Physiol Regulatory Integrative Comp Physiol, January 1, 2007; 292 (1): R527-R534. [Abstract] [Full Text] [PDF] Role of Extracellular Matrix in Adaptation of Tendon and Skeletal Muscle to Mechanical Loading M. KJAeR Physiol Rev, April 1, 2004; 84 (2): 649-698. [Abstract] [Full Text] [PDF] Medline items on this article's topics can be found at http://highwire.stanford.edu/lists/artbytopic.dtl on the following topics: Physics .. Elasticity Physiology .. Biomechanics Veterinary Science .. Mammalia Medicine .. Body Mass Additional material and information about American Journal of Physiology - Regulatory, Integrative and Comparative Physiology can be found at: http://www.the-aps.org/publications/ajpregu
This information is current as of March 15, 2008 .
The American Journal of Physiology - Regulatory, Integrative and Comparative Physiology publishes original investigations that illuminate normal or abnormal regulation and integration of physiological mechanisms at all levels of biological organization, ranging from molecules to humans, including clinical investigations. It is published 12 times a year (monthly) by the American Physiological Society, 9650 Rockville Pike, Bethesda MD 20814-3991. Copyright © 2005 by the American Physiological Society. ISSN: 0363-6119, ESSN: 1522-1490. Visit our website at http://www.the-aps.org/.
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The effect of running, strength, and vibration strength training on the mechanical, morphological, and biochemical properties of the Achilles tendon in rats K. Legerlotz, P. Schjerling, H. Langberg, G.-P. Bruggemann and A. Niehoff J Appl Physiol, February 1, 2007; 102 (2): 564-572. [Abstract] [Full Text] [PDF]
Relationship between body mass and biomechanical properties of limb tendons in adult mammals COLLEEN M. POLLOCK AND ROBERT E. SHADWICK Department of Biology, University of Calgary, Calgary, Alberta Biology Research Division, Scripps Institution of Oceanography,
Canada; and Marine California 92093-0204
SITUATED DISTALLY in the limbs of mammals, such as the ankle extensors and digital flexors, are thought to function as stiff biological springs that are stretched during the support and deceleration phase and that recoil during the swing and acceleration phase of each stride cycle (4). With every impact, a running animal loses and then regains kinetic and gravitational potential energy. Some of this energy is degraded as heat by the muscles being stretched and is later replaced by muscular contraction. Some is stored, however, as elastic strain energy in stretched tendons and then released in elastic recoil, thus providing a savings of metabolic energy that would otherwise be required (3, 4, 7, 14). The quantity of strain energy stored in a tendon depends on the amount of extension that occurs, which itself is determined by the force applied and the dimensions and material properties of the tendon. Of particular interest here are the elastic modulus, a measure of tendon stiffness, and the mechanical hysteresis, an indication of the proportion of viscous energy losses in cyclic loading. An allometric decrease in the net cost of transport (the metabolic energy required per kg per m traveled) as body mass increases has been well documented for mammals and birds (27-31, 33). The possibility that this results, in part, from a size-dependent increase in the contribution from strain energy storage in limb
tendons has been raised (11, 27, 29). Previous studies have demonstrated that many large mammals experience significant energy savings due to elastic energy storage in the tendons (1, 7, 8, 15, 16), whereas small species do not (l&12). Similarly, the suggestion that the importance of elastic strain energy storage in tendons increases with body size is supported by allometric analyses based on anatomic measurements of the digital flexors and ankle extensors of numerous mammals (2,5, 22). In these studies, however, the derived scaling of strain energy storage in limb tendons was based on the critical assumption that tendon stiffness was constant (i.e., mass and species independent). Because there has been no systematic study of the biomechanical properties of mammalian tendons in relation to body mass, it is unclear whether this assumption is valid. Thus our primary objective was to measure the elastic modulus and hysteresis of distal limb tendons from a large size range of quadrupedal mammals to determine what scaling relationship might exist in the material properties of these tendons. There is also some discrepancy in the literature regarding the mechanical properties of tendons that do not experience high stress loading during the support phase of the stride and do not act as springs in the skeletal system. Evidence from studies involving exercise and limb immobilization suggests that ground reaction forces may influence the growth and structure of tendons (20, 32, 34, 35), and therefore it seems possible that tendons normally experiencing high stresses may develop different mechanical properties than those that are less stressed. One such low-stress muscletendon unit is the digital extensor, which is presumably active only during the swing phase of the stride and is subjected to relatively low stresses. Woo et al. (39, 40) and Shadwick (26) showed that the digital extensor tendons of mature pigs have a much lower elastic modulus and higher hysteresis than the digital flexors. However, these differences were greatly diminished after long-term exercise training (39, 40). Ker et al. (18) found no difference between the mechanical behavior of the cow digital extensor tendon and that of any of the high-stress tendons, including digital flexors, as reported by Bennett et al. (9). Thus the question of whether tendons with different functions have different mechanical properties remains unresolved. A second objective of this study was, therefore, to determine if the digital extensor tendons of adult mammals were mechanically similar to those tendons that act as springs (i.e., the digital flexors and ankle extensors), and whether these properties varied with body size.
R1016
the American
flexor tendon; extensor tendon; esis; strain energy; locomotion
modulus
of elasticity;
hyster-
TENDONS
0363-6119/94
$3.00
Copyright
o 1994
Physiological
Society
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Pollock, Colleen RI., and Robert E. Shadwick. Relationship between body mass and biomechanical properties of limb tendons in adult mammals. Am. J. PhysioZ. 266 (Regulatory Integrative Comp. Physiol. 35): R1016-R1021, 1994.-We investigated the allometric relationship between the mechanical properties of various limb tendons and body mass. The elastic modulus (i.e., stiffness) and hysteresis (i.e., energy dissipation) of digital flexor, ankle extensor, and digital extensor tendons from 18 species of adult quadrupedal mammals ranging in body mass from 0.5 to 545 kg were determined by cyclic tensile testing in vitro. The results show that these elastic properties do not vary significantly among tendons from animals of different body mass, nor do they differ between the digital flexor and ankle extensor tendons (those situated to act as springs during locomotion) and the digital extensor tendons (those not likely to function as springs during locomotion). Consequently, the inherent capability of different limb tendons to store elastic energy, based on their material properties, is the same for large and small animals. The relationship between tendon elastic modulus (E; in GPa) and body mass (M b; in kg) is described by the allometric equation E = 1.22Mb ‘*O”. The hysteresis (H), as a percentage of total strain energy, is related to body mass as H = 8.89M;“.03.
T2N lN4, La Jolla,
BODY
MASS
AND
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BIOMECHANICAL
METHODS
Table 1. List of species used in study Species
Body
Cursorial Plantigrade White-tailed
jackrabbit
(Lepus
townsendii
>*
canadensis)“”
Cow (Bos taurus) Camel (Camelus
dromedarius) Ambulatory
represented
by more
than
2.2 3 338 6.9 34 36 200 3.9 11.1 20.4 28.5 97.36 76.64 97.68 159.5 205 454 545
species
Richardson’s ground squirrel (Spermophilus richardsonii ) Ferret (Mustela nigripes) Grey squirrel (Sciurus carolinensis) * Species
kg
CT= f/A,
species
Grizzly bear (Ursus arctos horribilis) Digitigrade Domestic cat (FeZis catus) Snow leopard (Uncia uncia) Domestic dog (Canis familiaris) Lion (Panthera Zeo) Unguligrade Kirk’s dik-dik (Madoqua kirkii ) Muntjac (Muntiacus muntjak) Pronghorn Antelope (AntiZocapra americana) Russian Saiga (Saiga tartarica) Mule deer (Odocoileus hemionus) White tail deer (Odocoileus virginianus)* Elk (Cervus
Mass,
the tensometer). It also prevents tissue damage at the clamp site. During testing the tendon was kept moist by dripping a 0.9% NaCl solution over the specimen. For the very thin tendons, however, the entire specimen was immersed in a saline-filled chamber to prevent drying out during testing. The crosshead of the tensometer was moved cyclically, alternately stretching the tendon and then allowing it to recoil, at a rate of 5-10 mm/min up to 5-6% strain, which is the range of strain to which most tendons can be extended reversibly without damage (13, 37). Ker ( 17) and Shadwick (26) have shown that at cycle frequencies ranging from 0.05 to 11 Hz, tendon material properties are frequency independent, i.e., stiffness and hysteresis do not vary with strain rate; thus these tests should give a reasonable representation of the tendon properties at their various in vivo loading rates. In each case, the tendon was load-cycled continuously until a stable hysteresis loop was recorded for at least 10 successive cycles. Forces were measured by using one of three load cells (loo-, l,OOO-, and 10,000-N ranges) mounted in series with the tendon. Extension measurements were made by a real-time video dimension analyzing system (Instrumentation for Physiology and Medicine), which determines the distance between two parallel surface markers (l-mm-wide black tape) glued perpendicular to the tendon axis (26, 38). These extension measurements were made in the central body of the tendon sample, well away from the clamps where slippage, tissue distortion, and stress concentrations may occur (17, 36, 38). Force and extension signals were recorded continuously on an X-Y plotter and digitized simultaneously at sampling rates of 10 Hz for long tendons and 50 Hz for shorter tendons by either a 80386 PC or a Digital PDP 11/23 lab computer and stored on disk. The force-extension cycles were smoothed by using a moving-point average of 3-10 points and then converted to stress and strain (see below). Next, one average cycle for each tendon was calculated by averaging stress values at strain intervals of 0.001 (obtained by linear interpolation between successive points) from 5-10 consecutive cycles. The average curve was then used to calculate the elastic modulus and hysteresis for reach specimen. Tensile stress was calculated as
one specimen.
0.47 0.485 0.55
(1)
where f is the force (in N) and At is the tendon cross-sectional area (in m2>. Stress is expressed in megapascals (1 MPa = lo6 N/m2). Tendon cross-sectional areas were calculated by dividing the wet mass of a sample by its length and density (assumed to be 1,120 kg/m”; Refs. 17, 26). Strain was calculated as E = Al/l,
(‘a
where AZ is the change in length and lo is the initial length, as measured between the surface markers. Stress-strain curves were obtained from these data, and slope of the linear portion of the loading curve was defined as the elastic modulus (E), a measure of the elastic stiffness of a material (see Fig. 1)
E = Aa/Ae
(3)
where E is expressed in gigapascals. Together, the loading and unloading curves produce a loop because tendons are viscoelastic. The area within the loop represents the energy lost in one cycle as heat due to internal damping, while the area under the unloading curve is the energy recovered in elastic recoil. Mechanical hysteresis (H) represents the fraction of strain energy lost and may be calculated as the ratio of the area within the stress-strain loop (strain energy dissipated) to the area beneath the loading curve (total strain energy input).
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Eighteen quadrupedal species, ranging in mass from 470 g to 545 kg, and represented by 21 specimens, were used in this study (see Table 1). All were considered mature adult animals. With the exception of the domestic species, all animals were either zoo specimens, obtained from the Calgary and San Diego Zoological Societies, or wild, obtained with the help of the Alberta Fish and Wildlife Service. No laboratory-raised specimens were used. Carcasses were obtained after the animals died or had been killed for other purposes. All specimens and tissues were collected fresh and stored at -20°C until required for dissection and mechanical testing. Tendons from hindlimbs only were used (with the exception of the Kirk’s dik-dik: only one forelimb was made available for this specimen). The mechanical properties of excised tendons were determined in vitro by cyclic tensile tests. The excised tissue was elongated at a constant rate while the changes in force and extension were simultaneously recorded, using a materials testing machine (Monsanto lo-kN Tensometer). The tendons studied were originating from the digital flexor muscles [plantaris, deep digital flexors (i.e., flexor hallucis and flexor digitorum longus)], ankle extensor muscles (gastrocnemius and soleus, if present), and common digital extensor muscles. Measured segments of these tendons were clamped in the machine in various ways, with the mode of clamping dependent on tendon size. The smallest tendons were clamped between flat aluminum blocks (2.5 x 3.5 cm) that had either fine-grit carbide abrasive paper glued to the gripping surfaces or interlocking sinusoidally serrated clamping surfaces. Larger steel clamps (5 x 5 cm) with serrated gripping surfaces were used for the midsized tendons. For the largest tendons a cryo-jaw clamp was used, as described by Riemersa and Schamhardt (24). This clamp resists slippage of tissue within the jaws for forces in excess of 10 kN (the maximum capacity of
R1017
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B
60
60 ..:: ..:.’ ,’
D
z
Q) 30zto 20 -
20
I
10 I 0.00
0.02
0.04
1
I
0.06
I I I
I
1
0.08
1
0.00
I
I
0.02
I
0.06
0.04
0.08
strain
Fig. 1. Typical stress-strain curve for mammalian tendon. Arrows beside curves indicate direction of loading. Elastic modulus is calculated as slope of linear portion of loading curve. Hysteresis (represented by area A) is 5.1% of total strain energy input (area A + area B).
Fig. 2. Plots of stress-strain behavior for a of tendon tested, showing their mechanical from a 28.5kg russian saiga (A), plantaris deep digital flexor from a 0.49-kg ferret (C), 200-kg lion (D).
Allometric equations were obtained by least-squares regression after transformation of the data to logarithms. Body mass was treated as the independent variable. The allometric equations are reported in the form Y = aXb, where Y is the dependent variable, X is body mass (in kg), the coefficient a is the value of Y at 1 kg, and the exponent b is the slope of the log-log regression line (21, 25). A Student’s t test and the standard error of the slope were used to assign 95% confidence limits to the allometric exponent, b (41). The correlation coefficient (r) for each equation was also determined. Analysis of covariance (41) was applied to the data to determine whether statistically similar scaling relationships were observed for the four tendon types.
After a few conditioning cycles, the curves became quite reproducible, with virtually no variation between successive cycles (see Ref. 26). The average elastic modulus and mechanical hysteresis (from 5 to 10 cycles) was then determined for each tendon, and these values were used to calculate the allometric equations. Figure 2 shows typical loading curves for the four different types of tendons tested, each from a different species, illustrating the overall trend that all tendons tested had similar stress-strain behavior. Our results show that in adult mammals, tendons associated with functionally different muscles, such as the ankle extensor, digital flexors, and digital extensors, are materially similar, and their material properties appear to be independent of body mass. Tables 2 and 3 and Figs. 3 and 4 show that for each of the tendon types, both E and H are relatively constant among 18 speciesranging from 0.50 to 500 kg. E ranged from approximately 0.9 to 1.8 GPa, with an average value of 1.24 t 0.23 GPa for all
RESULTS
A representative cyclic stress-strain curve for a tendon is shown in Fig. 1. All tendons tested, whether they functioned primarily as ankle extensors, digital flexors, or digital extensors, yielded similar J-shaped curves. The initially compliant “toe” region is associated with the straightening of crimped collagen fibers making up the tendon and typically occupies the first l-2% of elongation in adult tendons (17, 26, 36). Continued stretching results in a stiffening of the tissue as the straightened parallel collagen fibers are strained, and the loading curve becomes linear at stresses above 20-35 MPa. The elastic modulus is the slope of the linear portion of this curve and thus is a measure of the tendon stiffness. Because these data are normalized for tendon dimensions, the modulus is a property of the material that comprises the tendon. As long as the tendon was not extended beyond the linear region of the stress-strain curve, cyclic loading produced an elastic response, i.e., unloading restored the tendon to its original length. Hysteresis is represented by the area (A) enclosed by the loop, relative to the area under the loading curve (A + B), and is also a material property.
representative of each type similarity: gastrocnemius from a 545kg camel (B), and digital extensor from a
Table 2. Analysis of data for elastic modulus of 4 tendon types
Plantaris Deep digital flexor Gastrocnemius Digital extensor
N
a
b
19 21 10 17
1.32 1.18 1.16 1.25
-0.01 0.01 0.00 -0.01
95%
0.04 0.04 0.06 0.06
CI
r
-0.09 0.09 0.00 -0.11
Values of allometric parameters a and b for relation E = aI@, where i&, is body mass in kg, E is elastic modulus in units of GPa, a is proportionality coefficient, and b is allometric exponent. Equations were determined by least-squares regression after logarithmic transformation. N, no. of specimens used in each category; 95% CI, 95% confidence interval of allometric exponent b; r, correlation coefficient. Analysis of covariance revealed a common exponent and proportionality coefficient; thus entire dataset may be represented by a common allometric equation, E = 1.22 Mi.O”.
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strain
1
I
BODY
Table 3. Analysis of 4 tendon types
MASS
AND
TENDON
BIOMECHANICAL
of data for hysteresis P
Plantaris Deep digital flexor Gastrocnemius Digital extensor
N
a
b
95% CI
r
18 21 10 17
9.08 9.44 8.00 8.24
-0.10 0.01 0.05 -0.01
0.14 0.08 0.34 0.13
-0.36 0.03 0.11 -0.06
D
0
H = 9.08
,,db-”
H=
Mb’-”
n
10 P
0
-
D
n
E =
1.32
Mb-o’o’
G
v
E = 1.76
E=
7.18
Mpo7
c
q
E =
M,“O”
1. 25 M -oaol b
zi E !!.i 7 B E
t
’
’
“““I
’
’
“““I
1
’
’
10 body
mass
v
H = 8.00
,,$,“‘05
C
•I H = 8.24
Mb-o’o’ v
b n B
no
n 0
-0 53
8
VO
0
0
v
1
0
m n
0
100
10 body mass
1000
(kg)
Fig. 4. Log-log plot of relationship between esis (H) and &, in kg for all tendons tested.
tendon
mechanical
hyster-
coefficients (Tables 2 and 3) denote that there is no linear association between the magnitudes of the X and Y variables; that is, a change in magnitude in one does not imply a change in magnitude of the other (41). DISCUSSION
This study provides the first systematic assessment of the biomechanical properties of four anatomically different leg tendons from a group of mammals spanning three orders of magnitude in body mass. This dataset is large enough to allow statistical analysis that demonstrates two important new findings about limb tendons in adult mammals. First, the digital flexor and ankle extensor tendons (those likely to act as springs during the support phase of locomotion) have, on average, the same material properties (i.e., elastic modulus and hysteresis) as the digital extensors (those not likely to function as springs) and therefore the same inherent capacity for elastic energy storage. Second, the material properties of these anatomically and functionally distinct tendons are independent of species or body mass
Tendon
Species
0.1
G
Table 4. Peak in vivo stresses calculated for ankle extensor or digital flexor tendons during moderate to fast locomotion
?
0
”
“““I
’
100
’
“““I
1000
(kg)
Fig. 3. Log-log plot of relationship between tendon elastic modulus (E) in GPa and body mass (i&) in kg, for all tendons tested. Points for each tendon are represented by different symbols, and regression lines are labeled by letters: plantaris (P), deep digital flexors (D), gastrocnemius (G), and common digital extensor (C). Allometric equations for each tendon are shown.
Wallaby hopping Kangaroo hopping Dog jumping Camel pacing Deer galloping Donkey trotting Antelope galloping Buffalo galloping Kangaroo rat (hopping and jumping) *Corrected stress higher. as an incorrect
Stress, MPa
values; value
original for tendon
Literature Source
15-41 39-78 84 18 28-74 28-37 27-51 13-48
8*, 19 8”” 1”” 7 16 15 2” 6’”
lo-36
12
published values are slightly densitv was used (see Ref. 15).
Downloaded from ajpregu.physiology.org on March 15, 2008
tendons. H typically ranged from 3 to 20%, with an average value of 9.3 t 5.0% for all tendons. This means that, on average, over 90% of the strain energy absorbed by the tendon is recovered in elastic recoil. With the use of Student’s t test, we found that for all tendon types the scaling exponent b for both elastic modulus and hysteresis was not significantly different from zero (P > 0.05), indicating no dependence between these variables and body size. It is interesting to note that the hysteresis of the plantaris tendon appears to follow a decreasing trend with greater body mass (Fig. 4), although this is not statistically significant overall. Analysis of covariance applied to the elastic modulus data yields a common allometric exponent of 0.00 and a common proportionality coefficient of 1.22 for all tendon types tested. Similarly, analysis of covariance applied to the hysteresis data yields a common scaling exponent of -0.03 and a common proportionality coefficient of 8.89 for all tendon types. Furthermore, the low correlation
9.44
ch
Values of allometric parameters a and b for relation H = where & is body mass in kg, H is hysteresis expressed as a@, percentage of total strain energy lost, a is proportionality coefficient, and b is allometric exponent. Equations were determined by leastsquares regression after logarithmic transformation. Analysis of covariance revealed a common exponent and proportionality coefficient, giving a common allometric equation, H = 8.89 Mb0.03.
-
R1019
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R1020
BODY
MASS
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BIOMECHANICAL
showed that the digital extensor tendons increased significantly in stiffness, whereas no effect was seen on the digital flexors. Consequently, after 12 mo of exercise, the stress-strain behavior of digital flexor and extensor tendons was virtually the same and comparable to that reported here. If we assume that the exercised pigs used by Woo and colleagues are physiologically comparable to the adult animals used here, then there is consistency in the results of these studies. Our observations, on a large group of almost entirely wild species, clearly show that the material properties of tendons associated with functionally distinct muscles are all the same in adult mammals. How these properties change with loading during growth and development is still unclear. Thanks go to Professor A. P. Russell for helpful discussion, support, and humor. Specimen dissection was aided by Randolph Lauff. We are grateful to the Calgary and San Diego Zoological Societies and to the Alberta Fish and Wildlife Service for providing specimens for this study. Financial support was provided by a research grant and fellowship from the Natural Sciences and Engineering Research Council of Canada (to R. E. Shadwick), a grant from the University of California Biomedical Research Funds (to R. E. Shadwick), and Graduate Assistantships from the University of Calgary (to C. M. Pollock). Address for reprint requests: R. E. Shadwick, Marine Biology Research Div., Scripps Institution of Oceanography, La Jolla, CA 92093-0204. Received
6 November
1992;
accepted
in final
form
25 August
1993.
REFERENCES 1. Alexander, R. M. The mechanics of jumping by a dog (Canis familiaris). J. 2001. Lond. 173: 549-573, 1974. 2. Alexander, R. M. Allometry of the limbs of antelopes (Bovidae). J. ZooZ. Lond. 183: 125-146,1977. 3. Alexander, R. M. Elastic energy stores in running vertebrates. Am. ZooZ. 24: 85-94,1984. 4. Alexander, R. M. Elastic Mechanisms in AnimaZ Movement. Cambridge, UK: Cambridge Univ. Press, 1988. 5. Alexander, R. M., A. S. Jayes, G. M. 0. Maloiy, and E. M. Wathuta. Allometry of the leg muscles of mammals. J. ZooZ. Lond. 194: 539-552,198l. R. M., G. M. 0. Maloiy, B. Hunter, A. S. Jayes, 6. Alexander, and J. Nturibi. Mechanical stresses in fast locomotion of buffalo (Syncerus caffer) and elephant (Loxodonta africana). J. Zool. Lond. 189: 135-144,1979. 7. Alexander, R. M., G. M. 0. Maloiy, R. F. Ker, A. S. Jayes, and C. N. Warui. The role of elasticity in the locomotion of the camel (Camelus dromedarius). J. ZooZ. Lond. 198: 293-313, 1982. 8. Alexander, R. M., and A. Vernon. The mechanics of hopping by kangaroos (Macropodidae). J. ZooZ. Lond. 177: 265-303, 1975. M. B., R. F. Ker, N. J. Dimery, and R. M. Alex9. Bennett, ander. Mechanical properties of various mammalian tendons. J. ZooZ. Lond. 209: 537-548,1986. 10. Biewener, A. A. Bone strength in small mammals and bipedal birds: do safety factors change with body size? J. Exp. BioZ. 98: 289-301,1982. 11. Biewener, A. A., R. M. Alexander, and N. C. Heglund. Elastic energy storage in the hopping of kangaroo rats (Dipodomys spectabilis). J. Zool. Lond. 195: 369-383, 1981. 12. Biewener, A. A., and R. Blickhan. Kangaroo rat locomotion: design for elastic energy storage or acceleration? J. Exp. BioZ. 140: 243-255,1988. 13. Butler, D. L., E. S. Grood, F. R. Noyes, and R. F. Zernicke. Biomechanics of ligaments and tendons. In: Exercise Science and Sport Reviews, edited by E. S. Grood and F. R. Noyes. Philadelphia, PA: Franklin Institute, 1978, vol. 6, p. 125-183. 14. Cavagna, G. A., N. C. Heglund, and C. R. Taylor. Mechanical work in terrestrial locomotion: two basic mechanisms for minimiz-
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(Figs. 3 and 4; T a bl es 2 and 3). Consequently, if .metabolic energy savings due to elastic energy storage increase with body mass in running mammals, as previously suggested (5, 22), this does not result from a scaling of tendon material properties. Rather, differences in the level of tensile loading imposed on these tendons in larger animals must occur. The companion study (23) addresses this idea by considering the allometry of muscle and tendon dimensions. Interestingly, the material properties of mammalian limb bones also do not vary with differences in body size (10). These observations suggest the general finding that adjustments in the structural properties of the skeletal system in terrestrial mammals to accommodate increasing body size occur by changes in dimensions or shape, not material properties. For all tendons tested, the stress-strain curves were J-shaped, and the elastic modulus averaged 1.24 GPa while the mean hysteresis, or energy dissipation, was 9.3%. Similar stress-strain behavior has been reported for other mammalian tendons (9, 15, 17). These properties suggest that limb tendons in adult mammals are well suited to act as springs in the skeletal system. Table 4 shows that ankle extensor and digital flexor tendons experience stresses during moderate to fast locomotion that will stretch the tendons into the linear region of the stress-strain curve where large amounts of strain energy are stored and recovered elastically. The quantity of energy stored will increase in proportion to the level of stress imposed on the tendons. Our results are comparable to those of Bennett et al. (9), who found no consistent differences in the material properties of tendons from different anatomic sites of 10 species of mammals; the elastic modulus averaged 1.5 GPa at stresses above 30 MPa, hysteresis ranged from 6 to ll%, and the ultimate strength ranged from 80 to 100 MPa. The tendons included in their study represented only those believed to function as elastic energy stores during locomotion (e.g., ankle extensors and digital flexors of terrestrial mammals and the sacrocaudalis of a porpoise). They suggested that other tendons associated with muscles of different functions may have different properties. The current study expands the sample set to include the digital extensor tendons, whose muscles are thought to be active during the swing phase of locomotion as opposed to the support phase and can therefore be expected to experience less stress (18, 26). We find that the material properties of digital extensors are no different from those of the digital flexors and ankle extensor tendons. This is in contrast to previous studies (26, 39, 40), in which the digital flexor tendons of mature pigs had a much higher capacity for elastic energy storage than did the digital extensor tendons, because of the relatively low elastic modulus and high hysteresis of the latter. Shadwick (26) postulated that the differences in material properties between these tendons in the pig were correlated with their physiological functions, i.e., the flexors being adapted, with growth, to sustain higher stresses than the extensors. However, in a long-term exercise study on pigs, Woo et al. (39,40)
PROPERTIES
BODY
15.
16.
17. 18. 19.
20.
21. 22.
24.
25. 26.
27.
28.
AND
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