Rheological properties of canine anterior cruciate ligaments

J. Biomechanics, Voi.2, pp. 289-298. PergamonPress, 1969. Printedin GreatBritain

R H E O L O G I C A L P R O P E R T I E S OF C A N I N E A N T E R I O R CRUCIATE LIGAMENTS*? R O G E R C. HAUT:~ and ROBERT W. LITTLE Department of Metallurgy, Mechanics and Materials Science, Michigan State University, East Lansing, Mich. 48823, U.S.A. Abstract--The mechanical properties of canine anterior cruciate ligaments are studied at different strain rates and in different environments. A tibia-anterior cruciate ligament-femur preparation is tested preventing rupture at points of attachment. The data is compared with other investigations of ligaments and tendons and is plotted by use of the constitutive equation proposed by Y. C. Fung. Good agreement is obtained using Fung's exponential relationship and two numerical parameters are suggested for evaluation of future test data.

INTRODUCTION

THE STUDY of the rheological properties of connective tissues has been an area of interest since Annovazzio's (1928) investigations of ligaments (Stucke, 1950, 1951). Connective tissue is the most predominant and diversified tissue in the animal kingdom, appearing as bone, cartilage, ligament and tendon. Although blood is also so classified, it will not be discussed in this paper. Connective tissue has the distinguishing characteristic of large amounts of intercellular material being present. This intercellular material may consist of collagenous, elastic or reticular fibers and varying amounts of an amorphous ground substance. Since elastic fibers contain the low modulus material elastin (Carton, Dainauskas and Clark, 1962), the high modulus effects of tendons and ligaments is due to the collagenous material present. The particular connective tissue which is of interest at present is the anterior cruciate ligament. This ligament is composed almost entirely of collagenous fibers which appear as long wavy ribbons which are not branched. The fiber production is apparently in the form

of a secretion process in which an aggregate of extracellular material is secreted by starshaped cells called fibroblasts. The primary building blocks of these fibers are the collagen molecules: three chains of amino acids in certain sequences which coil into left-hand helices and intertwine to form a right-handed superhelix (Rich and Crick, 1961). The wavy pattern of a fiber will be considered later with reference to its effects on the stress-strain curve. Bundles of these fibers lie in a somewhat irregular arrangement parallel to the central axis of the ligament. These collagen bundles are presumably as long as the tendons or ligaments (Harris, Walker and Bass, 1966). They are surrounded by a woven mesh of loose connective tissue, the peritendineum internum, containing elastic fibers that tend to draw the bundle into a wavy formation in the relaxed condition. Tendon and ligament fibers are continuous with the fibers of the bones and at this point are called the fibers of Sharpey. Since the properties of ligaments and tendons vary depending upon their location in the body, it is necessary to concentrate

*Received 13 January 1969. ?Presented at the A S M E Third Biornechanical and Human Factors Division Conference at the University of Michigan, Ann Arbor, June 12-13, 1969. SPart of this paper is taken from the M.S. thesis of the first author, submitted to Michigan State University.

289 B.M. VoL 2No. 3--F

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R . C . H A U T and R. W. LITTLE

this examination to the particular ligament with a subsequent medial rotation of the femur in question. This ligament, the anterior takes place, the anterior cruciate ligament and cruciate, is located in the stifle joint. This the collateral ligaments are under extreme joint, located in the lower or hind limb, is tension. The most common type of injury is the most complicated joint in the body. It when the tibia is rotated laterally, as the joint must transmit forces of a much larger magni- is flexed. This type of injury is frequently tude than any other joint in the body, so that encountered in football and skiing accidents a high degree of support must be present to (Abbott, 1944). It has been suggested that stabilize it. To comply with the rigid require- similar movements may be the cause of the ments of stabilization as well as freedom to ruptures of the anterior cruciate ligaments flex and extend under large forces, the largest in canines. articulating surface in the body is present. The rheological properties of ligaments The bones meeting at this joint are the femur, and tendons has been the subject of many which inserts into the pelvic girdle, and the papers since Annovazzi's (1928) work. Much tibia, which articulates with the talus to form of this information is conflictive and many the ankle joint. Collateral ligaments lie along of the tests are subject to question. Cronkite the medial and lateral borders of the joint, (1936) conducted tests on almost every tendon while the quadriceps femoris muscle encases in the human body. He reported no signifithe knee cap which protects the anterior cant difference between tendons in their tensile region of the joint. Posteriorly, the biceps strengths which ranged from 2 × 10s to 2 × femoris and the gastrocnemius muscles help 109dyn/cm2. Gratz (1931) conducted similar support the joint. The entire joint is encircled tests on three tendons and obtained tensile with hyaline cartilage which serves as a strengths within this range and Young's cushion and as a capsule for the encasement modulus of 3 × 10s-4 × 10s dyn/cm2. He also of the lubricant, synovial fluid. Interior to the noted that immersion in Ringer's solution joint are cruciate ligaments, so named because made no significant difference in the results. Hardy (1951) noted the difference in these two ligaments form a cross in the joint. The posterior cruciate ligament extends modulus between ligaments containing from the posterior intercondylar fossa of the large amounts of collagenous material and tibia, a depression between the contact those containing elastic fibers. Smith (1954) surfaces, upward and forward to the lateral examined the properties of the anterior cruside of the medial condyle of the femur. The ciate ligaments of rabbits. He noted histoanterior cruciate ligament extends from the logical changes within the 1st hr after death. front of the intercondylar eminence of the His testing apparatus suspended the cruciate tibia upward and backward to the medial side ligament in a position such that the femur, of the lateral condyle of the femur. Isolation tibia and anterior cruciate were in a line of the anterior cruciate ligament without coinciding with the applied load. This resulted damage is possible due to this central in ruptures at the tibial insertion of the ligament. positioning in the joint. Rigby (1959, 1964) studied the mechanical Injuries to the collateral and cruciate ligaments of the stifle joint are very common. properties of rat tail tendons. He found that During hyperextension, the anterior cruciate the mechanical properties were reproducible ligament and the collateral ligaments are under within a strain range of 0-4 per cent. Varilarge tensile forces. The posterior cruciate ation of temperature from 0 to 37°C produced ligament is apparently under a certain degree no effects while increase in strain rate proof tension at all times. From clinical studies duced a slight shift of the stress-strain curve of the stifle joint it is noted that when flexion toward the stress axis. The average maximum

R H E O L O G I C A L PROPERTIES OF C A N I N E A N T E R I O R C R U C I A T E L I G A M E N T S

modulus for a strain rate of 10%/rain was from 6 to I0 × 109 dyn/cm2. Walker, Harris and Benedicts (1964) and VanBrocklin and Ellis (1965) performed tests on tendons of the human foot. Harris, Walker and Bass (1966) also tested human tendons but from the upper extremity of the body. Their tests yielded results within the range of those obtained previously. Abrahams (1967) attempted to correlate the shape of the stress-strain curve to the behavior of the collagen fibers. He found that the stress-strain curves of horses and human tendons described 3 distinct regions. The primary region was that of 0-1.5 per cent strain in which there was a considerable increase in length with only a slight increase in stress. In this region it is thought that the collagen fibers begin to straighten their wavy pattern. The secondary region was that of 1.5-3.0 per cent strain where the collagen fibers are thought to become fully oriented and begin to assume most of the load. In the final region, that of 3.0-5.0 per cent strain, it is thought that the entire response is due to the collagen fibers in pure tension. The stressstrain curve is a straight line in this region. Visible ruptures of the collagen fibers begin at 5.0 per cent strain level. Viidik and co-workers (1965, 1966, 1967), studied the properties of anterior cruciate ligaments in rabbits. He stored the ligaments in four different manners including saline baths of 20°C, formaldehyde baths, saline baths at 4°C and deep-freezing. He found variation in properties stored in any of these methods to those of fresh specimens. He suggested that future tests be run immediately after death in environments of blood plasma or synovial fluid. To correlate properties of any material, it is desirable to establish constitutive equations describing its behavior. Fung (1968) has done this for the thin connective tissue membrane in the abdomen: the mesentery. He was able to establish an exponential type of constitutive equation which he suggests might be

291

applicable to other biological materials. We will show that this equation is in excellent agreement with our test results. EXPERIMENTAL METHODS

In order to study the mechanical properties of the anterior cruciate ligament of canines, a femur-anterior cruciate ligament-tibia preparation was chosen. Using this type of preparation the end effects caused by direct clamping to the ligament can be neglected. The fixtures used for these tests were designed such that the preparation could be flexed so that the anterior cruciate ligament could be tested in a natural position. The angle formed by the fixtures was set at approximately 140° for all of the tests. In the natural standing position, a dog flexes the stifle joint from approximately 135° to 140° (Fig. 1). Three different testing environments were used consisting of the following: (1) Moistened slightly during the test with a saline solution (Lock's). (2) Immersion in a saline bath at room temperature. (3) Immersion in a saline bath at the canine body temperature of 101°F. The specimens were tested within 6 hr after the death of the animals. Initial tests were started within 2 hr after death of the animals with individual tests requiring approximately 1 hr. While one specimen was being tested, the remaining specimens were kept at room temperature with the knee capsule intact. Each specimen was subjected to the temperature bath for approximately 30rain before the beginning of the test. Due to its central location in the stifle joint, the anterior cruciate ligament was easily isolated. All interior cartilage and surrounding tendons and ligaments were removed from the joint area before testing, and the specimen was clamped to a table where the measurement of area was made. The cross-section of the anterior cruciate ligament was assumed to be elliptical. Since the anterior cruciate ligament has a 90° twist as it passes from the

292

R . C . H A U T and R. W. LITTLE

femur to the tibia, it was necessary to adjust the clamps so that the ligament was as uniform as possible when the measurements of the major and minor diameters were being taken. A special set of micrometer probes were designed for easy access into the intact joint. The probes were made from steel pins were designed for easy access into the intact joint. The probes were made from steel pins that were ground to a dia. of ~ of an in. and had an overall length of 1 in. The probes were then attached to a 2-3 in. micrometer (Fig. 6). The testing machine used for these tests was an Instron Model TT-CM metric with a 0-50 kg load cell inserted into the head. A cell range of 0 - 1 0 k g was sufficient for these tests (Fig. 3). As described earlier, the testing fixture held the specimen in a flexed position. The fixtures were also designed such that either the femur or the tibia could be rotated to allow for better alignment of the ligament during the tests. Attached to the stationary upper fixture was a system of coordinate axes. Using a pair of highly versatile calipers, 3 radii were drawn from the coordinate axes to the points of insertion of the anterior cruciate ligament on the tibia and on the femur (Fig. 4). The initial length of the ligament was established by solution of the resulting quadratic equations involving these three radii. In order to eliminate false strains due to slipping of the femur and the tibia in the fixture, a clip gage was inserted into the joint (Fig. 1). The clip gage was constructed from a strip of spring steel 0.01 in. thick and 0.25 in. wide. Two waterproofed SR-4 strain gages were attached to either side of the clip gage. Slipping of the clip gage in the joint was avoided by the puncture of holes in the femoral and tibial intercondyles to receive the pointed tips of the clip gage. The calibration fixture used for calibration of the clip gage consisted of a dial gage graduated in 0.001 in. intervals attached to a sliding frame (Fig. 5). With this particular design for the

clip gage, the calibration curve was linear throughout the range of interest. The procedure used for testing the anterior cruciate ligament was one of a step loading pattern. Applying a constant strain rate, the load was allowed to reach a predetermined level and then there was a subsequent stress relaxation at this particular strain level. This type of loading was applied until the strain level reached approximately 10 per cent where the loading was reversed back to the point of a zero strain level. At each particular load level the specimen was relaxed for 4 min. at which time the amount of relaxation approached an asymptotic value. After the completion of the first test cycle, the specimen was subjected to a second identical test. DISCUSSION AND CONCLUSIONS

The shape of the stress-strain curves follow the same pattern given most often in the literature. As seen in Figs. 7-9, the shape of the stress-strain curves is not altered by various strain rates, except for high strain o

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RHEOLOGICAL

PROPERTIES

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CRUCIATE

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293

rates where the toe region appears at an early strain level. Unlike the range of 0-1.5 per cent strain for the toe regions of tendons given by Abrahams (1967), the anterior cruciate ligament of dogs displays a toe region which varies with strain rate up to 6 per cent strain. Also, in these figures the increase in the apparent Young's modulus with increasing strain rate is quite pronounced. For slow strain rates the modulus changes rapidly with strain rate, but for higher values of strain rate only a gradual increase can be seen. Results similar to these were described by VanBrocklin and Ellis (1965) and Abrahams (1967). The average apparent Young's Modulus given by Frasher (1966) for collagen fibers in blood vessels ranged from 3.0 × 107 to 1.0 × 109 dyn/cm 2. Values of approximately 2.0 × 109 dyn/cm z were obtained in these experiments on the anterior cruciate ligaments of dogs (Fig. 10). Y. C. Fung (1968) described the elastic properties of the mesentery of the abdomen of rabbits by an exponential function. He used the value of stress after a complete relaxation of the specimen at each stress level and plotted this value versus the value of strain (Figs. 17-19), This relationship describes the so-called 'elastic' test condition corresponding to an infinitely slow application of load. H e obtained an equation which may be written in the form o-= C [ e { 1 - e + 4 e 2 } ] e a ~

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where 'C' and 'a' are undetermined constants. This form of Fung's Law was plotted for various values of 'a' and 'C' in Figs. 7-9. In Table 1 the constants which were used to draw these curves are given. It can be seen that Fung's Law very closely represents the results which were obtained in the tests. If one examines Table 1, it may be noted that the value of the constant 'a' depends on the strain rate. Since the strain rate was measured by the machine speed which may not be the strain rate in the specimen, the values of

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RHEOLOGICAL

PROPERTIES

OF CANINE

strain rate should be used only to indicate trends. In the tests for the moistened specimens the constant 'a' increases with the strain rate, whereas for the immersed specimens the constant decreases with an increase in the strain rate. With the limited amount of data available at this time it is difficult to determine the exact nature ,of this dependence. Also in Table 1 the constants for the static test are given. These constants are used in the curves which are plotted in Fig. 13. Again, Fung's Law represents the extrapolated data very well. The constant 'C' increases with an increase in strain rate and there is very little difference between the moistened and immersed at 72°F tests (Figs. 11 and 12).

ANTERIOR

CRUCIATE

LIGAMENTS

295

other than collagen fibers was ruptured in this conditioning. After this procedure, he claimed that the tendons were elastic beyond the strain level of 4 per cent. If one considers the description of the toe region given by Abrahams (1967), it could be possible that the rupturing of these other constituents might cause the toe region to become extended during the second test of a specimen. Furthermore, the fact that the slopes of the linear portions of the curves are identical for both of the tests indicates that the actual collagen fiber response is not affected by the testing of the same specimen twice in the range considered. In Figs. 14-16 the cumulative relaxation in percent of initial stress vs, the initial

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The difference between the first and second tests on the same specimen was noted (Fig. 20) to be an extended toe region for the second test. Rigby (1959, 1964) first reported this result in his tests for the mechanical properties of tendons. He 'preconditioned' the specimen by straining it to a given value of strain before each test. H e suggested that material

stress for varying strain rates is plotted. For lower strain rates it can be seen that the percent relaxation changes rapidly with the value of stress. At higher values of stress, above 20 kg/cm 2, the curves become linear. ~O'rela x = Coor

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296

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RHEOLOGICAL

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temperature tests must be made to complete the investigation. In Fig. 2 an apparent organized pattern of the fibers may be seen which took place while the specimen was being strained. Even though this was only observed and was not dealt with in any detail, there is a possibility that a recrystalization might take place under tensile forces similar to that which has been seen to occur at the so-called 'recrystalization temperature' of biological materials. A c k n o w l e d g e m e n t s - T h e work described here was carried out with the cooperation of the College of Veterinary Medicine of Michigan State University. In particular, Dr. Wade Brinker gave considerable assistance and valuable contributions to this study. This work was supported by N I H through the Michigan State University Biomedical Sciences Support Grant for 1967-68. REFERENCES

Abbott, L. C. (1944) Injuries to the knee joint. J. Bone a n d J t Surg. 26, 503-517. Abrahams, M. (1967) Mechanical behavior of tendon in

vitro, a preliminary report. Med. and biol. Engng 5, 433 -443. Annovazzi, G. (1928) Osservazioni sulla elasticity dei legamenti. Archs Sci. biol. Napoli 11,467-501. Carton, R. W., Dainauskas, J. and Clark, J. W. (1962) Elastic properties of single elastic fibers. J. appl. Physiol. 17, 547. Cronkite, A. E. (1936) The tensile strength of human tendons. Anat. Rec. 64, 173-186. Frasher, W. G. (1966) What is known about the physiology of larger blood vessels. Biomechanics. (Edited by Y. C. Fung), pp. 1-19, ASME, New York. Fung, Y. C. (1968) Biomechanics. Appl. Mech. Rev. 21, 1-20. Gratz, C. M. (1931) Tensile strength and elasticity tests on human fascia lata. J. Bone a n d J t Surg. 13, 334-340. Hardy, R. H. (1951) Observations on the structure and properties of the plantar calcaneonavicular ligament in man.J.Anat. 85,135-139. Harris, E. H., Walker, L. B. and Bass, B. R. (1966) Stress-strain studies in cadaveric human tendon and an anomaly in the Young's modulus thereof. Med. and biol. Engng 4, 253-259. Rich, A. and Crick, F. H. C. (1961) The molecular structure of collagen. J. molec. Biol. 3, 483-506. Rigby, B. J., Hairai, N., Spikes, J. C. and Eyring, H. (1959) The mechanical properties of rat tail tendon. J. gen. Physiol. 43, 265-283. Rigby, B. J. (1964) Effect of cyclic extension on the physical properties of tendon collagen and its possible relation to Nological aging of collagen. Nature, Lond. 202, B-2. Smith, J. W. (1954) The elastic properties of the anterior cruciate ligament of the rabbit. J. Anat. 88, 369-380. Stucke, K. (1950) The elasticity of the achilles tendon in loading experiments. Langebeck Arch. klin. Chir. 265, 579-599. Stucke, K. (1951) Tendon loads and rupture in animal experiments. Chirurgie 22, 16. VanBrocklin, J. D. and Ellis, D. G. (1965) A study of the mechanical behavior of toe extensor tendons under applied stress. Archs phys. Med. Rehabil. 46, 369-373. Viidik, A. Sandqvist, L. and M~igi, M. (1965) Influence of postmortal storage on tensile strength characteristics and histology of rabbit ligaments. Acta. orthop, scand. Suppl. 79. Viidik, A. (1966) Biomechanics and functional adaptation of tendons and joint ligaments. Studies on the Anatomy and Function o f Bone and Joints. (Edited by F. G. Evans), pp. 17-40. Springer, Heidleberg. Viidik, A. (1967) Experimental evaluation of the tensile strength of isolated rabbit tendons. Bio-med. Engng 2, 31-36. Viidik, A. and Lewin, T. (1966) Changes in tensile strength characteristics and histology of rabbit ligaments induced by different modes of postmortal storage. A cta orthop, scan& 37, 141-155. Walker, L. B., Harris, E. H. and Benedicts, J. V. (1964) Stress-strain relationships in human plantaris tendons: a preliminary study. Med. Electron. biol. Engng 2, 31-38.