Effect of age and distance from the articular surface on the tensile mechanical properties of articular cartilage [English translation]

Collagen fibers constitute one of the main components of articular cartilage. They form a network in which the gel formed by the interaction of the negative charges of proteoglycans and the liquid phase’s positive charge is entrapped. Collagen fibers, with their rope like structure, have the properties to resist tensile load and they have a major role in the tensile properties of articular cartilage. Tensile tests of articular cartilage enable to find the behavior of collagen fibers.

Mathematical models, developed from unconfined compression tests, provide information on cartilage microstructure by curve fitting experimental mechanical results. These models, base on unconfined compression test results, provide theoretical collagen fiber properties. These models assume collagen fiber non-linearity, which means that their modulus increases with deformation. The main objectives of the tensile tests are to verify this non-linear effect.

Few studies on tensile mechanical properties of articular cartilage were performed previously. One of these studies mentioned that, when doing a stress relaxation; the relaxation may take up to 7 hours to reach equilibrium. Despite this observation, their relaxation time was of 15 minutes. Our protocol was established in order to isolate as most as possible the collagen fiber’s behavior. The protocol we used enables the cartilage to relax for several hours (5½ to 10½) between each deformation, which are of small amplitude. Also, to increase the amount of information provided by the mechanical test, the analytical mathematic model was applied to the tensile test geometry. The model predicts a quasi-elastic behavior mainly based on the collagen fiber’s behavior.

Tensile tests had never been done in our laboratory so the development of some methods and an adaptation of the mechanical tester were needed. The method to obtain the samples is mainly base on the method used for compression tests with the exception that the samples were kept attached to the bone and were cut at the wanted dimension just before the tests. Also, the mechanical tester was adapted with a ring system, which enables the actuator to stretch the sample by pushing. Finally, pieces were design to perform stretching under a light microscope while using the same gripping system as the mechanical tester in order to determined the real deformation occurring when stretching a sample.

The main objectives of this study are to obtain information on collagen fibers that are present in articular cartilage. More specifically, this study has three objectives:

• To show that tensile equilibrium modulus of articular cartilage with uniaxial tensile strain
• To show that tensile stiffness decreases with depth from the articular surface
• To show that tensile stiffness increases with age

In order to characterize the curve obtained, the peak’s rigidity and the equilibrium’s modulus were calculated using infinitesimal deformation theory. These data were calculated for each stretching (total of 5), which also gives the slope of these 5 stretching. For young cartilage, peak’s rigidity and equilibrium modulus are, respectively, of 10.0 ± 3.3 MPa and 0.0 ± 0.5 MPa. The slope of the peak’s rigidity and equilibrium modulus are, respectively, of 0.8 ± 0.4 MPa/% and -0.09 ± 0.19 MPa/%. For adolescent cartilage, peak’s rigidity and equilibrium modulus are, respectively, of 18.7 ± 5.9 MPa and 4.7 ± 3.8 MPa. The slope of their peak’s rigidity and equilibrium modulus are, respectively, of 1.8 ± 0.4 MPa/% and 0.28 ± 0.22 MPa/%. For adult cartilage, peak’s rigidity and equilibrium modulus are, respectively, of 28.3 ± 16.6 MPa and 15.6 ± 10.2 MPa. The slope of their peak’s rigidity and equilibrium modulus are, respectively, of 3.1 ± 1.7 MPa/% and 1.75 ± 1.02 MPa/%. Also, a linear fit was made to found the ratio equilibrium-modulus/peak stiffness. It gave an extremely significant difference between the three age groups. The values of these slopes are, respectively for adolescent and adult shoulders, of 0.257 et 0.588. Because the equilibrium modulus of the young was near zero, the linear fit did not give good results. Mechanical test on the deeper zone in cartilage did not gave good quantitative results because, once install in the device, the samples showed a non-negligible curvature between the grips, which did not allow us to establish if the force was from decurvature or tensile properties of the samples. Nevertheless, the rigidity obtained from last stretching was smaller then the rigidity from the articular surface. The results from the stretching under light microscopy showed that the computed longitudinal deformation between each strain showed a constant deformation within the length and the width of the sample. An average of 1.5% deformation was computed between successive stretches and the overall computed deformation (0% to 10%) had an average of 7.7 ± 1.0%. The overall computed transversal deformation (0 to 10%) shows a large variation along the length of the sample. Near the grips, the deformation is -4.7 ± 3.0 % and -4.6 ± 1.6 %, and the largest deformation was in the center of the sample, with an average of -16.5 ± 4.2 %. The ratio of the computed transversal deformation on the longitudinal deformation (Poisson’s ratio for elastic, isotropic and homogeneous materials) is approximately 2,1 in the center of the sample.

For the adolescent and adult shoulders, the results are showing an increase of both peak’s rigidity and equilibrium modulus with increasing strains, while only peak’s rigidity increases for the young shoulders. Increased cross-linking of collagen fibers leads to a decrease in flexibility and an increase in the networks toughness. For a similar displacement, the highly cross-linked collagen fiber network will show higher resistance than a low cross-linked network, and vice-versa. The decrease in rigidity with depth correlates with results in literature. Also, the computed longitudinal deformation is homogenous and constant with stretching and corresponds to 77% of the applied deformation. Transverse deformation shows a big difference, being near zero near the grips, and being of 16.5% in the center.

An analytical mathematical model was applied to the tensile test geometry. The force-displacement curve does not correspond to the experimental curve, the amplitude of the relaxation being too small. First, the frontier conditions did not correspond to the real ones. Second, the hypothesis and assumption implies that the relaxation is caused by fluid entering in the cartilage, while a literature review strongly suggests that the relaxation is caused by a fluid exudation. On the other hand, theoretical equilibrium modulus results obtained are at the same magnitude of experimental results, varying from ~6 Mpa et ~13 Mpa. The non-linear effect found with the finite element method is a lot higher then what is found in this study. This discrepancy might by cause by the geometrical difference of the sample used in compression tests (cylindrical) and tensile test (rectangular).