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Shear Properties of the Temporomandibular Joint Disc in Relation to Compressive and Shear Strain
1 Department of Orthodontics and Craniofacial Developmental Biology, Hiroshima University Graduate School of Biomedical Sciences, 1-2-3 Kasumi, Minami-ku, Hiroshima 734-8553, Japan; Correspondence: * corresponding author, etanaka{at}hiroshima-u.ac.jp
Shear stress can result in fatigue, damage, and irreversible deformation of the temporomandibular joint disc. Insight into the dynamic shear properties of the disc may give insight into the mechanism inducing tissue failure due to shear. We tested the hypothesis that the dynamic shear properties of the disc depend on the amount of shear and compressive strain. Twenty-four porcine discs were used for dynamic shear tests. The specimens were clamped between the plates of a loading apparatus under compressive strains of 5%, 10%, and 15%. Dynamic shear was applied to the specimen by a sinusoidal strain of, respectively, 0.5%, 1.0%, and 1.5%. Both the dynamic elasticity and viscosity were proportional to compressive strain and inversely proportional to shear strain. These shear characteristics suggest a significant role of compressive and shear strain on the internal friction of the disc.
Key Words: temporomandibular joint disc • dynamic shear • compressive strain
It is very likely that, during loading, shear stresses occur in the temporomandibular joint (TMJ) disc, because the articular surfaces that compress the disc are not parallel. As a result, not all areas of the disc are deformed in the same direction, leading to local shear. Another reason why shear stress occurs in the disc is its non-homogeneous structure. Its inner layer consists mainly of anteroposteriorly running collagen fibers and the "leaflet-like" proteoglycans (Kuc and Scott, 1994; Nakano and Scott, 1996), whereas the superior and inferior surface layers consist mainly of anteroposteriorly and mediolaterally running collagen fibers and small proteoglycans (Nakano and Scott, 1996; Minarelli et al., 1997). Therefore, these layers are considered to have different biomechanical properties, which might lead to shear stress (Mizoguchi et al., 1998). Shear stress can result in fatigue, damage, and irreversible deformation of cartilage (Spirt et al., 1989; Zhu et al., 1993, 1994). The relationship between loading of the TMJ disc and the occurring shear stresses, however, has not been fully assessed. This relationship is largely dependent on its shear modulus. Previous work from this laboratory has demonstrated that the shear behavior of porcine discs was dependent on the frequency and direction of shear load, which implies a significant dependency on the collagen fiber orientation within the disc (Tanaka et al., 2003). In other studies, it was reported that the shear stress in cartilage is very sensitive, not only to the frequency and direction of the loading, but also to the amount of shear and compressive strain (Spirt et al., 1989; Mow et al., 1992; Zhu et al., 1994). This implies that the shear stress induced in the disc may be dependent on the compressive strain when the frequency and direction of the shear loading are kept constant. Thus far, however, both the quantitative and qualitative aspects of this dependency in the TMJ disc have not been assessed. Since the disc is an anisotropic and viscoelastic structure like articular cartilage, the question was asked whether and how the dynamic shear properties of the disc are dependent on the amount of shear and compressive strain. This may give more insight into the possible mechanism leading to tissue failure due to shear. In this study, therefore, we investigated the dynamic shear properties of the porcine disc in relation to compressive and shear strain.
Description of the Sample Twenty-four TMJ discs from 12 pigs (ages, 6 to 9 mos; unknown gender) were obtained from a slaughterhouse (Japan Agriculture, Hiroshima, Japan). The protocol of the experiment was approved by the Animal Care and Use Committee at Hiroshima University. The discs were carefully dissected within 1 hr after the animals’ death and were placed in 0.1 M phosphate buffer (pH 7.3) at 4°C.
From the central region of the intermediate zone of each disc, 2 specimens with approximately the same thickness were dissected (Fig. 1A
Testing Procedure The dynamic shear properties of the specimens were determined with the use of an automatic dynamic viscoelastometer (Rheovibron DDV-25FP, Orientec Corp., Tokyo, Japan). The loading apparatus was similar to that used in a previous study (Tanaka et al., 2003). Briefly, the chucking device consisted of 1 inner and 2 outer metal plates (Fig. 1B  ). The 2 specimens from the same disc were clamped between the inner and outer plates under a compressive strain of, respectively, 5, 10, and 15%. The instantaneous stress and strain were measured by means of load and displacement detectors, respectively. All experiments were performed in a bath with 0.1 M phosphate buffer (pH 7.3) at room temperature.
During the shear tests, the outer plates were displaced perpendicular to the compressive strain and relative to the inner plate by a tension control motor in the driver unit. Shear was applied to the specimens by a sinusoidal strain of
Dynamic Viscoelastic Parameters The magnitude of the complex modulus |G*| is determined by
where
where i =
In each test, the mean and standard error of G*, G', G'', and tan
The magnitudes of the dynamic shear moduli G*, G', and G'' were found to be dependent on the frequency and the amplitude of shear loading and on the compressive strains (Fig. 2  , for a shear amplitude 0.5%). At each compressive strain, the dynamic moduli increased with the loading frequency. In all experiments, the dynamic moduli increased with compressive strain. At 15% compressive strain, they were about twice as large as at 5% (p < 0.05); a similar difference was found at 1% and 1.5% shear strain (data not shown). The loss tangent tan  was also dependent on the compressive strain. It was largest at low compressive strain (5%) and slightly decreased with increasing compressive strain. Tan ranged from 0.2 to 0.3, which means that the disc is primarily elastic and has a small but not negligible viscosity.
The specimens exhibited a slight, but not significant, decrease in the values of G* and G' with increase of shear strain (Fig. 3 , for a compressive strain of 10%). The values of G* and G' at a shear strain amplitude of 0.5% were 1.2 times larger than those at 1.5%, regardless of the excitation frequency. The loss modulus G'' hardly depended on shear strain amplitude. The loss tangent tan d remained almost constant with an increase of excitation frequency, but became larger with an increase of the shear strain amplitude.
The two-way ANOVA revealed a significant effect (p < 0.001) of the compressive strain on the values of G' and G'' (Table ). For tan , a significant effect (p < 0.01) of shear strain was found. For all parameters, no significant interactions between compressive and shear strains were observed. At an excitation frequency of 1.0 Hz, the values of G' at 5% compressive strain were 1.04 ± 0.10 MPa, 0.87 ± 0.11 MPa, and 0.78 ± 0.10 MPa (mean ± SE) at 0.5%, 1.0%, and 1.5% shear strain, respectively. At 15% compressive strain, these values increased to 1.99 ± 0.33 MPa, 1.68 ± 0.30 MPa, and 1.47 ± 0.26 MPa (mean ± SE); these values were significantly (p < 0.05) larger than those at 5% compressive strain. The loss moduli G'' also exhibited the largest values at 0.5% shear strain and 15% compressive strain. The values of G'' at 15% compressive strain were 0.40 ± 0.06 MPa, 0.37 ± 0.06 MPa, and 0.36 ± 0.06 MPa (mean ± SE), which were significantly (p < 0.05) larger than those at 5% compressive strain. Concerning the loss tangent tan , the values at 5% compressive strain were 0.21 ± 0.01, 0.24 ± 0.01, and 0.25 ± 0.01 at 0.5%, 1.0%, and 1.5% shear strain, respectively. The value at 0.5% shear strain was significantly smaller (p < 0.05) than the one at 1.5% shear strain. At 15% compressive strain, the values of loss tangent were 0.21 ± 0.01 at 0.5%, 0.22 ± 0.01 at 1.0%, and 0.24 ± 0.01 at 1.5% shear strain, and the values of tan were almost similar, regardless of the magnitude of compressive strain (p > 0.05).
In our study, the dynamic shear moduli increased with the loading frequency, regardless of the shear amplitude and accompanying compressive strain. This dependency on frequency is in accordance with the results of our earlier study (Tanaka et al., 2003) and is probably related to water movement within the matrix of the disc. The present study aimed to clarify the effects of shear and compressive strain on the dynamic shear properties of the disc. An important finding was that the resistance to shear is dependent on the amount of compression of the disc. This finding is fully consistent with the results of Zhu et al.(1993, 1994) for bovine meniscus and articular cartilage. The increased shear stiffness during compression could be caused by an outflow of interstitial fluid due to pressurization of the compressed area. This could lead to smaller pores in the solid matrix, which in turn puts a brake on fluid flow ("lubrication") in response to shear. In tensile and compressive tests, the disc became stiffer with an increase of the applied strain (Beek et al., 2001; Tanaka et al., 2002). The possible explanation for this increase is the stretching of collagen fibers. In contrast, in the present shear tests we observed a shear softening of the disc, with an increase of the shear strain amplitude from 0.5% to 1.5%. This characteristic feature has also been recognized in the bovine meniscus (Zhu et al., 1994). In previous studies (Emery et al., 1997, 1998), this strain softening has been explained by shear displacement of adjacent tissue layers and the resultant disruption of the collagen fibers. Our result of shear softening at very low shear strain amplitudes is less readily explained in this way. In addition, we confirmed that the results of a second series of shear tests did not differ significantly from those of the first series, which implies that an irreversible disruption of collagen fibers is not likely. The possible explanation for the shear softening could be that the matrix (proteoglycans and water) within the disc has non-Newtonian properties similar to those of synovial fluid, i.e., at low shear rates its viscosity is much larger than at high rates. Indeed, in the present study, the loss tangent became significantly larger with increasing shear strain, although both the storage and loss moduli of the disc decreased with an increase of shear strain. This finding indicates that the viscosity of the disc increased due to a decrease of its elastic response. This shear-softening quality may contribute to one of the physiological functions of the disc, i.e., to obtain a congruence between the disc and the stiffer condylar and temporal articular surfaces. Our measurements were not performed at body temperature, but at room temperature (about 30°C). The dynamic properties of the TMJ disc are borne by the collagen and proteoglycan components, which are temperature-sensitive. A higher temperature (the body temperature of a pig, 39°C) may reduce stiffness and strength of the disc (Detamore and Athanasiou, 2003; Tanaka and van Eijden, 2003). In conclusion, analysis of the present results shows that the shear behavior of the porcine TMJ disc is dependent on the frequency and amplitude of the applied shear strain, and also on the compressive strain. The observed shear characteristics suggest a significant role for compressive and shear strain on the internal friction within the disc.
This research was supported by a grant (No. 14571950) for Science Research from the Ministry of Education, Science and Culture, Japan. Received for publication March 31, 2003. Revision received March 17, 2004. Accepted for publication March 18, 2004.
Journal of Dental Research, Vol. 83, No. 6,
476-479 (2004) This article has been cited by other articles:
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ABSTRACT
INTRODUCTION
, angular velocity). The sinusoidal strain produced by a tension control motor and the subsequent stress are measured by means of load and displacement detectors and transmitted to a data processor. In a viscoelastic material, the time difference between dynamic stress 
and dynamic strain 
is recognized and calculated as 
/2). The complex modulus G* is resolved into 2 components: the storage modulus G' and the loss modulus G'', shown vectorially. The tangent of the phase angle 
= 
-1 and 
10% compressive strain; 
15% compressive strain.
