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J Dent Res 83(5): 404-407, 2004
© 2004 International and American Associations for Dental Research

RESEARCH REPORT
Biomaterials & Bioengineering

The Frictional Coefficient of the Temporomandibular Joint and Its Dependency on the Magnitude and Duration of Joint Loading

E. Tanaka*, N. Kawai, M. Tanaka1, M. Todoh1, T. van Eijden2, K. Hanaoka, D.A. Dalla-Bona, T. Takata3, and K. Tanne

Department of Orthodontics and Craniofacial Developmental Biology and
3 Department of Oral Maxillofacial Pathobiology, Hiroshima University Graduate School of Biomedical Sciences, 1-2-3 Kasumi, Minami-ku, Hiroshima 734-8553, Japan;
1 Department of Mechanical Science and Bioengineering, Graduate School of Engineering Science, Osaka University, Osaka, Japan; and
2 Department of Functional Anatomy, ACTA, Amsterdam, The Netherlands; Hiroshima University Graduate School of Biomedical Sciences, Hiroshima, Japan;

* corresponding author, etanaka{at}hiroshima-u.ac.jp


   ABSTRACT
TOP
 ABSTRACT
INTRODUCTION
 MATERIALS & METHODS
 RESULTS
 DISCUSSION
 REFERENCES
 
In synovial joints, friction between articular surfaces leads to shear stress within the cartilaginous tissue, which might result in tissue rupture and failure. Joint friction depends on synovial lubrication of the articular surfaces, which can be altered due to compressive loading. Therefore, we hypothesized that the frictional coefficient of the temporomandibular joint (TMJ) is affected by the magnitude and duration of loading. We tested this by measuring the frictional coefficient in 20 intact porcine TMJs using a pendulum-type friction tester. The mean frictional coefficient was 0.0145 (SD 0.0027) after a constant loading of 50 N during 5 sec. The frictional coefficient increased with the length of the preceding loading duration and exceeded 0.0220 (SD 0.0014) after 1 hr. Application of larger loading (80 N) resulted in significantly larger frictional coefficients. In conclusion, the frictional coefficient in the TMJ was proportional to the magnitude and duration of joint loading.

KEY WORDS: temporomandibular joint • frictional coefficient • loading duration


   INTRODUCTION
TOP
 ABSTRACT
 INTRODUCTION
MATERIALS & METHODS
 RESULTS
 DISCUSSION
 REFERENCES
 
In many species, including pigs and humans, the articular surfaces of the temporomandibular joint (TMJ) are highly incongruent. Due to this incongruence, the contact areas of the opposing articular surfaces are very small. At joint loading, this may lead to large peak loads, which may cause damage to the cartilage layers on the articular surfaces. The presence of a fibrocartilaginous disc in this joint is believed to prevent these peak loads (Tanne et al., 1991; Scapino et al., 1996), since it is capable of deforming and adapting its shape to that of the articular surfaces. These deformations ensure that loads are absorbed and spread over larger contact areas.

During jaw movement, the disc moves with respect to both the mandibular condyle and the articular eminence. When the disc slides along the articular surfaces, shear loading of the disc has been considered to be negligible, due to very low friction (Nickel and McLachlan, 1994b), since the coefficient of friction can be assumed to be almost zero by the presence of synovial fluid (Forster and Fisher, 1996, 1999). When this fluid degrades and its viscosity decreases, it could easily be expelled from between the articular surfaces during joint loading. This could lead to a reduction in boundary lubrication between the articular surfaces, resulting in an increase of the frictional coefficient (Forster and Fisher, 1996, 1999; Nitzan, 2001). As a consequence, the frictional coefficient can be considered of great importance for an understanding of the dynamics of the TMJ and of the onset of internal derangement.

The normal frictional coefficient between the cartilage surfaces of synovial joints is reported to be range from 0.001 to 0.1 (Linn, 1967; Mabuchi et al., 1994, 1999; Forster and Fisher, 1999). This coefficient may increase due to deterioration in the lubrication mechanism (Linn, 1967; Ateshian et al., 1994; Ateshian, 1997). This mechanism is primarily dependent on the synovial fluid, where hyaluronic acid is considered to be the primary effective constituent (Schurz and Ribitsch, 1987; Mabuchi et al., 1994). However, the composition of the lubricant may change upon joint loading, because then it mixes with water, which is exuded from the cartilaginous tissue when it is compressed (Forster and Fisher, 1996). It is still unknown, however, how this affects the lubrication mechanism in the TMJ. Moreover, the literature has no available studies in which the frictional coefficient has been measured in the intact TMJ.

Thus far, it is suggested that the frictional coefficient between the articular surfaces in synovial joints becomes larger during compressive loading. In the TMJ, a cartilaginous disc is situated between the articular surfaces. It is not known how this structure interferes with the proposed effect of joint loading on lubrication. In this study, therefore, we measured the frictional coefficients of porcine TMJ after periods of compressive loading varying from 5 sec to 1 hr. The aim was to assess the influence of the loading magnitude and duration on the frictional coefficient in the intact joint.


   MATERIALS & METHODS
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS & METHODS
RESULTS
 DISCUSSION
 REFERENCES
 
Twenty TMJs from 10 pigs (Sus domesticus; ages 6–9 mos; no known gender) were obtained at a slaughterhouse (Japan Agriculture Hiroshima, Hiroshima, Japan). The protocol of the experiment was approved by the Animal Care and Use Committee at Hiroshima University. The joint was separated from the skull by an osteotomy on the temporal bone and from the mandible by an osteotomy through the condylar neck at the level of the coronoid process. Except for the joint capsule, all soft tissues were carefully removed. During the experiments, the joints were kept moist with injection of physiologic saline solution on the outside of the joints. The sizes of the condyle were 14.3 ± 1.6 mm and 24.0 ± 2.6 mm (mean and SD) in the anteroposterior and mediolateral directions, respectively.

The experimental apparatus developed for this study was a pendulum-type friction tester with an oscillation cycle of about 1–2 sec (Fig. 1Go). The temporal bone of the TMJ was fixed to the lower plate connected to the base column by means of gypsum, and the condyle was attached to the upper plate connected to the frame of the pendulum. The direction of loading was carefully aligned to match the natural posture at the jaw-closed position. The total mass of the upper plate and the frame of the pendulum was 40 N. The number of weights placed on the weight plate allowed the compressive load on the joint to be adjusted to various values-50 and 80 N, respectively, in the present study.



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  		Figure 1. Schematic illustration of the pendulum-type friction tester and a sample of damping curve recorded by the three-dimensional dynamic angle-sensor. The total compressive load was 50 N or 80 N, and the initial swing was approximately 5°, which was commenced immediately after the load was set. By the three-dimensional dynamic angle-sensor, three angular velocities and three angles are measured round three axes, i.e., a roll, a pitch, and a yaw axis. From the total six measurements obtained, the three-dimensional movements of the condyle along the articular surface were calculated.

 
The distance L between the center of gravity and the fulcrum was 40–100 mm, depending on the different number of weights, and its effective value was calculated based on the observed cycle time of oscillation, T = 2{pi}(L/g)1/2, where g is the acceleration of gravity. The angular displacement was measured by a three-dimensional dynamic angle-sensor (GU-3024, Data Tek, Tokyo, Japan) mounted on the upper plate (Fig. 1Go). The roll-pitch-yaw angles—i.e., the rotation angles with respect to, respectively, antero-posterior, medio-lateral, and vertical axes—were measured as the digital output of the sensor (sampling rate, 60 Hz; resolution, 0.5°) and were transmitted to the data processor. After confirming that the yaw angle was constant, we calculated the resultant three-dimensional swing angle of the pendulum from the roll and pitch angles.

Based on the damping oscillation curve of the pendulum, the frictional coefficient µ was calculated by the following equation:


where r is the radius of the condylar head, and {Delta}{theta} is the average decrease in amplitude of the pendulum swing. We evaluated it by averaging the values from the 3rd to the 12th swings.

As different conditions of the loading magnitude, compressive loads of 50 N and 80 N were applied on 10 right and 10 left joints, respectively. The main test variable, the period of loading prior to friction measurement, was varied between 5 sec and 1 hr (5 sec, 5 min, 10 min, 20 min, 40 min, and 1 hr). This was the amount of time that the disc spent loaded against the articular cartilage prior to the measurement of frictional coefficients.

We used a two-way ANOVA to determine whether statistically significant differences existed among loading magnitude, loading duration, and frictional coefficient. The differences of these values among the loading magnitudes and those among the loading durations were tested with Scheffé’s test.


   RESULTS
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS & METHODS
 RESULTS
DISCUSSION
 REFERENCES
 
The magnitude and duration of loading had a significant effect (ANOVA, p < 0.0001) on the frictional coefficient (TableGo). No significant interaction between loading magnitude and duration was observed.


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  		Table. Two-way ANOVA for the Coefficient of Friction
 
The mean frictional coefficient was 0.0145 (SD 0.0027) in the joints after a five-second period of loading with 50 N (Fig. 2Go). The frictional coefficient increased with the duration of loading and exceeded 0.0220 (SD 0.0014) after 1 hr. The mean values were 0.0168, 0.0184, 0.0191, and 0.0209 after 5 min, 10 min, 20 min, and 40 min, respectively (Fig. 2Go).



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  		Figure 2. Means and standard deviations of the frictional coefficients for the TMJ after 5 sec, 5 min, 10 min, 20 min, 40 min, and 1 hr of stationary loading duration, with 50 N and 80 N compressive loadings. Error bars are standard deviations (for each group, n = 10). *Significance of difference between the values (p < 0.01) as tested with Scheffé’s test. {dagger} p < 0.0001 compared with the frictional coefficient at 5 min, 10 min, 20 min, 40 min, and 1 hr. White bars = 50 N; black bars = 80 N.

 
With a load of 80 N, the mean frictional coefficient was 0.0191 (SD 0.0021) after a loading duration of 5 sec, which was significantly larger than that with a load of 50 N (Fig. 2Go). As was the case for the 50-N load, the frictional coefficient of the joint increased with the duration of loading and achieved a value of 0.0239 (SD 0.0023) after 1 hr. The Scheffé’s test showed that the coefficients of friction with a load of 50 N were significantly smaller than those with a load of 80 N (p < 0.0001). The frictional coefficients differed significantly (p < 0.01) between the durations of loading; the difference was most evident between the frictional coefficients after 5 sec of loading and those after more than 5 min of loading (p < 0.00001) (Fig. 2Go).


   DISCUSSION
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS & METHODS
 RESULTS
 DISCUSSION
REFERENCES
 
As far as we are aware, this is the first attempt to investigate the frictional coefficient in the intact TMJ. The only available information on the frictional coefficient in the TMJ is the study by Nickel and McLachlan (1994a), who measured the frictional coefficient between the dissected porcine disc and an acrylic resin plate. It is recognized that the frictional coefficient in synovial joints is associated with the lubrication mechanism (Ateshian, 1997; Linn, 1967). The lubricating ability is dependent on the joint components, including synovial fluid, disc, and articular surface cartilage. The synovial fluid is a viscous gel and contains mostly water. This fluid can move both inside and through the surface layer of the disc and articular cartilage. The collagen and proteoglycans are dispersed in the fluid, making the cartilage a microporous material with a certain permeability. The amount of permeability is particularly significant for compression, since the mechanical response of the disc will depend on it (Beek et al., 2001; Kim et al., 2003). A low permeability means that any substantial exchange of fluid between the inside and the outside of the disc must take place over a substantial period of time (e.g., min), compared with the physiological loading cycle (1 sec). As a consequence, the disc will maintain its stiffness under compression. In the case of high permeability, a rapid exchange of fluid is possible, which results in a substantial decrease in stiffness. The disc appears to be the principal means of reducing surface friction. Friction on the surfaces of the condyle, without the aid of the disc, is at least three times greater than when the disc is in place (Nickel and McLachlan, 1994a). In synovial joints, the frictional coefficients between the surfaces of cartilage are reported to be within a range of 0.001 to 0.1 (Linn, 1967; Forster and Fisher, 1996, 1999; Mabuchi et al., 1999). In this study, the mean frictional coefficient in the TMJ after 5 sec of loading with a compressive load of 50 N was 0.0145, which is within this range of frictional coefficients measured in other joints (Forster and Fisher, 1996, 1999; Mabuchi et al., 1999).

Furthermore, we found that the frictional coefficient in the TMJ increased with an increase of the compressive load. This increase leads to an increase of the contact area, which in turn might result in an increase of the frictional coefficient. Another possible explanation is that the shear modulus of the disc and the subsequent shear stress between the articular surfaces increase as the loading becomes larger. According to Zhu et al.(1993, 1994), the magnitude of the dynamic shear modulus increases with the amount of loading. These authors suggested that stationary compression might lead to stretching of the anteroposteriorly running collagen fibers. The stretched collagen fibers probably contribute to the resistance to shear, resulting in an increase of frictional coefficients (Tanaka et al., 2003). Furthermore, we also reported that the dynamic shear modulus of the TMJ disc increases with an increase of compressive strain (Tanaka et al., 2004). We suggested that the increased shear stiffness could be caused by an outflow of interstitial fluid due to pressurization of the compressed area. Considering these findings, the frictional coefficient in the TMJ is presumably dependent on the shear behavior of the disc.

It should be realized that the amount and nature of loading used in the present study do not represent the TMJ loading occurring in vivo. For example, TMJ loading during clenching and mastication in the monkey, human, and pig is reported to range from 10 to 170 N (Hohl and Tucek, 1982; Boyd et al., 1990; Ward et al., 1990; Nitzan, 1994). We used loading values of 50 and 80 N. It can be expected that, similar to the results obtained in other joints, the use of larger loads will lead to a further increment of the frictional coefficient. In addition, presumably, the effects of sustained static pre-loads on friction cannot be compared with that of repetitive dynamic loading.

The present results revealed an increase of the frictional coefficient in the TMJ as the period of stationary loading became longer. After prolonged loading, only solid contact may exist between the articular surfaces, and then there is probably no longer any lubrication of fluid film between them. However, comparing our results with those from other synovial joints, the increase of the frictional coefficient with the increase in loading time was very small. For example, in the articular cartilage from the bovine femoral condyle, the frictional coefficient became 27 times larger after 45 min of stationary loading (Forster and Fisher, 1996), while the frictional coefficient in the TMJ after 60 min of loading was only 1.25–1.5 times that measured after 5 sec. This difference may be explained by the presence of the disc. The disc contains much water and is a viscoelastic material, by which it functions to some extent as a fluid (Tanaka and van Eijden, 2003). It is therefore suggested that the lubricating function in the TMJ is relatively stable against prolonged compression, compared with other synovial joints without a disc.

In the initial stage of TMJ internal derangements, a dysfunctional biomechanical environment might be present in the TMJ (Dijkgraaf et al., 1995). A dysfunctional environment, such as sustained loading, is presumably associated with an increase in frictional coefficient. Because we found a relatively small effect of static sustained loading on the frictional coefficient, other factors might also be considered. We previously investigated the influence of prolonged stress on the viscoelastic properties of the disc, and suggested that a prolonged stress greatly affected the recovery of joint homeostasis and dramatically impairs viscoelastic properties such as energy dissipation and relative energy loss (Tanaka et al., 2002). In addition, it is well-known that intermittent hydrostatic compression of near-physiological magnitude has an anabolic effect on mineral metabolism in craniofacial components, and that continuous compression of higher magnitude has a catabolic effect (Burger et al., 1992). The subsequent increase of friction may induce increased shear stress in the disc. It is well-known that shear stress in a tissue can lead to fatigue and damage. Therefore, the resultant shear stress can lead to changes in glycosaminoglycan composition and thus to changes in mechanical properties of the disc.


   ACKNOWLEDGMENTS
 
We thank Japan Agriculture Hiroshima for provision of porcine TMJs. This research was supported in part by a grant (No. 14571950) for Science Research from the Ministry of Education, Science and Culture, Japan.

Received August 13, 2003; Last revision January 29, 2004; Accepted March 8, 2004


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 ABSTRACT
 INTRODUCTION
 MATERIALS & METHODS
 RESULTS
 DISCUSSION
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