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J Dent Res 82(3): 228-231, 2003
© 2003 International and American Associations for Dental Research

RESEARCH REPORT
Biomaterials & Bioengineering

Dynamic Shear Properties of the Temporomandibular Joint Disc

E. Tanaka1,*, K. Hanaoka1, T. van Eijden2, M. Tanaka3, M. Watanabe1, M. Nishi1, N. Kawai1, H. Murata4, T. Hamada4, and K. Tanne1

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;
2 Department of Functional Anatomy, Academic Centre for Dentistry Amsterdam (ACTA);
3 Division of Mechanical Science, Department of Systems and Human Science, Osaka University School of Engineering Science; and
4 Department of Prosthetic Dentistry, Hiroshima University Graduate School of Biomedical Sciences;

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


   ABSTRACT
TOP
 ABSTRACT
INTRODUCTION
 MATERIALS & METHODS
 RESULTS
 DISCUSSION
 REFERENCES
 
Shear stress might be an important factor associated with fatigue failure and damage of the temporomandibular joint disc. Little information, however, is available on the dynamic behavior of the disc in shear. Since the disc is an anisotropic and viscoelastic structure, in the present study the dependency of the dynamic shear behavior on the direction and frequency of loading was examined. Ten porcine discs were used for dynamic shear tests. Shear stress was applied in both anteroposterior (A-P test) and mediolateral (M-L test) directions. The dynamic moduli increased as the loading frequency increased. The dynamic elasticity was significantly larger in the A-P test than in the M-L test, although the dynamic viscosity was similar in both tests. The present results suggest that non-linearities, compression/shear coupling, and intrinsic viscoelasticity affect the shear material behavior of the disc, which might have important implications for the transmission of load in the temporomandibular joint.

KEY WORDS: temporomandibular joint disc • dynamic shear properties • viscoelasticity


   INTRODUCTION
TOP
 ABSTRACT
 INTRODUCTION
MATERIALS & METHODS
 RESULTS
 DISCUSSION
 REFERENCES
 
The temporomandibular joint (TMJ) disc, located between the articulating surfaces of the mandible and the temporal bone, has an important load-bearing, stress-absorbing, and joint-stabilizing function (Nickel and McLachlan, 1994; Scapino et al., 1996; Tanaka et al., 1999; Beek et al., 2001). The disc is subject to various types of loading, such as sustained loading during clenching and intermittent loading during mastication (Kuboki et al., 1997; Beatty et al., 2001). These loadings can generally be divided into compression, tension, and shear components.

The mechanical behavior of the disc is non-linear, anisotropic, and time-dependent, and its viscoelastic properties are dependent on the direction, rate, and frequency of the loads applied (Kuboki et al., 1997; Beatty et al., 2001; Beek et al., 2001; Tanaka et al., 2002). For example, the apparent Young’s modulus and ultimate tensile strength of the disc are larger for anteroposterior loading than for mediolateral loading (Beatty et al., 2001), and the loading frequency correlates positively with dynamic parameters, such as maximal stress, amount of dissipated energy, and various viscoelastic moduli (Beek et al., 2001; Tanaka et al., 2002). These characteristics are related to the collagen fiber orientation in the disc and the interstitial fluid flow.

Recent work reported by Gallo et al. (2000) suggests that, during mastication, fatigue failure of the disc could be caused by dynamic shear stress. Therefore, in addition to compressive and tensile stress, shear stress might be important for the normal or abnormal functioning of the disc. Thus far, however, relatively little information is available on the dynamic properties of the disc under shearing. In this study, we investigated the dynamic shear properties of the porcine disc over a wide range of loading frequencies. Since the disc is an anisotropic and viscoelastic structure, the aim was to evaluate the effects of frequency and direction of the applied load on these properties.


   MATERIALS & METHODS
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS & METHODS
RESULTS
 DISCUSSION
 REFERENCES
 
Description of the Sample
Ten TMJ discs from 10 pigs (ages 6-9 mos; no known gender) were obtained at 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 soon after the animals’ death. Immediately afterward, discs 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. 1AGo). To obtain equal mediolateral and anterolateral lengths, we trimmed these specimens using 2 parallel shavers (length, 6.7 mm). The anteroposterior and mediolateral lengths of the specimens and their thickness were measured by means of digimatic calipers (CCD-S20C, Mitutoyo Co., Kawasaki, Japan). For each disc, the lengths and thicknesses were determined by the average over 2 dissected specimens. For the 10 discs, the means and standard deviation values were 6.69 ± 0.28 mm, 6.86 ± 0.24 mm, and 2.08 ± 0.18 mm (n = 10) for the anteroposterior and mediolateral lengths and thicknesses, respectively. Shear tests were conducted within 6 hrs after resection of the specimens.



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  		Figure 1. Location of the two specimens (A) and block diagram (B) of the dynamic viscoelastometer with a schematic representation of the relationship between stress and strain of a viscoelastic material during a sinusoidal oscillating strain ({omega}, angular velocity). The sinusoidal strain is produced by a tension control motor in the driver, and the stress {sigma} and strain {gamma} are measured by means of load and displacement detectors and transmitted to a data processor. In a viscoelastic material, the phase difference between stress and strain is somewhere in between (0 < {delta} < {delta}/2), and the complex modulus G* is resolved into two components: the storage modulus G' and the loss modulus G'', shown vectorially. The tangent of the phase angle ({delta}) between stress and strain is a measure of the ratio of energy loss to energy stored during cyclic deformation.

 
Testing Procedure
The dynamic shear properties of the specimens were determined by means of an automatic dynamic viscoelastometer (Rheovibron DDV-25FP, Orientec Corp., Tokyo, Japan). The chucking device consisted of 2 outer and 1 inner metal plates (Fig. 1BGo), and the 2 specimens from a disc were clamped between the inner and outer plates under a constant compressive strain of 10%. The relative displacement was produced by a tension control motor in the driver unit; the time-dependent 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 tests, a dynamic shear was applied to the specimen by a sinusoidal strain of {gamma} = {gamma}0 + {delta}{gamma}sin({omega}76;t), with an applied strain of {gamma}0 = 0.5% and an oscillation amplitude 2{Delta}{gamma} = 0.2%; the resulting stress was described by {sigma} = {sigma}0 + {Delta}{sigma}sin({omega}t + {delta}). In the present study, the oscillation frequency ranged from 0.1 to 100 Hz. First, dynamic shear was applied in the anteroposterior direction of the specimen (A-P test). After a recovery time of 5 min, shear stress was applied in the mediolateral direction (M-L test). The A-P test was repeated 5 min after the M-L test. The results of the second series of A-P tests did not differ significantly from those of the first series, which implied that the testing order and recovery time had no effect on the stress-strain relationship.

Dynamic Viscoelastic Parameters
The relationship between stress and strain expresses the viscoelastic characteristics of the disc and yields several useful biomechanical parameters. Due to the viscoelasticity of the disc, the stress-strain response is in general out of phase, and the phase difference {delta} between the stress and strain falls in the range of 0 to 90° (Fig. 1Go). Based on the dynamic behavior of stress and strain, the complex dynamic shear modulus G*, the shear storage modulus G', the shear loss modulus G'', and the loss tangent tan{delta} were determined as dynamic viscoelastic parameters (Murata et al., 2000). The complex modulus G* is decomposed into G' and G''. The storage modulus (G') is the ratio of the stress in phase with the strain to the strain, and represents the elastic component of the material behavior. The loss modulus (G'') is the ratio of the stress 90° out of phase with the strain to the strain and represents the viscous component of the material behavior. The modulus G' is directly proportional to the energy storage in a cycle of deformation and G'' is proportional to the average dissipation or loss of energy. The loss tangent (tan{delta}) is the ratio of the energy lost to that stored during a single cycle of deformation; it thus represents the ratio of viscous/elastic properties.

The magnitude of the complex modulus |G*| is determined by

In this equation, {Delta}{sigma} represents the dynamic shear stress calculated by dividing the shear force by the area of the disc facing the metal plates of the testing apparatus. The dynamic shear strain {Delta}{gamma} was defined as displacement per average thickness of the two specimens. Using the phase angle {delta}, the storage and loss moduli, G' and G'', are determined by



where i = {surd}-1 and tan{delta} = G''/G' is the loss tangent.

For each frequency of each test (A-P or M-L), the mean and standard deviation of |G*|, G', G'', and tan{delta} were calculated. Paired Student t tests were performed for the A-P and M-L tests at the frequency of 1.0 Hz. This frequency reflects masticatory conditions during chewing (Druzinsky, 1993; Gallo et al., 2000).


   RESULTS
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS & METHODS
 RESULTS
DISCUSSION
 REFERENCES
 
In both the A-P and M-L shear tests, the magnitude of the complex modulus |G*|, the storage modulus G', and the loss modulus G'' increased as the frequency increased from 0.1 to 100 Hz (Fig. 2Go). Throughout the whole range of frequencies, the values of |G*| and G' for the A-P test were 1.5 times larger than those for the M-L test. The loss moduli G'' were almost the same for both tests.



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  		Figure 2. The complex modulus |G*|, storage modulus G', loss modulus G'', and loss tangent tan{delta} as a function of frequency. Error bars are standard deviations (for each group, n = 10). The frequency correlates positively with the values of the moduli.

A-P test: {circ} |G*| {triangleup} G' {square} G'' {diamond} tan{delta}

M-L test: • |G*| {blacktriangleup} G' {blacksquare} G'' {diamondsuit} tan{delta}

 
The loss tangent (tan{delta}) exhibited a relatively small change between 0.1 and 1 Hz, and gradually increased with frequencies beyond 1 Hz (Fig. 2Go). Throughout the entire range of frequencies tested, tan{delta} was larger in the M-L test than in the A-P test. The value of tan{delta} ranged from 0.15 to 0.25, which means that the disc is primarily elastic and has a small but not negligible viscosity.

At a frequency of 1.0 Hz, the moduli |G*|, G', and G'' were 1.44 ± 0.36 MPa, 1.41 ± 0.35 MPa, and 0.25 ± 0.06 MPa (mean ± SD), respectively, in the A-P test (Fig. 3Go). These values were smaller in the M-L test, especially those of |G*| and G' (p < 0.05). Concerning the loss tangent tan{delta}, the values at 1.0 Hz were 0.17 ± 0.01 in the A-P test and 0.20 ± 0.02 in the M-L test; the difference between the two directions was significant (p < 0.01).



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  		Figure 3. Means and standard deviations of storage modulus G', loss modulus G'', and loss tangent tan{delta} at 1.0 Hz. White and black bars are values in A-P and M-L tests, respectively. Error bars are standard deviations (for each group, n = 10). Asterisks: significance of difference between the groups (** p < 0.01; * p < 0.05) as tested with a paired Student t test.

 

   DISCUSSION
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS & METHODS
 RESULTS
 DISCUSSION
REFERENCES
 
Dynamic measurements on the disc have been carried out for frequencies ranging from 0.01 to 100 Hz (Beek et al., 2001; Tanaka et al., 2002). However, these measurements were restricted to compression or tension. Therefore, limited information is available on the viscoelastic properties in dynamic shear, particularly in a physiological range of frequencies and strains. The present study is, as far as we know, the first, in which the dynamic shear properties of the TMJ disc have been examined. Lai et al. (1998) investigated the shear modulus of the human TMJ disc, but, in contrast to the present study, they used a static shear loading.

Even when the disc slides along the articular eminence during jaw opening, shear loading of the disc has been considered to be negligible due to the very low friction (Nickel and McLachlan, 1994). By the presence of synovial fluid between the articular surfaces, the coefficient of friction in the joint is assumed to be almost zero (Linn, 1967; Foster and Fisher, 1996, 1999). However, there are several arguments supporting the view that the disc is subjected to shear stress. First, after prolonged loading such as clenching and grinding, only solid contact may exist between the disc and the articular surfaces, and there will be probably no boundary lubrication between them (Forster and Fisher, 1996, 1999; Tanaka et al., 2001). Second, the disc is an inhomogeneous structure (Kuc and Scott, 1994; Nakano and Scott, 1996; Minarelli et al., 1997). Three layers (two superficial, one deep) with a different mechanical behavior are generally distinguished (Nakano and Scott, 1996; Mizoguchi et al., 1998), resulting in shear. Indeed, finite element calculations, in which the disc was modeled to consist of three layers, demonstrated that relatively large shear stress is induced during clenching (Tanaka et al., 1994).

Zhu et al. (1994) investigated the viscoelastic shear properties of the bovine meniscus, and reported that the dynamic shear modulus |G*| increased non-linearly with an increase of frequency, regardless of the magnitude of compressive strain. In our study, the dynamic shear moduli also increased non-linearly with an increase of frequency, regardless of the direction of the applied force. A similar non-linear dependence on frequency was also observed during dynamic tensile tests (Tanaka et al., 2002). This dependence on frequency is due to water movement and squeezing within the matrix of the disc. Within small strains, the hydrostatic pressure in the interstitial fluid due to the hydrophilic character of the proteoglycans is in balance with the shear force. Therefore, the load acting on the disc can be assumed to be carried by pressurization of fluid without much deformation of the collagen network (Soltz and Ateshian, 1998). The loss tangent also increased with an increase of frequency. This implies that the dependence on frequency was greater for the elastic than for the viscous properties. A possible explanation for the increase may be heat-induced degradation of hydrogen bonds in the solid matrix which would reduce the fluid-solid drag coefficient. The increase in the moduli with frequency was not due to a time-dependent effect. We ruled this out by carrying out several experiments in which the moduli were also measured at several constant frequencies with increasing cycles (data not shown; see also Tanaka et al., 2002).

The dynamic shear properties of the disc differed between the A-P and M-L tests. The complex and storage moduli were significantly greater in the A-P test than in the M-L test. It is well-known that the viscoelastic properties of the disc are anisotropic (Nickel and McLachlan, 1994; Beatty et al., 2001). The present results support this characteristic of the disc. The anisotropic behavior of the disc is mainly dependent on the orientation of collagen fibers. In the intermediate zone, they mainly run anteroposteriorly (Mills et al., 1994; Scapino et al., 1996), and, consequently, the apparent modulus and ultimate tensile strength are anteroposteriorly an order of magnitude higher than mediolaterally (Beatty et al., 2001). In the present study, the loss moduli were similar in both directions, although the complex and storage moduli were significantly larger in the A-P test than in the M-L test. Furthermore, the loss tangent was significantly larger in the M-L test. Under mediolateral shearing, the elastic properties of collagen fibers decrease more than under anteroposterior shearing. The viscous properties of the proteoglycans are almost similar. Therefore, the ratio of the viscous/elastic properties (tan{delta}) was larger in the M-L shear test than in the A-P shear test.

The compressive strain of 10% used for clamping in the present study is in accordance with the amount of joint space reduction during maximum clenching (Kuboki et al., 1999). According to Zhu et al. (1993, 1994), the magnitude of the dynamic shear modulus |G*| increases with increasing compressive strain, which implies that the shear modulus is mainly dependent on the compressive strain. The possible explanation for this increase is that compression might lead to stretching of the anteroposteriorly running collagen fibers. The stretched collagen fibers probably contribute to the resistance to shear. To evaluate the influence of the amount of compressive strain on the dynamic shear modulus, more studies should be conducted in future.

In conclusion, the present results show that the TMJ disc exhibits a non-linear viscoelastic behavior in dynamic shear. This behavior is dependent on the frequency and direction of the shear load. The observed shear anisotropy implies a significant dependency on the collagen fiber orientation within the disc. Furthermore, it is suggested that the dynamic shear properties of the disc include the resistance to tension of collagen fibers and the resilience to shear between its superficial and deep layers.


   ACKNOWLEDGMENTS
 
This research was supported by a grant (No. 14571950) for Science Research from the Ministry of Education, Science and Culture, Japan.

Received July 19, 2002; Last revision November 18, 2002; Accepted December 5, 2002


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 ABSTRACT
 INTRODUCTION
 MATERIALS & METHODS
 RESULTS
 DISCUSSION
 REFERENCES
 
Beatty MW, Bruno MJ, Iwasaki LR, Nickel JC (2001). Strain rate dependent orthotropic properties of pristine and impulsively loaded porcine temporomandibular joint disk. J Biomed Mater Res 57:25–34.[ISI][Medline]

Beek M, Aarnts MP, Koolstra JH, Feilzer AJ, van Eijden TM (2001). Dynamic properties of the human temporomandibular joint disc. J Dent Res 80:876–880.[Abstract/Free Full Text]

Druzinsky RE (1993). The time allometry of mammalian chewing movements: chewing frequency scales with body mass in mammals. J Theor Biol 160:427–440.[ISI][Medline]

Forster H, Fisher J (1996). The influence of loading time and lubricant on the friction of articular cartilage. Proc Inst Mech Eng [H] 210:109–119.[Medline]

Forster H, Fisher J (1999). The influence of continuous sliding and subsequent surface wear on the friction of the articular cartilage. Proc Inst Mech Eng [H] 213:329–345.[ISI][Medline]

Gallo LM, Nickel JC, Iwasaki LR, Palla S (2000). Stress-field translation in the healthy human temporomandibular joint. J Dent Res 79:1740–1746.[Abstract/Free Full Text]

Kuboki T, Shinoda M, Orsini MG, Yamashita A (1997). Viscoelastic properties of the pig temporomandibular joint articular soft tissues of the condyle and disc. J Dent Res 76:1760–1769.[Abstract/Free Full Text]

Kuboki T, Takenami Y, Orsini MG, Maekawa K, Yamashita A, Azuma Y, et al. (1999). Effect of occlusal appliances and clenching on the internally deranged TMJ space. J Orofac Pain 13:38–48.[ISI][Medline]

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Linn FC (1967). Lubrication of animal joints. I. The arthrotripsometer. J Bone Joint Surg Am 49(A):1079–1098.[Abstract/Free Full Text]

Mills DK, Fiandaca DJ, Scapino RP (1994). Morphologic, microscopic, and immunohistochemical investigations into the function of the primate TMJ disc. J Orofac Pain 8:136–154.[Medline]

Minarelli AM, Del Santo Junior M, Liberti EA (1997). The structure of the human temporomandibular joint disc: a scanning electron microscopy study. J Orofac Pain 11:95–100.[Medline]

Mizoguchi I, Scott PG, Dodd CM, Rahemtulla F, Sasano Y, Kuwabara M, et al. (1998). An immunohistochemical study of the localization of biglycan, decorin and large chondroitin-sulphate proteoglycan in adult rat temporomandibular joint disc. Arch Oral Biol 43:889–898.[ISI][Medline]

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Scapino RP, Canham PB, Finlay HM, Mills DK (1996). The behaviour of collagen fibres in stress relaxation and stress distribution in the jaw-joint disc of rabbits. Arch Oral Biol 41:1039–1052.[ISI][Medline]

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Tanaka E, Tanne K, Sakuda M (1994). A three-dimensional finite element model of the mandible including the TMJ and its application to stress analysis in the TMJ during clenching. Med Eng Phys 16:316–322.[ISI][Medline]

Tanaka E, Tanaka M, Miyawaki Y, Tanne K (1999). Viscoelastic properties of canine temporomandibular joint disc in compressive load-relaxation. Arch Oral Biol 44:1021–1026.[ISI][Medline]

Tanaka E, Rogrigo DP, Tanaka M, Kawaguchi A, Shibazaki T, Tanne K (2001). Stress analysis in the TMJ during jaw opening by use of a three-dimensional finite element model based on magnetic resonance images. Int J Oral Maxillofac Surg 30:421–430.[ISI][Medline]

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