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J Dent Res 83(8): 650-654, 2004
© 2004 International and American Associations for Dental Research

RESEARCH REPORT
Biomaterials & Bioengineering

Laboratory Stresses and Tractional Forces on the TMJ Disc Surface

J.C. Nickel1,2,*, L.R. Iwasaki1,2, M.W. Beatty2,3, and D.B. Marx4

1 University of Nebraska Medical Center College of Dentistry, Departments of Growth and Development,
2 Oral Biology, and
3 Adult Restorative Dentistry, PO Box 683740, Lincoln, NE 68583-0755, USA; and
4 University of Nebraska, Department of Biometry, 103 Miller Hall, Lincoln, NE 68583-0712, USA;

* corresponding author, jnickel{at}unmc.edu


   ABSTRACT
TOP
 ABSTRACT
INTRODUCTION
 MATERIALS & METHODS
 RESULTS
 DISCUSSION
 REFERENCES
 
The etiology of degenerative disease of the TMJ may involve fatigue produced by surface tractional forces and compressive stresses. This study tested the time-dependent effects of compressive loading and stress-field translation on TMJ disc-surface tractional forces and stresses. In laboratory experiments with 50 porcine discs, an acrylic indenter imposed 10 N static loads for 10 and 60 sec, followed by translation of the loaded indenter along the mediolateral axis of the disc. Maximum tractional forces were found to occur following 60 sec of static loading (p < 0.001), and increased with translation velocity (R2 = 0.73); whereas maximum compressive stresses occurred after 10 sec of static loading (p < 0.001). Overall, the results were consistent with current mechanical theories of the time-dependent effects of compressive loading of cartilage.

KEY WORDS: TMJ • cartilage • mechanics • stresses • ploughing


   INTRODUCTION
TOP
 ABSTRACT
 INTRODUCTION
MATERIALS & METHODS
 RESULTS
 DISCUSSION
 REFERENCES
 
Degenerative joint disease (DJD) in synovial joints of young individuals is thought to be initiated by mechanical fatigue of the articulating tissues. Cracking of the cartilage surface by impact loading increases the rate of fatigue by concentrating peak stresses and strain energy in the cartilage matrix (Ateshian et al., 1994; Dunbar et al., 2001; Nickel et al., 2001). The mean age of onset of DJD in the temporomandibular joint (TMJ) is between 25 and 35 yrs (Heloe and Heloe, 1975; Solberg et al., 1979; Nilner, 1981; Pullinger et al., 1988), while in the hip it is a decade later (Lawrence et al., 1989; Felson et al., 1997; Vingard et al., 1997). The TMJ disc has the function of stress distribution and lubrication in the TMJ (Nickel and McLachlan, 1994a, b; Nickel et al., 2001); hence, mechanical failure of the disc may be an important predisposing factor leading to relatively early degenerative changes. Measurements of yield strength indicate that the TMJ disc is ten-fold stronger along the anteroposterior axis compared with the mediolateral axis, and that trauma increases rate of fatigue along the mediolateral axis (Beatty et al., 2001, 2003). The results suggest that mechanical fatigue of the disc is likely to cause failure of the cross-links between major, anteroposteriorly oriented, collagen fibers.

Tractional forces and compressive stresses applied repeatedly to the cartilage surface serve as sources of mechanical fatigue (Dunbar et al., 2001). Tractional forces are the result of frictional and ploughing forces produced by the deformation of the cartilage matrix as a stress-field translates over the surface (Linn, 1967; Mow et al., 1993). Tractional forces associated with static and dynamic friction on the surface of the TMJ disc are low (Nickel and McLachlan, 1994a; Nickel et al., 2001). Tractional forces associated with ploughing in the TMJ have not been characterized. However, stress-field translation, a pre-requisite for ploughing, has been demonstrated in vivo in humans (Gallo et al., 2000), where stress-field translation velocities were shown to exceed 100 mm/sec.

In general, loading of cartilage produces a "trampoline effect", where a portion of the total compressive load applied to the surface is supported by tangential forces on the cartilage surface (Donzelli et al., 1999). Consequently, compressive stress distribution over the cartilage surface will also affect the magnitudes of tractional forces imposed on articulating surfaces. Factors that increase compressive stresses on the TMJ disc during static loading include decreased cartilage thickness and decreased congruency between articulating surfaces (Nickel and McLachlan, 1994b; Beek et al., 2001).

Magnitudes of tractional forces and compressive stresses on hyaline cartilage surfaces are correlated according to time-dependent re-distribution of the fluid phase within the disc matrix. Re-distribution of the fluid phase accounts for stress-relaxation, a behavior typical of statically loaded cartilages, that is affected by factors such as rate of load application, matrix porosity, pressure gradient, and cartilage thickness (Li et al., 2003). In general, peak compressive stresses occur immediately after the disc is loaded (Huang et al., 2003), whereas peak tractional forces increase with the duration of loading (Mabuchi et al., 1998).

To date, no data have been reported regarding the effects of stress-field translation and duration of loading on tractional forces and compressive stresses on the surface of the TMJ disc. The specific aims of this project were to test the time-dependent effects of compressive loading and stress-field translation on TMJ disc surface tractional forces and stresses.


   MATERIALS & METHODS
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS & METHODS
RESULTS
 DISCUSSION
 REFERENCES
 
Ideally, the study of the effect of loading on the mechanics of the human TMJ disc requires human specimens. Due to the difficulty in procuring and maintaining non-preserved healthy human TMJ discs, we used porcine discs. The porcine model was chosen based on anatomical and biochemical similarities between pig and human TMJ discs in the areas normally subject to compressive loads (Herring, 1976; Strom et al., 1986; Sun et al., 2002). Fifty fresh TMJ discs from 25 pigs were obtained, in a manner consistent with UNMC regulations, from a local abattoir. Right and left discs were identified and stored separately in 0.1 M phosphate-buffered physiological saline solution (PBS, pH = 7.3) for approximately 45 min while in transport. In the laboratory, discs were maintained at 37°C in PBS.

Static loading of each TMJ disc was accomplished with the use of a hinged-beam apparatus (Figs. 1AGo, 1BGo). Loads placed at one end of the beam imposed a 10-N vertical compressive load on the disc via an acrylic indenter at the other end of the beam. The 10-N load reflected the minimum condyle load expected during a light bite force (Iwasaki et al., in press). The indenter was shaped to produce a mediolateral radius of contact similar to that measured in humans (Gallo et al., 2000). Indenter position and velocity were controlled through a hinged pendulum connected to a computer-controlled electromagnetic force generator. As the indenter moved along the mediolateral axis of the loaded TMJ disc, tractional forces were measured by an instrumented strut which supported the loaded indenter (Fig. 1BGo). Calibration of the instrumented strut permitted us to measure tractional forces to an accuracy of ± 0.05 N. We used a linear array of pressure transducers to measure compressive stresses beneath the TMJ disc according to previously described methods (Nickel and McLachlan, 1994b). Each transducer was accurate to within ± 10 kPa and had a saturation pressure of 2 mPa.



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  		Figure 1. Laboratory equipment used to produce compressive and tractional loads. (A) Schematic diagram of equipment and data acquisition system. (a) Pressure-sensitive array: An array of gauges lined the inside the loading tray and measured pressure along the mediolateral axis of the disc. (b) An acrylic indenter (major radius, 125 mm; minor radius, 31 mm) polished loading surfaces and milled holes to reduce the effect of mass on tractional force measurements. The indenter was connected to (c) a pendulum by an instrumented steel strut. Strain gauges attached to the surfaces of the strut (Fig. 1BGo) measured bending of the strut during movement of the indenter over the surface of the cartilage. Calibration of gauge output voltages for given loads made it possible for us to measure tractional forces in real time. (d) Electromagnetic force generator: A computer and custom-built software controlled the position and velocity of force generator displacement. (e) Mass platform on (f) loading beam: a hinged beam that facilitated placement of a static load at one end of the beam (e), and which caused the acrylic indenter to load the TMJ disc at the other end of the beam. We used linear voltage differential transformers (g) to measure real-time horizontal position of the indenter relative to the disc, while (h) was used to measure cartilage thickness during translation of the indenter over the surface of the disc. (i) Power supply. (j) 16-channel amplifier.

(B) Detail of (a) pressure transducer array and (b) acrylic indenter. During experiments, the disc was supported by a curved acrylic base and tray. The most medial portion of the disc was positioned over Pressure Gauge 1 (PG1). The acrylic indenter (b) placed a reactive compressive force on the TMJ disc in response to the 10-N load produced by the loading beam, and a tractional ploughing force produced by horizontal displacement by the electromagnetic force generator (Fig. 1AGo).

(C) Variation in indenter position, velocity, and tractional force with time. Normalized indenter position (•), velocity ({diamondsuit}), and tractional force ({blacksquare}) are plotted on the vertical axis vs. time on the horizontal axis. Large positive values indicate that the indenter was over the lateral portions of the disc. Velocity of translation of the stress-field was zero when the indenter movement stopped at the most medial or lateral position on the disc. (+) velocities occurred when the indenter was moving medially to laterally. Note that peak velocities occurred over the center of the disc.

 
All discs were tested at two different static loading periods, 10 sec on one experimental day and 60 sec on another experimental day for 25 discs, and the reverse order for the other 25 discs. Each disc was tested twice on each experimental day. After static loading of the disc for the designated time period, the indenter was oscillated at 3.5 Hz along the mediolateral axis of the TMJ disc to produce stress-field translation across the disc. The indenter started from the middle of the disc and moved laterally, then medially at peak velocities of 110 (± 5) mm/sec over a range of 10 mm. These values were chosen based on in vivo data recorded in healthy human joints (Gallo et al., 2000). Data were recorded at 300 Hz and stored on magnetic tape by means of commercial computer hardware and software.

Discs were warmed in 37°C PBS for all experiments. Before the tests were repeated on a given day, each disc was placed in 37°C PBS for 2 hrs so that the fluids which were lost during the loading experiments could be re-absorbed. We conducted preliminary studies to compare tractional forces and peak stresses measured on the surfaces of fresh discs with data measured on the surfaces of the discs that had been frozen at –15°C and thawed to a temperature of 37°C. Maximum differences in tractional forces and peak stresses were, on average, ± 15%. These differences were deemed small enough to allow the discs to be frozen for up to 4 days between experimental test days.

Using custom computer software, we analyzed data describing tractional forces and compressive stresses during the first 3 cycles of indenter translation over the TMJ disc to identify maximum tractional force, maximum compressive stress, and the average of pressure-gauge peak stresses per cycle. We used analysis of variance to evaluate the effects of load duration (10 sec, 60 sec), cycle number (1, 2, 3), and load duration and cycle number combined on tractional forces and compressive stresses. Disc location (right, left) and trial (1, 2) were used as measures of variability. Levels of significance were set conservatively at p ≤ 0.01. In addition, we performed a non-linear regression analysis on data from 20 discs to determine the relationship between peak tractional forces and velocity of stress-field translation. Criteria for inclusion of the data from a disc in the analysis were synchronization of peak tractional force with peak velocity and smooth time-dependent transitions of the tractional forces as the velocity of stress-field translation decreased to zero and then accelerated to peak velocity in the opposite direction (Fig. 1CGo). These criteria eliminated the transient effects of localized areas of cartilage compression. Static coefficients of friction reported for the TMJ disc were compared with coefficients of traction, calculated according to:



   RESULTS
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS & METHODS
 RESULTS
DISCUSSION
 REFERENCES
 
Averaged maximum tractional forces associated with initial movement of the indenter over the disc surface were 0.55 and 0.70 N following 10 and 60 sec of static loading, respectively (standard error of difference ± 0.026). Given that the vertical load was 10 N, this resulted in coefficients of traction (µtraction) of 0.06 and 0.07, respectively.

Duration of load alone had no significant effect, but number of cycles and the combined effects of load duration and cycle number significantly affected tractional forces (Appendix Table 1). Peak tractional force following 60 sec of static loading was greatest during the first cycle and was significantly greater than peak tractional force following 10 sec of static loading (p < 0.001, Fig. 2Go). There were significant cycle number effects, where peak tractional forces were reduced with increased cycling (p < 0.01–0.001). Overall, the results showed that peak tractional forces occurred at the start of movement and were greater following longer periods of static loading. During the second and third cycles of movement, peak tractional force was non-linearly related to velocity of stress-field translation (R2 = 0.73, Fig. 3Go). Peak tractional forces at stress-field translation velocities of 110 mm/sec were an order of magnitude greater than those at velocities less than 40 mm/sec. When the loaded indenter was at the lateral and medial extents of translation, indenter velocity was zero, yet small tractional forces of approximately 0.05 N were measured under the lateral portions of the disc.



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  		Figure 2. Effects of load duration and cycle number on peak tractional force. Cycle number is plotted on the horizontal axis, while mean peak tractional forces (N) are plotted on the vertical axis for static loading durations of 10 sec ({blacksquare}, n = 50) and 60 sec ({blacksquare}, n = 50). Significant differences between 10- and 60-second load-duration results for a given cycle number are indicated by * (p < 0.001). Lower-case letters represent comparisons between 10-second load-duration results for different cycle numbers, where different letters indicated significant differences (p < 0.001). Capital letters represent comparisons between 60-second load-duration results for different cycle numbers, where different letters indicate significant differences (p < 0.01). Error bars represent standard error.

 


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  		Figure 3. Peak tractional force vs. velocity of stress-field translation. The data were derived from the second and third cycles of movement over 20 discs following 10 sec of static loading. Criteria for inclusion of the data were synchronization of peak tractional force with peak velocity, and smooth transition of the tractional forces as the velocity of translation decreased to zero and then accelerated to peak velocity in the opposite direction (Fig. 1CGo). A second-order polynomial was fitted to the data (R2 = 0.73).

 
Stress-field translation produced an oscillation of compressive stresses under the discs (Fig. 4AGo). Peak stresses under each disc moved laterally, then medially, in concert with the movement of the loaded indenter over the surface. The duration of static loading before the start of movement significantly affected the maximum compressive stresses measured beneath the disc (Fig. 4BGo, Appendix Table 2), where the maximum compressive stresses after 10 sec of static loading were more than twice the maximum compressive stresses after 60 sec of static loading for all 3 cycles. Although cycle number had no effect on maximum stresses (Appendix Table 2), averages of pressure-gauge peak stresses were significantly greater during the first cycle (p < 0.001, Appendix Table 3) following 10 and 60 sec of static loading.



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  		Figure 4. Surface compressive stresses during stress-field translation. (A) Pressure distribution during stress-field translation following 60 sec of static loading. Data shown were recorded following 60 sec of loading of one disc. Time (sec) and Pressure Gauge Number are plotted on the horizontal axes. Pressure Gauge 1 was located under the most medial portion of the disc. Pressure (kPa) is plotted on the vertical axis. Following static loading, stress-field translation was initiated when the indenter moved toward the lateral portion of the disc (0.25–0.3 sec). On the return phase, the indenter moved toward the medial part of the disc (0.30–0.45 sec).

(B) Effect of load duration on maximum compressive stress. Cycle number is plotted on the horizontal axis, while mean maximum compressive stress is plotted on the vertical axis for static load durations of 10 sec ({blacksquare}, n = 50) and 60 sec ({blacksquare}, n = 50). Significant differences are indicated by * (p < 0.001). Error bars indicate standard error.

 

   DISCUSSION
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS & METHODS
 RESULTS
 DISCUSSION
REFERENCES
 
The tractional forces measured were the sum of classic frictional and ploughing forces on the disc surface. The coefficient of static friction (µs) for 1 min of loading on the TMJ disc was reported to be between 0.0025 and 0.005 (Nickel and McLachlan, 1994a; Nickel et al., 2001). Since the vertical loads during the current experiments were approximately 10 N, static frictional forces likely ranged from 0.02 to 0.05 N (µs = Ffriction/10 N). Subtraction of these frictional forces from the measured peak tractional forces indicated that ploughing forces were at least an order of magnitude greater than frictional forces. It was noted that the µtraction for 60 sec of loading was 27% greater than that for 10 sec of loading.

The tractional force-velocity of the stress-field translation relationship was developed with data from 20 discs that were statically loaded for 10 sec. Static loading for 60 sec created significant displacement and localized matrix consolidation. Subsequent measurements of tractional forces were influenced by residual localized matrix consolidation, which confounded the tractional force-velocity relationship. Discs loaded for 10 sec were less affected by residual strains during the second and third oscillatory cycles. This was likely due to the re-distribution of fluid produced by the movement of the loaded indenter back over the disc, which eliminated the localized areas of compression. Data from the second and third cycles met the inclusion criteria and permitted the "normal" viscoelastic behavior of the TMJ disc to be studied. Future studies should investigate the transient changes in ploughing forces produced by residual compression of the cartilage matrix.

Previous work has suggested that the magnitudes of ploughing mechanical work done to the cartilage varied by two orders of magnitude between individuals (Gallo et al., 2000). The ploughing forces used in these previous calculations were derived empirically from the effects of strain rate during tensile testing of discs, due to the lack of data describing the ploughing forces produced by stress-field translation. The current project provides more accurate data for the calculation of in vivo work in TMJ cartilage by ploughing forces.

Static loading for 10 sec typically produced maximum compressive stresses more than twice those measured following static loading for 60 sec. These differences may be due to stress-relaxation, which is typical of viscoelastic tissues. Mathematical models of cartilage poroviscoelasticity suggest that the time-dependent equilibration of stresses is due to re-distribution of the fluid phase within the biphasic viscoelastic matrix of the disc. Time-dependent re-distribution of load over a larger area produced lower stresses following 60 sec of loading. A similar phenomenon was shown in the hip (Macirowski et al., 1994) and in laboratory experiments on pieces of cartilage (DiSilvestro et al., 2001). In the current experiments, however, a consequence of longer periods of static loading was greater tractional forces due to localized consolidation of the cartilage matrix in the center of the stress-field, similar to results for ankle (Linn, 1967) and knee cartilage (Mabuchi et al., 1998). With respect to the effects of cycle number on peak tractional forces and peak compressive stresses, movement of the stress-field during indenter translation may have contributed to re-distribution of the fluid portion of the disc matrix, thereby increasing the area for distribution of load, and eliminating the localized region of matrix consolidation that resulted in large tractional forces at the start of movement.

It remains to be determined whether the effects of loading on tractional forces and compressive stresses in laboratory experiments are like those produced in vivo. The applied static loads of 10 N were lower than loads in the human TMJ during mastication and bruxism (Nickel et al., 1997). In addition, stress-relaxation behavior of cartilage is affected by the radius of the contact area relative to the thickness of the cartilage (Suh and Spilker, 1994). The standardized indenter did not exactly reproduce the area of loading that occurs in vivo. It is possible that the radius of contact area used was smaller than that found in vivo. This would tend to increase tractional forces.

In conclusion, the magnitudes of tractional forces and compressive stresses produced on the surface of the disc depended on duration of loading and were consistent with the stress-relaxation behavior of biphasic viscoelastic cartilage. As well, the tractional forces increased in a non-linear manner with increasing velocity of stress-field translation, and were significantly greater than classic frictional forces.


   ACKNOWLEDGMENTS
 
Dr. Laura Rothe helped in procuring the raw data while being supported through a UNMC College of Dentistry Summer Research Fellowship. Equipment funds were provided in part by the College of Dentistry Research Fund, the Office of the Dean, and Department of Growth and Development. Mr. Bobby Simetich provided technical help through the financial support of the Department of Adult Restorative Dentistry. Aaron Jacobsen, Krista Evans, Alistar Hoyt, and Adam Shaver developed the required computer programs and were supported by the College of Dentistry Work-Study Program. Mr. Kim Theesen, Learning Resources, UNMC College of Dentistry, produced the Figures.


   FOOTNOTES
 
A supplemental appendix to this article is published electronically only at http://www.dentalresearch.org.

Received July 24, 2003; Last revision May 16, 2004; Accepted June 1, 2004


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Beatty MW, Nickel JC, Iwasaki LR, Leiker M (2003). Mechanical response of the porcine TMJ disc to an impact event and repeated tensile loading. J Orofacial Pain 17:70–76.

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J.C. Nickel, L.R. Iwasaki, M.W. Beatty, M.A. Moss, and D.B. Marx
Static and Dynamic Loading Effects on Temporomandibular Joint Disc Tractional Forces
J. Dent. Res., September 1, 2006; 85(9): 809 - 813.
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