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J Dent Res 85(9):809-813, 2006
© 2006 International and American Associations for Dental Research

RESEARCH REPORT
Biomaterials & Bioengineering

Static and Dynamic Loading Effects on Temporomandibular Joint Disc Tractional Forces

J.C. Nickel1,2,*, L.R. Iwasaki1,2, M.W. Beatty2,3, M.A. Moss4, and D.B. Marx5

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;
4 private practice, 1817 17th St., Cody, WY 82414, USA; and
5 University of Nebraska, Department of Statistics, 340 Hardin Hall North, Lincoln, NE 68583-0963, USA

* corresponding author, jnickel{at}unmc.edu


   ABSTRACT
TOP
 ABSTRACT
INTRODUCTION
 MATERIALS & METHODS
 RESULTS
 DISCUSSION
 REFERENCES
 
Mechanical fatigue-related degeneration of the temporomandibular joint (TMJ) disc may be promoted by tractional forces. This study tested the hypotheses that tractional forces following static loading of the TMJ disc: (1) increase with compressive strain at the start of movement, and (2) are velocity-dependent during movement. Sixty-four porcine discs received a 10-N static load via an acrylic indenter for 1 or 30 sec before cyclic movement. Physical data were recorded and analyzed by ANOVA. The results showed that compressive strain and tractional forces were largest for the start of movement following 30 sec of static loading (p ≤ 0.0001) and were correlated (R2 = 0.84). Peak tractional forces were linearly and positively related to velocity of movement (R2 = 0.85), and were highest during Cycle 1 after 30 sec of loading (p ≤ 0.0067). The results demonstrated that tractional forces were strain-related at the start of movement and velocity-dependent during movement. Abbreviations: ANOVA = analysis of variance, PBS = phosphate-buffered physiological saline solution, TMJ = temporomandibular joint, µT =tractional coefficient, µs = static coefficient of friction.

KEY WORDS: TMJ • cartilage • mechanics • strain • plowing


   INTRODUCTION
TOP
 ABSTRACT
 INTRODUCTION
MATERIALS & METHODS
 RESULTS
 DISCUSSION
 REFERENCES
 
Degenerative joint disease in synovial joints of young individuals is thought to be initiated by mechanical fatigue of the articulating tissues. The mean age of onset of degenerative joint disease 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). Mechanical failure of the disc may be an important predisposing factor leading to the relatively early degenerative changes seen in the TMJ. Measurements of yield strength have indicated that the TMJ disc is 10-fold stronger along the anteroposterior axis compared with the mediolateral axis, and that trauma increases the rate of mechanical fatigue along the mediolateral axis (Beatty et al., 2001, 2003). This suggests that mechanical fatigue of the disc causes failure of the cross-links between major anteroposteriorly oriented collagen fibers.

Tractional forces applied repeatedly to the cartilage surface serve as sources of mechanical fatigue (Dunbar et al., 2001). Tractional forces are the result of frictional and plowing forces produced by the deformation of the cartilage matrix as a stress-field translates over the surface (Linn, 1967; Mow et al., 1993). For the TMJ disc, plowing forces are expected to be the dominant component of tractional forces. This is because static and dynamic frictional forces measured on the surface of the TMJ disc are low (Nickel and McLachlan, 1994a; Nickel et al., 2001). In addition, laboratory experiments have showed that tractional forces associated with plowing on the surface of the TMJ disc were 10 times greater than static frictional forces (Nickel et al., 2004). The tractional forces increased with the duration of static loading prior to the start of movement and with increasing velocity of stress-field translation. The tractional coefficients reported were consistent with the tractional forces measured in whole TMJ experiments (Kawai et al., 2004; Tanaka et al., 2004).

Currently, it is unknown how tractional forces at the initiation of movement after compressive loading compare with those associated with stress-field translation. That is, no data have been reported comparing tractional forces due to compressive strain at the start of movement, and limited data have been reported regarding tractional forces due to stress-field translation at different velocities (Nickel et al., 2004). This study tested the hypotheses that tractional forces following static loading of the TMJ disc: (1) increase with compressive strain at the start of movement, and (2) are velocity-dependent during movement.


   MATERIALS & METHODS
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS & METHODS
RESULTS
 DISCUSSION
 REFERENCES
 
Experiments were conducted on 64 TMJ discs from 32 pigs, which were obtained from a local abattoir in a manner consistent with institutional regulations. 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 39°C in PBS. Experiments for each disc pair were completed during the day of harvest.

Each disc was tested twice, where a load was applied to the condyle-facing surface, first statically for 1 or 30 sec, and then dynamically along the mediolateral axis of the disc. This was accomplished with the use of a hinged beam apparatus (Appendix Fig. 1Go) described previously (Nickel et al., 2004). A compressive load of 10 N was imposed on the disc via an acrylic indenter, shaped to produce a mediolateral radius of contact similar to that measured in humans (Gallo et al., 2000). The load reflected the minimum condylar load expected during a light bite force (Nickel and Iwasaki, 2004). Total translation of the center of the stress-field during dynamic loading was approximately 9 mm, and average peak velocity of translation was 80 mm/sec. All of these conditions were consistent with in vivo conditions (Gallo et al., 2000).


Figure 1
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  		Figure 1. Effects of duration of static loading of the TMJ disc on compressive strain (left vertical axis) and tractional coefficient at start of movement (right vertical axis). Average compressive strain was significantly larger (***p < 0.0001) following 30 sec (n = 32, SE = ± 0.012) of static loading than following 1 sec (n = 32, SE = ± 0.012 ) of static loading. Similarly, average tractional coefficients at the start of movement were significantly larger (a, b; p < 0.0001) following 30 sec (n = 32; SE = ± 0.032) than after 1 sec (n = 32, SE = ± 0.032) of static loading. Vertical bars indicate standard errors of the means. Measurements were made during the 0.003 sec following the start of movement. Velocities of movement during this time were less than 10 mm/sec.

 
Compressive strains of the TMJ disc were determined with the use of instantaneous disc thickness measurements. These were recorded continually by means of a calibrated linear voltage differential transformer (Appendix Fig. 1Go), which facilitated thickness measurements within 0.05 mm. Initial thickness of the disc was recorded upon the application of load, when an increase in pressure was first detected by a linear array of 9 pressure transducers, 3 mm apart, under the disc. Transducer sensitivities were ± 10 kPa (Appendix Figs. 1A, 1BGo).

Electrical output from a calibrated accelerometer indicated the start of movement of the indenter. Indenter position and velocity were determined by calibrated electrical output from a second linear voltage differential transformer, and were controlled through a hinged pendulum connected to an electromagnetic force generator and a computer. The sampling frequency allowed instantaneous velocities to be calculated every 0.003 sec with the use of custom software (Appendix Fig. 2Go). Tractional forces were measured during a 0.003-second period at the start of movement. Peak velocities within this period were less than 10 mm/sec. Following this, as the loaded indenter moved through 3 cycles back and forth along the mediolateral axis of the TMJ disc, tractional forces were measured continuously by an instrumented strut that supported the loaded indenter (Appendix Figs. 1A, 1BGo). Equal numbers of discs were loaded with either medial or lateral portions of the disc positioned over pressure transducer #1 (Appendix Fig. 1BGo). Calibration of the instrumented strut permitted tractional forces to be measured to an accuracy of ± 0.05 N. Data were recorded at 300 Hz and stored on magnetic tape with the use of commercial computer hardware and software.


Figure 2
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  		Figure 2. Compressive strain effects on tractional coefficient at the start of movement. Compressive strains of the TMJ discs ranged between less than 5% to greater than 40% of original thickness following 1 sec (n = 32) and 30 sec (n = 32) of static loading. Measurements were made during the 0.003 sec following the start of movement. Velocities of movement during this time were less than 10 mm/sec.

 
Tractional forces were expressed as starting, instantaneous, and peak tractional coefficients (µTstart, µTinstantaneous, and µTpeak, respectively). µT was equal to tractional force/normal loading force (10 N). Analysis of variance (ANOVA) was used to evaluate the effects of: (1) duration of load (1 sec, 30 sec) on the tractional coefficient at the start of movement (µTstart) and compressive strain; (2) duration of load and cycle of indenter movement (1, 2, 3) on peak tractional coefficient (µTpeak); and (3) velocity of stress-field translation and normalized instantaneous tractional coefficients (µTinstantaneous/µTpeak). Levels of significance were set conservatively at p ≤ 0.01. We used regression analyses to demonstrate the relationship between tractional coefficients at the start of movement (µ Tstart) and compressive strain, and normalized instantaneous tractional coefficients (µTinstantaneous/µTpeak) and velocity of movement.


   RESULTS
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS & METHODS
 RESULTS
DISCUSSION
 REFERENCES
 
Stress-field translation following static loading was confirmed by pressure transducer measurements of fluctuating compressive stresses with respect to time (Appendix Figs. 3A, 3BGo). The stress-field initially moved from a position over pressure transducer #5 toward #8. The indenter then stopped and reversed direction of movement toward pressure transducer #1, where the direction was reversed again, and the loaded indenter completed one cycle by returning to the original starting position. When the loaded indenter was at 90° and 270° positions, velocities of translation dropped to zero (Appendix Figs. 3C, 3DGo). At these positions, the indenter was over either the lateral or the medial aspect of the disc.


Figure 3
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  		Figure 3. Effects of cycle number and static loading duration on peak tractional coefficient. Results from two-way ANOVA. The error bar is the standard error of the mean. Data are presented for 1 sec (blank bars) and 30 sec (hatched bars) of static loading prior to pendulum movement (n = 32). The brackets compare 1 sec vs. 30 sec of static loading for a given cycle number. *** = significant differences at the p ≤ 0.01 confidence level; n.s. = non-significant differences (p ≥ 0.01). Letters denote comparisons of peak tractional coefficients for different cycles. Lower-case letters compare tractional coefficients for 1 sec of static loading vs. the cycle number, and upper-case letters compare tractional coefficients for 30 sec of static loading vs. cycle number. Groups with the same letters represent non-significant differences (p ≥ 0.01), and groups with different letters represent significant differences at a p ≤ 0.01 confidence level.

 
Average TMJ disc thickness at the time of loading was 1.92 mm, and ranged between 1.14 and 3.16 mm. Compressive strains of TMJ discs were approximately 1.5 times higher immediately following 30 sec of static loading compared with 1 sec of static loading (Fig. 1Go). That is, average strains were 27% after 30 sec of static loading and 16% after 1 sec of static loading, and were significantly different (p < 0.0001). Tractional forces varied continuously during each cycle (Appendix Figs. 2Go, 3Go, 4Go). Average tractional coefficients at the start of movement were 0.051 after 30 sec of static loading and 0.022 after 1 sec of static loading, and were significantly different (Fig. 1Go, p < 0.0001). Compressive strains immediately following 1 and 30 sec of static loading ranged from less than 5% to greater than 40% (Fig. 2Go). There was a non-linear relationship between compressive strain and tractional coefficients at the start of movement (Fig. 2Go, R2 = 0.84). This relationship demonstrated an inflection point at approximately 20% compressive strain, so that discs with strains of 40% compared with 20% had 3.5-times larger tractional coefficients at the start of movement.


Figure 4
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  		Figure 4. Relationship between normalized instantaneous tractional coefficient (instantaneous µT/peak µT) and velocity of stress-field translation during Cycles 2 and 3. Criteria for inclusion of the data were synchronization of peak tractional force with peak velocity during Cycles 2 and 3, and smooth transition of the tractional force as the velocity of translation decreased to zero and then accelerated to peak velocity in the opposite direction (n = 14 discs). Velocity of stress-field translation varied between +80 and -80 mm/sec. Positive velocities indicate movement of the stress-field toward pressure transducer #9, whereas negative velocities indicate movement toward pressure transducer #1.

 
The average of peak tractional coefficients during Cycle 1 of movement of the loaded indenter over the surface of the TMJ disc reflected the combined effects of compression and velocity of stress-field translation on tractional force (Fig. 3Go). The average of peak tractional coefficients during Cycle 1 of movement following 30 sec of static loading was 20% higher compared with that following 1 sec of static loading, and was significantly different (p = 0.0067, SE = 0.003). Peak tractional coefficients during Cycles 2 and 3 were mainly influenced by velocity, and were not significantly different. Peak tractional coefficients during Cycles 2 and 3 following 1 sec of static loading were significantly greater (p < 0.0001) than in Cycle 1. Peak tractional coefficients during Cycles 2 and 3 following 30 sec of static loading were significantly less (p < 0.0001) than in Cycle 1. The relationship between normalized instantaneous tractional coefficients and velocity of movement during Cycles 2 and 3 was linear (Fig. 4Go; R2 = 0.85).

The mechanical work done on the disc surface per cycle is proportional to the area encompassed by the data points in radial plots of phase-dependent changes in tractional forces for a given cycle (Appendix Figs. 3C, 3DGo). Mechanical work done on the surface of the disc was greatest during Cycle 1 compared with Cycles 2 and 3 (Appendix Fig. 4Go: A vs. B, C; D vs. E, F) and the following 30 sec compared with 1 sec of static loading (Appendix Fig. 4Go: D-F vs. A-C).


   DISCUSSION
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS & METHODS
 RESULTS
 DISCUSSION
REFERENCES
 
Ideally, the study of the effect of loading on TMJ disc mechanics requires the use of non-preserved human specimens. However, fresh porcine TMJ discs were used, due to the difficulty in procuring and maintaining fresh human specimens. The porcine model was chosen based on anatomical and biochemical similarities of pig and human TMJ discs in the areas normally subject to compressive loads (Herring, 1976; Strom et al., 1986; Sun et al., 2002). To date, there is a paucity of data to demonstrate similarities in the poroviscoelastic mechanics of porcine and human TMJ discs (Beatty et al., 2001, 2003; Beek et al., 2003; Detamore and Athanasiou, 2003; Tanaka and van Eijden, 2003).

The term ‘tractional coefficient’ was used in this study because the tractional forces measured were the sum of classic frictional and plowing forces on the disc surface. Coefficients of static friction ( µs), associated with 1 and 30 sec of static loading of an acrylic indenter on the TMJ disc, were reported to be 0.0025 and 0.005, respectively (Nickel and McLachlan, 1994a; Nickel et al., 2001). In the current study, the tractional coefficient at the start of movement was, on average, 0.022 and 0.051 following 1 and 30 sec of static loading, respectively, and therefore, an order of magnitude larger than the reported µs. In a study of whole TMJs, 5 sec of static loading with 50 and 80 N produced tractional coefficients of 0.0145 and 0.0191, respectively (Tanaka et al., 2004). These measurements were reported as ‘friction’, but were an order of magnitude greater than previously reported µs values (Nickel and McLachlan, 1994a; Nickel et al., 2001), and were comparable with the tractional coefficients at the start of movement in the current study. It has been noted that whole joint measurements of friction cannot eliminate the plowing forces produced by stress-field translation (Linn, 1967; Mow et al., 1993).

Peak tractional forces measured following 1 sec of static loading appeared to be primarily influenced by the velocity of stress-field translation. The peak tractional forces during Cycle 1 following 30 sec of static loading reflected the importance of compressive strain-related tractional forces. Similar experiments (Nickel et al., 2004) showed that peak tractional coefficients during Cycle 1 were 0.055 and 0.069 following 10 and 60 sec of static loading. Thus, it appears that there is a linear relationship between duration of static loading and peak tractional forces during Cycle 1.

Analysis of data previously reported (Nickel et al., 2004) showed a similar linear relationship between normalized instantaneous tractional coefficients and velocities of stress-field translation < 80 mm/sec, but a non-linear increase in tractional forces for velocities of translation > 80 mm/sec. The current results are more reflective of in vivo velocities of stress-field translation (Gallo et al., 2000). This previous study suggested that the magnitudes of plowing mechanical work done to the cartilage in the TMJ varied by 2 orders of magnitude between individuals (Gallo et al., 2000) and peaked at 709 mJ during symmetrical opening and closing of the mandible at 1.0 Hz. Plowing forces used in these work calculations were derived empirically from effects of strain rate during tensile testing of TMJ discs. In the current study, the greatest amount of work was done during the first cycle of movement following 30 sec of static loading, where peak work values approached 10 mJ for > 10 mm of movement across the disc surface. This work estimate is 25 times less than previously reported (Gallo et al., 2000). 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; Iwasaki et al., 2004), but were not unlike the loads typical of symmetrical opening and closing as previously described (Gallo et al., 2000). 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 used in the current study did not exactly reproduce the area of loading that occurs in vivo, and possibly had a smaller radius of contact area. These data, overall, resulted from a ‘best-case scenario’ for joint-loading conditions, and demonstrated that tractional forces occur even during low loading of the surface of the TMJ disc.

In conclusion, increased duration of static loading of TMJ discs resulted in a significant increase in the tractional forces at the start of movement. These forces were non-linearly and positively correlated with compressive strain of the TMJ disc in response to static loading. During movement, tractional forces due to plowing were linearly related to velocity of stress-field translation. In the current study, the highest average tractional forces occurred during Cycle 1 after 30 sec of static loading, where compressive strain and velocity of stress-field translation effects were combined. Clinically, however, tractional forces will depend on the velocity of stress-field translation associated with function in a given individual. Indications are that inter-individual differences in the velocity of stress-field translation during function are large (Gallo et al., 2000)). Alternatively, if static loading of the disc occurs before movement, as is the case for clenching, for example, large tractional forces can develop when the velocity of stress-field translation is relatively slow.


   ACKNOWLEDGMENTS
 
Equipment funds were provided by the UNMC College of Dentistry Research Fund and the Department of Growth and Development. Mr. Bobby Simetich provided technical help through the financial support of the Office of the Dean, and Departments of Adult Restorative Dentistry and Growth and Development. Mr. Kim Theesen, Graphic Artist, UNMC College of Dentistry, produced the Figures. The authors thank Farmland Foods Corporation, Crete, Nebraska, for their support of this project. This work was based in part on a thesis submitted to the Graduate Faculty, University of Nebraska Medical Center, in partial fulfillment of the requirements of the MS degree for M.A. Moss.


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

Received October 28, 2005; Last revision April 26, 2006; Accepted May 15, 2006


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TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS & METHODS
 RESULTS
 DISCUSSION
 REFERENCES
 
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