Temporomandibular joint (TMJ) diseases such as osteoarthritis and disc displacement have no permanent treatment options, but lubrication therapies, used in other joints, could be an effective alternative. However, the healthy TMJ contains fibrocartilage, not hyaline cartilage as is found in other joints. As such, the effect of lubrication therapies in the TMJ is unknown. Additionally, only a few studies have characterized the friction coefficient of the healthy TMJ. Like other cartilaginous tissues, the mandibular condyles and discs are subject to changes in friction coefficient due to fluid pressurization. In addition, the friction coefficients of the inferior joint space of the TMJ are affected by the sliding direction and anatomic location. However, these previous findings have not been able to identify how all three of these parameters (anatomic location, sliding direction, and fluid pressurization) influence changes in friction coefficient. This study used Stribeck curves to identify differences in the friction coefficients of mandibular condyles and discs based on anatomic location, sliding direction, and amount of fluid pressurization (friction mode). Friction coefficients were measured using a cartilage on glass tribometer. Both mandibular condyle and disc friction coefficients were well described by Stribeck curves (R2 range 0.87–0.97; p < 0.0001). These curves changed based on anatomic location (Δμ ∼ 0.05), but very few differences in friction coefficients were observed based on sliding direction. Mandibular condyles had similar boundary mode and elastoviscous mode friction coefficients to the TMJ disc (μmin ∼ 0.009 to 0.19) and both were lower than hyaline cartilage in other joints (e.g., knee, ankle, etc.). The observed differences here indicate that the surface characteristics of each anatomic region cause differences in friction coefficients.
Temporomandibular joint (TMJ) diseases, including osteoarthritis and disc displacement, collectively affect about 25% of the population [1–3], and have been linked to increased friction in the joint [4–6]. Since TMJ disease has no effective and durable treatment options, lubrication therapies used in other di-arthrodial joints to restore native healthy friction coefficients have been considered as potential alternatives [7–11]. However, the TMJ is a ginglymodiarthrodial joint and contains fibrocartilage (not hyaline) covering the articular surface . The TMJ also contains a unique disc that separates the temporal fossa from the mandibular condyle to redistribute loads and facilitate sliding (Fig. 1(a)). A more thorough understanding of the tribology of native healthy TMJ cartilage will identify therapeutic targets that could enhance the development of lubrication therapies for TMJ disease.
Only a handful of studies have measured the friction coefficients of tissues from the TMJ. These studies have shown that friction in the TMJ can change due to fluid pressurization, anatomic location, and sliding direction [13–17]. Pendulum devices, used to measure friction coefficients of the intact TMJ, have shown that whole joint friction increases with increasing loading duration [13,14]. This increase in friction is linked to fluid exudation from the articular cartilage and disc . Additional studies, which measured friction using migrating contact areas, have shown friction coefficients of condyles decreases with increases in speed and the Peclet number [16,17]. The disc also showed decreases in friction coefficient with increases in sliding speed [16,17]. In addition to speed, these changes in friction coefficient were dependent on the sliding direction of the condyle and disc, where medial–lateral (ML, orthogonal to the fiber direction) resulted in larger friction coefficients than anterior–posterior (AP) sliding . These studies indicate TMJ cartilaginous tissues exhibit changes in friction coefficients due to fluid pressurization at the tissue surface and fiber orientation. However, these friction tests have not determined how varying amounts of fluid pressurization, the tissue sliding direction, and the anatomic location of mandibular condyles and discs interact and change the observed friction coefficient.
The Sommerfeld number is calculated as the product of the fluid viscosity (ɳ), the sliding speed (v), and the sample width (w) divided by the normal load (P). Boundary mode friction is characterized by high friction coefficients due to the direct contact of the two sliding surfaces. In contrast, elastoviscous mode is associated with the lowest friction coefficient and the most fluid pressure at the tissue surface. Mixed mode is the transition from boundary mode to elastoviscous mode, where friction coefficient decreases with increases in speed, increases in fluid viscosity and/or decreases in normal load. This Stribeck framework has been documented for hyaline cartilage from the knee [18,20], and ankle  and is particularly useful to calculate the boundary friction, elastoviscous friction mode, and transition number (mixed mode). However, this framework has not been applied to cartilage from the TMJ.
A number of factors are likely to affect TMJ cartilage lubrication. The thick collagen fibers on the surface of the mandibular condyle and disc could cause the friction coefficient to change based on the sliding direction of the sample . Additionally, these surface fibers, their orientation, and concentration of boundary lubricants change based on anatomic location in both the mandibular condyle and disc [26,27]. As a result of these surface properties, this study will identify (1) if the Stribeck curve framework accurately describes the lubrication of mandibular condyles and discs and (2) if each boundary friction, elastoviscous friction, and transition friction mode changes based on sliding direction and anatomic location.
Cartilage and Disc Removal.
The mandibular condyle and disc were removed from both the left and the right side of seven porcine heads (six heads for condyle analysis and five heads for disc analysis) obtained from a local butcher (Shrader Meats, Romulus, NY, Fig. 1(a)). The animals were of mixed breed and unknown sex, with an average age of 6 to 7 months. During joint dissection, the inferior TMJ capsule was preserved with the disc attached to the condyle. Discs were carefully removed from the surface of the condyle and a 5 mm diameter biopsy punch was used to harvest samples from four anatomic regions of the disc (medial, lateral, anterior, posterior, Fig. 1(b)). The AP direction was marked on all disc samples. A total of 32 samples were taken from TMJ discs, with eight samples at each of the four anatomic locations (medial, lateral, anterior, and posterior, Fig. 1(b)). All samples were frozen immediately after joint dissection. Prior to testing, samples were thawed at room temperature in phosphate buffer saline (PBS, Corning Cellgro, Manassas, VA). The total thickness of each sample was measured with a micrometer and recorded. The inferior aspect of the disc (i.e., the surface in contact with the condyle) was later slid in both the AP (along the fibers) and the ML (against the fibers) directions.
To verify fiber directions in the TMJ discs, second harmonic generation microscopy was used as described previously . Images of collagen fibers were obtained using a Zeiss LSM 880 confocal/multiphoton inverted microscope with a 40×/1.2 C-Apochromat water immersion objective (Carl Zeiss Microscopy, White Plains, NY) at wavelengths between 437 and 464 nm.
Mandibular condyles were obtained by taking a 6 mm diameter biopsy punch at five anatomic regions of the joint (medial, lateral, anterior, posterior, and central, Fig. 1(b)). Since the condylar cartilage layer was very thin, each punch contained both cartilage and bone. Once removed from the joint, each osteochondral condyle sample was cut to a thickness of 2 mm. The AP direction on each sample was marked to keep track of the sliding direction. A total of 40 condyle samples were slid in both the AP and ML directions with eight samples from each of the five anatomic locations.
Dextran Formation and Viscosity Measurements.
To obtain a large span of viscosities, several concentrations of dextran were used. Increasing concentrations of dextran in solution increases the fluid viscosity and has previously been shown to provide similar Stribeck curves to those generated by solutions of hyaluronic acid at similar viscosities . Dextran solutions were made by mixing 20 MDa dextran (Sigma Aldrich, St. Louis, MO) with PBS at concentrations of 0%, 9%, and 23% (w/v). The viscosity of these solutions was determined using a commercial rheometer (Discovery Hybrid Rheometer 3, TA instruments, New Castle, DE) as previously described . Viscosity measurements were measured using a 40 mm cone-plate geometry with a 2 deg angle, and viscosity values were taken at a shear rate of = 1 s−1. This shear rate resulted in viscosity values of 1, 31.5, and 218 mPa·s for 0%, 9%, and 23% dextran concentrations, respectively.
Friction Coefficient Measurements.
Friction coefficients were measured using a custom cartilage-on-glass tribometer [18,19], as previously described. Briefly, samples were slid at speeds that spanned 2 orders of magnitude and in viscosities that spanned 2 orders of magnitude, generating conditions that spanned 4 orders of magnitude in the Sommerfeld number (S, Eq. (1)). Half the samples were tested in the AP direction first and half were tested in the ML direction first (Fig. 1(c)). Each sample was placed in 0% dextran, compressed, and allowed to relax for at least 30 min and until an equilibrium load of 100 g (35 kPa) for the condyle and 60 g (30 kPa) for the disc was obtained. Once equilibrium was reached, samples were slid at nine different speeds that spanned two orders of magnitude (0.1, 0.3, 0.5, 0.7, 1.0, 3.0, 5.0, 7.0, and 10 mm/s). During sliding, a biaxial load cell measured the instantaneous normal and shear loads, from which the friction coefficient was calculated.
After sliding in 0% dextran, the sample was removed from the tribometer and placed in PBS, while the media wells were cleaned to prevent any contamination from the previous test. Then, samples were placed back in the tribometer in 9% dextran and tested in the same sliding direction at the same nine sliding speeds. This process was repeated for the 23% dextran solution (Fig. 1(d)). Then, the sample was turned 90 deg and slid in the orthogonal direction using the same process of compressing, relaxing, and sliding in three concentrations of dextran at nine sliding speeds (Fig. 1(e)).
In this equation, μmin represents the elastoviscous (minimum) friction coefficient, μb is the boundary mode friction coefficient, St is the transition number between boundary and elastoviscous mode, and d indicates the slope of the curve between boundary and elastoviscous mode friction. These four parameters (μmin, μb, St, and d) were obtained by minimizing the error between predicted and measured friction coefficients using a least-squares fitting algorithm in matlab (Mathworks, Natick, MA). All fitting parameters were constrained to be greater than zero with initial guesses ranging from of 0.03, 0.2, 1, and 2 for μmin, μb, St, and d, respectively.
Stribeck curves were analyzed for goodness of fit using an R2 parameter and a root-mean-square error (RMSE). Differences in friction coefficients based on anatomic location and sliding direction for the disc and condyles were analyzed separately using a linear random effects model in R Studio (RStudio, Boston, MA). The random effects of this model accounted for variability between pigs, multiple samples from a single head (i.e., left and right sides), the repeated testing of samples in both the AP and ML directions, and the initial sliding direction. Differences between groups were calculated using a Tukey post hoc analysis and were considered statistically significant based on a p value of less than 0.05.
The friction coefficient of mandibular condyles and discs decreased with increases in sliding speed. These changes in friction coefficient were largest in the highest fluid viscosity for all sliding directions and anatomic locations. When tissue was slid in PBS, the lowest viscosity fluid, very small decreases in friction coefficient were observed with increases in sliding speed (Figs. 2(a) and 3(a)). In 9% dextran, friction coefficients dropped by a factor of 2 while the sliding speed changed from 0.1 mm/s to 10 mm/s (Figs. 2(b) and 3(b)). In the highest viscosity fluid (23% dextran), the friction coefficients dropped by almost an order of magnitude as sliding speed increased (Figs. 2(c) and 3(c)). These decreases in friction coefficient occurred in both sliding directions for all anatomic location as viscosity and sliding speed increased.
For all condyle and disc samples, plotting the friction coefficient versus the Sommerfeld number showed clear Stribeck curve behavior (Fig. 4). These Stribeck curve fits (Eq. (2)) yielded high R2 values (R2 range 0.90–0.97 and 0.87–0.95 for condyle and disc, respectively) and low RMSE (RMSE range 0.011–0.0195 and 0.016–0.023 for condyle and disc, respectively) in all TMJ tissues, at all anatomic locations, and all sliding speeds. The friction coefficients of condyles and discs in boundary mode (μb = 0.17–0.22) were almost an order of magnitude higher than the elastoviscous friction (μmin = 0.009–0.03) at all anatomic locations and sliding directions. The transition number ranged from 7.4 × 10−6 to 38 × 10−6 for all samples. This approach enabled direct measurements of the boundary friction, minimum friction, and transition number of TMJ tissues.
The Stribeck curve fit coefficients of condyles changed based on anatomic location. The boundary friction coefficient of mandibular condyles was highest in the anterior and central regions (μb ∼ 0.21 and μb ∼ 0.22, respectively, Fig. 5(a)). The posterior region of the condyle showed the lowest boundary friction coefficient and the largest differences when compared to the other anatomic locations (μb ∼ 0.17, Fig. 5(d)), but no significant differences were reported. The elastoviscous friction coefficient of mandibular condyles was lowest in the posterior region (μmin ∼ 0.009) but showed no statistical significance when compared to all other regions (Figs. 5(b) and 5(e), μmin ∼ 0.013 to 0.019 for all other anatomic regions). The transition number of mandibular condyles was almost two times larger in the anterior and posterior regions (St ∼ 22 × 10−6 and St ∼ 19 × 10−6, respectively) than both the lateral (St ∼ 11 × 10−6) and central regions (St ∼ 9.4 × 10−6, Figs. 5(c) and 5(f), p < 0.05 between the anterior and central regions, p = 0.05 between anterior and lateral regions). When compared to other anatomic locations, the posterior region of the mandibular condyle consistently had the lowest friction coefficient for multiple lubricating modes.
Similar to the mandibular condyles, TMJ discs showed changes in the friction modes based on anatomic location. The lateral region had the lowest boundary friction coefficient (μb = 0.17, Figs. 6(a) and 6(d)). All other anatomic regions had boundary friction coefficients that were 10–30% higher (p = 0.10, 0.17, and 0.40 for the lateral region versus the posterior, anterior, and medial region, respectively, Fig. 6(d)). The anterior and posterior regions consistently showed the lowest elastoviscous friction coefficients (μmin ∼ 0.011). The lateral region consistently showed the highest friction coefficient, which approached significance against the anterior region (Figs. 6(b) and 6(e), p = 0.09). The transition from boundary friction to elastoviscous friction did not change based on anatomic location (Figs. 6(c) and 6(f)).
Both tissues showed some small changes in friction due to the sliding direction, and no significant differences. The condyle central region showed a 20% higher boundary friction coefficient and a 60% lower transition number in the AP direction than the ML direction (Fig. 5(a)). These differences approached statistically significance (Table 1, p = 0.08). In the disc, three out of four anatomic locations resulted in 10% to 20% higher boundary friction coefficient due to sliding ML instead of AP (Fig. 6(a)). However, no statistical significance was found based on sliding direction (Table 1). The elastoviscous friction coefficient of the lateral and medial regions of the disc was 20% higher due to sliding in the ML direction rather than the AP direction (Fig. 6(b), Table 1). The other friction modes of the condyle and disc showed little to no differences based on sliding direction. Overall changing the sliding direction of each sample resulted in small changes in friction coefficients that were not statistically significant or consistent between anatomic locations.
When the friction modes of the condyle and disc were compared, the lateral region and the transition number showed the largest differences (Table 2). The lateral region of the disc had a 15% lower boundary friction coefficient, two times larger elastoviscous friction coefficient, and a three times larger transition number than the mandibular condyle in that same region (lateral). Similarly, the disc showed higher transition numbers (∼2 to 3 times larger) than the condyle in all anatomic regions except the anterior. These differences between the disc and the condyle indicate the two tissues behave differently at the same Sommerfeld number.
The objectives of this study were to determine if TMJ condylar cartilage and discs followed Stribeck curve behavior and to determine any differences between these curves based on anatomic location and sliding direction. Both tissues from all anatomic locations followed Stribeck curve behavior as indicated by the presence of multiple friction modes. The observed Stribeck curves were not identical for all anatomic locations. Very few differences in friction coefficients based on sliding direction were observed. These results identify differences in friction behavior based on anatomic location, sliding direction, and the friction mode, which were previously unknown for the mandibular condyle and disc.
Boundary friction coefficients have been correlated with multiple factors, including the surface roughness of the tissue. Because the surface roughness of the condyles is similar to the disc , we expected these two tissues to have similar boundary mode friction coefficients. Overall, the condyle and disc did have similar boundary mode friction coefficients. Additionally, the surface roughness of the mandibular condyles is higher than hyaline cartilage of other joints, and was expected to result in a larger boundary friction coefficient . Unexpectedly, the boundary friction coefficient of mandibular condyles in this study was lower than hyaline cartilage of other joints [18,20,24,29]. Other surface characteristics known to affect boundary lubrication such as lubricin concentration could cause the differences observed between mandibular condyles and hyaline cartilage. Both mandibular condyles and hyaline condylar cartilage have a high concentration of lubricin, a boundary lubricant, on their tissue surface [11,30]. These previous studies use immunohistochemical staining to visualize lubricin. Since this approach is inherently nonquantitative, it would be important in future work to directly quantify lubricin content on TMJ tissues.
The presence of a rough, oriented fibrous surface in these tissues was expected to result in large differences based on sliding direction. This thought was based on previous findings that the friction coefficients of mandibular condyles and discs changed based on sliding direction . This previous study was performed using migrating contact areas, which would most likely result in friction coefficient in the elastoviscous friction mode at high Sommerfeld numbers [31–33]. In contrast to previous work, we saw no significant changes in elastoviscous friction or any other friction mode due to sliding direction. If the circumferential orientation of the fibers on the edges of the TMJ disc and mandibular condyles is considered [34,35], sliding in the medial lateral direction should have resulted in higher friction coefficients for the anterior and posterior directions. However, this study did not observe these differences and noted no statistical significance based on sliding direction (some anatomic regions approached statistical significance, Table 1). This finding may be explained by examining the fiber directions on the surface of the samples (supplemental figures available in the Supplemental Materials on the ASME Digital Collection). Friction coefficients were not affected by the sliding direction or the fiber orientation in this study.
Using Stribeck curves, this study showed discs have a higher transition numbers than mandibular condyles (Table 2), and the mandibular condyles had a higher transition number than articular hyaline cartilage of other joints . Stribeck curves make these comparisons possible because of the use of the dimensionless Sommerfeld number, which provides the ability to directly compare friction coefficients of tissues that may have been tested under slightly different conditions . This pattern of transition numbers indicates it is more difficult to pressurize fluid on the surface of TMJ cartilage than in other joints containing hyaline cartilage. This phenomenon could be a result of the high surface permeability of mandibular condyles and the higher permeability of the TMJ disc [31,32]. A more permeable surface requires a larger amount of fluid flow to adequately pressurize fluid at the surface. In addition to transition number, the elastoviscous friction coefficients are lower in the TMJ (μmin ∼ 0.009 to 0.19), than hyaline cartilage of other joints (μmin ∼ 0.045 to 0.06) [16,20,36]. Also confirming that more fluid is pressurized at the surface of the mandibular condyle than in hyaline cartilage operating under elastoviscous friction mode. The increase in transition number of mandibular condyles and discs could indicate that these tissues are more likely to operate in boundary mode friction at physiologic sliding speeds (∼40 mm/s) . These differences in cartilage behavior could also indicate therapeutic injections might require a more viscous lubricant to reach elastoviscous friction coefficients.
Interesting the lateral region of the disc had both the lowest boundary friction coefficient recorded in this study and is the first region in the TMJ to exhibit signs of damage . Previous work using finite element models have shown this damage prior to disease could be due to the large stress and strain concentrated in the lateral zone of the disc [39,40] during normal joint movement. These large stresses indicate large normal loads and the potential for low fluid pressurization at the tissue surface, and more time under boundary mode friction. The healthy joint may have developed the ability to protect the lateral region of the disc from damage by localizing the lowest boundary friction coefficients in the region most likely to see tissue damage. To prevent TMJ disease, lubrication therapies may need to focus on restoring this ultralow boundary friction coefficient using regenerative medicine techniques such as hyaluronic acid or lubricin injections [8,9,41] or regenerative medicine technologies [11,42–44].
While this study has direct implications to understanding the lubricating mechanisms of the mandibular condyle and disc, there are several limitations that must be considered. First, this study uses porcine TMJ cartilage, which is not identical to humans. However, the porcine TMJ is one of the most commonly used animal models for TMJ research, because the joint morphology, internal structures (e.g., disc biochemical properties and compressive modulus) and attachments are similar to humans [45–47]. Additionally, a postprocessing power analysis revealed that some changes in the friction modes based on anatomic location were underpowered (supplemental Table 1 available in the Supplemental Materials on the ASME Digital Collection). An increase in sample size may increase statistical power and result in more statistically significant differences based on anatomic location, but it is unlikely that the magnitude differences will change drastically. Finally, friction coefficients in this study were plotted against the Sommerfeld number, which is a function of sliding speed, viscosity, and normal loads. The normal loads were not changed in this study. However, previous work using knee articular cartilage shows that altering normal loads scales friction coefficients as expected from the Stribeck framework. Future work involving changes to the normal loads of these tissues may solidify this system and these results for healthy mandibular condyles and discs.
This study provided insight into the friction coefficients required for healthy TMJ function. We observed differences in friction coefficients based on anatomic location, which implies multiple surface characteristics are also changing based on anatomic location. No differences based on sliding direction were observed, implying the orientation of the surface fibers may not greatly affect the friction coefficient. Similar to other cartilaginous tissues, the Stribeck framework accurately explains changes in the friction coefficients of TMJ cartilage; therefore, some lubrication therapies that increase fluid viscosity may be effective in treating TMJ disorders. However, the observed friction coefficients of the fibrocartilaginous TMJ tissues were less than hyaline cartilage and the transition number was higher than hyaline cartilage in other joints. Therefore, some hyaline cartilage lubrication therapies may need to be modified (more lubricin, higher viscosities, etc.) to treat TMJ diseases and restore joint function.
The authors would like to thank Sierra Cook and Professor Itai Cohen for the assistance in rheology testing. We also thank Marianne Lintz for the TMJ schematic and SHG images.
Cornell Center for Materials Research (CCMR) (Funder ID: 10.13039/100008585).
NSF (Grant Nos. DGE-1650441, DMR-1460428, DMR-1719875, and CMMI 1927197; Funder ID: 10.13039/100000001).