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Mechanical Work during Stress-field Translation in the Human TMJ
1 Clinic for Masticatory Disorders and Complete Dentures, Center for Oral Medicine, Dental and Maxillo-Facial Surgery, University of Zürich, Plattenstrasse 11, CH-8028 Zürich, Switzerland; and Correspondence: * corresponding author, luigi{at}zui.unizh.ch
The pathomechanics of degenerative joint disease of the temporomandibular joint (TMJ) may involve fatigue produced by mechanical work on the articulating tissues. This study tested the hypotheses that mechanical work in the TMJ (i) varies with the type of mandibular activity, and (ii) is evenly distributed over TMJ surfaces. Ten healthy human participants were recorded with Magnetic Resonance Imaging (MRI) and jaw tracking. The data were used to reconstruct and animate TMJ activity. Aspect ratios, instantaneous velocities, and distances of stress-fields translation were used to calculate work (mJ). The results were analyzed by least-squares polynomial regression and ANOVA. Work magnitudes were related to peak velocity (R2 = 0.92) and distance of stress-field translation (R2 = 0.83), and were distributed over the joint surfaces (p < 0.03). During mandibular laterotrusion, average mechanical work was 1.5 times greater in the contralateral joint. Peak magnitudes of work (> 3000 mJ) were 4 times that previously reported.
Key Words: temporomandibular joint • stress-fields • mechanical work • biomechanics • MRI
Degenerative joint disease (DJD) in synovial joints is thought to involve the mechanical fatigue of the articulating tissues (Ateshian et al., 1994; Dunbar et al., 2001; Nickel et al., 2001). Degenerative processes can occur at a relatively early age in the human temporomandibular joint (TMJ), where the mean age of onset of DJD is between 25 and 35 yrs (Ong and Franklin, 1996; Israel et al., 1998; Murakami et al., 1998). Studies on human cadavers have shown that macroscopic lesions of the TMJ articular surfaces, as well as disc perforations, are frequently found (Oberg et al., 1971; Stratmann et al., 1996). Animal experiments have shown that perforations or defects experimentally induced in the TMJ disc can increase in size according to their location and produce alterations in the TMJ tissues, as seen in DJD (Helmy et al., 1988; Lekkas et al., 1988; Axelsson et al., 1992). Mechanical failure of the TMJ disc appears to be a predisposing factor to DJD, because of the role of the disc as the principal mechanism of stress distribution and lubrication in the TMJ (Nickel and McLachlan, 1994a,b; Nickel et al., 2001; Beek et al., 2003). Measurements of yield strength of the TMJ disc indicate that the disc is ten-fold stronger along the anteroposterior axis compared with the mediolateral axis, and that trauma produces increased rates of fatigue along the mediolateral axis (Beatty et al., 2001, 2003; Detamore and Athanasiou, 2003). These results suggest that mechanical fatigue along the mediolateral axis of the disc is more likely to cause failure of the cross-linking between major collagen fibers. Tractional forces applied repeatedly to the surfaces of the TMJ disc are a potential source of mechanical fatigue. Tractional forces can result from frictional forces and plowing forces produced by the deformation of the cartilage matrix as a stress-field translates over the surface (Linn, 1967; Ateshian et al., 1994; Gallo et al., 2000). Frictional forces on the surface of the TMJ disc are low (Nickel and McLachlan, 1994a; Nickel et al., 2001). With respect to plowing forces, we have demonstrated, from in vivo data, that stress-field translation, a pre-requisite for plowing, occurs along the mediolateral axis of the disc in humans (Gallo et al., 2000). Calculations of the mechanical work done during symmetrical jaw-opening/-closing indicate that the energy input to the disc by mediolateral-stress-field translation is highly variable between different TMJs (from 6 to 706 mJ). It is reasonable to assume that a higher and abnormal amount of mechanical work done adds energy to the cartilage that ultimately contributes to the failure of these tissues. This research contributes to the long-term goal of identifying the important variables in the pathomechanics of degenerative disease of synovial joints in general, and of the TMJ in particular. The specific aims of this study were to test the hypotheses that mechanical work in the human TMJ (i) varies with the type of mandibular activity, such as protrusion and laterotrusion, and (ii) is evenly distributed over TMJ surfaces.
Ten human participants (eight females, two males), from 24 to 35 yrs of age, with healthy TMJs, as determined by history and clinical examination (Gallo et al., 2000), participated in this study. These participants also participated in a previous study where the same methods were used (Gallo et al., 2000). The movements analyzed in this study were recorded in the second part of the same jaw-tracking session. Five TMJs were excluded unilaterally, due to time constraints in Magnetic Resonance (MR) image acquisition or to technical difficulties in preparing and/or using the splints for jaw-tracking for any of the mandibular movements. The study protocol was approved by the University of Zürich Institutional Review Board, and informed consent was obtained from all participants. The method for the reconstruction and animation (dynamic stereometry) of the TMJ is briefly described as follows. Magnetic resonance imaging (MRI) scans, consisting of 14 parasagittal views made perpendicular to the condylar long axis, were recorded in a 1.5 T system (Gyroscan ACS-II Philips Medical System, Best, Netherlands). The position of the mandible was stabilized for this by a monobloc that fit over the participant’s maxillary and mandibular teeth. The monobloc was rigidly connected to an external frame reference system, which served to transform the MRI coordinates into those of the jaw-tracking system. The jaw-tracking system consisted of 3 linear cameras tracking the relative temporospatial changes of 2 sets of 3 light-emitting diodes attached to mandibular and maxillary teeth (Mesqui et al., 1985; Airoldi et al., 1994). MRI provided anatomical information, segmented by means of an interactive line editor, from which we could obtain the contours of mandibular condyle and fossa that were then joined into wire-frames approximating the articulating surfaces (Krebs et al., 1995; Krebs, 1997; Gallo et al., 2000). Motion data were applied to the reconstructed anatomical structures by means of custom-written software running on a graphics workstation (Indigo 2, Silicon Graphics, Mountain View, CA, USA). Errors in the method have been reported (Krebs, 1997) and are within the range of 1 mm. Mandibular movements of laterotrusion to the right and left sides and symmetric protrusion were recorded by the jaw-tracking system. The pace and amounts of mandibular movements were determined by the participant. No attempts were made to standardize the amount of condylar movement between tasks or participants. Each recording session was performed twice, and the data were averaged.
The center of the stress-field was determined by the area of minimum condyle-fossa distance (Nickel and McLachlan, 1994b; Gallo et al., 2000). Therefore, for each sampling time of mandibular motion, the 10 smallest adjacent condyle-fossa distances, measured between polygon vertices, were identified. We averaged these distances to determine the average minimum condyle-fossa distance, h. The centroid of the area defined by these 10 minimum distances was calculated, and determined the mediolateral position of the stress-field, D. The standard deviation of the positions of the 10 minimum distances about the centroid was also calculated, and determined the mean radius, a. The area A was then determined according to: A = The mechanical work, W (mJ), done to the cartilage was estimated according to the equation:
where:
Due to the paucity of human TMJ data regarding plowing forces associated with the movement of the stress
The basis of this formulation was the non-linear relationship demonstrated between stress and strain rate of porcine discs at physiological rates of tensile and compressive displacement (Beatty et al., 2001). This formulation was used previously (Gallo et al., 2000) to estimate mechanical work done.
We determined spatial distribution of work done by color-coding the intra-articular space to identify the position of the stress-field centroid at the beginning of movement and at maximum excursion. The location of
The strengths of the relationships between the estimated work done and the variables used to calculate it were determined for all mandibular activities in all participants, by least-squares polynomial regressions. We performed ANOVA on the data to investigate the effects of joint side (right or left), type of mandibular movement (contralateral or ipsilateral to direction of laterotrusion; either TMJ in symmetrical protrusion), and location of
We pooled the results for all mandibular movements (laterotrusion to right and left, protrusion) by 10 TMJs in 15 participants (Figs. 1  , 2). The amounts of work done were highly associated with peak velocity (Vp) of mediolateral stress-field translation (R2 = 0.92) and the amount of this translation ( D) (R2 = 0.83) (Figs. 1, 2). Similar plots of work done vs. variables such as  , A, and (a/h)–1 showed weak associations (R2) of 0.58, 0.32, and 0.09, respectively.
Average work done in each TMJ by mediolateral stress-field translation was calculated for all movements (Table 1 ). Data reported previously for symmetrical jaw-opening/-closing (Gallo et al., 2000) were included for comparison. Protrusion produced a mean ± SD work value of 340 ± 787 mJ. The mean ± SD work value of 374 ± 740 mJ for laterotrusion in the contralateral TMJ was similar, but the mean ± SD work value of 245 ± 446 mJ for laterotrusion in the ipsilateral TMJ was lower, although not significantly different (Table 2). Work values for all movements were less than 250 mJ for the majority of the joints. However, TMJs #8, #9, and #14 showed the largest outliers between 696 and 3126 mJ for laterotrusion and protrusion of the mandible (highlighted in Table 1). TMJ #14 had work values for the 3 movements that were an order of magnitude larger than means for a given movement for all TMJs studied. The peak work values for TMJ #14 were 4 times larger than those calculated previously for jaw-opening and -closing movements in this group of TMJs.
Results of ANOVA to elucidate the effects of various factors on the mechanical work done within the TMJ showed that joint side and type of movement did not have any significant effects (p = 0.555 and 0.066, respectively). However, significantly more mechanical work was done when D was located in both halves of the TMJ, as compared with when D was located in the medial or lateral half only (p < 0.005 and p < 0.030, respectively), whereas there was no significant difference in the amount of work done when D was in the medial compared with the lateral half of the TMJ (p = 0.483).
The results of this study show that the magnitude of work done to the TMJ during laterotrusive and protrusive movements was primarily influenced by the velocity and distance of mediolateral stress-field translation, rather than by the stress-field area (A) or aspect ratio a/h. Mediolateral stress-field translation and the subsequent plowing forces that impose mechanical work on the TMJ disc occur during almost any anteroposterior movements of the mandibular condyle. Mediolateral stress-field translation is mainly due to the incongruence between the articular surfaces of fossa and condyle. Such incongruence occurs because of the specific anatomy and the relative positions of joint components in an individual. In general, the main condylar axis in humans is not perpendicular to the sagittal plane; thus, for symmetrical movements, this axis is not perpendicular to the main direction of the condylar movement, and tends to enhance incongruent relationships during these movements. Analysis of the data also suggests that any type of movement of the mandibular condyles is likely to ’spend’ mechanical energy in the TMJ disc tissue, with great inter-individual variability. The fact that most extreme work values were found in the same TMJs #8, 9, and 14 for all types of mandibular movements, including jaw-opening/-closing at 2 different speeds, seems to indicate that individual-specific joint morphology may play a role in the way the TMJ tissues are loaded. In general, work was greater in the joint contralateral, rather than ipsilateral, to the direction of laterotrusion of the mandible. However, the influence of type of movement and joint side on the mean work done was not significant. This was probably due to the limited number of reconstructed joints.
The joints studied that were associated with the highest work done showed that stress-field translation We recognize that our method has some limitations, because we have used a simplified estimation of mechanical work and assumptions of rigid body mechanics. In general, all joint components undergo some sort of deformation during movement. However, the deformation of the bony and bone-supported components is likely to be far less than the deformation of the cartilaginous TMJ disk. Hence, we have used rigid body mechanics, as well as the inference of disc strains from the motion of bony surfaces, as a starting point. Nevertheless, in this analysis, we considered only mediolateral components of stress-field translation, which are most likely to cause mechanical fatigue. That is, the disc is normally tethered to its lateral ligaments, so mediolateral components of stress-field translation run transversely to the disc fibers and to the main component of its motion. Furthermore, even if the minimum intra-articular distance, h, may not be a perfect absolute measure of disc thickness and compression, it has been shown to vary consistently, depending on compressive effects such as in mastication (Fushima et al., 2003). The results presented in this study are initial data describing mechanical work in a synovial joint. This type of analysis has never been reported previously on a synovial joint system. We plan to extend the analysis of TMJ loading, using the accurate data delivered by the dynamic stereometry method, to chewing movements, in which numerical modeling of joint reaction forces will be needed (Iwasaki et al., 2003, 2004; Nickel et al., 2003; Nickel and Iwasaki, 2004), and parafunction (bruxism), in which static loading of the mandible lasts significantly longer than in normal chewing (Ware and Rugh, 1988). In the future, several aspects of the methods presented in this study will require further refinement. First, empirical data to describe the velocity-stress relationship should be replaced with data that specifically measure plowing forces during known velocities of stress-field translation. Second, the temporal dimension of loading will have to be taken into account, because we have seen that plowing forces, which are several orders of magnitude greater than the tractional forces produced by friction, increase as a consequence of increased condylar loading, duration of static loading before the start of movement, and velocity of stress-field translation (Nickel and Iwasaki, unpublished data). Combining the information from the dynamic stereometry of the TMJ with data from laboratory experiments, which demonstrate the effect of magnitude and duration of loading on plowing forces, will significantly improve the calculation of work values relevant to the in vivo situation.
Figures were prepared by K. Theesen, UNMC College of Dentistry. Dr. D. Marx, Department of Statistics, University of Nebraska-Lincoln, performed the ANOVA calculations. The authors are indebted to the individuals who participated in this study. The work was supported by the Department of Masticatory Disorders and Complete Dentures, University of Zürich School of Dentistry. Received for publication August 3, 2005. Revision received July 4, 2006. Accepted for publication July 18, 2006.
Journal of Dental Research, Vol. 85, No. 11,
1006-1010 (2006)
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ABSTRACT
INTRODUCTION
a2. The velocity of the stress-field translation, V, (mm/s), was calculated from discrete position information and smoothed by uniform averaging of 7 discrete values over 84 ms. 
