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Relationship between Kinematic Center and TMJ Anatomy and FunctionClinic for Masticatory Disorders, Removable Prosthodontics and Special Care, Center for Oral Medicine, Dental and Maxillo-Facial Surgery, University of Zürich, Plattenstrasse 11, CH-8032 Zürich, Switzerland Correspondence: * corresponding author, luigi{at}zui.uzh.ch
The kinematic center (KC)—defined by coinciding jaw-opening/-closing and protrusion-retrusion trajectories—has been proposed in the literature as a reference point to represent TMJ movements. In this study, we tested whether the KC lies in a peculiar anatomical point and whether its trajectory reflects intra-articular distance. In 11 asymptomatic individuals (seven females, four males, aged 24–37 yrs), 4 openings/closings and 4 protrusions/retrusions were tracked with dynamic stereometry. In a 3D lattice (0.5 mm grid) constructed solidly around each condyle, the KC was the point with maximal cross-correlation between opening-closing and protrusion-retrusion paths. KC trajectories were more cranial on closing than on opening, consistent with intra-articular distances being smaller on closing than on opening. However, KCs were never located on condylar main axes (distance, 4.5 ± 2.9 mm), nor did they coincide with points best approximating fossa shapes (distance, 12.5 ± 6.4 mm). The kinematic center’s anatomical and functional significance therefore appears to be questionable.
Key Words: biomechanics • kinematics • kinematic point • MRI • temporomandibular disorders • temporomandibular joint
The kinematic center (KC) has been proposed as a standardized reference point to represent condylar movements of the temporomandibular joint (TMJ) (Yatabe et al., 1995; Naeije, 2003). The KC has been presented as lying in the center of a spherical condyle (Huddleston Slater et al., 1999), and researchers thought it to be the only condylar point performing solely translatory movements "parallel" to the articular eminence during mandibular movements (Yatabe et al., 1995), with trajectories allegedly showing the smallest variability (Yatabe et al., 1997; Naeije et al., 1999). The KC trajectories were also believed to reflect variations in intra-articular distances (Huddleston Slater et al., 1999, 2002), since, during symmetric unloaded opening/closing movements, the opening trajectories were closer to the articular eminence than were the closing ones (Yatabe et al., 1997). Moreover, this discrepancy was found to disappear during loaded opening/closing movements (Huddleston-Slater et al., 2002). All these studies, as well as those using other condylar reference points, have the major drawback of being performed without relating the trajectories to the shape of the fossa. Therefore, the anatomical and functional significance of the kinematic center remains obscure, and it seems premature to infer variations in intra-articular distances solely from the trajectories of the kinematic center as proposed (Huddleston Slater et al., 2002). Dynamic stereometry permits the three-dimensional reconstruction of the anatomy of the TMJ and its animation with real kinematics acquired with 6 degrees of freedom (Krebs et al., 1995; Krebs, 1997). The system therefore allows the movement of the whole condyle within the fossa to be visualized, and the variations in the true distances between the condyle and fossa surfaces to be measured as movement progresses (Gallo et al., 2000; Fushima et al., 2003; Gossi et al., 2004). Thus, the system permits the elucidation of the significance of the kinematic center, since it relates its trajectories during any sort of mandibular movement to the joint anatomy. The aim of this study was therefore to assess the relationship between the KC trajectories and the TMJ anatomy. In particular, the following three hypotheses were tested in asymptomatic individuals: (a) The kinematic center lies in the condylar center, (b) the kinematic center coincides with the point that best follows the fossa shape, and (c) the variations in the trajectories of the kinematic center during unloaded jaw opening/closing movements correspond to those of the minimum intra-articular distance.
Participants Eleven persons (seven females, four males, age 20–38 yrs) with asymptomatic TMJs participated in the study (Table  ). Initially, all potential participants had a medical history recorded. They also responded to a questionnaire to uncover a past or present history of craniomandibular disorders (CMD). Those with a negative history underwent a clinical examination to exclude any CMD signs. Thus, to be included in the study, participants had to have non-reduced and non-painful jaw movements, and be free of palpatory tenderness of the TMJ area and masticatory muscles. Also, joint play had to be negative. Although the presence of pain-free clicking did not lead to exclusion, no participants had clicking joints. All participants were in good general health and gave informed consent before participation. The ethics committee of the State of Zürich approved the study.
Data Acquisition For each participant, TMJ anatomy was assessed by magnetic resonance imaging (MRI), and jaw movements were subsequently recorded while the participant performed 4 symmetric jaw opening/closing cycles and 4 symmetric protrusion/retrusion cycles at a deliberate rate. To reconstruct and animate real TMJ anatomy with its own motion, we combined MRI and jaw-tracking data by using a reference system consisting of 3 non-collinear plastic spheres surrounded by magnetic contrast liquid. This allowed for the transformation of MRI coordinates in the jaw-tracker coordinate system. Thus, the motion information obtained from the jaw-tracking system could be applied to the three-dimensional TMJ anatomy. Although the method has been thoroughly described elsewhere (Krebs et al., 1995; Krebs, 1997; Gallo et al., 2000), we will summarize it briefly here. Imaging was performed in a 1.5 T MRI scanner (Gyroscan NT, Philips, Eindhoven, the Netherlands) with the participant biting on an individually made occlusal splint attached to a face bow carrying the reference system laterally to the examined TMJ. Twelve slices were taken through the reference system and 14 slices through each TMJ perpendicular to the condylar long axis. The centers of the reference spheres were determined automatically. For the 3D reconstruction of the TMJ, its bony contours were input manually. After contour approximation by polylines and triangulation, the surface was described by a set of cubic parametric patches. Mandibular movements were tracked opto-electronically (Mesqui et al., 1986; Airoldi et al., 1994). Two triangular target frames (TTFs), carrying 3 light-emitting diodes (LEDs) each, were attached to the dental arches by means of splints not interfering with occlusion. The LEDs were pulsed sequentially at 70 Hz, and 3 linear cameras recorded their positions. The TTFs defined a maxillary {H} and a mandibular {M} coordinate system. The temporospatial changes of {M} were determined relative to {H}.
Data Analysis We constructed the main condylar axis by connecting the centroids of the most medial and most lateral condylar contour. The distance between the kinematic center and the center of the main condylar axis was calculated for each joint.
A 3D lattice with a 0.5-mm grid was defined, extending at least 10 mm in each spatial direction around each condyle and animated as if it was rigidly connected to it. Subsequently, opening-closing and protrusion-retrusion paths of each lattice point were calculated. The kinematic center was the lattice point with maximal cross-correlation between opening-closing and protrusion-retrusion paths. The difference between opening and closing trajectories in the caudocranial direction (
The point with trajectory best approximating the fossa shape (BA) was the lattice point maximizing the cross-correlation function between its trajectory and the shape of the fossa. This shape was determined from the sagittal MR images taken through the center of the main condylar axis. The vector pointing from the KC to BA was constructed for each joint.
The centroid of the 30 minimal distances between fossa and condyle at each time step throughout the opening/closing movements was computed. We then determined the path of the minimum intra-articular distance (h) between condyle and fossa by connecting the centroids at each time step, similarly to previous studies (Gallo et al., 2000; Gossi et al., 2004). The degree of coincidence of the paths of this centroid in the mediolateral direction on opening/closing was determined as previously described (Gossi et al., 2004). The dorso-ventral position (xh) corresponding to the maximum difference between h on opening and closing (
Statistical Analysis
The maximum differences
An example of the trajectory of the kinematic center and of the condylar point best approximating the fossa shape is shown in a sagittal view (Fig. 2A ). The size of the cubes represents the value of the cross-correlation between the opening/closing and protrusion-retrusion paths, i.e., the degree of coincidence between the paths of the two types of movement: the larger the cube, the higher the coincidence degree. The starting points of the trajectories lay within only 7 out of 22 condyles. Only for joint #2 are the trajectories of the KC and BA superimposed; for joints #8, #10, and #12, they are somehow similar, and for the other joints they are quite different (Fig. 2B). Thus, KC trajectories in general are different from the eminence shapes. The condyles never had a spherical shape.
The kinematic centers were, on average, at a distance d = 4.0 ± 2.2 mm (median, 3.8 mm; range, 0.3–8.3 mm) from the main condylar axis (95% confidence interval of the median of d: 2.2–5.2 mm). In 10 joints, the KC was located dorso-cranially (d = 5.3 ± 2.0 mm; median, 5.1 mm; range, 1.7–8.3 mm), in 6 ventro-caudally (d = 2.6 ± 1.1 mm; median, 2.2 mm; range, 2.2–3.8 mm), in 3 ventro-cranially (d = 3.5 ± 3.0 mm; median, 3.8 mm; range, 0.3–6.3 mm), and in 3 dorso-caudally (d = 2.8 ± 0.9 mm; median, 2.5 mm; range, 0.8–4.2 mm) (Fig. 3A ).
There was no correspondence of the KC and BA, the distance between these two points being, on average, 11.5 ± 5.3 mm (median, 12.6 mm; range, 2.4–22.3 mm) (Fig. 3B  ).
The paths of the minimum intra-articular distance coincided between opening and closing in the mediolateral direction in all joints. The minimum intra-articular distance h was significantly smaller during closing than during opening (
This study showed that the position of the kinematic center as defined in the literature (Yatabe et al., 1995, 1997; Catic and Naeije, 1999;Naeije et al., 1999; Naeije, 2002, 2003) was: (a) unrelated to condylar anatomy, its position being unpredictable and mostly located outside the condyle; (b) not following the fossa shape during mandibular movement; and (c) associated with, but neither identical to nor synchronized with, the variations in the minimum intra-articular distance. The observation that the kinematic center was unrelated to the lateral condylar pole had already been reported (Yatabe et al., 1997), but ours is the first study showing that the KC can lie even outside of the condyle. Analysis of preliminary data (unpublished) suggests that the distance between the KC and the condylar axis center depends on how the shape of the cranial part of the condyle deviates from that of a hemisphere: the larger the deviation, the greater the distance. Since the condyle has an inter-individually highly variable—and never spherical—shape, it is not surprising to find such large variations in the KC position relative to the condyle. Moreover, the simplified assumption of the condyle being a sphere or a cylinder rolling/sliding along the fossa does not consider: (1) the presence of soft compressible tissue between the articular surfaces, (2) the condyle-disc relationship likely being different on opening and closing, and (3) the difference in the relationship between rotation and translation on opening and closing (Salaorni and Palla, 1994). The KC trajectories were not "parallel" to the fossa and in some cases even crossed the eminence. Also, the KC trajectories in general did not lie on a circular arc. In many cases, they were not located dorso-caudally to the condylar center, as has been suggested (Morneburg and Proschel, 1998), but were also in more cranial positions. These facts seem to provide evidence against the theory of the KC as being placed at the condylar attachment of a taut temporomandibular ligament (Osborn, 1989, 1993; Morneburg and Proschel, 1998). It has been reported that, during unloaded opening/closing movements, the closing trajectory is further caudal than on opening (Huddleston Slater et al., 1999). This is in contrast to our results, which showed more cranial closing trajectories, consistent with the intra-articular distances being smaller on closing than on opening. This had also already been shown for mastication (Fushima et al., 2003; Palla et al., 2003). Since in this study we calculated the KC according to its proponents, one possible explanation for this discordance could be due to the fact that the mandible was more loaded by the weight of the jaw-tracking markers than by our TTFs (around 2 grams). Our finding that the intra-articular distance was smaller on closing than on opening may suggest that, during opening, at least in asymptomatic individuals, the elevator muscles do not actively counteract the mainly caudally directed pull of the suprahyoid muscles (Yamada et al., 2005). Nevertheless, KC trajectories, as measured in this study, indirectly reflect the variations in the intra-articular distance between jaw-opening and -closing phases, although the maximum differences do not occur simultaneously. In our protocol, we disregarded loaded movements, because we wanted to record movements as they occurred under normal conditions. In conclusion, our study shows that, although the traces of the TMJ kinematic center reflect to some extent the joint space variation, they are unrelated to joint anatomy, since they represent neither the movement of the whole condyle nor that of surface points.
This work was supported by the standard financial plan of the University of Zürich and by Grant # 325200-110067 of the Swiss National Science Foundation, Berne, Switzerland. The authors thank Ms. Diana Gössi for her help in collecting and analyzing the data. Received for publication June 13, 2007. Revision received February 26, 2008. Accepted for publication May 7, 2008.
Journal of Dental Research, Vol. 87, No. 8,
726-730 (2008)
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ABSTRACT
INTRODUCTION
Z) was calculated, and the time step (tz) at the maximum difference (
