Biomechanical analysis of stress distribution in the human temporomandibular-joint

ANNALS OF ANATOMY

Biomechanical analysis of stress distribution in the human temporomandibular-j oint Rainer Breul 1, Gita Mall 2, Johannes Landgraf 1, and Roland Scheck 3 1Anatomisches Institut, Ludwig-Maximilians-Universit~it,PettenkoferstraBe 11, D-80336 Mtinchen, Germany, 2 Institut fiir Rechtsmedizin, Ludwig-Maximilians-Universit~it, Frauenlobstrage 7 a, D-80046 Mtinchen, Germany, and 3 Institut far Radiologische Diagnostik, Ludwig-Maximilians-Universitfit, Frauenlobstrage 8, D-80046 Miinchen, Germany

Summary. The positions of the head of the mandible, of the articular disc and the outline of the temporal surface are digitized from sagittal MRI-scans of the temporomandibular joint of a 32-year-old subject in 5 different positions of occlusion. The stress distribution in the joint is calculated on the basis of these data. For each position of the condyle, the momentary center of rotation in the head of the mandible and the tangent attached to the temporal surface are determined. The line connecting these two points indicates the direction of the resulting compressive force. Furthermore, the extension of the area available to the force transmission is estimated. By means of these parameters the stress distribution is calculated independently from the position. The analyses show that the temporomandibular joint is slightly eccentrically loaded in all positions. The increase of the stresses is in all cases oriented caudo-ventrally. The results are verified in an anatomical specimen of the articular tuberculum. The trabecular structures as well as the subchondral bone-lamella of the articular tuberculum are functionally adapted to the analyzed stress situations. Key words: Temporomandibular-joint - Biomechanics Stress analysis - Stress distribution - MRI

Introduction In recent years a series of fundamental studies on the biomechanics of the temporomandibular joint have appeared Barbenel 1974; Brehnan et al. 1981; Kubein-Meesenburg 1985; Kang et al. 1993). Nevertheless, there is still a vivid Correspondence to: R. Breul

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AnnAnat(1999)181:55-60 © Urban& FischerVerlag

discussion on the loading situation in the mandibular joint. In-vivo investigations (Hylander 1979) are extremely difficult because of the mechanical complexity of the joint and its neuro-muscular regulation (Kubein-Meesenburg 1985). Most studies are therefore restricted to experimental or analytical methods. Molitor (1969), in his very detailed biomechanical analysis, compared the mandible to a balance beam resting with its momentary center of rotation on the articular tuberculum. The suspension of the beam is ensured by the masticatory muscles, which, according to the lever principle, balance out the mastication forces on the alimentary bolus and the compressive force on the articular tuberculum. Molitor showed by vector analyses, that the direction of the compressive force is more or less rostral with respect to the shape of the ascending ramus of the mandible and the momentary position of the condyle on the articular tuberculum. He was further able to prove theoretically that the temporomandibular joint with its multiple muscle functions can in case of a certain specific combination of muscle forces be free from forces during mastication. Kubein-Meesenburg, N/~gerl and Fangh~inel (1990) and Nggerl et al. (1991) have intensively analyzed the kinematics and biomechanies of the mandibular movements during mastication. They have also characterized the anatomical structures of the temporomandibular joint under differential-geometric aspects. They mention 2 fundamentally different functional properties of the joint. On the one hand, the joint serves to transmit forces from the mandible to the maxilla; on the other hand it represents a space for movements of the condyle. Since the force is transmitted by the bolus in the sense of a hypomochlion, the joint is force-free. The above studies are contrasted by observations of Hylander (1979) and Brechnan et al. (1981) in macacas.

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They were able to prove by direct m e a s u r e m e n t s in the m a n d i b u l a r j o i n t that considerable forces are exerted on the joint during the phase of occlusion as well as during the process of mastication. Dos Santos (1995) further showed in a biomechanical m o d e l that during a strong occlusion o n splints, 30 to 45% of the total muscle force is transmitted to the m a n d i b u l a r joint. Because of the partially contrary statements on the loading condition of the m a n d i b u l a r joint, the present study aims to analyze the kinds of stresses acting on the t e m p o r o m a n d i b u l a r joint by M R I u n d e r defined occlusion conditions. The results are morphologically verified in an anatomical specimen.

Materials and methods _2 Proton-weighted MRI-sequences of the temporomandibular joint of a 32-year old subject were scanned under defined conditions Fig. 2. Scheme of the measurement of the MRLimages for deterusing modified coils for the temporomandibular joint (Fig. 1). By mining the parameters of the stress distribution analyses: this method it was possible to present all anatomical structures T= tangent attached to the temporal surface, S t - $ 3 secants for rich in contrast. The resolution was 0.4 mm. The head of the sub- determining the momentary center of rotation D of the head of ject was fixed in a compressive of foam rubber to avoid move- the mandible, PRA = resultant compressive force on the articular ment during the acquisition time of 3 minutes and 20 seconds. tuberculum, the connection between D and T determines the diThe orientation of the acquisition plane was right-angled in the rection of PR~b a and b = sections for the force transmission to middle of the articular tuberculum. The scan thickness was the articular tuberculum. 2 ram. A total of 5 scans of the temporomandibular joint were taken. meters (Fig. 2) are determined from the position of the articular The distance ot the incisor teeth of 0 ram, 6 mm, 9 mm, 12 mm surfaces: 1. A tangent T is attached to that particular location on the arand 15 mm was kept constant by an individually shaped form of Permagum (Espe Comp.). The form at the same time served as a ticular tuberculum which is nearest to the condyle. 2. The momentary center of rotation D in the articular condyle bolus. During the acquisition time the subject was asked to exert is located with the help of the three secants $1 - $3. a constant pressure on the bolus. 3. The line between T and D indicates the direction of the comThe MRI-scans were prepared for the analyses by an image processing system (Adobe Photoshop 3.0). The following para- pressive load A on the articular tuberculum. 4. The lengths of the sections a and b on both sides of the intersection center of A are measured. The sections together with the articular disc contribute to the force transmission in the mandibulax joint. 5. The following force components are calculated from the parameters a, b and A for formulating the stress profile:

Pa = A'2(2 b - a)/a + b)2 as lateral border of section a Pb ~ A'2(2 a - b ) / ( a + b) 2 as lateral border of section b as force component in the intersection center of the compressive force A, These 3 approaches take into account the hypothesis of Navier (Schreyer 1957), according to which the increase of all force components is linearly limited in the case of an eccentric position of A. Since the absolute value of the compressive force A is unknown, it is replaced by the unit vector PRA. The absolute value is thereby changed into a relative value, which still allows to determine the kind of the stress distribution in the joint. The force components P1 are further divided into their normal components and projected onto the circular outline to present the stress distribution. The results of the analyses of the stress distribution are differentiated with respect to the position of PRA. In the case of a centric position of PRA the normal components PIN (Fig. 3 a) are almost equal leading to an even stress distribution. In the case of a slightly eccentric position of PRA the stress diagram shows a

Fig. 1. MRI-image of a proton weighted sequence (Siemens Vision, 1.5 Tesla, TE/TR 20/2000) of the temporomandibular joint of a 32-year old subject in complete occlusion. In the center of the image: articular tubereulum, articular disc and head of the mandible. 56

stress value on Pa which is almost twice as high as that o n / ' b . The joint is subjected to higher stresses. If PRA assumes an extremely eccentric position, the stress values are very high on P~ while they are almost equal to zero on Pb. Especially high and excentric stresses lead to a destruction of the articular cartilage.

PRA PIN

Results In the 1st analysis, the stress distribution in the t e m p o r o m a n d i b u l a r joint is calculated and graphically p r e s e n t e d (Figs. 4 a, b) in c o m p l e t e occlusion (distance b e t w e e n incisor teeth: 0 mm). The condyle lies on the p o s t e r i o r and lower 3rd of the articular tuberculum; the compressive force runs slightly inclined in a rostro-occipital direction. The sections are a = 65 units and b = 51 units. The stress distribution is slightly eccentric and increases in a caudalventral direction. In the 2rid analysis, the distance b e t w e e n the incisor teeth is 6 ram, the condyle is positioned a n t e r i o r to and below the articular t u b e r c u l u m (Figs. 5 a, b). The sections are a = 72 units and b = 38 units. The stress distribution is slightly eccentric and increases in a caudal-ventral direction.

PRA

°\

1

b

a PRA

0 turn PR~

1

1

0 mrn

Fig. 3. a) Example of a centric strain of the joint. The intersection of the resultant compressive force PRA divides the compressive line ab into two sections a and b of equal length. This leads to an even stress distribution of the force components P1 (stress profile on the baseline) and P~N (stress profile on the circular outline): P, and Pb = lateral borders of the stress profile. b) Example of a slightly eccentric stress distribution. Section a is shorter than section b. PRA does not meet ab in the center. c) Example of a highly eccentric stress distribution. PRA is clearly eccentric; section a is considerably shorter. The values of the force components P , increase towards PA. 57

Fig. 4. a) Position of the head of the mandible in complete occlusion (incisor teeth distance: 0 mm). T= tangent attached to the temporal surface, D momentary center of rotation of the head of the mandible, sections a and b for force transmission to the articular tuberculum. PRA = resultant compressive force on the articular tuberculum. b) Stress distribution on the articular tuberculum in complete occlusion (incisor teeth distance: 0 ram). The intersection of the resultant compressive force PRA divides the line ab into two sections a and b causing a slightly eccentric stress distribution of the force components Pz (in the stress profile on the base line) and Pm (in the stress profile on the circular outline). PA and PB = lateral borders of the stress profile.

9 mm a

6 mm PltA

a b

PRa

b a

6 mm

9 mm

b

Fig. 5. a) Position of the head of the mandible for an incisor teeth distance of 6 mm. For further explanations see Fig. 4 a. b) Stress distribution on the articular tuberculum for an incisor teeth distance of 6 mm. The stress values slightly increase caudoventrally.

Fig. 6. a) Position of the head of the mandible for an incisor teeth distance of 9 mm. For further explanations see Fig. 4 a. b) Stress distribution on the articular tuberculum for an incisor teeth distance of 9 mm. The stress values slightly increase caudoventrally.

In the 3rd analysis (Figs. 6 a, b), the distance between the incisor teeth is 9 mm; the condyle has almost the same position as in the 2nd analysis. The sections are a = 51 and b = 42 units. The stress distribution is slightly eccentric on a relatively higher level of stress values and increases in a caudo-ventral direction as well. In the 4th analysis (Figs. 7 a, b), the distance between the incisor teeth is 12 ram; the condyle has passed the lower vertex on the articular tuberculum ventrally. The sections are a = 58 units and b = 55 units. The stress distribution is almost centric; a slight increase is observed in a ventral direction. In the 5th analysis (Figs. 8 a, b), the distance between the incisor teeth is 15 ram; the condyle has the same position as in the 4th analysis. The sections are a = 62 units and b = 58 units. The stress distribution is almost centric and slightly increases ventrally.

Discussion The present biomechanical analysis of the loading conditions in the temporomandibular joint is based on the assumption that the head of the mandible is supported by the articular tuberculum during occlusion. The compressive force is the resultant of the forces of all muscles inserting in the mandibular joint. It causes a pressure in the m o m e n t of occlusion which is transmitted to the articular tuberculum through the articular disc. The assumptions made are supported by in-vivo measurements in the temporomandibular joint and the condyle in macacas (Hylander 1979; B o y d et al. 1990), which showed considerable pressure forces. For the presented analyses of the stress distribution it is essential to know the parameters for the direction of the resulting compressive force RA as well as the lengths 58

!

15 m m

12 mm PI~

PRA

1

a

12 m m

a

b

15 m m

b

Fig. 7. a) Position of the head of the mandible for an incisor teeth distance of 12 mm. For further explanations see Fig. 4 a. b) Stress distribution on the articular tuberculum for an incisor teeth distance of 12 mm. The stresses slightly increase caudo-ventrally.

Fig. 8. a) Position of the head of the mandible for an incisor teeth distance of 15 ram. For further explanations see Fig. 4 a. b) Stress distribution on the articular tuberculum for an incisor teeth distance of 15 ram. The stresses slightly increase caudo-ventrally.

of the sections a and b. They can be determined from the MRI-scans of the temporomandibular joint for the different distances of the incisor teeth of 0, 6, 9, 12 and 15 mm according to the rules of Pauwels (1965, 1973) and Kummer (1968, 1985). The 5 stress analyses show that the temporomandibular joint is subjected to a more or less eccentric stress distribution in all positions. Under eccentric stress the resultant force in the joint has a caudo-ventral direction. Since our investigation did not include an exact measurement of the pressure force in the mandibular joint, the pressure force is uniformly assumed as 100%. This method is justified because it allows to evaluate the kind of loading (centric or eccentric) for the stress analysis if the sections a and b for the force transmission are known. Higher or lower forces only shift the level of the stress profile but do not change the kind of the stress distribution. As the positions 1 to 5 show, the force transmission between the corresponding components takes place in a comparatively small area in the lower re-

gion of the articular tuberculum, which is referred to as major force-transmitting zone. Dos Santos (1995) came to the result that of an assumed total force of 100%, nearly 31% have to be attributed to the temporomandibular joint and 69% to the occluding teeth. Observations of occlusion splints led to the same conclusions. No analysis however succeeded in proving a complete unloading of the temporomandibular joint under equilibrium conditions. Klesper et al. (1987, 1989) found clear densitometrical indications that in more than 98% of the mandibular joints investigated the subchondral bone showed the highest density in this region. Our own finding (Fig. 9) shows as well that there is a pronounced subchondral plate, to which some trabecular structures lead, transmitting the pressure forces from the articular tuberculum to the cranial base. Oberg et al. (1971) observed distinct arthrotic changes in this region with thinning out and perforations of the disc as a sign of high stresses. Koop (1976) was able to 59

References

Fig. 9. 2 mm section of a tuberculum articulare with pronounced subchondral plate and trabecular structures, v = ventral, d = dorsal, F = Fossa mandibulae. find glycosaminoglycanes in the anterior part of the articular disc, which occur only in pressure-exposed parts of joints. Our analyses as well as the results of the investigations cited above indicate that the temporomandibular joint is subjected to pressure forces during occlusion as well as during mastication. The specific geometrical conditions of the articular surfaces in the different positions during the process of occlusion lead to a more or less eccentric stress distribution in the joint. Despite the results presented it has to be taken into account that the temporomandibular joint is, in the mechanical sense, part of an overdetermined system because of the masticator muscles inserting in the mandible. In such a system the compressive force in the temporomandibular joint can, according to Molitor (1969), be equal to zero in the phase of occlusion since certain combinations of forces can free the joint from forces. Observations in patients having the head of the mandible resected, support this finding. These patients are able to develop a physiologically appropriate masticatory pressure. The masticatory apparatus seems to be able to fulfill this special task to varying degrees because of its exceptional muscular construction. The 2 functional states mentioned in the introduction (Kubein-Meesenburg, Nfigerl and Fangh~inel 1990; Nfigerl et al. 1991) refer to this special ability.

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