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Jaw Clenching: Muscle and Joint Forces, Optimization Strategies

¹ Research Group Biomechanics, Faculty for Mathematics, University of Karlsruhe, D-76128 Karlsruhe, Germany;
² Department of Reconstructive Dentistry and Temporomandibular Disorders, Dental School, University of Basel, Switzerland;
³ Department of Prosthodontics, University of Heidelberg, Germany; and
⁴ Department of Prosthodontics, Dental School, University Hospital Freiburg, Germany

^* corresponding author, myo.schindler{at}t-online.de

	ABSTRACT

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Realistic masticatory muscle and temporomandibular joint forces generated during bilateral jaw clenching are largely unknown. To determine which clenching directions load masticatory muscles and temporomandibular joints most heavily, we investigated muscle and joint forces based on feedback-controlled electromyograms of all jaw muscles, lines of action, geometrical data from the skull, and physiological cross-sectional areas acquired from the same individuals. To identify possible motor control strategies, we applied objective functions. The medial pterygoid turned out to be the most heavily loaded muscle for all bite directions. Biting with accentuated horizontal force components provoked the highest loading within the medial and lateral pterygoids. The largest joint forces were also found for these bite directions. Conversely, the lowest joint forces were detected during vertical biting. Additionally, joint forces with a clear posterior orientation were found. Optimization strategies with the elastic energy as objective function revealed the best fit with the calculated results.

KEY WORDS: jaw muscles • joint forces • muscle forces • EMG • optimization

	INTRODUCTION

TOP ABSTRACT INTRODUCTION MATERIALS & METHODS RESULTS DISCUSSION REFERENCES

 
Clenching forces are generated by complex co-activation of masticatory muscles. Their individual contributions to the motor task are traditionally estimated by electromyography (EMG) (Gibbs et al., 1984; Wood, 1986). However, only biomechanical modeling permits masticatory muscle and temporomandibular joint forces to be calculated. In principle, two different methods are available: (1) optimization algorithms, based on physiologically reasonable neuromuscular objectives for coordinated muscle co-contraction, e.g., minimization of joint forces, minimization of overall muscle forces, or minimization of applied muscle energy (Pruim et al., 1980; Throckmorton et al., 1990; Koolstra and van Eijden, 1992; Osborn, 1995; Trainor et al., 1995; Raikova, 1999; Iwasaki et al., 2004); and (2) simultaneous in vivo measurement of EMGs of all relevant masticatory muscles and the resultant bite force, and subsequent calculation of all forces from the static equilibrium conditions (van Eijden, 1990; van Eijden et al., 1990; Iwasaki et al., 2004). Pre-conditions for both methods are geometric data from the skull, lines of action, physiological cross-sectional areas (A_i) of the muscles, their pennation angles, and intrinsic muscle strength (P). Commonly, P is used as a fixed conversion constant based on generic mammalian skeletal muscle properties (Koolstra and van Eijden, 1992; Langenbach and Hannam, 1999). With optimization strategies, joint force directions are usually pre-supposed. The second method allows them to be calculated. To date, however, no such computations are available for bilateral biting with all essential measurements acquired from one sample.

Jaw clenching is assumed to be a risk factor for temporomandibular disorders (Velly et al., 2003; Magnusson et al., 2005). Biomechanical modeling based on all feasible in vivo measurements from a group of individuals may provide realistic insight into joint and muscle loads generated during clenching activities. Furthermore, it broadens the insight into control strategies of the motor system during clenching, and may help to reveal risk factors for the structures involved.

We undertook this study to determine the realistic loading of masticatory muscles and temporomandibular joints during biting under various resultant force vectors. Additionally, we used optimization algorithms to investigate possible control strategies for muscle co-contractions. Muscle and joint forces were calculated based on feedback-controlled electromyograms of all jaw muscles, their lines of action and physiological cross-sectional areas, geometric data from the skull, and individually calculated P gathered from one defined sample.

	MATERIALS & METHODS

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Participants
Ten healthy males (average age, 31 ± 2.3 yrs) gave written informed consent to participate in this study. They had Angle class I or mild class II dentition. Exclusion criteria were skeletal anomalies (e.g., short-faced or long-faced) or distinct malocclusions. The study was approved by the Ethics Committee of the University of Freiburg, Germany (No. 25/02, amendment 04).

In vivo Measurements
    Intra-oral Force Measurement
Bite force was transmitted by an intra-oral "bearing pin device" equipped with strain gauges and mounted parallel to the occlusal plane of the mandible on a metal splint (Schindler et al., 2005b). A perforation in the contact plate midway between the lower first molars facilitated a joint connection of the pin for force transmission in the central jaw position. Jaw separation at the incisors was adjusted to 5 mm. The transducer measured forces in 3 orthogonal directions relative to the occlusal plane (Fig. 1A).

View larger version (23K): [in this window] [in a new window]   Figure 1. Exerimental set-up and fundamentals for the muscle and joint force calculations. (A) Scheme of intra-oral force-measuring device used in the experiments: x', y', z' = coordinates of the occlusal plane; sg = strain gauge; bp = base plate; cp = contact plate; ms = metal splints bearing bp and cp. (B) Reference planes and their orientation to the location of force measurement: x, y, z = coordinates of the Frankfort horizontal plane; Jr, Jl = right and left joint reaction forces; Fres,maxilla = resultant force acting on the maxilla; Fres,mand = resultant force acting on the mandible; = circumferential angle; = cranial angle.

    EMG
Bipolar surface electrodes measured bilaterally the EMG of the masseter, anterior temporalis, posterior temporalis, and anterior digastric. Ag/AgCl electrodes (diameter, 14 mm; center to center, 20 mm) were placed parallel to the longitudinal axes of the muscles. Before electrode application, the skin was cleaned with 70% ethanol. We used an extra-oral approach to gain access to the medial and inferior lateral pterygoids by bipolar wire electrodes, as previously described (Schindler et al., 2005a). The common electrode was positioned in the neck above the 7th vertebra. The EMG signals were differentially amplified (EM 100 Biopac, Santa Barbara, CA, USA; frequency response, 1–5000 Hz) and sampled at 1000 Hz simultaneously with the force signals.

    Tasks
The participants generated bite forces with F = 50 N and F = 150 N. Force vectors were produced in random order at six angles (anteriorly, 0°; anteromedially, 60°; medially [left], 90°; posteriorly, 180°; laterally [right], 270°; anterolaterally, 300°) and four angles (tilt to the vertical: 0°, 20°, 40°, 60°). Additionally, the participants performed purely vertical biting with F = 250 N and at maximum voluntary contraction. After the experiments, the muscles were activated in different directions at maximum effort (intercuspal clenching, retrusion, jaw opening, and protrusion/laterotrusion against resistance). All activations were repeated three times.

    Analysis of EMG Data
We determined the point in time when the test person was closest to the given force vector, i.e., at which the error e = |_measured – _target|/|_target| was minimal. The root mean square value of a 400-ms interval around this point was used and normalized with the maximum EMG activity for the respective muscle (MVC%). The measured parameters were described by the mean values (Mean) and standard deviations (SDs). Intra-individual scatters for the same tasks were clarified by coefficients of variation (cv). Right-and left-side data for corresponding tasks were averaged. The complete results have been published previously (Schindler et al., 2005a). The results for F = 150 N were used for the calculations.

Force Calculations
    Anatomical Geometry
For each participant, a 3D model of the musculature and structures relevant to the calculations was reconstructed, by horizontal and frontal magnetic resonance tomography (slice distance: 4 mm). From the muscle models, the lines of action [lines through the centers of the muscle attachment areas (Hems and Tillmann, 2000)] were acquired. For calculation of A_i = V_i/l_f,i [V_i, reconstructed muscle volume; l_f,i, fiber length (van Eijden et al., 1997)], the tendinous tissue was subtracted from the muscle volume, based on previous studies (van Eijden et al., 1997). The model also served to identify the Frankfort horizontal plane, the occlusal planes, and the position of the bearing pin.

    Computation of Muscle and Joint Forces
The resultant bite force and muscle and joint forces must fulfill the 6 (scalar) equilibrium conditions (cf. APPENDIX, Table 1A, Eq. 1), facing (12+2)·3 = 42 unknown muscle and joint force components. Based on the force law (Eqs. 2,3), muscle forces are given by _i = P·A_i·cos_i·(c₁·U_rel,i+c₂·U²_rel,i) _i, where c₁ and c₂ are gained by a least-squares fit based on the data for vertical biting [pennation angle _i was based on previous studies (van Eijden et al., 1997)]. Since line of action, physiological cross-section, and relative electric activity were determined for each muscle, P was the only parameter needed to compute the 36 muscle force components. The joint forces, which are supposed to intersect the line connecting the centers of the condyles (y-axis), can be transmitted only by compression. Assuming negligible deformations of the mandible and condylar movements along the y-axis to be restricted in the medial direction only, it can be concluded that the y-component of the reaction force must vanish for one joint (Eq. 9). This led to a system of 6 equations for 6 unknowns. Because the joint force components disappeared from the balance of momentum with respect to the y-axis, P could be determined directly (Eq. 4). Relations for the joint force components are given by the remaining equilibrium conditions (Eqs. 5–9). The solution method clarifies that P must be calculated for each motor task to fulfill static equilibrium, i.e., an a priori chosen constant value could not be used.

For ~ 40°–60° and = 180°, small errors of the parameters have a great influence on P, because the numerator and denominator in Eq. 4 are both close to zero. Therefore, posterior forces were not considered in the calculations.

    Optimization Strategies
We applied several optimization strategies to determine the muscle and joint forces. The following objective functions (cf. APPENDIX Table 1B) were used: minimization of (1) joint force magnitude, (2) overall muscle force, (3) elastic energy of the contractile tissue, considering _i, l_f,i, and A_i. Joint force directions were taken from the results based on the in vivo data.

Data Analysis and Statistics
The calculated forces under the various conditions were described by the mean values (Mean) and standard deviations (SDs) for the joints and muscles of the right side. Participants with the lowest and highest cumulative deviations from the means were also illustrated. The influence of the angles and on the muscle and joint forces was examined with two-way analysis of variance with repeated measures (ANOVA). Mean differences between the results of the optimization strategies and in vivo data calculations were tested by paired t tests.

	RESULTS

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Variability of Measured EMG and Force Data
The mean cv of maximum EMG amounted to 8.3 ± 5.5%, and for the task repetitions, 12.3 ± 8.5%. The mean deviation of the measured force vectors from the target force vectors was 6.7 ± 7.9%.

Calculations Based on the in vivo Measurements
The individually calculated P averaged over all tasks and all participants amounted to 0.32 ± 0.12 N/mm² (for geometric data and A_i, see APPENDIX Tables 2A, 2B).

ANOVA revealed a significant influence of angle (p < 0.001) and angle (p < 0.001) on the muscle and joint forces. Additionally, a significant interaction (p < 0.001) was apparent.

Depending on the muscle and the task, pronounced decreases or increases of the forces with growing angle could be observed (Fig. 2A). Lateral pterygoid and posterior temporalis showed a largely increasing behavior, whereas masseter and anterior temporalis revealed the reverse pattern. Laterally directed biting ( = 270°, 300°) elicited the highest muscle force in the ipsilateral anterior and posterior temporalis (90–100 N) and simultaneously in the contralateral medial pterygoid, lateral pterygoid, and masseter.

View larger version (37K): [in this window] [in a new window]   Figure 2. Group means and standard deviations of the muscle and joint forces illustrated for the participants’ right side. Data for identical tasks (see text) of the left and right sides are pooled. Best-fitting () and worst-fitting () cases are also depicted. (A) Muscle and joint forces calculated with in vivo data (n = 10). (B) Muscle and joint forces computed with minimization of elastic energy as an objective function (n = 10). For (A) and (B): lFl/lFresl = forces as a fraction of the resultant force Fres = 150 N; = angle of the resultant force in the horizontal plane; different shades of bar plots (left to right) encode angle = 0°, 20°, 40°, 60°; motor task = 180°/ = 60° is not illustrated (see text).

View larger version (42K): [in this window] [in a new window]   Figure 3. Joint reaction forces generated during different motor tasks at Fres = 150 N. (A) Frequency distribution of the joint force angles found for the different resultant force directions defined by angle and angle (n = 10). (B) Range of joint reaction forces in the sagittal plane: J = force exerted by the condyle onto the articular eminence; = joint force angle in the sagittal plane (n = 10).

Calculations with Optimization Strategies
The optimizing calculations for muscle and joint forces based on minimal elastic energy as an objective function repeated with good approximation the characteristics found in the calculations based on the in vivo data (Fig. 2B). The mean deviation from the in vivo data was 9.8 ± 2.1 N. The other optimizing strategies showed significantly (p < 0.001) higher mean differences compared with the in vivo data (minimization of joint forces, 18.2 ± 4.6 N; minimization of muscle forces, 15.9 ± 3.4 N).

	DISCUSSION

TOP ABSTRACT INTRODUCTION MATERIALS & METHODS RESULTS DISCUSSION REFERENCES

 
Masticatory muscle and temporomandibular joint forces were significantly influenced by the horizontal (angle ) and vertical (angle ) bite directions. In addition, angle changed the muscle forces in various horizontal bite directions in different ways.

The individually calculated P averaged over the participants (0.32 ± 0.12 N/mm²) differed somewhat from the commonly used constant (0.37 N/mm²) (Weijs and Hillen, 1985). The latter, however, was calculated on the basis of different samples, one providing muscle volume, the other one bite forces. This might explain the observed differences.

The medial and lateral pterygoids of the contralateral side were the most heavily loaded muscles during biting in an anterolateral to lateral direction at large angles (40°–60°). In these directions, favorably to their line of action, they generated a higher amount of force than the masseter, although their A_i amounted to only about 1/3 to 1/2 of that of the masseter (van Eijden et al., 1997). This substantiated the relevance of both muscles for horizontal force development, as recently postulated (Murray et al., 2001; Schindler et al., 2005a). Due to its essentially lower A_i, the medial pterygoid was also the most loaded muscle at vertical biting, as compared with the temporalis and masseter. Thus, the medial pterygoid is obviously the most heavily loaded muscle relative to all biting activities. In contrast, the calculated forces for the masseter and temporalis at vertical and anterior biting corresponded fairly well with results of simulations at unilateral vertical molar biting (Koolstra and van Eijden, 1992; Iwasaki et al., 2004).

The reaction forces of the joints were substantially larger in bite directions with a large angle . This demonstrated that the joints are loaded clearly more at biting with distinct horizontal force components. The direction of the reaction forces exerted by the condyles on the articular eminence ranged from 5° to 130°, i.e., anterior as well as posterior force components were obvious. Bite forces generating a posteriorly oriented force component (> 90°) may contribute to anterior disc displacement. In general, the values of the joint loads for vertical biting were in the range found at simulations for unilateral vertical molar biting (Iwasaki et al., 2004). A restriction in our experimental model was that the force transfer was managed mid-sagittally on the level of the first molars. This specific factor limits the direct comparison with activation states in maximum intercuspation. Nonetheless, as recently shown (Schindler et al., 2005a,b), the good match of the mean EMG data during maximum contraction, with and without the bearing pin device, speaks for a similar "equilibrating behavior" of the system under the two conditions.

Another limitation might be the morphological and functional heterogeneity of the jaw muscles, i.e., the possible differential contraction behavior of muscle subunits (Belser and Hannam, 1986; Blanksma and van Eijden, 1995; Murray et al., 1999; van Eijden and Turkawski, 2001). Thus, the activation ratio from single recording sites may not reflect the activation level of a whole muscle, i.e., the real line of action might vary somewhat from the reconstructed one.

A further significant finding was the good fit of the calculated results of the in vivo data with those obtained by minimization of the elastic energy. This could provide substantial evidence for a realistic motor control strategy of the masticatory system for bilateral biting. Yet, this is in contrast to results from Iwasaki et al.(2003) for unilateral molar biting. Those investigators found an equivalent fit for minimization of joint load and minimization of muscle effort. The different equilibrating conditions and changed sensory input from the involved tissues (Hattori et al., 2003) could explain these differences. Energy consumption, i.e., minimization of elastic energy, might represent a general control principle, whereas minimization of joint load might rather be a protective control mechanism, e.g., more relevant under unilateral than under bilateral biting.

	ACKNOWLEDGMENTS

 
This investigation was supported by the Deutsche Forschungsgemeinschaft by grants SCHW 307/15-1 and STRU 675/1-1.

	FOOTNOTES

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

Received June 16, 2006; Last revision March 23, 2007; Accepted April 16, 2007

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