Lenz, J.

Rues, S.

Schindler, H. J.

Schweizerhof, K.

English

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Joint And Muscle Forces During ClenchingStefan Rues∗1, Jürgen Lenz1, Hans J. Schindler1, and Karl Schweizerhof21 Research Group Biomechanics, University of Karlsruhe (TH), Kaiserstraße 12, 76128 Karlsruhe2 Institute for Mechanics, University of Karlsruhe (TH), Kaiserstraße 12, 76128 KarlsruheThe masticatory system is highly redundant. Therefore, complete knowledge about the activation patterns of the chewingmuscles belonging to a specific resultant bite force can only be gained either by simultaneous force- and EMG-measurementor with the help of optimization strategies. In this study, such EMG and force measurements were carried out with 10 testpersons and the results compared to those computed with several objective functions.The results show an increase of the joint forces with an increase of the horizontal component of the resultant bite force. Thetest persons seem to favor energy minimization as control mechanism.1 IntroductionThe human masticatory system consists of twelve essential muscles connecting the mandible to the maxilla. Each muscle cangenerate a force vector with an a priori unknown magnitude but a line of action which can approximately be constructed fromits geometry. For the joint forces, however, the magnitude as well as the line of action are unknown. Thus, there are 12 (muscleforces) + 6 (joint force components) = 18 unknown parameters in comparison with 6 equilibrium conditions. Therefore, thesystem is highly redundant, i.e., a specific resultant force can be generated by an infinite variety of activation patterns. In thisstudy, the activation patterns and the resultant bite force were measured simultaneously during specific clenching tasks. Theresults based on the measured data were compared to those calculated with the help of different optimization strategies.2 Materials and MethodsSo far, no data were available from experiments in which the activities of all masticatory muscles and the resultant force hadbeen recorded simultaneously. This complete knowledge is, however, indispensable to determine the direction and amount ofthe reaction forces transferred to the condyles.For that purpose, in ten healthy male subjects (average age: 29 ± 2.6 years) the intraoral force transfer and the electromyo-graphic activities of the masseter, anterior and posterior temporalis, medial and lateral pterygoid, and anterior digastric wererecorded simultaneously in simulated clenching tasks during the generation of various resulting force vectors [1]. A feedbacksystem enabled the test persons to perform 19 specific clenching tasks (circumferential angle ϕ = 0◦, 60◦, 90◦, 180◦, 270◦,300◦; cranial angle θ = 0◦, 20◦, 40◦, 60◦ with respect to the normal z’ on the occlusal plane) at different magnitudes of theresultant force Fres (cf. Fig. 1, left). The centrally transmitted resultant force was determined with an intraoral measuringdevice also illustrated in Fig. 1 (bearing pin device fixed on custom made metal splints and equipped with strain gauges).Fig. 1 Left: Used coordinate systems and force measuring device. Right: Determination of a muscle’s elastic energy.Additionally, for each test person a 3D-model of the musculature was constructed using horizontal and frontal magneticresonance tomograms (MRTs) which also served to identify the occlusal plane as well as the position of the bearing pin. Fromthese models the centroids of the muscles’ origin and insertion areas whose connection lines coincide with the muscles’ linesof action for a homogeneous activation, were determined as well as the physiological cross-sectional areas Ai = Vi/lf,i(Vi:volume of the contractile tissue of the ith muscle, lf,i: fibre length, values taken from [2]). Now, a force law relating themuscle forces to the EMG-activities [3] can be derived and all remaining unknowns be computed under the assumptions thatthe mandible behaves like a rigid body and that joint forces can only be transferred to the fossa mandibularis by compression.∗ Corresponding author: e-mail: stefan.rues@ifm.uni-karlsruhe.de, Phone: +49 721 608 2615, Fax: +49 721 608 7990© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, WeinheimPAMM · Proc. Appl. Math. Mech. 6, 139–140 (2006) / DOI 10.1002/pamm.200610050 © 2006 WILEY-VCH Verlag GmbH & Co. KGaA, WeinheimFirst published in:EVA-STAR (Elektronisches Volltextarchiv – Scientific Articles Repository) http://digbib.ubka.uni-karlsruhe.de/volltexte/1000009400 All objective functions but one were taken from literature (e.g. [4], [5]). In this study, additionally the elastic energy of thecontractile tissue of a pennated muscle (pennation angle αi) was derived as elucidated in Fig. 1 (right). Most authors, namely,only take into account the squared muscle force as an equivalent for the elastic energy.3 ResultsOver all tasks and all test persons, the intrinsic muscle stress was found to be P = 0.32 ± 0.13 N/mm2. This corresponds wellwith the value P = 0.37 N/mm2 given in [6]. The results displayed in Fig. 2 show that the interval of joint force magnitudesranges from about 60 to 100% of the resultant bite force. Highest joint forces occur under large angles θ, i.e., under bite forceswith marked horizontal components. Furthermore, muscles whose lines of action nearly coincide with the actual bite forcedirection are highly activated. This behavior can best be observed for the lateral pterygoid muscle.masseter anterior temporallateral pterygoid digastric joint0120100806040200120100806040200IFI/IFI[%]res60 90[°]180 270 300posterior temporalIFI/IFI[%]resmedial pterygoid0 60 90[°]180 270 3000 60 90[°]180 270 3000 60 90[°]180 270 300 = 0°= 20°= 40°= 60°Fig. 2 Mean muscle and joint forces normalized to the resultant bite force (Fres = 150 N) for the right side of all test persons.Table 1 summarizes the mean differences ∆Fmean between the calculations based on the measured data (as reference) andthe results gained with the help of different optimization strategies. Best correlation is found for the proposed minimization ofthe elastic energy of the contractile tissue.Table 1 Differences between results based on optimization strategies and those based on the measured data (Fres = 150 N)opt. strategy joint forces muscle forces max. activity — — ’el. energy’ el. energyobj. function Σ Ji Σ Fi max (Fi) ΣF2iA2iΣF3iA3iΣ F2iΣF2i·lF,iAi·cos2αi∆Fmean [N ] 27.4 23.8 18.7 17.4 16.6 16.2 14.74 ConclusionsFor the intrisic muscle stress a mean value P = 0.32 N/mm2 was determined. High joint forces occurred under large angles θwith magnitudes partially greater than that of the resultant bite force. The test persons favored energy minimization as controlmechanism.Acknowledgements The authors express their gratitude to cand. ing. Frank Eckardt and cand. math. Andrea Otzen for their assistance.References[1] H. J. Schindler, S. Rues, J. C. Türp, J. Lenz, Activity patterns of the masticatory muscles during feedback-controlled simulated clen-ching activities, Eur. J. Oral Sci. 113, 469–478 (2005).[2] T. M. G. J. van Eijden, J. A. M. Korfage, P. Brugman, Architecture of the human jaw-closing and jaw-opening muscles, The AnatomicalRecord 248, 464–474 (1997).[3] S. Rues, H. J. Schindler, J.C. Türp, K. Schweizerhof, J. Lenz, Masticatory muscle and joint forces during clenching based on simulta-neous force and EMG measurement, in: 3rd European Medical and Biological Engineering Conference (EMBEC’ 05), Proceedings ofthe International Federation for Medical and Biological Engineering, 11 (2005).[4] P. G. Trainor, K. R. McLachlan, W. D. McCall, Modelling of forces in the human masticatory system with optimization of the angula-tions of the joint loads. J. Biomech. 28, 829–43 (1995).[5] L. R. Iwasaki, P. E. Petsche, W. D. McCall Jr., D. Marx, J. C. Nickel, Neuromuscular objectives of the human masticatory apparatusduring static biting. Arch. Oral Biol. 48, 767–77 (2003).[6] W. A. Weijs, B. Hillen, Cross-sectional areas and estimated intrinsic strength of the human jaw muscles, Acta morph. nederl.-scand.,23, 267–274 (1985).© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, WeinheimSection 2 140 

Joint and muscle forces during clenching

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Joint and muscle forces during clenching

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