0003-9969/91$3.00+ 0.00 Copyright 0 1991Pergamon Press plc
Archs oral Biol. Vol. 36, No. 7, pp. 535-539,1991 Printed in Great Britain. All rights reserved
THREE-DIMENSIONAL ANALYSES OF HUMAN BITE-FORCE MAGNITUDE AND MOMENT T. M. G. J.
VAN
EIJDEN
Department of Functional Anatomy, Academic Center for Dentistry Amsterdam (ACTA), University of Amsterdam, 15 Meibergdreef, 1105 AZ Amsterdam, The Netherlands (Accepted
8 January
1991)
Summary-The effect of the three-dimensional orientation of occlusal force on maximal bite-force magnitude was examined in seven human subjects at three different unilateral anteroposterior bite positions (canine, second premolar and second molar). At each position, bite-force magnitude was registered in 17 precisely defined directions using a three-component force transducer and a feedback method. In addition, to assess the efficiency of transfer of muscle to bite force, for bites produced in the
sagittal plane, moment-arm length was determined and the produced bite-force moment calculated. The results showed that the largest possible bite force was not always produced in a direction perpendicular to the occlusal plane. Generally, maximal bite force in medial and posterior directions was larger than that in, respectively, corresponding lateral and anterior directions. In each direction the produced force was larger at the posterior bite point than at the anterior bite point. The combined moment produced by the jaw muscles was largest for vertical bites, smallest for posteriorly directed bites and intermediate for anteriorly directed bites. In the case of vertically and anteriorly directed bites the produced moment did not vary significantly with the bite position. Hence, for these bite positions the jaw closing moment of the muscles must have kept constant. In the case of posteriorly directed bites the produced moment decreased when bite position changed from the anterior to the posterior side of the dentition. This indicated that jaw muscle activity had declined. Key words: masticatory muscles, jaw mechanics, biomechanics bite force. occlusion.
INTRODUCTION
muscles of mastication have different orientations relative to the occlusal plane. The masseter and medial pterygoid exert a forward force and the posterior temporalis exerts a backward force on the mandible. The orientation of the anterior temporalis is close to perpendicular to this plane. Theoretically, this diversity enables the system to produce bite forces in different directions during a static bite. Koolstra et al. (1988b) recently explored the threedimensional directions in which bite forces can in theory be exerted. Although information is available on bite-force direction during voluntary maximal effort (Hylander, 1978) and on the direction of force exerted on the teeth during chewing (Graf, Grass1 and Aeberhard, 1974), no data exist on the relationship between bite-force direction and the maximal force humans are able to produce. In almost all bite-force studies, the bite force is restricted to a single vertical direction (Mansour and Reynik, 1975; Pruim, Ten Bosch and De Jongh, 1978; Fields et al., 1986). We earlier described a method for recording maximum bite forces in predefined directions (van Eijden et al., 1988b) and used it to describe changes in activity level of the jaw muscles as a function of change in bite-force magnitude in several specified directions (van Eijden et al., 1990) and of an alteration in bite point (van Eijden, 1990). We have now investigated the magnitude of maximum bite force in a number of directions. It has been claimed (Mansour and Reynik, 1975; Pruim, De The human
Jongh and Ten Bosch, 1980) that bite-force magnitude decreases at more anterior bite points. The lower force, registered at the anterior teeth, would be the result of (1) a longer resistance arm of the bite force in the lever system and/or (2) a lower level of activity of the jaw-closing muscles. In our experimental protocol, the position of the mandible relative to the skull was the same for the tested canine, secondpremolar and second-molar bites. Furthermore, if bite forces in different directions are exerted at a single bite point the resistance arm of the bite force (i.e. the perpendicular distance between temporomandibular joint and bite-force direction) varies. Our data can therefore test the hypothesis whether the total moment exerted by the jaw elevators is influenced by the location of the bite point and the direction of the bite force. Obviously, the conditions under which these muscles can exert the largest moments determine the optimal working conditions for the masticatory system. MATERIALS
AND METHODS
For a detailed description of the apparatus and the participating subjects we refer to van Eijden et al. (1988b) and van Eijden (1990) respectively. In brief, a three-component force transducer (24 x 24 x 10 mm, length x width x height) registered both the direction and magnitude of bite force in seven Caucasian males, age 31.1 f 4.9 yr (mean f SD). They had normal class I occlusions and showed no signs of craniomandibular dysfunction; most subjects were 535
536
T. M.G.J.
missing some of their third molars and two of them a lower left premolar. Placement of the transducer between occlusal clutches yielded an interincisal distance of 16 + 2.3 mm (mean + SD of the subjects). Forces were measured at the right-hand side of the dentition of the upper canine, second premolar and second molar. The degree of mouth opening was the same in the three bite positions. The upper occlusal clutch was kept parallel to the upper dentition. Hence, the distance between the transducer and the lower teeth was larger at the anterior side of the dentition than at the posterior side. If this distance becomes too large, medially directed bite forces pass outside the supporting element of the lower teeth, so that tilting of the transducer occurs. This was the case in two subjects for bite-force angles larger than 30” relative to the vertical. For this reason, bite-force directions exceeding an angle of 20” were not investigated. At each of the three bite positions, force was produced in 17 different directions, the vertical one (along the z-axis, i.e. perpendicular to the occlusal plane of the upper teeth) and 16 non-vertical ones. The direction of the non-vertical bites was defined with respect to the z-axis and the antero-posterior x-axis. The latter was oriented in a sagittal plane and was parallel to the upper occlusal plane. Eight directions were defined relative to the x-axis: anterior (angle relative to x-axis: 0’) antero-lateral (45”), lateral (go”), postero-lateral (135”), posterior (180”), postero-medial (225”), medial (270”) and anteromedial (315”). In each of these eight directions, two bite-force angles relative to the vertical z-axis were examined: 10” and 20”. Our feedback method was based on simultaneous visualization of both the actual and desired force direction on a computer screen (van Eijden et al., 1988b). The subjects made a maximal voluntary contraction in a particular direction. They were instructed to bite as hard as possible, keeping the direction of their actual bite force closely (within 53) matched to that of the desired force. They were not vocally encouraged. After each bite the transducer and clutches were removed for a rest period of at least 3 min. The sequence of the trials for the different bite points and force directions was chosen randomly. Measurements were made on three successive days, one for each bite point. After the experiment was completed (51 bites, 3 bite points x 17 directions), the entire procedure was repeated, with another randomized sequence. Hence, each subject produced two maximal bites per force direction. The output of the force transducer (three signals, one for each force component) was recorded on FM analogue tape and subsequently digitized (1000 samples/s/channel) using a DEC 1l/73 minicomputer system. By means of a computer program the magnitude of maximal bite force, averaged over an epoch of 0.5 s, was determined for each bite. Of the two available force values per direction, the larger one was chosen to calculate mean and SD of force over the 7 subjects. In addition, the difference between the two values, expressed as a percentage of their average, was also calculated. Mean value and SD of these differences were calculated for each bite point (n = 119, 7 subjects x 17 directions) and used as a
VAN
EIJDEN
measure for the repeatability of the results. Finally, an analysis of variance was used to test for the influence of bite-point location and bite-force direction on maximal bite-force magnitude. Calculations were done with the BMDP statistical package. To determine moment-arm length of bite forces produced in the sagittal plane, a routine orthodontic lateral cephalometrlc X-ray film (film-focus distance: 3.5 m) was made for each subject. From the closed jaw position on the film, the open position with the transducer and occlusal clutches in situ was reconstructed. Moment arm length was defined as the perpendicular distance between the temporomandibular contact point (i.e. point of shortest distance between condyle and articular eminence) and the bite-force vector. In addition, for each force direction the produced moment was determined by calculating the product of moment arm and measured bite force. RESULTS
The reproducibility of the measurements of the magnitude of the bite force was 9.4 f 10.1% (mean f SD) for the canine, 10.8 + 10.7% for the second premolar, and 10.4 f 12.5% for the second molar. The direction of bite force had no systematic effect on reproducibility. Of the two bite trials the magnitude of the second attempt was generally (in 80% of the bites) larger than that of the first. For each tooth and force direction, Table 1 gives mean + SD value of maximal bite force. Mean maximal bite-force magnitude ranged dependent on its direction between 323 and 485 N at the canine, 424 and 583 N at the second premolar and 475 and 749 N at the second molar. The analysis of variance demonstrated that both the bite position and force direction had a significant (p < 0.01) effect on maximal bite force magnitude. To visualize the results, a so-called bite-force envelope was constructed for each bite position (Koolstra et aZ., 1988b). This is a threedimensional shape created by connecting the far ends of the mean maximal bite-force vectors. The following points deserve special attention (see Table 1 and Fig. 1). First, for a particular direction, maximal bite force was largest at the second molar, smallest at the canine and intermediate at the second premolar. Bite-force magnitude at the second premolar and canine was on average (n = 17), 82.3 i 6.3% and 66.8 f 9.4%, respectively, of that produced at the second molar. The relative change in bite-force magnitude that occurred with a changing bite position was, broadly speaking, the same for the various bite-force directions. An exception was the 20” posteriorly directed bite where the force increase was smaller than 10%. Secondly, there was a clear relationship between bite-force direction and magnitude. On average, highest levels were attained in vertical, posterior and medial directions. Generally, an increase of bite-force angle relative to the vertical resulted in a decrease (maximally 35%) of bite-force magnitude. The direction of the largest possible bite force was slightly posterior at the anterior bite position (canine) and slightly medial at the posterior position (second molar).
Bite-force magnitude in three dimensions
537
Table 1. Mean maximal bite-force magnitude (N) for different bite positions and force directions Canine
!Gxond premolar
(mean f SD)
(mean f SD)
Second molar (mean f SD)
469*85 4llk83 358 f 81 434 f 72 381*64 430 f 83 393 f 52 448&78 386 f 51 485 f 93 481 f 93 465*82 336* 110 438 f 98 323 f 130 419 f 85 355*99
583*99 516 f 87 424*84 525 f 83 44Of83 525 f 72 454 f 67 536 f 81 446*71 579 f 103 523 f 77 561 f 126 498*113 575 f 133 496 f 84 529* 118 442* 100
723 f 138 652 f 132 503 f 150 690&97 536 f 142 66of 102 571 f 85 653k90 475 f 57 686&84 508 f 139 724 f 86 607*75 749 f 119 612f89 663 f 128 524f 111
Bite force direction Vertical Anterior (10’) Anterior (20”) Antero-lateral (10”) Antero-lateral (20”) Lateral (lo”) Lateral (20”) Postero-lateral (10’) Postero-lateral (20”) Posterior (lo”) Posterior (20”) Postero-medial (10”) Postero-medial (20”) Medial (10”) Medial (20”) Antero-medial (10”) Antero-medial (20”)
Vertical: force perpendicular to the occlusal plane of the upper teeth, anterior, posterior, etc.: direction relative to the antero-posterior x-axis; 10” and 20”: angle relative to the vertical.
The lengths of the moment arms of the bite forces produced in the sagittal plane are given in Fig. 2. It should be realized that the larger the moment arm, the smaller the efficiency of transfer of muscle to bite force. For all directions the moment arm increased from posterior to anterior bite points. Anteriorly directed bite forces had the largest moment arms. The difference in moment-arm length between 20” anteriorly and 20” posteriorly directed
n P2
bites was about 2Scm, irrespective of the bite point. The produced bite-force moments are given in Fig. 3. Generally, largest moments were produced by vertical forces. An increase of the bite-force angle coincided with a decrease of the bite-force moment. The decrease was more obvious for posteriorly than for anteriorly directed bites. Note that for a particular bite-force direction the produced moments
I Ca
Fig. 1. Bite-force envelopes for each of the investigated bite positions. Top row: lateral views, bottom row: frontal views. The line intersections indicate the mean maximal bite forces. A : origin of bite force vectors; *: end-point of maximal bite-force vector perpendicular to the occlusal plane of the upper teeth. C!az canine, P2: second premolar, M2: second molar. Vertical bar: lOON.
538
T. M. G. J.
post (20”)
post (IO”)
vert (0”)
ant (IO”)
Bite-Force
ant (20”)
Direction
Fig. 2. Mean moment-arm length (small black bars: standard deviations) of bite forces produced in the sagittal plane at different teeth. Ca: canine (obliquely dashed bars); P2:
second premolar (vertically dashed bars); M2: second molar; post: posterior bite-force direction; vert: vertical; ant: anterior; lo” and 20”: angle relative to the vertical (0”).
differed only slightly between the bite points. An exception to this was the 20” posteriorly directed bite, where the moment at the second molar was consideraly smaller than the one produced at the other teeth. DISCUSSION For a given bite-point and bite-force direction the maximum force. showed marked interindividual variability. Causes of this variability can be (1) variability in the strength of the jaw muscles, due to differences in cross-sectional area (Weijs and Hillen, 1984) and/or fibre-type composition (Ringqvist, 1973); (2) variability in moment-arm length of individual jaw muscles (Throckmorton, 1985; Koolstra, van Eijden and Weijs, 1988a) and/or resistance-arm length of bite force (van Eijden et al., 1988a); and (3) factors
post (200)
post (10”)
vert (0”) Bite-gorce
ant (10”)
ant (20°)
Direction
Fig. 3. Mean moment (moment arm x bite force) of bite forces produced in the sagittal plane. Same symbols as in Fig. 2.
VAN EIJDEN
associated with voluntary or reflex inhibition of full recruitment (Kroemer and Marras, 1980). Anatomical differences probably underlie the observed differences in maximal bite force between long- and short-faced persons (Ingervall and Helkimo, 1978). In our experiments another factor might have affected interindividual variability, namely the differences between subjects in the separation between the teeth, necessary to accommodate the transducer and splints. This might have affected bite-force magnitude via the length-tension relationships of the muscles and via differential changes in their lines of action (Koolstra et al., 1988b). Manns, Miralles and Palazzi (1979) and MacKenna and Turker (1983) demonstrated that bite force is the largest at an interincisal distance of 15-20 mm, about the same range in which the present registrations were carried out. Our study has shown that the total moment of the bite force, which is equal and opposite to the one produced by jaw muscles, is not constant, but depends on bite-point location and bite-force direction. It appeared that the produced moment in the sagittal plane, and hence the mechanical effect of the combined musculature, was largest in vertically, intermediate in anteriorly and smallest in posteriorly directed bites. From anteriorly to vertically to posteriorly directed bites the resistance arm of the bite force decreased. However, to produce a force in the desired direction, the jaw muscles must exert forces that approximate that direction, The final moment is determined by the extent to which the different jaw muscles participate in generating the desired bite force. As the majority of muscles have a large vertical component, the moment is largest for vertical bite forces. The second largest force component is the anterior one, and the smallest force can be generated in posterior direction (only the posterior temporalis). Consequently, the number of muscles participating in generating a moment decreases from vertically, to anteriorly to posteriorly directed bites, and this is seen for the moments. Despite this, the bite force in a posterior direction is larger than in an anterior direction. This is the direct result of the small resistance arm of the posteriorly directed bite force and thus the more efficient transfer of muscle to bite force. Our findings are that the largest possible bite force was not necessarily produced in a direction perpendicular to the occlusal plane. Koolstra et al. (1988b) found that posteriorly and medially directed forces generally reach higher values than, respectively, anteriorly and laterally directed forces. This is in agreement with our experimental results. The produced force in a particular direction was always larger at the posterior side of the dentition than at the anterior side. As far as vertical bite forces are concerned, this agrees with the findings of Pruim et al. (1980) and Mansour and Reynik (1975). In contrast to Mansour and Reynik (1975), we found that the location of the bite point had almost no effect upon the exerted moment if the bite force was vertically or anteriorly directed. In our experimental set-up the mandible does not have to change position if the bite point is changed. It must be concluded that the decrease in muscle moment in vertical bites as observed by Mansour and Reynik
Bite-force magnitude in three dimensions
was a result of the change in mandibular position, possibly effected by changed muscle length. The often described (Msller, 1966) decreased activity of the anterior temporalis muscle did not occur in our experiments (van Eijden, 1990). However, for posteriorly directed bites a marked decrease in moment with a shift in bite point from canine to second molar was indeed observed. We have demonstrated earlier (van Eijden, 1990) that this must be caused by a decrease of the activity of the posterior temporalis muscle. A cause or a functional explanation for this behaviour is still lacking. Acknowledgements-I am indebted to Dr W. A. Weijs for his comments on the manuscript, to J. Ferwerda and P. Brugman for technical assistance, to A. van HorssenMedema and C. J. Hersbach for the illustrations and photography, and to H. Rollernan-ter Heurne for preparing the manuscript.
REFERENCES
van Eijden T. M. G. J. (1990) Jaw muscle activity in relation to the direction and point of application of bite force. J. dent. Res. 69, 901-905. van Eijden T. M. G. J., Brugman P., Weijs W. A. and Oosting, J. (1990) Coactivation of jaw muscles: recruitment order and level as a function of bite force direction and magnitude. J. Biomechan. 23, 475485. van Eijden T. M. G. J., Klok E. M., Weijs W. A. and Koolstra J. H. (1988a) Mechanical capabilities of the human jaw muscles studied with a mathematical model. Archs oral Biol. 33, 819-826. van Eijden T. M. G. J., Koolstra J. H., Brugman P. and Weijs W. A. (1988b) A feedback method to determine the three-dimensional bite force capabilities of the human masticatory system. J. dent. Res. 67, 45&454. Fields H. W., Proffit W. R., Case J. C. and Vig K. W. L. (1986) Variables affecting measurements of vertical occlusal force. J. dent. Res. 65, 135-138. Graf H., Grass1 H. and Aeberhard H. J. (1974) A method for measurement of occlusal forces in three dimensions. Helv. odont. Acto 18, 7-l 1. Hylander W. L. (1978) Incisal bite force directions in humans and the functional significance of mam-
539
malian mandibular translation. Am. J. phys. Anrhropof. 48, l-8. Ingervall B. and Helkimo E. (1978) Masticatory muscle force and facial morphology in man. Archs oral BioZ. 23, 203-206. Koolstra J. H., van Eijden T. M. G. J. and Weijs W. A. (1988a) Three-dimensional performance of the human masticatory system: the influence of the orientation and physiological cross-section of the masticatory muscles. In International Series on Biomechanics 7-A (Eds de Groot G., Hollander A. P., Huijing P. A. and van Ingen Schenau G. J.), pp. 99-106. Free Univ. Press, Amsterdam. Koolstra J. H., van Eijden T. M. G. J., Weijs W. A. and Naeije M. (1988b) A three-dimensional mathematical model of the human masticatory system predicting maximum nossible bite forces. J. Eiomechan. 21. 563-576. Kroemer K. H. E. and Marras W. S. (1980)‘Towards an objective assessment of the “maximal voluntary contraction” component in routine muscle strength measurements. Eur. J. appl. Physiol. 45, 1-9. MacKenna B. Rand Turker K. S. (1983) Jaw separation and maximum incising force. J. prosrhet. Dent. 49, 726-730. Manns A., Miralles R. and Palazzi C. (1979) EMG, bite force, and elongation of the masseter muscle under isometric voluntary contractions and variations of vertical dimension. J. prosthet. Dent. 42, 674-682. Mansour R. M. and Reynik R. J. (1975) In uivo occlusal forces and moments: 1. forces measured in terminal hinge position and associated moments. J. dent. Re.s. 54, 114120. Meller E. (1966) The chewing apparatus. Acra physiol. stand. 69, l-229. Pruim G. J., De Jongh H. J. and Ten Bosch J. J. (1980) Forces acting on the mandible during bilateral static bite at different bite force levels. J. Biomechan. 13, 755-763. Pruim G. J., Ten Bosch J. J. and De Jongh H. J. (1978) Jaw muscle EMG-activity and static loadine of the mandible. J. Biomechan. 11, 389-395. Ringqvist M. (1973) Fiber sizes of human masseter muscle in relation to bite force. J. Neurosci. 19, 297-305. Throckmorton G. S. (1985) Quantitative calculations of temporomandibular joint reaction forces-2. The importance of the direction of the jaw muscle forces. J. Biomechan. 18, 453-46 1. Weijs W. A. and Hillen B. (1984) Relationship between the physiological cross-section of the human jaw muscles and their cross-sectional area in computer tomograms. Acta anal. 118, 129-138.
Archs oral Biol. Vol. 36, No. 7, pp. 535-539,1991 Printed in Great Britain. All rights reserved
THREE-DIMENSIONAL ANALYSES OF HUMAN BITE-FORCE MAGNITUDE AND MOMENT T. M. G. J.
VAN
EIJDEN
Department of Functional Anatomy, Academic Center for Dentistry Amsterdam (ACTA), University of Amsterdam, 15 Meibergdreef, 1105 AZ Amsterdam, The Netherlands (Accepted
8 January
1991)
Summary-The effect of the three-dimensional orientation of occlusal force on maximal bite-force magnitude was examined in seven human subjects at three different unilateral anteroposterior bite positions (canine, second premolar and second molar). At each position, bite-force magnitude was registered in 17 precisely defined directions using a three-component force transducer and a feedback method. In addition, to assess the efficiency of transfer of muscle to bite force, for bites produced in the
sagittal plane, moment-arm length was determined and the produced bite-force moment calculated. The results showed that the largest possible bite force was not always produced in a direction perpendicular to the occlusal plane. Generally, maximal bite force in medial and posterior directions was larger than that in, respectively, corresponding lateral and anterior directions. In each direction the produced force was larger at the posterior bite point than at the anterior bite point. The combined moment produced by the jaw muscles was largest for vertical bites, smallest for posteriorly directed bites and intermediate for anteriorly directed bites. In the case of vertically and anteriorly directed bites the produced moment did not vary significantly with the bite position. Hence, for these bite positions the jaw closing moment of the muscles must have kept constant. In the case of posteriorly directed bites the produced moment decreased when bite position changed from the anterior to the posterior side of the dentition. This indicated that jaw muscle activity had declined. Key words: masticatory muscles, jaw mechanics, biomechanics bite force. occlusion.
INTRODUCTION
muscles of mastication have different orientations relative to the occlusal plane. The masseter and medial pterygoid exert a forward force and the posterior temporalis exerts a backward force on the mandible. The orientation of the anterior temporalis is close to perpendicular to this plane. Theoretically, this diversity enables the system to produce bite forces in different directions during a static bite. Koolstra et al. (1988b) recently explored the threedimensional directions in which bite forces can in theory be exerted. Although information is available on bite-force direction during voluntary maximal effort (Hylander, 1978) and on the direction of force exerted on the teeth during chewing (Graf, Grass1 and Aeberhard, 1974), no data exist on the relationship between bite-force direction and the maximal force humans are able to produce. In almost all bite-force studies, the bite force is restricted to a single vertical direction (Mansour and Reynik, 1975; Pruim, Ten Bosch and De Jongh, 1978; Fields et al., 1986). We earlier described a method for recording maximum bite forces in predefined directions (van Eijden et al., 1988b) and used it to describe changes in activity level of the jaw muscles as a function of change in bite-force magnitude in several specified directions (van Eijden et al., 1990) and of an alteration in bite point (van Eijden, 1990). We have now investigated the magnitude of maximum bite force in a number of directions. It has been claimed (Mansour and Reynik, 1975; Pruim, De The human
Jongh and Ten Bosch, 1980) that bite-force magnitude decreases at more anterior bite points. The lower force, registered at the anterior teeth, would be the result of (1) a longer resistance arm of the bite force in the lever system and/or (2) a lower level of activity of the jaw-closing muscles. In our experimental protocol, the position of the mandible relative to the skull was the same for the tested canine, secondpremolar and second-molar bites. Furthermore, if bite forces in different directions are exerted at a single bite point the resistance arm of the bite force (i.e. the perpendicular distance between temporomandibular joint and bite-force direction) varies. Our data can therefore test the hypothesis whether the total moment exerted by the jaw elevators is influenced by the location of the bite point and the direction of the bite force. Obviously, the conditions under which these muscles can exert the largest moments determine the optimal working conditions for the masticatory system. MATERIALS
AND METHODS
For a detailed description of the apparatus and the participating subjects we refer to van Eijden et al. (1988b) and van Eijden (1990) respectively. In brief, a three-component force transducer (24 x 24 x 10 mm, length x width x height) registered both the direction and magnitude of bite force in seven Caucasian males, age 31.1 f 4.9 yr (mean f SD). They had normal class I occlusions and showed no signs of craniomandibular dysfunction; most subjects were 535
536
T. M.G.J.
missing some of their third molars and two of them a lower left premolar. Placement of the transducer between occlusal clutches yielded an interincisal distance of 16 + 2.3 mm (mean + SD of the subjects). Forces were measured at the right-hand side of the dentition of the upper canine, second premolar and second molar. The degree of mouth opening was the same in the three bite positions. The upper occlusal clutch was kept parallel to the upper dentition. Hence, the distance between the transducer and the lower teeth was larger at the anterior side of the dentition than at the posterior side. If this distance becomes too large, medially directed bite forces pass outside the supporting element of the lower teeth, so that tilting of the transducer occurs. This was the case in two subjects for bite-force angles larger than 30” relative to the vertical. For this reason, bite-force directions exceeding an angle of 20” were not investigated. At each of the three bite positions, force was produced in 17 different directions, the vertical one (along the z-axis, i.e. perpendicular to the occlusal plane of the upper teeth) and 16 non-vertical ones. The direction of the non-vertical bites was defined with respect to the z-axis and the antero-posterior x-axis. The latter was oriented in a sagittal plane and was parallel to the upper occlusal plane. Eight directions were defined relative to the x-axis: anterior (angle relative to x-axis: 0’) antero-lateral (45”), lateral (go”), postero-lateral (135”), posterior (180”), postero-medial (225”), medial (270”) and anteromedial (315”). In each of these eight directions, two bite-force angles relative to the vertical z-axis were examined: 10” and 20”. Our feedback method was based on simultaneous visualization of both the actual and desired force direction on a computer screen (van Eijden et al., 1988b). The subjects made a maximal voluntary contraction in a particular direction. They were instructed to bite as hard as possible, keeping the direction of their actual bite force closely (within 53) matched to that of the desired force. They were not vocally encouraged. After each bite the transducer and clutches were removed for a rest period of at least 3 min. The sequence of the trials for the different bite points and force directions was chosen randomly. Measurements were made on three successive days, one for each bite point. After the experiment was completed (51 bites, 3 bite points x 17 directions), the entire procedure was repeated, with another randomized sequence. Hence, each subject produced two maximal bites per force direction. The output of the force transducer (three signals, one for each force component) was recorded on FM analogue tape and subsequently digitized (1000 samples/s/channel) using a DEC 1l/73 minicomputer system. By means of a computer program the magnitude of maximal bite force, averaged over an epoch of 0.5 s, was determined for each bite. Of the two available force values per direction, the larger one was chosen to calculate mean and SD of force over the 7 subjects. In addition, the difference between the two values, expressed as a percentage of their average, was also calculated. Mean value and SD of these differences were calculated for each bite point (n = 119, 7 subjects x 17 directions) and used as a
VAN
EIJDEN
measure for the repeatability of the results. Finally, an analysis of variance was used to test for the influence of bite-point location and bite-force direction on maximal bite-force magnitude. Calculations were done with the BMDP statistical package. To determine moment-arm length of bite forces produced in the sagittal plane, a routine orthodontic lateral cephalometrlc X-ray film (film-focus distance: 3.5 m) was made for each subject. From the closed jaw position on the film, the open position with the transducer and occlusal clutches in situ was reconstructed. Moment arm length was defined as the perpendicular distance between the temporomandibular contact point (i.e. point of shortest distance between condyle and articular eminence) and the bite-force vector. In addition, for each force direction the produced moment was determined by calculating the product of moment arm and measured bite force. RESULTS
The reproducibility of the measurements of the magnitude of the bite force was 9.4 f 10.1% (mean f SD) for the canine, 10.8 + 10.7% for the second premolar, and 10.4 f 12.5% for the second molar. The direction of bite force had no systematic effect on reproducibility. Of the two bite trials the magnitude of the second attempt was generally (in 80% of the bites) larger than that of the first. For each tooth and force direction, Table 1 gives mean + SD value of maximal bite force. Mean maximal bite-force magnitude ranged dependent on its direction between 323 and 485 N at the canine, 424 and 583 N at the second premolar and 475 and 749 N at the second molar. The analysis of variance demonstrated that both the bite position and force direction had a significant (p < 0.01) effect on maximal bite force magnitude. To visualize the results, a so-called bite-force envelope was constructed for each bite position (Koolstra et aZ., 1988b). This is a threedimensional shape created by connecting the far ends of the mean maximal bite-force vectors. The following points deserve special attention (see Table 1 and Fig. 1). First, for a particular direction, maximal bite force was largest at the second molar, smallest at the canine and intermediate at the second premolar. Bite-force magnitude at the second premolar and canine was on average (n = 17), 82.3 i 6.3% and 66.8 f 9.4%, respectively, of that produced at the second molar. The relative change in bite-force magnitude that occurred with a changing bite position was, broadly speaking, the same for the various bite-force directions. An exception was the 20” posteriorly directed bite where the force increase was smaller than 10%. Secondly, there was a clear relationship between bite-force direction and magnitude. On average, highest levels were attained in vertical, posterior and medial directions. Generally, an increase of bite-force angle relative to the vertical resulted in a decrease (maximally 35%) of bite-force magnitude. The direction of the largest possible bite force was slightly posterior at the anterior bite position (canine) and slightly medial at the posterior position (second molar).
Bite-force magnitude in three dimensions
537
Table 1. Mean maximal bite-force magnitude (N) for different bite positions and force directions Canine
!Gxond premolar
(mean f SD)
(mean f SD)
Second molar (mean f SD)
469*85 4llk83 358 f 81 434 f 72 381*64 430 f 83 393 f 52 448&78 386 f 51 485 f 93 481 f 93 465*82 336* 110 438 f 98 323 f 130 419 f 85 355*99
583*99 516 f 87 424*84 525 f 83 44Of83 525 f 72 454 f 67 536 f 81 446*71 579 f 103 523 f 77 561 f 126 498*113 575 f 133 496 f 84 529* 118 442* 100
723 f 138 652 f 132 503 f 150 690&97 536 f 142 66of 102 571 f 85 653k90 475 f 57 686&84 508 f 139 724 f 86 607*75 749 f 119 612f89 663 f 128 524f 111
Bite force direction Vertical Anterior (10’) Anterior (20”) Antero-lateral (10”) Antero-lateral (20”) Lateral (lo”) Lateral (20”) Postero-lateral (10’) Postero-lateral (20”) Posterior (lo”) Posterior (20”) Postero-medial (10”) Postero-medial (20”) Medial (10”) Medial (20”) Antero-medial (10”) Antero-medial (20”)
Vertical: force perpendicular to the occlusal plane of the upper teeth, anterior, posterior, etc.: direction relative to the antero-posterior x-axis; 10” and 20”: angle relative to the vertical.
The lengths of the moment arms of the bite forces produced in the sagittal plane are given in Fig. 2. It should be realized that the larger the moment arm, the smaller the efficiency of transfer of muscle to bite force. For all directions the moment arm increased from posterior to anterior bite points. Anteriorly directed bite forces had the largest moment arms. The difference in moment-arm length between 20” anteriorly and 20” posteriorly directed
n P2
bites was about 2Scm, irrespective of the bite point. The produced bite-force moments are given in Fig. 3. Generally, largest moments were produced by vertical forces. An increase of the bite-force angle coincided with a decrease of the bite-force moment. The decrease was more obvious for posteriorly than for anteriorly directed bites. Note that for a particular bite-force direction the produced moments
I Ca
Fig. 1. Bite-force envelopes for each of the investigated bite positions. Top row: lateral views, bottom row: frontal views. The line intersections indicate the mean maximal bite forces. A : origin of bite force vectors; *: end-point of maximal bite-force vector perpendicular to the occlusal plane of the upper teeth. C!az canine, P2: second premolar, M2: second molar. Vertical bar: lOON.
538
T. M. G. J.
post (20”)
post (IO”)
vert (0”)
ant (IO”)
Bite-Force
ant (20”)
Direction
Fig. 2. Mean moment-arm length (small black bars: standard deviations) of bite forces produced in the sagittal plane at different teeth. Ca: canine (obliquely dashed bars); P2:
second premolar (vertically dashed bars); M2: second molar; post: posterior bite-force direction; vert: vertical; ant: anterior; lo” and 20”: angle relative to the vertical (0”).
differed only slightly between the bite points. An exception to this was the 20” posteriorly directed bite, where the moment at the second molar was consideraly smaller than the one produced at the other teeth. DISCUSSION For a given bite-point and bite-force direction the maximum force. showed marked interindividual variability. Causes of this variability can be (1) variability in the strength of the jaw muscles, due to differences in cross-sectional area (Weijs and Hillen, 1984) and/or fibre-type composition (Ringqvist, 1973); (2) variability in moment-arm length of individual jaw muscles (Throckmorton, 1985; Koolstra, van Eijden and Weijs, 1988a) and/or resistance-arm length of bite force (van Eijden et al., 1988a); and (3) factors
post (200)
post (10”)
vert (0”) Bite-gorce
ant (10”)
ant (20°)
Direction
Fig. 3. Mean moment (moment arm x bite force) of bite forces produced in the sagittal plane. Same symbols as in Fig. 2.
VAN EIJDEN
associated with voluntary or reflex inhibition of full recruitment (Kroemer and Marras, 1980). Anatomical differences probably underlie the observed differences in maximal bite force between long- and short-faced persons (Ingervall and Helkimo, 1978). In our experiments another factor might have affected interindividual variability, namely the differences between subjects in the separation between the teeth, necessary to accommodate the transducer and splints. This might have affected bite-force magnitude via the length-tension relationships of the muscles and via differential changes in their lines of action (Koolstra et al., 1988b). Manns, Miralles and Palazzi (1979) and MacKenna and Turker (1983) demonstrated that bite force is the largest at an interincisal distance of 15-20 mm, about the same range in which the present registrations were carried out. Our study has shown that the total moment of the bite force, which is equal and opposite to the one produced by jaw muscles, is not constant, but depends on bite-point location and bite-force direction. It appeared that the produced moment in the sagittal plane, and hence the mechanical effect of the combined musculature, was largest in vertically, intermediate in anteriorly and smallest in posteriorly directed bites. From anteriorly to vertically to posteriorly directed bites the resistance arm of the bite force decreased. However, to produce a force in the desired direction, the jaw muscles must exert forces that approximate that direction, The final moment is determined by the extent to which the different jaw muscles participate in generating the desired bite force. As the majority of muscles have a large vertical component, the moment is largest for vertical bite forces. The second largest force component is the anterior one, and the smallest force can be generated in posterior direction (only the posterior temporalis). Consequently, the number of muscles participating in generating a moment decreases from vertically, to anteriorly to posteriorly directed bites, and this is seen for the moments. Despite this, the bite force in a posterior direction is larger than in an anterior direction. This is the direct result of the small resistance arm of the posteriorly directed bite force and thus the more efficient transfer of muscle to bite force. Our findings are that the largest possible bite force was not necessarily produced in a direction perpendicular to the occlusal plane. Koolstra et al. (1988b) found that posteriorly and medially directed forces generally reach higher values than, respectively, anteriorly and laterally directed forces. This is in agreement with our experimental results. The produced force in a particular direction was always larger at the posterior side of the dentition than at the anterior side. As far as vertical bite forces are concerned, this agrees with the findings of Pruim et al. (1980) and Mansour and Reynik (1975). In contrast to Mansour and Reynik (1975), we found that the location of the bite point had almost no effect upon the exerted moment if the bite force was vertically or anteriorly directed. In our experimental set-up the mandible does not have to change position if the bite point is changed. It must be concluded that the decrease in muscle moment in vertical bites as observed by Mansour and Reynik
Bite-force magnitude in three dimensions
was a result of the change in mandibular position, possibly effected by changed muscle length. The often described (Msller, 1966) decreased activity of the anterior temporalis muscle did not occur in our experiments (van Eijden, 1990). However, for posteriorly directed bites a marked decrease in moment with a shift in bite point from canine to second molar was indeed observed. We have demonstrated earlier (van Eijden, 1990) that this must be caused by a decrease of the activity of the posterior temporalis muscle. A cause or a functional explanation for this behaviour is still lacking. Acknowledgements-I am indebted to Dr W. A. Weijs for his comments on the manuscript, to J. Ferwerda and P. Brugman for technical assistance, to A. van HorssenMedema and C. J. Hersbach for the illustrations and photography, and to H. Rollernan-ter Heurne for preparing the manuscript.
REFERENCES
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