AMERICAN JOURNAL OF PHYSICAL ANTHROPOLOGY 80:429-445 (1989)

Relationships Between the Size and Spatial Morphology of Human Masseter and Medial Pterygoid Muscles, the Craniofacial Skeleton, and Biomechanics

A.G. HANNAM AND W.W. WOOD Faculty of Dentistry, The Uniuersity of British Columbia, Vancouuer, British Columbia, Canada V6T 127 KEY WORDS Jaw muscles, Cross-sectional area, Muscle angula- tion, Bite force

ABSTRACT The relationship between human craniofacial morphology and the biomechanical efficiency of bite force generation in widely varying muscular and skeletal types is unknown. To address this problem, we selected 22 subjects with different facial morphologies and used magnetic resonance imaging, cephalometric radiography, and data from dental casts to reconstruct their craniofacial tissues in three dimensions. Conventional cephalometric analyses were carried out, and the cross-sectional sizes of the masseter and medial pterygoid muscles were measured from reconstituted sections. The potential abilities of the muscles to generate bite forces at the molar teeth and mandibular condyles were calculated according to static equilibrium theory using muscle, first molar, and condylar moment arms. On average, the was about 66% larger in cross section than the medial pterygoid and was inclined more anteriorly relative to the functional occlusal plane. There was a significant positive correlation (P < 0.01) between the cross-sectional areas of the masseter and medial pterygoid muscles (r = 0.75) and between the bizygomatic arch width and masseter cross-sectional area (r = 0.56) and medial pterygoid cross-sectional area (r = 0.69). The masseter muscle was always a more efficient producer of vertically oriented bite force than the medial pterygoid. Putative bite force from the medial pterygoid muscle alone correlated positively with mandibular length and inversely with upper face height. When muscle and tooth moment arms were considered together, a system efficient at producing force on the first molar was statisti- cally associated with a face having a large intergonial width, small intercondy- lar width, narrow dental arch, forward maxilla, and forward . There was no significant correlation between muscle cross-sectional areas and their respective putative bite forces. This suggests that there is no simple relation- ship between the tension-generating capacity of the muscles and their me- chanical efficiency as described by their spatial arrangement. The study shows that in a modern human population so many combinations of biomechanically relevant variables are possible that subjects cannot easily be placed into ideal or nonideal categories for producing molar force. Our findings also confirm the impression that similar bite-force efficiencies can be found in subjects with disparate facial features.

Received June 27,1988; accepted November 16,1988.

@ 1989 ALAN R. LISS, INC. 430 A.G. HA"AM AND W.W. WOOD During chewing and tooth clenching in the force is greatest in the same facial types primate, muscle forces are resisted both at (Ringqvist, 1973; Proffit and Fields, 1983). the bite point and at the temporomandibular However, the degree of activity recorded articulations (Hylander, 1975, 1985a). Re- from a muscle may reflect both its absolute cent observations from mathematical mod- size and its mechanical efficiency for the els simulating jaw biomechanics indicate task at hand. Whereas a high level of activity that muscle cross-sectional sizes and pat- might be expected from a large muscle mass, terns of activation, as well as the moment a low recorded level is more ambiguous in arms ofmuscles, bite points, and mandibular that it may be generated either by a small condyles, are the major determinants of bite muscle mass or by a lessened need to activate and articular forces (Nelson and Hannam, a large one. Both factors may vary from 1982, 1983, 1986; Osborn and Baragar, subject to subject since they are related to 1985; Smith et al., 1986; Hatcheret al., 1986; morphology. Throckmorton and Throckmorton, 1985; Muscle moment arms almost certainly dif- Throckmorton, 1985; Nelson, 1986; Iwasaki, fer between subjects, but data describing 1987; Baragar and Osborn, 1987; Faulkner human jaw muscle locations and angula- et al., 1987; Koolstra et al., 1988). Since tions are sparse and at best inferential. modern human populations show consider- When individuals with hyperdivergent able diversity in craniofacial form (Solow, are viewed laterally, their masseter muscles 1966; Brown et al., 1965; Bjork, 1963; Cleall appear more vertically inclined to the man- et al., 1979; Anderson and Popovitch, 19831, dibular plane than normal; and, as the man- corresponding variations in some or all of dibular plane becomes steeper, the muscles' these determinants of tooth and articular angulations relative to the porion-orbitale forces are likely. It also seems theoretically (Frankfort horizontal) plane and sella-na- possible for subjects with apparently differ- sion line become more acute (Proctor and De ent craniofacial morphologies to function Vincenzo, 1970; Tetz, 1983). The masseter with equal biomechanical efficiency pro- and medial pterygoid muscles insert more vided the correct combinations of determi- posteriorly on the mandibular corpus and nant variables exist. Here, a recent demon- more superiorly on the ramus in these sub- stration of comparable jaw mechanics in jects (Horaist, 1974). Radiographic land- dolichocephalic and brachycephalic subjects marks assumed to represent muscle attach- (Iwasaki, 1987) is pertinent. ments in subjects with short posterior facial Jaw muscle cross-sectional sizes have heights, steep mandibular planes, and large been shown to alter with skeletal shape gonial angles suggest that they have mas- (Weijs and Hillen, 198413, 1986). Temporal seter muscles with a more superior insertion and masseter cross-sectional areas increase on the mandibular ramus than normal with facial width; those of the masseter and (Takada et al., 1984). Whether masseter pterygoid muscles increase with mandibular muscle angulation is constant relative to the length (Weijs and Hillen, 1986). These rela- occlusal plane is controversial. Some con- tionships are independent of a general size sider this to be so (Proctor and De Vincenzo, effect, and their specificity argues for differ- 1970), but others suggest that the masseter ences in the tension-generating capacities of muscle is more anteriorly inclined relative to muscles according to facial type. the occlusal plane in subjects with short Muscle use may differ between subjects posterior facial heights, steep mandibular apparently performing similar chewing and planes, and large gonial angles (Takada et clenching tasks (Moller, 1966; Hannam and al., 1984). Wood, 1981; MacDonald and Hannam, It is difficult to explain how the major 1984a,b;Wood et al., 1986; Wood, 1986; Ma- determinants of tooth and articular forces han et al., 19831, and distinct patterns of interact in living subjects with different fa- muscle contraction have been correlated cial morphologies. Many combinations of with facial morphology (Moller, 1966; Inger- muscle cross-sectional sizes and muscle, Val1 and Thilander, 1974; Lowe and Takada, tooth, and articular moment arms are possi- 1984). For example, jaw closing muscle activ- ble, especially when these are considered in ity is greatest in subjects with long posterior three dimensions of space. It is equally un- facial heights, short anterior facial heights, certain whether muscle cross-sectional sizes long , flat mandibular planes, and vary predictably with given combinations of small gonial angles (Moller, 1966; Ingervall moment arms and whether these biome- and Thilander, 1974; Tabe, 19761, and bite chanical variables correlate in any way with RELATIONSHIPS IN JAW BIOMECHANICS 43 1 conventional measures of craniofacial form. In each subject, MR images were obtained To address these problems, we combined by means of a 0.15T superconducting scan- data from magnetic resonance (MR) images, ner (Picker Vista MR1100). Spin-echo se- dental casts, and cephalometric radiographs quences were used with an echo time of 40 in living subjects with different craniofacial msec and repetition times ranging from 1.5 morphologies. We used three-dimensional to 3 sec. Sixteen contiguous sections spaced reconstructions to measure masseter and approximately 9 mm apart were sampled in medial pterygoid muscle cross-sectional ar- both the axial and coronal planes. In the eas and relevant moment arms and carried axial plane, four sections lay rostral to the out a biomechanical assessment of the tooth porion-orbitale (Frankfort horizontal) plane, and articular force-generating capacities of one passed throughit, and 11 lay caudal to it. the two muscles. In the coronal plane, four sections lay dorsal to an orthogonal plane passing through the MATERIALS AND METHODS centers of the mandibular condyles, one Our sample consisted of 22 fully dentate passed through it, and 11 lay ventral to it. adults between 22 and 48 years of age. It Figure 1 shows typical axial and coronal included 16 males and six females, with sections depicting the masseter and medial different facial characteristics. Two females pterygoid muscles, mandibular condyles, were identical twins. and maxillary teeth. Differences in head size

Fig. 1. MR images representative of those used to reveal the craniofacial tissues, with arrows indicating the relevant structures. The axial section at the level of the maxillary tooth crowns (top left) shows the masseter and medial pterygoid muscles, and that at the level of the mandibular condyles (top right) shows a condylar head. The coronal section at the level of the mandibular coronoid notch (bottom left) shows the masseter and rostral part of the medial pterygoid muscles, and that at the level of the mandibular condyles (bottom right) shows a condylar head. 432 A.G. HA"AM AND W.W. WOOD and practical limitations in head positioning known distances from both tube and film. sometimes limited the numbers of coronal Cephalometric data were merged with the sections obtained. We imaged only those reconstructed MR data so that, viewed sagit- muscles mainly responsible for generating tally, they were superimposed at the same bite force near the first molars, and excluded scale. Selected conventional linear and an- the because, like others, we gular cephalometric variables were then found its angulation and cross-sectional size measured according to criteria and defini- difficult to measure with confidence (Weijs tions described by Lowe (1980). In confor- and Hillen, 1984a). Whatever the plane of mity with his abbreviations, the anterior section employed, the fan shape of the tem- position of the maxilla was defined by the poral muscle and its variation in thickness angle SNA, anterior position of the mandible mediolaterally made calculations unreli- by the angle SNB, relative mandibular prog- able. We also chose to analyze data from nathism by the angle ANB, gonial angle by right-sided muscles only because we had no the lower border of the mandible and the reason to believe, a priori, that there would posterior border of the ramus, palatal angle be any consistent trends in the data from by the lines ANS-PNS and SN, mandibular sidedness alone. Accordingly, sections that plane angle by the lower border of the man- included details of the right masseter and dible and the line SN, ramus height by the medial pterygoid muscles, their sites of at- distance from the superior condylar point to tachment, the right and left mandibular gonion measured perpendicular to the line condyles, and the right and left first molar SN, mandibular length by the linear dis- teeth were selected for analysis. Other struc- tance from the midcondylar point to pogo- tures were included to assist orientation and nion, upper face height by the linear distance reconstruction of the data. between nasion and a projection from ANS Acetate overlays were used to trace the along a perpendicular to the nasion menton relevant outlines, which were verified by a line, and lower face height by the linear second investigator. Calibration bars on distance between menton and the same pro- each section were used to reference a given jection of ANS. Additionally, from the com- series of sections to a common origin. All bined cephalometric and MR data, bizygo- tracings were then digitized by means of a matic width was measured as the largest computer system capable of rotational distance between the zygomatic arches in graphics (Hewlett-Packard lOOOE and pe- the coronal plane, bigonial width as the dis- ripherals). Digitizing was carried out with a tance between the gonions, and intercondy- resolution of one point per 0.3 mm on the lar width as the distance between the centres original tracing, and from these data 50 of the condyles viewed coronally. points were selected to describe the bound- Dental casts of the maxillary and mandib- ary of each structure excepting the teeth, ular teeth were also made for each subject. which were represented by 10 points each. The locations of all cusp tips making contact All data were coded numerically and by color with opposing teeth when the dental arches according to the structures they represented were positioned in the maximum intercuspal and arranged within a common three-dimen- position, as well as the centers of the incisal sional coordinate system. Graphics software edges of all anterior teeth, were digitized permitted retrieval of individual sections, three-dimensionally by means of an optical assembly of a series of sections in any combi- system (Takada et al., 1983). Data were nation, and their graphical representation in rotated and merged so that points represent- three dimensions. It included an interactive ing discrete contacts between the occluded cursor for retrieving the spatial coordinates teeth superimposed at the same scale on of any points of interest. both the MR and the cephalometric images. A lateral cephalometric radiograph of each Thus the dental cast data could be rotated subject was taken to permit comparisons of and displayed with the MR images in any our sample with those of others. Conven- plane. Figure 2 shows computer reconstruc- tional skeletal orthodontic landmarks were tions viewed sagittally, coronally, and axi- traced from each film, digitized, and scaled ally. The reconstructions include the mandi- to allow for X-ray beam divergence. During ble and the condyles, the right masseter and scaling, the assumption was made that the medial pterygoid muscles, a superimposed traced images lay on a midline plane passing cephalometric tracing, and tooth cusp tips. through the center of the cephalostat at Combining data from several sources made RELATIONSHIPS IN JAW BIOMECHANICS 433

0

** I* L1 %

Fig. 2. Three-dimensional computer reconstructions of craniofacial morphology. A sagittal view of the mandible is shown at the top left and a similar view of the masseter muscle at the top right. In each, the corresponding cephalometric tracing and maxillary and mandibular cusp tips digitized from dental casts have been superimposed. The coronal view (bottom left) includes the right masseter and medial pterygoid muscles, the left condyle and mandible, and the cusp tips. The axial view from below (bottom right) includes the right masseter and medial pterygoid muscles, right and left condylar heads, left mandible, and cusp tips. The calibration bar represents 2 cm. All data are from the same subject. it possible to obtain the best possible resolu- even thickness. The superimposed sections tion for each feature being measured and provided reconstructions of muscle borders, provided an internal calibration for each which were regular enough to permit linear reconstruction. Thus we defined a “func- approximations of their slopes both sagit- tional’’ occlusal plane (FOP), described by tally and frontally. These slopes were consid- contacts between the cusps of the second ered representative for the muscle as a premolar and first and second molar teeth whole and were used to define a hypothetical and measured the first molar arch width, three-dimensional resultant, which passed defined as the distance between the mesio- through the muscle’s geometric center. Sin- palatal cusps of the maxillary first molars. gle vectors positioned and aligned in three We considered our definition of the occlusal dimensions of space therefore described the plane to be more truly representative of a masseter and medial pterygoid muscles of resistance plane related to bite force in the each subject (Fig. 3). These vectors were region of the first molars than the one con- used for two purposes: first, to help estimate ventionally used in cephalometric analyses the cross-sectional areas of the muscles; sec- since the latter is partly defined by the inci- ond, to calculate muscle moment arms dur- sor teeth. ing the analysis of jaw mechanics. A given muscle was usually defined by Human jaw muscles present special prob- four or five sections in each plane. By means lems when efforts are made to measure their of the graphics cursor, it was possible to true anatomical cross sections with imaging determine its geometric center with reason- devices. Although a given plane of section able accuracy because both muscles were may be appropriate for one muscle, it is essentially quadrate in form and of fairly inappropriate for another. It is possible to 434 A.G. HA”AM AND W.W. WOOD

select more than one imaging plane, but, unless this is done for every muscle in every subject, cross-sectional area calculations are erroneous (Weijs and Hillen, 1984a). To overcome the problem, we reconstructed the R. MASSETER surface outline of each muscle in three di- mensions, used its central vector as a mea- sure of its orientation in space, and resec- tioned the reconstruction perpendicular to this line of orientation. This was done by - F.H. arranging the 50 points outlining each axial section of a muscle to common polar coordi- SAGITTAL CORONAL nates. Corresponding points in the four cen- tral sections of each muscle were joined to provide a surface representation of its cen- tral region. A program then determined the points of intersection between this surface R. MEDIAL and a new plane of section chosen to pass PTERYGOID through the muscle’s center point perpendic- ular to the muscle’s long axis (Fig. 4). The area of the planar figure described by these intercepts was considered the true cross- Fig. 3. Vectorsdrawn through the centers of the right sectional area of the muscle independent of masseter and medial pterygoid muscles viewed both sagittally and coronally. Each vector is further described its spatial orientation. Tests of the method by its angulations relative to the Frankfort horizontal carried out with rectangular objects of com- plane (the plane of section) and the muscle center (solid parable size sectioned at 30” to their long arrow origins).

z/

Fig. 4. Derivation of the cross-sectionalarea of a muscle. Four contiguous axial sections (stippled) were joined by lines connecting each of 50 equally spaced points on the perimeter of each section. A new plane passing through the center point of the muscle and perpendicular to its long axis intersected these lines to form the perimeter of the reconstructed area used for measurement. RELATIONSHIPS IN JAW BIOMECHANICS 435 axes revealed estimation errors of less than sion produced by the muscle. Thus a mas- 3% of the true cross-sectional areas. seter muscle assumed to be acting alone with To calculate the theoretical molar and ar- a tension of 10 arbitrary units might typi- ticular forces that could be produced by each cally produce a compressive force of 6.4 units muscle in each subject, we used static equi- on the right molar; a compressive force of 4.4 librium theory according to principles previ- units on the ipsilateral, working-side man- ously described by others (Weijs and Dan- dibular condyle; and a distractive force of tuma, 1981; Osborn and Baragar, 1985; 5.6 units on the contralateral, balancing Hatcher et al., 1986; Smith et al., 1986; condyle. Note that the sum of the units rep- Nelson, 1986; Koolstra et al., 1988). We as- resenting the magnitudes of the tooth and sumed that under isometric or near- condylar reaction forces does not equal the isometric conditions of jaw muscle function, assigned muscle tension. This is because the all forces applied to the mandible were in force vectors are not parallel; the muscle static balance, so that the sums of all mo- vector, for example, is oriented differently ments and forces were zero irrespective of from the tooth force vector. However, when the viewing plane. Each muscle was treated the components of all the resultants involved as an independent case and was initially are expressed in three orthogonal planes, the assigned an arbitrary tension vector of 10 sum of all forces and the sum of their mo- units. Tooth resistance forces were consid- ments are zero. ered possible at two independent sites lo- The contribution of each muscle to tooth cated at either the right or the left first and articular forces was first assessed inde- molar. Compressive (positive) forces at both pendently of muscle size, each calculation sites on the tooth row were considered to be being determined entirely by the three-di- aligned perpendicular, in three dimensions, mensional spatial configuration of the struc- to the FOP in that region. Compressive (pos- tures involved. However, we also wished to itive) or distractive (negative) forces were observe the effect of individual variations in assumed to be possible at both condylar muscle size on this relationship. Therefore, sites. in a separate step, we normalized each mus- The indeterminate nature of the distribu- cle cross section to the mean for the group tion of lateral components of force between and used these relative values to scale the 10 the two mandibular condyles has been de- units initially assigned to each muscle. Bite scribed by others (Weijs and Dantuma, 1981; and articular forces were then recalculated Smith et al., 1986; Nelson, 1986) and is due as before, this time involving muscle values to the coaxial nature of the condyles when that reflected proportional muscle cross-sec- viewed in the lateral plane. In some studies, tional sizes. this problem has been overcome by arbi- Product moment correlations were calcu- trarily distributing the total lateral compo- lated between muscle cross-sectional areas, nent of articular force (which is calculable) muscle and first molar moment arms, puta- evenly between both condyles (Faulkner et tive bite forces, and selected skeletal vari- al., 1987; Koolstra et al., 1988). In our calcu- ables. Subsequently, stepwise multiple re- lations, we assumed that forces on the left gression was used to estimate significant condyle were always resisted perpendicular correlations, with ct set at 0.05 to enter and to the FOP when viewed coronally. This remove variables. This was followed by an approach supposed that the floor of the left analysis of variance. glenoid fossa was flat mediolaterally. No other angular constraints were placed on RESULTS condylar resistance forces, nor indeed was Descriptive statistics for all skeletal and this possible, since such a procedure would dental measurements are found in Table 1. have overconstrained the number of un- These include mean values, standard devia- known variables that required solution. For tions, and ranges of the variables. mathematical convenience in these calcula- Skeletally, our sample appeared to be typ- tions, the center of the right condyle was ical of an adult modern human population. selected as the point about which all mo- Of the 14 variables we chose to describe the ments were calculated. In this way, it was sample, eight were identical to, and there- possible to describe the contribution of each fore directly comparable with, those re- individual muscle to any bite point as well as ported by Weijs and Hillen (1986).Their data both articular forces and to express these are provided in parentheses in Table 1. Our forces as a proportion of the theoretical ten- mean values for bizygomatic width, bigonial 436 A.G. HA"AM AND W.W. WOOD width, anterior position of the maxilla, ante- parenthesis. There is a mean discrepancy of rior position of the mandible, gonial angle, about 1 cm between these two linear dis- palatal plane angle, mandibular plane an- tances. gle, and mandibular length, and the ranges The cross-sectional areas of both muscles, of these values, were similar to theirs, al- including means and standard deviations for though our sample showed a greater vari- the sample, are shown in Table 2. The mean ance. A further measurement in our study, cross-sectional area of the masseter muscle ramus height, was made from the most supe- was 5.76 k 1.11 cm', with a range of rior point on the mandibular condyle to go- 3.57-7.89 cm'. That of the medial pterygoid nion. A comparable but different measure- muscle was 3.48 ? 0.88 cm', with a range of ment was made from articulare to gonion by 2.01-4.90 cm'. The masseter muscles were Weijs and Hillen (1986) and is also shown in thus about 66% larger in cross section than

TABLE 1. Skeletal parameters for the 22 subjects (comparable data from Weijs and Hillen [I9861 in parenthesis; units are mm and degrees) Mean S.D. Min Max Bizygomatic width 133.6 (139.7) 7.70 (4.8) 119.7 (129) 147.4 (149) Bigonial width 97.0 (106.1) 8.10 (5.8) 82.4 (94) 118.6 (119) Intercondylar width 102.6 7.22 89.4 116 Anterior position of maxilla 82.8 (82.8) 5.22 (3.50) 76.2 (74.4) 98.3' (90.7) Anterior position of mandible 80.4 (79.6) 5.72 (3.80) 71.8 (71.5) 97.9" (88.9) Relative mandibular prognathism 2.4 2.38 -1.3 8.6' Gonial angle 125.1 (125.6) 7.42 (4.00) 112.6 (117.8) 139.1" (133.0) Palatal angle 7.5 (6.8) 4.29 (3.4) 0.1 (0.4) 13.9" (15.6) Mandibular plane angle 30.4 (24.0) 6.83 (5.3) 20.1 (12.4) 43.4' (35.6) Ramus height 64.7 (53.3) 5.77 (4.70) 50.7 (40) 75.4 (62) Mandibular length 83.3 (80.6) 5.68 (4.3) 74.5 (71) 95.5 (93) Umer face height 55.7 3.56 47.3 61.5 Lower face height 71.0 5.85 59.7 83.0 First molar arch width 41.5 4.80 30.5 53.1

TABLE 2. Muscle aneles fdeerees relatiue to FOP) and cross-sectional areas fern') Masseter Medial pterygoid Sagittal Coronal Cross-sectional Sagittal Coronal Cross-sectional Subject angle angle area angle angle area 01 77 98 6.03 84 63 4.10 02 78 99 6.04 84 72 3.86 03 69 99 7.89 67 49 4.86 04 70 98 5.47 71 65 4.58 05 80 102 5.44 85 70 3.48 06 73 107 7.55 83 56 4.07 07 69 107 6.84 87 56 4.90 08 67 95 6.95 61 57 4.71 09 88 103 7.39 67 58 3.91 10 84 106 5.24 82 71 2.58 11 73 103 5.81 79 62 3.25 12 70 104 5.58 73 62 3.81 13 75 98 4.91 74 57 2.92 14 75 101 5.44 95 54 3.09 15 71 97 4.81 82 53 2.01 16 76 103 4.47 83 56 2.31 17 78 100 5.68 88 69 4.00 18 78 99 3.57 80 48 2.29 19 63 97 4.36 75 70 3.32 20 76 95 4.68 80 54 2.50 21 72 100 5.93 77 51 2.57 22 74 95 6.70 99 61 3.38 Mean 74 100 5.76 80 60 3.48 S.D. 6 4 1.11 9 7 0.88 RELATIONSHIPS IN JAW BIOMECHANICS 437 the medial pterygoid muscles for the sample pterygoid muscles with almost equal cross- as a whole. There was a significant positive sectional areas. These atypical muscle sizes correlation (r = 0.75) between the sizes ofthe did not result from consistent undersizing or two muscles (P< 0.01).However, some nota- oversizing of one muscle relative to the other. ble variations in proportional muscle size For example, two subjects had medial ptery- were observed from subject to subject, and goid cross-sectional sizes that were almost these are evident as deviations from the equal at 3.3 and 3.4 cm2 but differing mas- regression line in Figure 5. Occasionally, seter sizes of 4.4 and 6.7 cm2, respectively; subjects demonstrated masseter and medial another two had masseter cross-sectional sizes of 5.5 and 5.9 cm2 but medial ptewgoid

o.1006 + o.586x R = 0.74 medially (60" k 7.30). In both planes, medial pterygoid muscle angulations varied more

the medial pt

TABLE 3. Moment arm lengths (mm)from the center of the right condyle Masseter Masseter Medial pterygoid Medial pterygoid Right molar Right molar Subject lateral coronal lateral coronal lateral coronal 01 34.4 3.4 26.2 34.5 61.3 32.2 02 36.2 4.6 28.9 33.9 58.7 33.0 03 29.0 7.1 17.6 31.0 49.8 23.7 04 32.9 7.5 26.8 31.4 54.8 31.6 05 35.8 6.3 23.8 33.3 61.6 35.6 06 37.9 8.3 22.1 33.8 56.9 38.5 07 39.2 2.4 21.0 37.8 57.2 44.1 08 44.2 7.8 34.1 33.5 59.8 32.2 09 34.8 6.9 32.7 35.6 58.5 32.2 10 29.0 15.9 21.4 23.1 54.4 24.3 11 36.5 0.9 24.0 35.6 61.7 35.0 12 39.1 7.6 24.8 35.6 53.3 35.6 13 32.7 4.1 24.0 37.3 50.6 36.7 14 44.2 13.1 26.0 24.8 57.3 31.1 15 35.7 0.0 23.0 28.5 53.2 31.0 16 33.7 2.3 20.8 33.1 50.0 30.5 17 42.7 5.9 25.7 33.9 63.8 31.1 18 33.3 8.0 21.6 37.8 50.0 32.7 19 45.6 2.6 31.2 32.4 60.1 32.7 20 32.5 5.2 22.7 43.0 49.7 40.7 21 30.3 8.1 22.1 38.4 60.6 28.2 22 44.1 3.2 15.1 34.6 60.7 33.3 Mean 36.5 6.0 24.4 33.8 56.6 33.0 sn 52 3.7 4.6 4.4 4.6 4.6 438 A.G. HA”AM AND W.W. WOOD Viewed sagittally, the first molar moment 0.5 units and the mean compressive force on arms were longest, followed by those of the the ipsilateral condyle was 6.3 2 0.6 units. masseter and medial pterygoid muscles. On When the bite point was contralateral to this average, masseter moment arms were 50% muscle, the mean distractive force on the longer than the medial pterygoid moment contralateral condyle was 5.1 t 0.7 units and arms. Viewed coronally, right molar and me- the mean compressive force on the ipsilat- dial pterygoid moment arms were almost eral condyle was 8.7 k 0.6 units (Table 4). identical and showed a significant (P< 0.01) For the medial pterygoid muscle, forces on positive correlation (r = 0.64). both condyles were always positive (com- Estimations of putative first molar bite pressive). When the bite point was ipsilat- forces and corresponding articular forces eral to the muscle, the mean compressive from the isolated contributions of the mas- force on the contralateral condyle was 2.1 t seter and medial pterygoid muscles are 0.4 units and the mean compressive force on found in Tables 4 and 5, respectively. Mean the ipsilateral condyle was 6.2 5 0.7 units. values, standard deviations, and ranges are When the bite point was contralateral to the given for first molar bite points on sides muscle, the mean compressive force on the ipsilateral and contralateral to the muscle contralateral condyle was 0.5 rfi 1.0 units and involved. The masseter was always a more the mean compressive force on the ipsilat- efficient producer of bite force than the me- eral condyle was 7.0 * 0.4 units, (Table 5). dial pterygoid muscle because of its longer Product moment correlation coefficients moment arm. For biting on the ipsilateral between skeletal variables and masseter side, the mean putative bite force from the and medial pterygoid muscle cross-sectional masseter acting alone was 6.4 i 0.8 units areas and muscle and tooth moment arms, (range 4.9-7.61, whereas it was only 3.7 rfi 0.7 and the putative tooth forces generated by units (range 2.24.9) for the medial ptery- these muscles, are presented in Table 6. goid muscle. This difference was statistically There were significant correlations (P < significant (P < 0.01). 0.01) between masseter muscle cross-sec- Forces on the condyles also reflected the tional area and bizygomatic arch width (r = effect each muscle would have had had it 0.56) and between medial pterygoid cross- acted alone. For the masseter muscle, forces sectional area and bizygomatic arch width (r on the balancing condyle contralateral to the = 0.69). Stepwise multiple regression at the muscle were always negative (distractive) 0.05 level of significance failed to reveal any and forces on the working side ipsilateral to other contribution from skeletal variables to the muscle were always positive (compres- the variance of the cross-sectional areas. sive). When the bite point was ipsilateral to There was a significant correlation (P < the masseter muscle, the mean distractive 0.01) between the masseter sagittal moment force on the contralateral condyle was 2.6 2 arm and both intergonial width (r = 0.62)

TABLE 4. First molar bite force and condylar reaction forces generated by 10 units of right masseter muscle force Mean S.D. Min Max Bite force 6.4 0.8 4.9 7.6 Right condylar force (right molar bite) 6.3 0.6 5.5 8.1 Left condylar force (right molar bite) -2.6 0.5 -3.6 -1.5 Right condylar force (left molar bite) 8.7 0.6 7.9 10.4 Left condylar force (left molar bite) -5.1 0.7 -6.7 -3.4

TABLE 5. First molar bite force and condylar reaction forces generated by 10 units of right medial pterygoid muscle force Mean S.D. Min Max Bite force 3.8 0.7 2.2 4.9 Right condylar force (right molar bite) 6.2 0.7 4.6 7.2 Left condylar force (right molar bite) 2.1 0.4 1.3 2.5 Right condylar force (left molar bite) 7.0 0.4 6.2 7.7 Left condylar force (left molar bite) 0.5 1.o -1.8 1.9 RELATIONSHIPS IN JAW BIOMECHANICS 439

TABLE 6. Correlations between skull variables and muscle cross-sectional areas, muscle moment arms, tooth moment arms, and putative bite forces' Cross-sectional Moment arms Rieht molar areas bite forces _____ Mass Mass Med Pt MedPt RMol RMol _____ Mass Med Pt. (Sag) (Cor) (Sag) (Cor) (Sag) (Cor) Mass Med Pt. Bizygomatic width .56** .69** .47 .09 31 .12 .62 .24 .I1 .16 Bigonial width .44 .56 .a** .14 .35 .04 .62 .21 .29 .20 Intercondylar width .28 .42 .51 -.21 22 .49 .55* .60 23 .08 Anterior position of -.13 .17 .52** -.13 .47 -.03 .47 .18 .27 .46 maxilla Anterior position of -.18 .07 .45 .07 .55** -.09 .31 .I4 .29 .56 mandible Relative mandibular .I5 .21 .06 -.45* p.29 .I4 .29 .05 -.lo -.34 prognathism Gonial angle -.lo p.27 .14 .07 -.lo -.18 .06 .16 .I0 -.15 Palatal angle .02 -.09 p.14 -.34 -.41 -.02 -.I8 -.I3 .oo -.44 Ramus height .06 .29 .15 .18 .33 -.21 50 -.08 -.20 .31 Mandibular length .20 .39 .37 -.14 .34 -.I7 .42 .06 .13 .34** Upper face height .32 .I2 -.09 -.I7 -.49 -.01 .I8 .07 -.21 -.55** Lower face height -.09 .07 .27 .20 .I8 -.25 .47 .10 -.04 .13 First molar arch .31 .37 .42 -.03 .33 -.34 .74** -.21 -.05 .20 width

lAbbreviations: Mass, masseter muscle; Med Pt, medial pterygoid muscle; RMol, right first molar; Sag, sagittal; Cor, coronal. * P < 0.05. **P < 0.01.

and the anterior position of the mandible (r able to demonstrate any statistically signifi- = 0.52). These two variables entered the cant correlations at the 0.05 level between stepwise multiple regression to produce an the cross-sectional size of either muscle and R2 of 0.54. There was a significant correla- its moment arm or its associated bite force tion (P< 0.01) between the medial pterygoid and articular forces. This was true irrespec- sagittal moment arm and the anterior posi- tive of the bite point chosen. Thus there was tion of the mandible (r = 0.55) and between no association between the mechanical effi- the right molar sagittal moment arm and ciency of the system imparted by the spatial both first molar arch width (r = 0.74) and arrangement of its components and the sizes intercondylar width (r = 0.55). The latter of two of its major elevator muscles. two variables entered the stepwise regres- In Figure 6, putative right molar bite sion to produce an R2 of 0.67. There was a forces calculated with muscle tensions of 10 significant negative correlation (P < 0.05) units (unscaled) are compared with those between the masseter coronal moment arm calculated with muscle tensions propor- and relative mandibular prognathism (r = tioned according to muscle cross-sectional 0.45). There were no significant correlations size (scaled). Data are presented for both the between any skeletal variables and the puta- masseter and medial pterygoid muscles. As tive bite forces generated by the masseter might be expected, when cross-sectional pro- muscle. However, there was a significant portions were included in the calculations, negative correlation (P < 0.01) between the the distribution of forces produced by the putative bite force generated by the medial sample widened considerably. When un- pterygoid muscle and upper face height (r = scaled masseter muscle tensions were used, -0.55) and a positive correlation between bite forces ranged from 4.9 units to 7.5 units bite force and mandibular length (r = 0.34). but widened their range from 4.3 units to 9.0 Both skeletal variables entered the stepwise units when muscle tensions were scaled ac- regression to produce an R2 of 0.50. Stepwise cording to muscle size. The same trend was regression also selected the anterior position evident in the data for the medial pterygoid of the mandible as an initial correlate in this muscle, suggesting that large differences in relationship but rejected it when it failed to bite force might be expected in this sample of contribute to the variance any more than the subjects, not only as a consequence of spatial next two variables entered, viz, upper face relationships but also as a result of muscle height and mandibular length. We were un- size. That the latter acted as an independent 440 A.G. HANNAM AND W.W. WOOD

MASSETER x UNSCALED attachment to bone, theoretically make lo1 SCALED many tension vector locations and angula- tions available. Functional heterogeneity has already been demonstrated during mas- tication in the masseter muscles of rabbit (Weijs and Dantuma, 1981), pig (Herring et al., 1979), monkey (Hylander et al., 19871, and man (Belser and Hannam, 1986). In the present study, however, there were valid reasons for selecting single muscle vectors. SURIECTS First, they provided a useful quantitative means for comparing major lines of action in muscles that visibly differed in both position and angulation from subject to subject, and for which little information is presently available. Hitherto, no satisfactory method MEDIAL PTERYGOID seems to have existed for determining mus- w 6 cle lines of action in living humans (Throck- Cf0 morton, 1985). Second, although the imaging B technique used in this study provided a sig- w nificant technical advantage, its resolution k nevertheless did not permit any more de- tailed approach to quantification. We are confident that increased resolution is but a matter of time and that muscle compartmen- SUBJECTS talization can and eventually will be re- vealed by magnetic resonance. Third, repre- Fig. 6. Putative bite forces for muscles assigned iden- sentation of a whole muscle by its single tical units of tension and for the same muscles with central axis was the only satisfactory way to tension scaled proportionately to the mean muscle size for the group. Data are shown for the masseter (top) and align the plane of section used to estimate its medial pterygoid muscles (bottom).For each, bite forces cross-sectional area. This method was an calculated with unscaled muscle values are ranked in improvement over previous radiographic ascending order. Solid lines connect these with forces scanning techniques used in living subjects obtained when muscle values were scaled for cross- (Weijs and Hillen, 1986) because it ensured sectional size. slice orientations which were independent of variations in muscle angulation. Our measurements of the cross-sectional areas of the masseter and medial pterygoid muscles proved to be quite similar to those of variable can be seen from the random direc- Weijs and Hillen (1984a,b), who obtained tions of shifts in bite force from the unscaled theirs by single-slice computed tomography. to the cross-sectionally scaled state. It is Our mean values were slightly greater with clear that not all subjects with inherently less deviation for the masseter muscle (5.76 less efficient systems improved their rank k 1.11 cm2 vs. their 5.33 2 1.43 cm2), and order on the bite force scale by having larger slightly smaller with more deviation for the muscles, even though some did. Some effi- medial pterygoid (3.48 ? 0.88 cm2 vs. their cient individuals actually had a lower rank 3.76 k 0.72 cm'). The masseter muscle, order on the bite force scale when muscle when viewed coronally, makes a near verti- cross-sectional size was taken into account. cal angle (100") with the Frankfort horizon- tal plane. Thus a single slice axial tomogram DISCUSSION rotated 30" inferiorly to the Frankfort plane There are limitations in assuming that the will produce a masseter cross-sectional area human masseter and medial pterygoid mus- similar to that derived from a reconstructed cles can be represented biomechanically by muscle sectioned perpendicular to its long single vectors of force (Weijs, 1980; Throck- axis. Such is not the case for the medial morton and Throckmorton, 1985; Throck- pterygoid. This muscle makes an angle of 60" morton, 1985). The multipinnate nature of relative to the Frankfort plane (viewed coro- these jaw muscles, and their broad areas of nally). Planar orientation of a single slice RELATIONSHIPS IN JAW BIOMECHANICS 44 1 tomogram similar to that used for the mas- references are taken into account. Our re- seter muscle can lead to an overestimation of sults differ from those obtained by Iwasaki medial pterygoid cross-sectional area by (1987). She estimated masseter muscle an- 10%.For this reason, our estimates of medial gulation indirectly using cephalometric ra- pterygoid areas may be more reliable than diographic landmarks based on observations those of Weijs and Hillen (1984a,b). made on dry skulls. Her smaller mean mas- On the basis of its position and angulation, seter angulations of 57" reported for doli- the masseter muscle seems to be a much chocephalics and 53" for brachycephalics more effective producer of bite force than the may be explained in part by the different medial pterygoid. This relationship is mag- occlusal plane used in her study and in part nified when their respective cross-sectional by her definition of the origin of the masseter areas are taken into account, because the muscle. Within the limitations inherent in masseter is the larger muscle. The data show single vector analysis our data, in common that some subjects had larger muscle cross- with those of Horaist (19741, Takada et al. sectional areas than others. This trait could (19841, and Iwasaki (1987), suggest that be familial or simply a consequence of habit- there is no fixed relationship between mas- ual muscle use. Enlarged jaw muscles are seter muscle angulation and the occlusal not uncommon in subjects prone to vigorous plane. This contrasts with the views of Proc- mastication or nocturnal tooth grinding. Nor tor and de Vincenzo (1970). Two-dimen- can we explain why, in some cases, there sional model analysis predicts minimum ar- were unexpected variations in the propor- ticular loading during symmetrical molar tional sizes of the two muscles. Perhaps biting when the masseter muscle is aligned these reflect different and highly specific between 70" and 75" to the occlusal plane patterns of jaw use. Although it is not re- (Throckmorton, 1985). It is tempting to spec- ported here, we compared the muscles of ulate that, irrespective of facial type, mas- both sides in these subjects and found such seter muscle angulation may permit the gen- disparities in size to be bilateral when they eration of maximum molar bite force with occurred. The significant correlation found minimum articular loads. If so, this would be between the cross-sectional areas of the mas- best accomplished when muscle locations seter and medial pterygoid muscles and bizy- were well anterior to the articulation (Th- gomatic width differs from observations rockmorton, 1985). made by Weijs and Hillen (1986). However, Viewed sagittally, the mean medial ptery- they reported a correlation between mas- goid muscle angulation of 80" 2 9" relative to seter cross-sectional area and head width, FOP can be compared with the a mean value which is not a dissimilar indicator of of 85" * 10" we derived from Horaist's (1974) brachycephaly. Taken together, the studies data. suggest that increased masseter and medial The standard deviations around the mean pterygoid cross-sectional size is highly likely angulations of the masseter muscles are in brachycephalic subjects. about half those of the medial pterygoid Viewed sagittally, the mean masseter muscles viewed in both sagittal and coronal muscle angulation was 74" ? 5.6"relative to planes. One possible explanation for this is FOP. Proctor and de Vincenzo (1970) re- the greater number of sections used to esti- ported mean angulations of 69" ? 6" for a mate the angulation of the masseter muscle. sample of 54 normal subjects, 70" 2 7"for 14 Another is a possible closer association be- skeletal open-bit subjects, and 69" ? 4" for 12 tween the positions of the attachment sites of closed-bite subjects. The discrepancy be- the masseter muscles compared with those tween the studies may be explained by the of the medial pterygoid muscles, at least difference between FOP and the occlusal viewed in the coronal plane. plane used in their study. Our data can also Although a biomechanical analysis of iso- be compared with a mean value of 78" k 11" lated jaw muscles is unrealistic functionally, that we extracted from data provided by it is a convenient way to analyze complex Horaist (1974).In his study, the anterior and interactions that occur between muscle, posterior borders of 26 cadaver masseter tooth, and articular forces. Such interac- muscles were measured relative to an oc- tions, for example, those controlled by the clusal plane partly defined by the anterior various moment arms involved, can be de- teeth. Here, the discrepancy between the scribed by relative forces presumed to occur results of the two studies would increase at selected bite and articular points, and when the different occlusal planes used as these may be considered a means for ex- 442 A.G. HA"AM AND W.W. WOOD pressing the potential biomechanical effi- significance for the medial pterygoid muscle ciency of a given system irrespective of how it than for the masseter. If it is assumed that is actually used in practice. In jaw mechan- during normal, vigorous medial pterygoid ics, efficiency can be expressed in different muscle use bite force is directed downward ways. It can be estimated by maximizing bite from medial to lateral on the mandibular force at a specified location while minimiz- first molar of the ipsilateral side, then, even ing the sum of the muscle forces, or while though the vertical component of bite force is minimizing articular forces, or while maxi- unchanged (since it is determined by sagittal mizing the work done for a given sum of view dimensions), its lateral component will muscle forces (Baragar and Osborn, 1987). alter according to the mediolateral angle of In this study, we expressed bite force effi- the force vector. This increases the overall ciency as the ratio of bite force to the max- resultant for bite force, rendering the medial imum (arbitrary) tension produced by a pterygoid muscle more efficient than our single reference muscle. This approach per- calculations suggest. A bite force angled 60" mitted an assessment of efficiency that re- to the FOP in the coronal plane, for example, flected muscle location and angulation rela- would increase medial pterygoid-generated tive to key resistive elements in the system bite force to 3.9 units from a present calcula- (the bite point and the mandibular condyles), tion of 3.4 units. Nevertheless, we are con- and it avoided the problem of assigning phys- tent with our assumption that all bite forces iological variables that are notoriously diffi- were directed perpendicular to FOP because cult to measure with precision, such as mus- little is known about functional bite force cle "physiological" cross-sectional areas, angulation in man, and, in any event, small muscle tension constants per unit of cross deviations would have a small effect. section, and muscle activation levels. A ma- Although our subjects showed wide varia- jor advantage of the approach was that it tions in unilateral bite force for both muscles allowed an objective assessment of at least tested, bite force magnitudes were always some functional correlates of morphology. identical on each side of the dental arch. The extent to which groups of muscles or Viewed sagittally, the mandibular condyles muscle subunits combine, under physiologi- are coaxial, and the sum of all rotational cal conditions, to produce bite and articular moments about them must be zero to achieve forces depends on their individual tension- static equilibrium. By taking moments about generating capacities and the extent to the centers of the condyles, bite force is which they are activated in a coordinated determined solely by muscle moments and manner during function. These combined the length of the bite point moment arm. Bite actions were not considered here. force magnitude will always be determined Our selection of a bite force angle perpen- by these relationships, since static equilib- dicular to FOP in the region of the mandibu- rium in this particular plane must be satis- lar first molar was based on the natural axial fied irrespective of any other viewing plane alignment of these teeth, the frequent use of considered. Thus our first molar bite forces, the region during mastication, and the fact which were derived from these anteroposte- that human molar bite forces are often mea- rior and superoinferior spatial dimensions sured this way (Proffit and Fields, 1983). alone, had to have been the same irrespec- Recently, it was reported that maximum bite tive of the side of the bite point. On the other force angulation in the molar region seldom hand, condylar forces, their ratios relative to deviates more than 10" from a perpendicular each other, and their ratios relative to bite to the occlusal plane (van Eijden et al., 1988). force are determined entirely by the medio- It has also been suggested that for condylar lateral and superoinferior spatial dimen- fossa angles between 30" and 50" (inclined sions of the face and jaws and would be anteriorly relative to the occlusal plane) first expected to differ according to variations in molar bite force angles between 90" and 95" coronal facial dimensions. That articular are also the most work-efficient (Baragar forces apparently vary less than bite forces and Osborn, 1987). In practice, however, bite can be explained only by the way the factors force angles may vary considerably, espe- responsible for them interact. Presumably cially mediolaterally, and it has been shown high bite forces (from anteriorly inclined or that medially directed forces on the maxil- positioned muscles) tend to occur in broad lary teeth reach higher magnitudes than faces, thereby reducing condylar forces, forces in corresponding lateral directions which would otherwise be very high. Con- (van Eijden et al., 1988). This has more versely, low bite forces (from more posteri- RELATIONSHIPS IN JAW BIOMECHANICS 443 orly inclined or positioned muscles) might muscles and consequently longer muscle mo- occur in narrower faces and produce pro- ment arms. However, the lack of significant portionally higher condylar forces. Such correlations between putative bite forces trends could result in wide variations in bite generated by the masseter muscle and skel- forces in a mixed population like ours but etal variables indicates that the combined less variation in corresponding condylar influences of the moment arms of the mas- forces. seter muscles and the first molars are inde- The results emphasize the advantages of pendent of conventional cephalometric mea- bilateral muscle use across a fused symphy- sures of skeletal structures. The significance sis, a feature noted by others (Hylander, of the negative correlation between putative 1975,1985b; Beecher, 1977; Greaves, 1978; bite force generated by the medial pterygoid Weijs, 1980). For a given molar bite, any muscle and upper face height is unclear; masseter and medial pterygoid contribu- however, its positive correlation with man- tions from both sides of the jaw would be dibular length may relate to the increase in additive at both the bite point and the tem- the moment arm with a forward placed go- poromandibular articulation. Distractive nial angle and attachment of the muscle to balancing side and compressive working side the ramus of the mandible. In the latter condylar forces produced by one masseter instance, it is relevant to note that Weijs and muscle would be reduced by similar forces of Hillen (1986) have reported a positive corre- opposite sign from the masseter of the other lation between the cross-sectional area of the side. At the same time, compressive forces medial pterygoid muscle and mandibular produced at the bite point by both muscles length. would be additive. In this sense, bilateral A masticatory system consisting only of masseter activation offers considerable bio- masseter and medial pterygoid muscles, if mechanical benefits, although it should be ideally suited to produce large molar bite stressed that during human mastication forces, would have the following characteris- these muscles are not activated equally (Mol- tics. Viewed from the side, the masseter and ler, 1966; Belser and Hannam, 1986). In the medial pterygoid muscles would be placed case of the medial pterygoid muscle, all bite anteriorly as far as possible and angled ante- point and condylar forces are compressive. riorly as far as possible to increase their However, during the power stroke of masti- moment arms. The occlusal plane would be cation, this muscle normally acts unilater- flat to keep the bite point as close as possible ally (Hannam and Wood, 1981; Wood, 1986). to the articulation and to reduce its moment Thus, even allowing for functional differ- arm. Viewed coronally, the intercondylar ences in muscle behavior and contributions width would be as large as possible and the from muscles not considered in our study, a dental arch narrowed to distribute the loads general principle of enhanced bite force with on the mandibular condyles more evenly, relatively lessened compressive forces at the since wide intercondylar distance maximizes articulation seems likely during normal condylar moment arms, and the narrow den- function. tal arch maximizes the bite point moment The lack of any significant correlation be- arm. A low occlusal plane would also be tween the cross-sectional areas of each of the advantageous if bite forces were directed two muscles and their respective moment obliquely during function; this could add arms or the moment arm of the right molar dramatically to bite point moment arms in when viewed sagittally suggests that the the coronal plane and minimize articular force-generating ability of an individual oc- loading. Finally, it would be ideal to have jaw curs by a random mix of principal force- elevator muscles with large cross-sectional generating factors. High force generation at areas. Many of these traits are evident in the first molar ideally requires large muscle brachycephalic subjects with flat mandibu- moment arms and a small tooth moment lar and occlusal planes, long mandibular arm, which in the present study seem to be bodies, small gonial angles, long posterior associated with large intergonial width, facial heights, and short anterior facial small intercondylar width, narrow dental heights (Proctor and De Vincenzo, 1970; Ho- arch, forward maxilla, and forward mandi- raist, 1974; Tetz, 1983; Takada et al., 1984; ble. Of these variables, only the forward Weijs and Hillen, 1984b, 1986). Predictably, position of the maxilla and mandible have subjects with these characteristics produce any direct meaning in terms of bite force; strong muscle activity and high bite forces they can result in more anteriorly placed (Moller, 1966; Ringqvist, 1973; Ingervall and 444 A.G. HA"AM AND W.W. WOOD

Thilander, 1974; Tabe, 1976; Proffit and Greaves WS (1978) The jaw lever system in ungulates: a Fields, 1983). new model. J. Zool. 184:271-283. Hannam AG, and Wood WW (1981) Medial pterygoid Our study shows, however, that in a mod- muscle activity during the closing and compressive ern human population so many combina- phases of human mastication. Am. J. Phys. Anthropol. tions of biomechanically relevant variables 55:359-367. are possible that subjects cannot easily be Hatcher DC, Faulkner MG, and Hay AA (1986) Develop- placed into ideal or nonideal categories for ment of mechanical and mathematical models to study loading. J. Prosthet. Dent. producing molar bite force. There are wide 55:377-384. variations in mechanical efficiency and mus- Herring SW, Grimm AF, and Grimm BR (1979) Func- cle cross-sectional size, and specific combi- tional heterogeneity in a multipinnate muscle. Am. J. nations of these variables are difficult to Anat. 154563476. predict because they do not appear to be Horaist FJ (1974)A cephalometricand anatomical study of the relationship between the masseter muscle, the associated. Our observations may help to medial pterygoid muscle and gonial angle of the hu- explain why large variations in unilateral man mandible: A continuing study. MSc Thesis, Fair- molar bite force can be found in subjects with leigh Dickinson University. apparently similar skeletal patterns deter- Hylander WL (1975) The human mandible: lever or link? mined by conventional cephalometry (Proffit Am. J. Phys. Anthropol. 43:227-242. Hylander WL (1985a) Mandibular function and temporo- and Fields, 1983). Variations in muscle size, mandibular joint loading. In D.S. Carlson, J.A. McNa- tooth position, and FOP by themselves can mara, and K.A. Ribbens (eds.):Developmental Aspects profoundly affect bite force production in the of Temporomandibular Joint Disorders (Monograph first molar region even when other muscu- #16, Craniofacial Growth Series). Ann Arbor, Michi- gan: Center for Human Growth and Development,The loskeletal features appear similar. University of Michigan, pp. 19-35. Our findings also confirm the impression Hylander WL (1985b) Mandibular function and biome- that similar efficiency in bite force produc- chanical stress and scaling. Am. J. Zool. 25:315-330. tion can be found in subjects with disparate Hylander WL, Johnson KR, and Crompton AW (1987) skeletal features (Iwasaki, 1987). In some, Loading patterns and jaw movements during mastica- variations in 'muscle size can apparently tion in Macaca fascicularis: A bone-strain, electromyo- graphic and cineradiographic analysis. Am. J. Phys. compensate for mechanical inefficiency. 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