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Biomechanics of differences in lower facial height
Biomechanics of differences in lower facial height Gaylord S. Throckmorton, Ph.D., Richard A. Finn, D.D.S., and William H. Bell, D.D.S. Dallas, Texas A two-dimensional model which allows calcuhtion of mechanical advantage ot the human temporalis and masseter muscles is presented. The model is manipulated to demonstrate how selected dtrerences in facial morpholog? affect the nrec~hanic~trl advantage of the muscles. The model is then used to evaluute the d~fj%~rtnce.~in mechanical advantage between patients with the long face syndrome and those with the short face sydrome. Differences in facial morphology between these /NW groups result in sign@cant dtfjerences in the mechanical advantages of their muschs. Mec,hanical advantage may, in part, explain observed dryerences in bite force betrz,een the two groups. The model suggests that some surgical procedures used to correct ,finkl disharmonies may have u significant e@ect on the mechanical advantugr of’ the ,ja~, muscles. Key words: maxillofacial
Biomechanics, surgery
masticating muscles, facial height, bite force
I
n recent years, several studies have attempted to classify variation in facial height. Schendel and associates2odefined a long face syndrome in which there is excessive height of the maxilla and a relatively large mandibular plane angle. Opdebeek and Be1118 have described a short face syndrome with the vertical height of the maxilla less than normal and a relatively small mandibular plane angle. These classifications are similar to Sassouni ‘slg classification of skeletal open-bite (similar to long face syndrome) and skeletal deep bite (similar to short face syndrome). From lateral cephalometric radiographs, a number of morphologic criteria can distinguish the two groups. In patients with the long face syndrome,20 both the anterior and posterior maxillary heights are greater than normal. In addition, there is a clockwise rotation of the entire face so that the mandibular plane angle and the gonial angle tend to be greater than normal, while the mandibular ramus tends to be shorter than normal.” These features are most marked in patients with open-bite. 2oIn patients with the short face syndrome the dentoalveolar height is reduced anteriorly, both the mandibular plane angle and the gonial angle are relatively small, and ramus height is increased. Physiologic differences between the two groups have also been reported. Sassouni’” From the Departments of Cell Biology and Oral Surgery, The University of Texas Health Science Center at Dallas.
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OfIOZ-9416/80/040410+11$01.10/0
0
1980 The C. V. Mosby
Co.
Volume 77 Number 4
Biomechanics
of differences
in lower
facial
height
411
FT
B.
--------1
FB
Fig. 1. The human mandible functioning as a lever. A, Two-dimensional model of mandibular system. B, Stylized lever system. CN, Tip of coronoid process; CO, condyle and fulcrum; FB, bite force vector; muscle force vector for masseter; FT, muscle force vector for temporalis; a, moment arm for masseter; b, moment arm for temporalis; c, moment arm for bite force.
FM,
noted that persons with skeletal open-bite had a molar biting force clustering around 50 to 80 pounds (22.7 to 36.3 kg.) while persons with skeletal deep bite had a molar biting force clustering around 150 to 200 pounds (68.1 to 90.8 kg.). Several factors could produce the observed differences in bite forces, including (1) total muscle size,lg (2) differences in the morphology of the jaw muscles, either in their architectures or in the size and distribution of different types of muscle fibers,6* lo* l1 (3) the activity level of the muscle,‘, 5* 14,15,l7 and (4) the mechanical advantage of the jaw muscles. The purpose of the present study was twofold: (1) to determine how the morphologic differences between patients with long and short face syndromes affected the mechanical advantage of their jaw muscles and (2) to determine if differences in mechanical advantage between the groups could account for reported differences in maximum bite force. Materials and methods The lever model of mandibular mechanics. In order to examine differences between the two groups, a two-dimensional lever model (Fig. 1) of the mandible was developed. (See the article by Hylander13 for a review of the lever action of the human mandible.) The mandible is represented by a lever with the fulcrum at the summit of the condyle, forces from the temporalis and masseter muscles applied distal to the fulcrum, and the bite force or load applied distal to the muscle forces. This model was used to calculate the me-
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chanical advantage for the temporalis and masseter muscles during molar bites. As in any model, simplifying assumptions have been made in order to demonstrate certain key features. The model corresponds to the situation in which an isometric bite is performed between the first molars. During isometric bites, the jaw system is in static equilibrium. Initially the position of the bite force on the model passes through the mesiobuccal cusp of the upper first molar. In manipulations of the model the position of the bite force is held in a constant position on the maxilla when the height of the maxilla is changed (Fig. 3), but it is held in a constant position on the mandible when gonial angle and ramus height are changed (Figs. 4 and 5). This is necessary to avoid trivial cases in which manipulation of the elements result in no change in the length of the load arm. For example, if the bite point were held constant on the mandible as the maxilla was moved, the distance of the bite force from the condyle would also remain constant and little effect on mechanical advantage would be observed. Thus, in the present model the positioning of the bite force maximizes the effect of manipulation of the model on mechanical advantage. The direction of the bite force is assumed to be perpendicular to the mandibular plane (GO to ME) in the sagittal plane. The directions of the muscle forces are assumed to be along single lines of action. For the temporalis, the line of action (line FT of Fig. 1) is defined as a line intersecting the coronoid tip and running tangent to the ascending ramus. For the masseter, the line of action (line FM of Fig. 1) is defined as a line connecting gonion to the intersecting point of the frontal and squamous processes of the zygoma.2’ During an isometric bite, the jaw-elevating muscles tend to produce a counterclockwise rotation of the mandible (when viewed from the right) which is termed a torque. The strength of the torque is the product of the magnitude of the muscle force (FM and FT) times the perpendicular distance (termed moment arm) of the muscle from the condyle (line segments a and b, respectively). The object being bitten also produces a torque which, in an isometric bite, is equal to but opposite in direction to the sum of the torques produced by the jaw-elevating muscles. This torque is the product of the bite force (FB) times its moment arm (line segment c). The total torque applied to the jaw is 0 because the bite-force torque cancels exactly the muscle-force torques. Thus, there is no movement of the jaw. The mechanical advantage of a muscle is the ratio of the moment arm of the muscle to the moment arm of the load or, in this case, the bite force.* In normal jaw mechanics the mechanical advantage of the jaw adductors is always less than 1 because the moment arm of the muscles is always shorter than that of the load. As mechanical advantage increases and approaches 1, it becomes easier for the muscle to produce a particular bite force. For example, it is easier to perform a bite of a given force at the molars than at the incisors because moving the bite force to the molars from the incisors shortens the moment arm of the load, thus increasing the mechanical advantage of the jaw adductors. I6 Two types of studies were undertaken with the model. In the first study a general model based on values from Bolton’s standard2* was constructed. In this model various morphologic parameters were gradually altered and the temporalis and masseter mechanical advantages were calculated for each change. The height of the maxilla was increased and decreased by 20 mm. at 10 mm. intervals (Fig. 3). Gonial angle was changed from 90 degrees to 150 degrees at lo-degree intervals (Figs. 4 and 5). Ramus height was changed from 50 mm. to 70 mm. at 5 mm. intervals (Fig. 6).
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Biomechunics
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\
-\
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b
me
Fig. 2. Diagrammatic demonstration of mandibular changes necessary to keep teeth in occlusion if the maxilla is elevated. co, Condylar summit; go, gonion; me, mentale; m, molar bite point; i, incisor bite point; Of, occlusal plane. Solid line represents original mandible position. Broken lines represent jaw position if (a) gonial angle changes or(b) the mandible rotates anteriorly-superiorly to match new molar bite point.
Ideally, one would like to isolate each morphologic change and determine its effect alone on mechanical advantage. This is not always possible in analyses of jaw mechanics, however, since changing only one parameter may prevent the teeth from coming together. For example, if one changes the height of the maxilla (Fig. 2), then in order for the teeth to occlude either the gonial angle must also change or the entire jaw must rotate. Therefore, it was sometimes necessary to use two different analyses of one parameter to gain a full understanding of the effects of making changes. In the second study the mechanical advantages of twenty long-face and twenty-seven short-face patients were compared. These patients had been used in previous cephalomettic studies,‘*, 2o and their cephalometric data are stored on magnetic tape in the Medical Computing Resources Center, The University of Texas Health Science Center at Dallas. By means of graphics programs developed for previous studies,‘** *O plots of the cephalometric profiles for each patient were generated. Values for each of the morphologic parameters in the model were taken from each profile and were plugged into the model. Thus, the mechanical advantage of the temporalis and masseter muscles of each patient were calculated. The mean value for the mechanical advantage of each muscle was then calculated for the long-face and short-face groups and the means were compared by using the Student t test. Results Effects of changing maxilla height. Fig. 3, A demonstrates the effect of changing maxillary height. The beginning position represents the model values for Bolton’s standard for 18-year-old males. The maxilla is then elevated and depressed at 10 mm. intervals without changing the orientation of the plane of the maxilla to allow for mandibular autorotation. The bite point is assumed to have a constant position on the maxilla. No other morphologic changes occur, but the lower jaw is allowed to rotate anterosuperiorly
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und Bell
FT f
Fig. 3. Changes in mechanics of the temporalis and masseter muscles with shortening of the maxilla. A, Diagram of changes in the model as maxillary height is increased and decreased from Bolton’s standard. FT, Line of action of temporalis; FM, line of action of masseter; f-B, line of action of bite force; S, sella; A! nasion; CO, summit of condyle. 6, Mechanical advantage of temporalis (r) and masseter (M) muscles versus change in maxillary height (in mm.).
so that the tooth rows will remain in contact. This type of “autorotation” is seen clinically when the vertical position of the maxilla is altered. Lowering of the maxilla causes a posteroinferior rotation of the mandible, and the maxillary bite point moves anteriorly relative to the mandible. The result is a 50 percent increase in the length of the moment arm of the load over a 40 mm. change in the position of the maxilla. Rotation of the mandible as the maxilla is lowered causes gonion to move posteriorly and the tip of the coronoid process to move inferiorly. These movements result in a 7 percent decrease in moment arm length for the temporalis and an 18 percent decrease for the masseter. The results of these changes are a decrease in mechanical advantage of 36 percent for the temporalis and 44 percent for the masseter (Fig. 3, B). These results suggest that the greater maxillary height in long-faced patients should produce a decreased mechanical advantage for the temporalis and masseter muscles. Effect ofchanging genial angle. Two separate analyses are needed for a full appreciation of the effect of the gonial angle on mechanical advantage. In the first analysis (Fig. 4, A), the gonial angle is changed without rotation around the mandibular joint. In order for the bite point to remain in position, the maxilla must shift to remain with the lower jaw. In addition, the position of the tip of the coronoid process was kept constant. Therefore, in this analysis the mandible does not change position, but the shape of both the mandible and the maxilla must change to keep the teeth in contact. The position of the
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FT A S-
lN
‘i 90
GONIAL
120 ANGLE
150
Fig. 4. Effect of gonial angle on mechanical advantage I. A. Diagram of changing gonial angle from Bolton’s standard without rotation of the mandible; 17, line of action of temporalis; FM, line of action of masseter; 19, line of action of bite force; S, sella; N, nasion; CO, summit of condyle; GO, gonial angle. B, Mechanical advantage of temporalis (T) and masseter (M) muscles versus gonial angle.
bite point is constant for both the mandible and the maxilla. The effect of these changes on mechanical advantage is shown in Fig. 4, B. For both muscles, mechanical advantage is inversely proportional to the gonial angle because increasing the gonial angle lengthens the load arm while the moment arms of both muscles remain unchanged. As the gonial angle increases from 90 degrees to 150 degrees, mechanical advantage, as measured by this model, decreases by 55 percent for both temporalis and masseter muscles. Note that the effect of changes in the gonial angle is greatest when the gonial angle is relatively small. These results suggest that an increased gonial angle combined with greater maxillary height in long-face patients should sharply reduce the mechanical advantage in both muscles. In the second analysis (Fig. 5, A) the mandible rotates to maintain tooth-to-tooth contact and the maxilla and mandible do not change in shape (except, of course, for the gonial angle). As gonial angle increases, the mandible rotates anteriorly. In this analysis the bite point is assumed to have a constant position on the mandible while moving posteriorly along the maxilla as the gonial angle increases. Because the jaw must rotate anteriorly as the gonial angle increases from 90 degrees to 150 degrees, the moment arm of the load is lengthened by 115 percent. However, anterior
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Fig. 5. Effect of gonial angle on mechanical advantage II. A, Diagram of changing gonial angle from Bolton’s standard with rotation of the mandible; FT, line of action of temporalis; FM, line of action of masseter; FB, line of action of bite force; S, sella; N, nasion; CO, summit of condyle; GO, gonial angle. 8, Mechanical advantage of temporalis (T) and masseter (IV) muscles versus gonial angle.
rotation of the mandible moves gonion anteriorly and the tip of the coronoid process superiorly, thus increasing the moment arms of the muscles by 10 percent for the temporalis and 40 percent for the masseter. The over-all effect on mechanical advantage is shown in Fig. 5, B . Increasing the gonial angle from 90 degrees to 150 degrees causes a 48 percent decrease in mechanical advantage for the temporalis and a 35 percent decrease for the masseter, according to this model. This analysis also suggests that the long-face patient with a larger gonial angle will have a smaller mechanical advantage for the temporalis and masseter muscles. Effects of changing ramus height. The effect of changing ramus height is shown in Fig. 6, A. In this analysis the ramus is lengthened and shortened at 5 mm. intervals and the mandible is rotated to allow the teeth to remain in contact. In this model the bite point maintains a constant position along the mandible. As ramus height increases, the jaw must rotate anterosuperiorly in order for the teeth to remain in contact. Anterior movement of the mandible lengthens the moment arm of the load by 17 percent while lengthening the moment arm of the masseter by 34 percent. Superior movement of the tip of the coronoid process produces only a very slight increase of 4 percent of the moment arm of the temporalis. The over-all results (Fig. 6, B) are a decrease of 10 percent in the mechanical advantage of the temporalis but an increase of 15 percent in the mechanical advantage of the masseter, for a change in ramus height of 20 mm. The effects of the various morphologic changes on mechanical advantage can be
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417
FT
6 .9 z 4 .a k $ .7 2 .6 4 :
I :-‘a-
.5
'-*-.T
u ; .4 4 ; .3 :
.2 .l 0-
-10
-5 RAMUS
Fig. 6. rotation nasion; versus
0 t5
t10
HEIGHT
Effect of ramus height on mechanical advantage. A, Diagram of changing ramus height with of the mandible. IT, Line of action of temporalis; FM, line of action of masseter; S, sella; N, CO, summit of condyle. B, Mechanical advantage of temporalis (T) and masseter (A4) muscles ramus height.
summarized as follows: (1) Any change which moves the bite point away from the condyle will decrease the mechanical advantage of the adductor muscles by increasing the moment arm of the load; (2) any change which moves gonion anteriorly and/or inferiorly will increase the mechanical advantage of the masseter because its line of action is moved away from the condyle and thus its moment arm is lengthened; and (3) any change which moves the coronoid process superiorly and/or anteriorly will increase the mechanical advantage of the temporalis for the same reasons given above for the masseter. Comparison ofpatient groups. In Fig. 7 the models for three groups Bolton standard 1%year-old males; mean long face (20 patients ~3,20), and mean short face (27 patients”) are superimposed so that their condylar summits match and the mandibular ramus lines are aligned. This type of comparison shows the morphologic differences among the groups: (1) The height of the maxilla (as measured relative to S-N) is greater in the long-face group than in either of the other groups. The short-face group appears to have greater maxillary height than that of the Bolton standard, but this is because of its higher condylar position relative to S-N. (2) Ramus height is greatest in the short-face group and least in the long-face group. (3) The gonial angle is greatest in the long-face group and least in the
Fig. 7. Comparison of muscle mechanics of Bolton standard for 1 &year-old males (solid lines), mean long face group (dashed lines), and mean short face group (dotted lines). S, Sella; N, nasion; CO, condyle summit; CN, tip of coronoid process; GO, gonion; ME, mentale; FT, line of action of temporalis; FM, line of action of masseter; FB, line of action of bite force.
Table I. Comparison of mechanical advantage between long face and short face patients Group
Long face Bolton standard Short face
Mean
temporalis
mechanical
adwntage
0.494 k S.D. = 0.060 0.507 0.520 2 S.D. = 0.048
Mean
masseter
mechanical
advantage
0.545 t S.D. = 0.056 0.601 0.633 f S.D. = 0.050
short-face group. The length of the bite force moment arm is greatest in the long-face group but is also greater in the short-face group than for Bolton’s standard. The moment arm for the temporalis is longest for the Bolton standard and shortest in the short-face group. The moment arm for the masseter is also longest in the short-face group. The differences in mean mechanical advantage between the two groups are shown in Table I. For the temporalis muscle, the short-face group tends to have a larger mechanical advantage than either Bolton’s standard or the long-face group. The differences, however, are not significant (P < 0.098). The short-face group does have a significantly larger mechanical advantage (P < 0.001) for the masseter muscle when compared to the longface group. The masseter mechanical advantage is also larger in the short-face group than Bolton’s standard, although the significance of that difference is not presently evident. Discussion These results suggest that the greater bite force reported for patients with the short face syndrome may be due, at least in part, to the greater mechanical advantage of their adductor muscles. Each of the morphologic differences between the long and short face
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syndromes produces an increased mechanical advantage for the adductor muscles of the short-face patient, with the one exception of the decreased temporalis mechanical advantage when ramus height is lengthened. These results also suggest that surgical alteration of the facial skeleton may produce significant changes in the mechanical advantage of the jaw muscles. For example, moving the maxilla upward in correction of the long face syndrome3 will tend to increase the mechanical advantage of the adductor muscles, but lengthening the maxilla in the correction of the short face syndrome4 will have the opposite effect. Anterior and posterior repositioning of the maxilla also will affect mechanical advantage by changing the relationship of the bite positions to the condyle. Surgical procedures on the mandible may produce even greater changes in mechanical advantage. Mandibular advancement, for example, will decrease mechanical advantage of the adductors by increasing the length of the load arm. * To date, no studies have linked surgically induced changes in mechanical advantage to postoperative changes in muscle function, possible alterations in skeletal morphology in response to these muscle changes, or tendencies toward relapse. However, such studies should be undertaken. At present, surgeons may want to consider changes in mechanical advantage as an additional factor when planning procedures to correct facial disharmonies. These results differ somewhat from those of a previous study7 in which the lines of actions of the temporalis and masseter muscles were determined in a different way. The earlier model was designed to correspond to experiments in which electrodes recorded muscle activity during isometric bites. The direction chosen for the lines of actions of a muscle have profound effects upon calculations of mechanical advantage. In the earlier study mechanical advantage was calculated for the specific portion of the muscle from which recordings were made. In the present study the lines of action have been drawn from anatomic points which more closely reflect the function of the entire muscle.‘l Nevertheless, because muscle force vectors do not necessarily correspond to single lines of action, particularly in complex muscles which may exhibit differential activity,” it is important that interpretations of models of the jaw apparatus be made with caution. In spite of these difficulties, models can lead to useful insights or suggest significant problems requiring experimental investigation. Summary
We have presented a two-dimensional model which allows calculation of mechanical advantage of the human temporalis and masseter muscles. The model is manipulated to demonstrate how selected differences in facial morphology affect mechanical advantage of the muscles. The model is then used to evaluate the differences in mechanical advantage between patients with the long face syndrome and those with the short face syndrome. Differences in facial morphology between these two groups result in significant differences in mechanical advantages of their muscles. Mechanical advantage may, in part, explain observed differences in bite force between the two groups. The model suggests that some surgical procedures used to correct facial disharmonies may have a significant effect on mechanical advantage of the jaw muscles. Dr. J. B. Brammer and Mr. J. Adams helped make tracings of the cephalometric data used in the study. Dr. D. J. Mishelevich
donated computer time to retrieve some of the computer data used in
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the study. suggestions.
Dr.
Walter
Finn, ud Bell Greaves
read
an earlier
version
of this
manuscript
and
made
many
helpful
REFERENCES 1. Ahlgren, J., Ingervall, B. F., and Thilander, B. L.: Muscle activity in normal and post normal occlusion. AM. J. ORTHOD. 64: 445-456, 1973. 2. Alexander, R.: Animal mechanics, Seattle, 1968, University of Washington Press, pp. 13-15. 3. Bell, W. H., Creekmore, T. D., and Alexander, R. G.: Surgical correction of the long face syndrome, AM. J. ORTHOD. 71: 40-67, 1977. 4. Bell, W. H.: Correction of the short face syndrome-vertical maxillary deficiency: A preliminary report, J. Oral Surg. 35: 110-120, 1977. 5. CarIs%, S.: Nervous coordination and mechanical function of the mandibular elevators. Acta Odontol. Stand. 10 (Supp. 11): 1-131, 19.52. 6. Edgerton, V. R.: Neuromuscular adaptation to power and endurance work, Can. J. Appl. Sport Sci. 1: 49-58, 1976. 7. Finn, R. A., Thmckmorton, G. S., Gonyea, W. J., Barker, D. R., and Bell, W. H.: Neuromuscular characteristics of vertical maxillary dysplasias. In Bell, W. H., Proffitt, W. R., and White, R. P. (editors): Surgical correctionof dentofacial anomalies, Philadelphia, 1980, W. B. SaundersCompany, pp. 1112-l 130. 8. Finn, R. A., Throckmorton, G. S., and Bell, W. H.: Biomechanics of mandibular deficiency, J. Oral Surg. (In press.) 9. Gans, C., and Bock, W.: The functional significance of muscle architecture, a theoretical analysis, Ergeb. Anat. Entw. Gesch. 38: 116-142, 1965. 10. Gonyea, W., and Bonde-Petersen, F.: Contraction properties and fiber types of some forelimb and hindlimb muscles in the cat, Exp. Neurol. 57: 637-644, 1977. 1 I. Gonyea, W., and Bonde-Petersen, F.: Alterations in muscle contractile properties and fiber composition after weight-lifting exercise in cats, Exp. Neurol. 59: 75-84, 1978. 12. Herring, S. W., Grimm, A. F., and Grimm, B. R.: Functional heterogeneity in a multipennate muscle, Am. J. Anat. 154: 563-576, 1979. 13. Hylander, W. L.: The human mandible, lever or link? Am. J. Physiol. Anthropol. 43: 227-243, 1975. 14. Ingervall, B. F.: Facial morphology and activity of temporal and lip muscles during swallowing and chewing, Angle Orthod. 46: 372-380, 1976. 15. Ingervall, B. F., and Thilander, B. L.: Relation between facial morphology and activity of the masticatory muscles, J. Oral. Rehabil. 1: 131-147, 1974. 16. Mansour, R. F., and Reynick, R. J.: In vivo occlusal forces and moments. I. Forces measured in terminal hinge position and associated moments, J. Dent. Res. 53: 114-120, 1975. 17. Moller, E.: The chewing apparatus, Acta Physiol. Stand. 69: Supp. 280, 1953. 18. Opdebeek, H., and Bell, W. H.: The short face syndrome, AM. J. ORTHOD. 73: 499-511, 1978. 19. Sassouni, V.: A classification of skeletal facial types, AM. J. ORTHOD. 55: 109-123, 1969. 20. Schendel, S. A., Eisenfeld, J., Bell, W. H., Epker, B. N., and Mischelevich, D. J.: The long face syndrome: Vertical maxillary excess, AM. J. ORTHOD. 70: 398-408, 1976. 21. Sicher, H., and DuBrul, E. L.: Oral anatomy, ed. 5, St. Louis, 1970, The C. V. Mosby Company, pp. 170-178. 22. Broadbent, B. H., Sr., Broadbent, B. H., Jr., and Golden, W. H.: Bolton standards of dentofacial developmental growth, St. Louis, 1976, The C. V. Mosby Company.
Biomechanics, surgery
masticating muscles, facial height, bite force
I
n recent years, several studies have attempted to classify variation in facial height. Schendel and associates2odefined a long face syndrome in which there is excessive height of the maxilla and a relatively large mandibular plane angle. Opdebeek and Be1118 have described a short face syndrome with the vertical height of the maxilla less than normal and a relatively small mandibular plane angle. These classifications are similar to Sassouni ‘slg classification of skeletal open-bite (similar to long face syndrome) and skeletal deep bite (similar to short face syndrome). From lateral cephalometric radiographs, a number of morphologic criteria can distinguish the two groups. In patients with the long face syndrome,20 both the anterior and posterior maxillary heights are greater than normal. In addition, there is a clockwise rotation of the entire face so that the mandibular plane angle and the gonial angle tend to be greater than normal, while the mandibular ramus tends to be shorter than normal.” These features are most marked in patients with open-bite. 2oIn patients with the short face syndrome the dentoalveolar height is reduced anteriorly, both the mandibular plane angle and the gonial angle are relatively small, and ramus height is increased. Physiologic differences between the two groups have also been reported. Sassouni’” From the Departments of Cell Biology and Oral Surgery, The University of Texas Health Science Center at Dallas.
410
OfIOZ-9416/80/040410+11$01.10/0
0
1980 The C. V. Mosby
Co.
Volume 77 Number 4
Biomechanics
of differences
in lower
facial
height
411
FT
B.
--------1
FB
Fig. 1. The human mandible functioning as a lever. A, Two-dimensional model of mandibular system. B, Stylized lever system. CN, Tip of coronoid process; CO, condyle and fulcrum; FB, bite force vector; muscle force vector for masseter; FT, muscle force vector for temporalis; a, moment arm for masseter; b, moment arm for temporalis; c, moment arm for bite force.
FM,
noted that persons with skeletal open-bite had a molar biting force clustering around 50 to 80 pounds (22.7 to 36.3 kg.) while persons with skeletal deep bite had a molar biting force clustering around 150 to 200 pounds (68.1 to 90.8 kg.). Several factors could produce the observed differences in bite forces, including (1) total muscle size,lg (2) differences in the morphology of the jaw muscles, either in their architectures or in the size and distribution of different types of muscle fibers,6* lo* l1 (3) the activity level of the muscle,‘, 5* 14,15,l7 and (4) the mechanical advantage of the jaw muscles. The purpose of the present study was twofold: (1) to determine how the morphologic differences between patients with long and short face syndromes affected the mechanical advantage of their jaw muscles and (2) to determine if differences in mechanical advantage between the groups could account for reported differences in maximum bite force. Materials and methods The lever model of mandibular mechanics. In order to examine differences between the two groups, a two-dimensional lever model (Fig. 1) of the mandible was developed. (See the article by Hylander13 for a review of the lever action of the human mandible.) The mandible is represented by a lever with the fulcrum at the summit of the condyle, forces from the temporalis and masseter muscles applied distal to the fulcrum, and the bite force or load applied distal to the muscle forces. This model was used to calculate the me-
472
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chanical advantage for the temporalis and masseter muscles during molar bites. As in any model, simplifying assumptions have been made in order to demonstrate certain key features. The model corresponds to the situation in which an isometric bite is performed between the first molars. During isometric bites, the jaw system is in static equilibrium. Initially the position of the bite force on the model passes through the mesiobuccal cusp of the upper first molar. In manipulations of the model the position of the bite force is held in a constant position on the maxilla when the height of the maxilla is changed (Fig. 3), but it is held in a constant position on the mandible when gonial angle and ramus height are changed (Figs. 4 and 5). This is necessary to avoid trivial cases in which manipulation of the elements result in no change in the length of the load arm. For example, if the bite point were held constant on the mandible as the maxilla was moved, the distance of the bite force from the condyle would also remain constant and little effect on mechanical advantage would be observed. Thus, in the present model the positioning of the bite force maximizes the effect of manipulation of the model on mechanical advantage. The direction of the bite force is assumed to be perpendicular to the mandibular plane (GO to ME) in the sagittal plane. The directions of the muscle forces are assumed to be along single lines of action. For the temporalis, the line of action (line FT of Fig. 1) is defined as a line intersecting the coronoid tip and running tangent to the ascending ramus. For the masseter, the line of action (line FM of Fig. 1) is defined as a line connecting gonion to the intersecting point of the frontal and squamous processes of the zygoma.2’ During an isometric bite, the jaw-elevating muscles tend to produce a counterclockwise rotation of the mandible (when viewed from the right) which is termed a torque. The strength of the torque is the product of the magnitude of the muscle force (FM and FT) times the perpendicular distance (termed moment arm) of the muscle from the condyle (line segments a and b, respectively). The object being bitten also produces a torque which, in an isometric bite, is equal to but opposite in direction to the sum of the torques produced by the jaw-elevating muscles. This torque is the product of the bite force (FB) times its moment arm (line segment c). The total torque applied to the jaw is 0 because the bite-force torque cancels exactly the muscle-force torques. Thus, there is no movement of the jaw. The mechanical advantage of a muscle is the ratio of the moment arm of the muscle to the moment arm of the load or, in this case, the bite force.* In normal jaw mechanics the mechanical advantage of the jaw adductors is always less than 1 because the moment arm of the muscles is always shorter than that of the load. As mechanical advantage increases and approaches 1, it becomes easier for the muscle to produce a particular bite force. For example, it is easier to perform a bite of a given force at the molars than at the incisors because moving the bite force to the molars from the incisors shortens the moment arm of the load, thus increasing the mechanical advantage of the jaw adductors. I6 Two types of studies were undertaken with the model. In the first study a general model based on values from Bolton’s standard2* was constructed. In this model various morphologic parameters were gradually altered and the temporalis and masseter mechanical advantages were calculated for each change. The height of the maxilla was increased and decreased by 20 mm. at 10 mm. intervals (Fig. 3). Gonial angle was changed from 90 degrees to 150 degrees at lo-degree intervals (Figs. 4 and 5). Ramus height was changed from 50 mm. to 70 mm. at 5 mm. intervals (Fig. 6).
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\
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b
me
Fig. 2. Diagrammatic demonstration of mandibular changes necessary to keep teeth in occlusion if the maxilla is elevated. co, Condylar summit; go, gonion; me, mentale; m, molar bite point; i, incisor bite point; Of, occlusal plane. Solid line represents original mandible position. Broken lines represent jaw position if (a) gonial angle changes or(b) the mandible rotates anteriorly-superiorly to match new molar bite point.
Ideally, one would like to isolate each morphologic change and determine its effect alone on mechanical advantage. This is not always possible in analyses of jaw mechanics, however, since changing only one parameter may prevent the teeth from coming together. For example, if one changes the height of the maxilla (Fig. 2), then in order for the teeth to occlude either the gonial angle must also change or the entire jaw must rotate. Therefore, it was sometimes necessary to use two different analyses of one parameter to gain a full understanding of the effects of making changes. In the second study the mechanical advantages of twenty long-face and twenty-seven short-face patients were compared. These patients had been used in previous cephalomettic studies,‘*, 2o and their cephalometric data are stored on magnetic tape in the Medical Computing Resources Center, The University of Texas Health Science Center at Dallas. By means of graphics programs developed for previous studies,‘** *O plots of the cephalometric profiles for each patient were generated. Values for each of the morphologic parameters in the model were taken from each profile and were plugged into the model. Thus, the mechanical advantage of the temporalis and masseter muscles of each patient were calculated. The mean value for the mechanical advantage of each muscle was then calculated for the long-face and short-face groups and the means were compared by using the Student t test. Results Effects of changing maxilla height. Fig. 3, A demonstrates the effect of changing maxillary height. The beginning position represents the model values for Bolton’s standard for 18-year-old males. The maxilla is then elevated and depressed at 10 mm. intervals without changing the orientation of the plane of the maxilla to allow for mandibular autorotation. The bite point is assumed to have a constant position on the maxilla. No other morphologic changes occur, but the lower jaw is allowed to rotate anterosuperiorly
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FT f
Fig. 3. Changes in mechanics of the temporalis and masseter muscles with shortening of the maxilla. A, Diagram of changes in the model as maxillary height is increased and decreased from Bolton’s standard. FT, Line of action of temporalis; FM, line of action of masseter; f-B, line of action of bite force; S, sella; A! nasion; CO, summit of condyle. 6, Mechanical advantage of temporalis (r) and masseter (M) muscles versus change in maxillary height (in mm.).
so that the tooth rows will remain in contact. This type of “autorotation” is seen clinically when the vertical position of the maxilla is altered. Lowering of the maxilla causes a posteroinferior rotation of the mandible, and the maxillary bite point moves anteriorly relative to the mandible. The result is a 50 percent increase in the length of the moment arm of the load over a 40 mm. change in the position of the maxilla. Rotation of the mandible as the maxilla is lowered causes gonion to move posteriorly and the tip of the coronoid process to move inferiorly. These movements result in a 7 percent decrease in moment arm length for the temporalis and an 18 percent decrease for the masseter. The results of these changes are a decrease in mechanical advantage of 36 percent for the temporalis and 44 percent for the masseter (Fig. 3, B). These results suggest that the greater maxillary height in long-faced patients should produce a decreased mechanical advantage for the temporalis and masseter muscles. Effect ofchanging genial angle. Two separate analyses are needed for a full appreciation of the effect of the gonial angle on mechanical advantage. In the first analysis (Fig. 4, A), the gonial angle is changed without rotation around the mandibular joint. In order for the bite point to remain in position, the maxilla must shift to remain with the lower jaw. In addition, the position of the tip of the coronoid process was kept constant. Therefore, in this analysis the mandible does not change position, but the shape of both the mandible and the maxilla must change to keep the teeth in contact. The position of the
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FT A S-
lN
‘i 90
GONIAL
120 ANGLE
150
Fig. 4. Effect of gonial angle on mechanical advantage I. A. Diagram of changing gonial angle from Bolton’s standard without rotation of the mandible; 17, line of action of temporalis; FM, line of action of masseter; 19, line of action of bite force; S, sella; N, nasion; CO, summit of condyle; GO, gonial angle. B, Mechanical advantage of temporalis (T) and masseter (M) muscles versus gonial angle.
bite point is constant for both the mandible and the maxilla. The effect of these changes on mechanical advantage is shown in Fig. 4, B. For both muscles, mechanical advantage is inversely proportional to the gonial angle because increasing the gonial angle lengthens the load arm while the moment arms of both muscles remain unchanged. As the gonial angle increases from 90 degrees to 150 degrees, mechanical advantage, as measured by this model, decreases by 55 percent for both temporalis and masseter muscles. Note that the effect of changes in the gonial angle is greatest when the gonial angle is relatively small. These results suggest that an increased gonial angle combined with greater maxillary height in long-face patients should sharply reduce the mechanical advantage in both muscles. In the second analysis (Fig. 5, A) the mandible rotates to maintain tooth-to-tooth contact and the maxilla and mandible do not change in shape (except, of course, for the gonial angle). As gonial angle increases, the mandible rotates anteriorly. In this analysis the bite point is assumed to have a constant position on the mandible while moving posteriorly along the maxilla as the gonial angle increases. Because the jaw must rotate anteriorly as the gonial angle increases from 90 degrees to 150 degrees, the moment arm of the load is lengthened by 115 percent. However, anterior
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Fig. 5. Effect of gonial angle on mechanical advantage II. A, Diagram of changing gonial angle from Bolton’s standard with rotation of the mandible; FT, line of action of temporalis; FM, line of action of masseter; FB, line of action of bite force; S, sella; N, nasion; CO, summit of condyle; GO, gonial angle. 8, Mechanical advantage of temporalis (T) and masseter (IV) muscles versus gonial angle.
rotation of the mandible moves gonion anteriorly and the tip of the coronoid process superiorly, thus increasing the moment arms of the muscles by 10 percent for the temporalis and 40 percent for the masseter. The over-all effect on mechanical advantage is shown in Fig. 5, B . Increasing the gonial angle from 90 degrees to 150 degrees causes a 48 percent decrease in mechanical advantage for the temporalis and a 35 percent decrease for the masseter, according to this model. This analysis also suggests that the long-face patient with a larger gonial angle will have a smaller mechanical advantage for the temporalis and masseter muscles. Effects of changing ramus height. The effect of changing ramus height is shown in Fig. 6, A. In this analysis the ramus is lengthened and shortened at 5 mm. intervals and the mandible is rotated to allow the teeth to remain in contact. In this model the bite point maintains a constant position along the mandible. As ramus height increases, the jaw must rotate anterosuperiorly in order for the teeth to remain in contact. Anterior movement of the mandible lengthens the moment arm of the load by 17 percent while lengthening the moment arm of the masseter by 34 percent. Superior movement of the tip of the coronoid process produces only a very slight increase of 4 percent of the moment arm of the temporalis. The over-all results (Fig. 6, B) are a decrease of 10 percent in the mechanical advantage of the temporalis but an increase of 15 percent in the mechanical advantage of the masseter, for a change in ramus height of 20 mm. The effects of the various morphologic changes on mechanical advantage can be
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FT
6 .9 z 4 .a k $ .7 2 .6 4 :
I :-‘a-
.5
'-*-.T
u ; .4 4 ; .3 :
.2 .l 0-
-10
-5 RAMUS
Fig. 6. rotation nasion; versus
0 t5
t10
HEIGHT
Effect of ramus height on mechanical advantage. A, Diagram of changing ramus height with of the mandible. IT, Line of action of temporalis; FM, line of action of masseter; S, sella; N, CO, summit of condyle. B, Mechanical advantage of temporalis (T) and masseter (A4) muscles ramus height.
summarized as follows: (1) Any change which moves the bite point away from the condyle will decrease the mechanical advantage of the adductor muscles by increasing the moment arm of the load; (2) any change which moves gonion anteriorly and/or inferiorly will increase the mechanical advantage of the masseter because its line of action is moved away from the condyle and thus its moment arm is lengthened; and (3) any change which moves the coronoid process superiorly and/or anteriorly will increase the mechanical advantage of the temporalis for the same reasons given above for the masseter. Comparison ofpatient groups. In Fig. 7 the models for three groups Bolton standard 1%year-old males; mean long face (20 patients ~3,20), and mean short face (27 patients”) are superimposed so that their condylar summits match and the mandibular ramus lines are aligned. This type of comparison shows the morphologic differences among the groups: (1) The height of the maxilla (as measured relative to S-N) is greater in the long-face group than in either of the other groups. The short-face group appears to have greater maxillary height than that of the Bolton standard, but this is because of its higher condylar position relative to S-N. (2) Ramus height is greatest in the short-face group and least in the long-face group. (3) The gonial angle is greatest in the long-face group and least in the
Fig. 7. Comparison of muscle mechanics of Bolton standard for 1 &year-old males (solid lines), mean long face group (dashed lines), and mean short face group (dotted lines). S, Sella; N, nasion; CO, condyle summit; CN, tip of coronoid process; GO, gonion; ME, mentale; FT, line of action of temporalis; FM, line of action of masseter; FB, line of action of bite force.
Table I. Comparison of mechanical advantage between long face and short face patients Group
Long face Bolton standard Short face
Mean
temporalis
mechanical
adwntage
0.494 k S.D. = 0.060 0.507 0.520 2 S.D. = 0.048
Mean
masseter
mechanical
advantage
0.545 t S.D. = 0.056 0.601 0.633 f S.D. = 0.050
short-face group. The length of the bite force moment arm is greatest in the long-face group but is also greater in the short-face group than for Bolton’s standard. The moment arm for the temporalis is longest for the Bolton standard and shortest in the short-face group. The moment arm for the masseter is also longest in the short-face group. The differences in mean mechanical advantage between the two groups are shown in Table I. For the temporalis muscle, the short-face group tends to have a larger mechanical advantage than either Bolton’s standard or the long-face group. The differences, however, are not significant (P < 0.098). The short-face group does have a significantly larger mechanical advantage (P < 0.001) for the masseter muscle when compared to the longface group. The masseter mechanical advantage is also larger in the short-face group than Bolton’s standard, although the significance of that difference is not presently evident. Discussion These results suggest that the greater bite force reported for patients with the short face syndrome may be due, at least in part, to the greater mechanical advantage of their adductor muscles. Each of the morphologic differences between the long and short face
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syndromes produces an increased mechanical advantage for the adductor muscles of the short-face patient, with the one exception of the decreased temporalis mechanical advantage when ramus height is lengthened. These results also suggest that surgical alteration of the facial skeleton may produce significant changes in the mechanical advantage of the jaw muscles. For example, moving the maxilla upward in correction of the long face syndrome3 will tend to increase the mechanical advantage of the adductor muscles, but lengthening the maxilla in the correction of the short face syndrome4 will have the opposite effect. Anterior and posterior repositioning of the maxilla also will affect mechanical advantage by changing the relationship of the bite positions to the condyle. Surgical procedures on the mandible may produce even greater changes in mechanical advantage. Mandibular advancement, for example, will decrease mechanical advantage of the adductors by increasing the length of the load arm. * To date, no studies have linked surgically induced changes in mechanical advantage to postoperative changes in muscle function, possible alterations in skeletal morphology in response to these muscle changes, or tendencies toward relapse. However, such studies should be undertaken. At present, surgeons may want to consider changes in mechanical advantage as an additional factor when planning procedures to correct facial disharmonies. These results differ somewhat from those of a previous study7 in which the lines of actions of the temporalis and masseter muscles were determined in a different way. The earlier model was designed to correspond to experiments in which electrodes recorded muscle activity during isometric bites. The direction chosen for the lines of actions of a muscle have profound effects upon calculations of mechanical advantage. In the earlier study mechanical advantage was calculated for the specific portion of the muscle from which recordings were made. In the present study the lines of action have been drawn from anatomic points which more closely reflect the function of the entire muscle.‘l Nevertheless, because muscle force vectors do not necessarily correspond to single lines of action, particularly in complex muscles which may exhibit differential activity,” it is important that interpretations of models of the jaw apparatus be made with caution. In spite of these difficulties, models can lead to useful insights or suggest significant problems requiring experimental investigation. Summary
We have presented a two-dimensional model which allows calculation of mechanical advantage of the human temporalis and masseter muscles. The model is manipulated to demonstrate how selected differences in facial morphology affect mechanical advantage of the muscles. The model is then used to evaluate the differences in mechanical advantage between patients with the long face syndrome and those with the short face syndrome. Differences in facial morphology between these two groups result in significant differences in mechanical advantages of their muscles. Mechanical advantage may, in part, explain observed differences in bite force between the two groups. The model suggests that some surgical procedures used to correct facial disharmonies may have a significant effect on mechanical advantage of the jaw muscles. Dr. J. B. Brammer and Mr. J. Adams helped make tracings of the cephalometric data used in the study. Dr. D. J. Mishelevich
donated computer time to retrieve some of the computer data used in
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and
made
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helpful
REFERENCES 1. Ahlgren, J., Ingervall, B. F., and Thilander, B. L.: Muscle activity in normal and post normal occlusion. AM. J. ORTHOD. 64: 445-456, 1973. 2. Alexander, R.: Animal mechanics, Seattle, 1968, University of Washington Press, pp. 13-15. 3. Bell, W. H., Creekmore, T. D., and Alexander, R. G.: Surgical correction of the long face syndrome, AM. J. ORTHOD. 71: 40-67, 1977. 4. Bell, W. H.: Correction of the short face syndrome-vertical maxillary deficiency: A preliminary report, J. Oral Surg. 35: 110-120, 1977. 5. CarIs%, S.: Nervous coordination and mechanical function of the mandibular elevators. Acta Odontol. Stand. 10 (Supp. 11): 1-131, 19.52. 6. Edgerton, V. R.: Neuromuscular adaptation to power and endurance work, Can. J. Appl. Sport Sci. 1: 49-58, 1976. 7. Finn, R. A., Thmckmorton, G. S., Gonyea, W. J., Barker, D. R., and Bell, W. H.: Neuromuscular characteristics of vertical maxillary dysplasias. In Bell, W. H., Proffitt, W. R., and White, R. P. (editors): Surgical correctionof dentofacial anomalies, Philadelphia, 1980, W. B. SaundersCompany, pp. 1112-l 130. 8. Finn, R. A., Throckmorton, G. S., and Bell, W. H.: Biomechanics of mandibular deficiency, J. Oral Surg. (In press.) 9. Gans, C., and Bock, W.: The functional significance of muscle architecture, a theoretical analysis, Ergeb. Anat. Entw. Gesch. 38: 116-142, 1965. 10. Gonyea, W., and Bonde-Petersen, F.: Contraction properties and fiber types of some forelimb and hindlimb muscles in the cat, Exp. Neurol. 57: 637-644, 1977. 1 I. Gonyea, W., and Bonde-Petersen, F.: Alterations in muscle contractile properties and fiber composition after weight-lifting exercise in cats, Exp. Neurol. 59: 75-84, 1978. 12. Herring, S. W., Grimm, A. F., and Grimm, B. R.: Functional heterogeneity in a multipennate muscle, Am. J. Anat. 154: 563-576, 1979. 13. Hylander, W. L.: The human mandible, lever or link? Am. J. Physiol. Anthropol. 43: 227-243, 1975. 14. Ingervall, B. F.: Facial morphology and activity of temporal and lip muscles during swallowing and chewing, Angle Orthod. 46: 372-380, 1976. 15. Ingervall, B. F., and Thilander, B. L.: Relation between facial morphology and activity of the masticatory muscles, J. Oral. Rehabil. 1: 131-147, 1974. 16. Mansour, R. F., and Reynick, R. J.: In vivo occlusal forces and moments. I. Forces measured in terminal hinge position and associated moments, J. Dent. Res. 53: 114-120, 1975. 17. Moller, E.: The chewing apparatus, Acta Physiol. Stand. 69: Supp. 280, 1953. 18. Opdebeek, H., and Bell, W. H.: The short face syndrome, AM. J. ORTHOD. 73: 499-511, 1978. 19. Sassouni, V.: A classification of skeletal facial types, AM. J. ORTHOD. 55: 109-123, 1969. 20. Schendel, S. A., Eisenfeld, J., Bell, W. H., Epker, B. N., and Mischelevich, D. J.: The long face syndrome: Vertical maxillary excess, AM. J. ORTHOD. 70: 398-408, 1976. 21. Sicher, H., and DuBrul, E. L.: Oral anatomy, ed. 5, St. Louis, 1970, The C. V. Mosby Company, pp. 170-178. 22. Broadbent, B. H., Sr., Broadbent, B. H., Jr., and Golden, W. H.: Bolton standards of dentofacial developmental growth, St. Louis, 1976, The C. V. Mosby Company.