A biomechanical analysis of craniofacial form and bite force Ordean d. Oyen, PhD* and T. Peter Tsay, Dipl Dent, MS, PhD, DDS** C/eve~and, Ohio In vivo measurements of bite force and bone strain obtained in growing African green monkeys were used to study skull biology and geometry. Strain values and distributional patterns seen in association with forceful jaw elevation were inconsistent with most conventional explanations that link upper facial morp.hology with masticatory function and use beam models of craniofacial architecture. The results mandate careful use of concepts about skeletal geometry based on static analysis that have not been experimentally verified with in vivo procedures. In particular, a reevaluation of conventional ideas about the generation and dissipation of forces during contraction of the jaw elevator muscles seems called for. (AM J ORTHOD DENTOFACORTHOP 1991;99:298-309.)
O n e of the structural responsibilities of the skeleton is to withstand and distribute the loads engendered during physiologic movements. The design of the human facial skeleton is also expected to serve the function of distributing masticatory forces without endangering the integrity of facial structures. Following on the work of Benninghoff, t Sicher and Tandler2 proposed a "beam" hypothesis, suggesting the transmission of masticatory force through several "routes" along the facial skeleton (Fig. 1). This view persists essentially unchanged in several textbooks. 3-5 In this model, force generated in the molar area when the jaw closes is said to be transmitted through the key ridge and along the zygomatic bone and lateral border of orbit until it is finally dissipated over the skull. The forces referred to in this model apparently are universally compressive in nature, at least insofar as the cranium is concerned. (Force transmission in the mandible is more problematic. Even though it is not of concern in this discussion, it should be noted that, according to the model, the compressive "dental trajectory" is the most important route of the mandible because it conducts masticatory pressure to the skull.) Forces emanating from the molar region are also transmitted through the maxillary tuberosity along the posterior border of the maxilla and "pterygoid buttress" upward and dissipated over the base of skull. In the premaxillary area, bite force is said to be transmitted through the canine root eminence From Case Western Reserve University School of Dentistry. Supported by National Science Foundation Grants BNS 8217034 and 8520078, O.l. Oyen, P.I.; by National Institutes of Health Grant NIDR DE07182, M.F. Teaford, P.I.; and R.I. Reynolds Company. *Assistant Director. Office of Research Administration; Associate Professor of Orthodontics, Oral Biology, and Anthropology. **Assistant Professor and Vice Chairman, Department of Orthodontics.
298
Fig. 1. Stress trajectories, or "routes," that masticatory forces dissipate in the middle face and cranium. (From Sicher H, Tandler J. Anatomie for Zahnarzte. Wien, Verlag von Springer, 1929.)
and along the Idteral border of the piriform aperture and nasal bone, to be dissipated over the skull. The concepts just described are logical inferences drawn from static analyses of the masticatory apparatus. Moreover, this explanatory model is based on the premise that any impact generated by chewing is not drastically diminished when food is crushed between teeth. Since the architectural design of the skeleton also serves a very important function in providing stimulation to facial growth in growing persons and maintaining homeostasis of facial structure in adults, the pillar-andbeam model can have a profound influence on attempts
Volume 99 Number 4
Biochemical analysis of bite force 299
T a b l e I. Bite force measurements (kg) Monkeys with mixed dentition
Monkeys with permanent dentition Monkey Sex Body
weight Lt M2 Lt MI Lt dm2 L(dml Lt Pm4 dl I
Rt Pro4 Rt dml Rt dm2 Rt MI Rt M2
003 M 4.0 (kg)
006 M 3.7 (kg)
012 M 7.0 (kg)
016 M 3.6 (kg)
593 F 1.7 (kg)
594 M 1.7 (kg)
606 F 1.3 (kg)
27.9 23.9
19.5 15.3
28.5 23.4
20.3 19.1 14.3
8.2 6.7
8.6 7.5
6.4 6.0 5.2
20.6
14.3
21.3 6.0
5.3
3.7
9.8
7.8 14.1
11.4
7.5 8.3
7.5 10.5
5.2 6.0 6.7
24.9 28.1
15.2 17.2
9.6
25.5 28.3 35.4
18.0 21.3
Lt = Left; Rt = right; M I I M 2 = permanent first/second molar; Pro4 = permanent fourth premolar; 1 = permanent incisor; dl = deciduous incisor; d m l l d m 2 = deciduous first/second molar.
to apply the functional matrix concept 6 for the purpose of understanding the mechanisms that regulate and maintain facial harmony. Investigators have shown that tensile forces may be more critical than compressive forces in evoking nontraumatic remodeling changes in long bone. ~ If this concept of tensile forces is correct and can be transferred to the facial skeleton, we are left with the problem of explaining how the pillar-andbeam model works if it relies solely on the predominance of compressive forces. This analysis was designed to examine the nature of the forces transmitted to the lateral orbital margin of the facial skeleton during maximum contraction of masticatory muscles, thereby providing some insights into the validity of the pillar-and-beam model. In this study we tested the hypothesis that the force/remodeling relationship is site-specific and is predominantly tensile in nature. In contrast to earlier studies, which used dry skulls of adults more than two decades ago, ~~° this analysis used in vivo bite force and bone strain data obtained from growing animals. MATERIALS AND METHODS Experimental animals
In this report, results obtained from seven growing African green monkeys (Cercopithecus aethiops) are considered. The animals ranged from those with deciduous teeth and occluding first permanent molars to animals with occluding second permanent molars and erupting third molars. Additional information about each monkey is provided in Table I.
Bite force measurement
Masticatory bite force data were collected through a bite force transducer and according to protocols established by Hylander n and Dechow and CarlsonJ 2 The bite force transducer consists of a 6 x 1.5 × 0.2 cm aluminum beam sandwiched between two other beams of the same width (1.5 cm) but 10 cm in length. Each 10 cm beam has two single-element strain gauges mounted in series on its free inner surface. Leads from the strain gauges pass along the long axis of the instrument through channels milled in the surface of the aluminum spacer beam and exit at the nonworking end, where they are connected with leads to a strain amplifier. Compressive forces acting to bring the 10 cm working beams closer to each other are recorded by t h e strain gauges as the beams are bent. The researcher calibrated the transducer by applying known amounts of force to the working beams and recording the strain output. The strain gauges were calibrated before and after each laboratory recording session. The system is relatively small and easily manipulated, thereby enabling the operator to position it for biting at specific tooth positions. The transducer resists the amount of deformation that would bring the working beams into contact with each other, yet it is precise enough to record even low-level strain. The arrangement of the two gauges in series per beam reduces both variability in bite force data caused by the position of the transducer relative to the tooth row and variability in the direction of bite force. Also, because the strain gauges are loaded on the inner surfaces of the working
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Oyen and Tsay
bite force transducer was then placed between maxillary and mandibular teeth at selected points. Attainment of full tetany, or maximum isometric closure of the mandible, as demonstrated by a plateau in bite force level, was recorded and verified through use of the transducer. It should be noted that in all cases this method of stimulation of the muscles yields forces in excess of those obtained through "natural stimuli" (i.e., normal motor innervation). If no other measurements were required, the animal was then allowed to recover from the anesthesia. Because of the nature of the stimulus, as well as the mildness of the anesthesia, the monkeys usually recovered within 20 to 30 minutes and began to eat immediately upon recovery. Bite force measurements were repeated approximately every 6 months. The bite forceeiectrostimulation procedures were used in conjunction with bone strain measurement techniques described below.
a
a,b,c depict o r i e n t a t i o n ofelementsfirst, second, and t h i r d gauges of a rosette.
Forr~ula f o r detefi~ining Maximum P r i n c i p a l S t r a i n [Ca+Co
"L
~ ' 'V ~ 2 ( , . - -
Cb)Z+2(¢.,
--
Cc) 2] J
¢a,b.c - s t r a i n s measured a t r e s p e c t i v e gauges Formula f o r d e t e r m i n i n g Angle o f Raxinxim P r i n c i p a l
Strain
Bone strain measurement }tan - I [
z%
C 8
(% * --
co)
E c
Fig. 2. Diagrammatic representation of the arrangement of three strain gauges in a rosette and the formula used to derive the maximum principal strain and the principal angle.
beams and coated with water-repellent materials, the instrument effectively withstands strenuous handling in the laboratory. The following procedure was used to obtain maximum unilateral bite force: The monkeys were anesthetized with subcutaneous injections of 5 to 7 mg/kg of Ketaset (Ketamine HCI, Bristol, Syracuse, N.Y.) and 1 to 2 mg/kg of Rompun (Xylazine, Mobay, Syracuse, N.Y.). Unipolar platinum needle electrodes (Grass Instruments E28 subdermal electrodes, Quincy, Mass.) were inserted into the right and left masseter and temporalis muscles through the skin. The electrodes were then attached to a stimulator (Grass Instruments Model 55) and electric current was applied. On the basis of an earlier study of macaques by Dechow and Carlson'-" and on our own work with the vervets, three levels of stimulation were used: 60, 70, and 80 volts (all at 0.8 milliseconds, 60 hertz) during dental loading. In animals with smaller body weights, maximum tetany was attainable with lower stimulation (i.e., 60 or 70 volts). Each level of stimulation is applied for 0.5 to 1.0 second, with 5 to 7 seconds separating episodes of stimulation. This procedure has consistently achieved full tetany of the jaw elevator muscles, presumably including the pterygoids by volume conduction. The
Mechanical (engineering) strain is the deformation of a specimen caused by an external force; it is measured in terms of change in overall dimension per unit dimension (e = 1/1o, where e = strain, 1 = change in specimen length, 1o = original length). Strain is thus a dimensionless unit referring to the ratio of change (elastic deformation) to some basic size in response to applied force. A strain gauge allows measurement, both quantitatively and qualitatively, of this deformation when the specific geometry and resistance of its wire grid are modified by deformation of the solid to ~,vhich the gauge is attached. The strain gauge measures strain in only one direction, along the length of its grid wires, in the plane of the gauge. The sensitivity of a gauge to transverse forces can be adjusted for, and in this study a gauge type that minimized sensitivity to such transverse forces was selected. At the onset of the study, the principal axis of in vivo strain in the circumorbital region was unknown. Thus, rosettes of three identical gauges stacked one upon another, and two gauges oriented 45 ° to'the primary gauge were used to determine maximum and minimum strains and the principal axis of strain. The actual strain calculations are described below and in Fig. 2. Short-term implantable strain gauge techniques were used to measure in vivo bone strains in the facial skeleton in each monkey. The methods used were patterned after studies by Weijs and deJongh '3 and Hylander t~~6 and were developed in direct cooperation with Hylander. Strain gauge implantation. Rosette strain gauges
Volume 99 Number 4
Biochemical analysis of bite force 301 Figs. 3 to 11. Principal strain values and graphic (vectored) representations of maximum principal strains and angles for the seven monkeys reported in this study. For clarity, only vectors of maximum principal strains associated with selected bite points have been drawn. Abbreviations are defined in Table I. i~Rt. M2 I I
I~ I I
II II II
Bite Force
Bite
Point 006
012
Principa] Strains
006
006
012
Lt M2
20
29
35
189/- 59
-65
23
Lt MI
15
23
86/- 46
145/- 54
20
17
Lt Pm4
14
21
56/-
141/- 61
53
17
8
11
261/-118
178/°125
1
25
Rt Pm4
14
26
294/-135
200/-127
3
23
Rt MI
15
28
281/-125
233/-136
2
23
Rt M2
17
35
264/-111
272/-157
0
23
I
1!81
012
Principal Angle
6
II iJ
II| |
.t.M2
ii 11 ||
II Lt,M2
s ~"
Fig. 3. comparison of bite force and bone strains from monkeys 006 (sofid line) and 012 (broken line).
(WA-p6-030WR-120, Measurements Group, Inc., Raleigh, N.C.) were implanted on a short-term basis (several hours) on the frontal process of the zygoma. The position and orientation of each implanted gauge were standardized to allow collection of comparable data about bone strain patterns from different persons. When implanted, each rosette was positioned approximately at the midpoint along the lateral border of the orbit anteroposteriorly and superoinferiorly. One element of the rosette was oriented parallel to the lateral orbital rim; the second element was approximately perpendicular to the axis of the first and parallel with the orbital rim, and the third element of the rosette was oriented 45 ° from the other two elements. The axis of intersection of the rosettes was directed medially. The actual strain gauge bonding procedure was as follows: After the animals were anesthetized by means of the procedure described above, a 3 cm incision was made along the lateral orbital margin (under aseptic conditions) parallel to and approximately I cm from the orbital rim. The soft tissues, including the periosteum, were de-
flected and hemostasis was achieved. The bonding site on the exposed bone was degreased and dehydrated with acetone. The bonding site was then flooded with surface activator and a rosette strain gauge, which had been previously treated with a moisture-resistant coating (M-coat A, Micro-Measurements, Raleigh, N.C.), was bonded to the cortical surface with a cyanoacrylate adhesive (Perma-Bond 910, Micro-Measurements). Before closure of the surgical incision, the strain gauge was temporarily used to form one ann of a Wheatstone bridge by being connected to a strain gauge amplifier, and the functioning of the gauge was confirmed. To prevent lead wire movements that would affect gauge readings, during the installation process the wires were cemented to the cortical bone surface for a distance of at least 5 mm beyond the rosette. The effectiveness of this preventive measure was tested in every instance by tugging on the wires with the gauges activated. Once it was confirmed that good anchorage had been obtained, the free components of the leads were then tagged to the overlying tissue with a single silk stitch
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Oyen and Tsay
Rt.M2
Bite Position
Principal Strains
Principal Angle
Lt M2
145/- 25
41
Lt M1
99/- 20
62
Lt Pm4
76/- 21
89
I
156/-102
4
Rt M1
213/-139
9
Rt M2
211/-134
- 7
L t . M2
a
Fig. 4. Monkey 003, body weight 4.0 kg. Principal strains and angles, with vectors for loading at the incisor and right and left second permanent molars.
and a cadaver needle was used to pass the leads under the skin and out at a point in the region of the right dorsal quadrant of the neck. Strain recording. The anesthetized monkeys, with strain gauges in place, were subjected to the bite forceelectrostimulation procedures described above. With the strain gauge connected to the amplifier, the bite force transducer was placed at a given location between the upper and lower teeth. An electric stimulus was applied to the jaw elevator musculature and simultaneous recordings of bite force and bone strain were obtained. This procedure was repeated with the bite force transducer placed between the incisors and then between the molars. Following bone strain recordings, the strain rosette was removed and the wound was closed. The monkeys were treated with antibiotics, allowed to recover from the anesthesia, and returned to their quarters. Maximum and minimum principal strains and principal angles were algebraically derived from the values of the strains measured at each of the single foil gauges in a stacked rosette (Fig. 2). Maximum principal strain characterizes the maximum deformation that occurs in a material under given loading conditions. The specific orientation of a maximum principal strain in relation to the a axis is referred to as the principal angle. Minimum principal strain is an algebraically derived value of the
strain that occurs perpendicular to the line of maximum principal strain. Both maximum and minimum principal strains can be either tensile or compressive. Because these values are algebraically derived, the absolute value of the minimum principal strain can exceed that of the maximum principal strain. ~7 RESULTS Maximum bite force
Data from the seven monkeys are reported in Table I. The data are arranged into two subgroups--one of monkeys with permanent teeth except third molars and another group of monkeys with mixed dentition. In the table, bite forces in the mixed-dentition group are always less than those in the other group. When the location of the bite point shifts anteriorly from the most posterior bite point (i.e., the molars), the bite force consistently decreases, with the values at the first molars approximately 102% greater than those at the incisors. At the second deciduous molars, the bite force exceeds incisor loads by 40.5%. Bilateral symmetry in maximum bite force is seen, but symmetrical distributions are less apparent in larger animals. A relative difference of some 20% between the "weak" and "strong" sides occurs in posterior bite forces in the larger monkeys (data not shown). Fig. 3 and its table allow a direct comparison of
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Biochemical analysis of bite force 303
I
Bite Position
Principal Strains
Et M2
118/
Principal Angle
34
-65
Lt Ml
861- 46
20
Lt Pm4
56/-
6
53
I
261/-118
1
Rt Pm4
294/-135
3
Rt MI
281/-125
2
Rt M2
264/-111
0
\ ,,.M2
Fig. 5. Monkey 006, body weight 3.7 kg. Principal strains and angles, with vectors for loading at the incisor and right and left second permanent molars.
bite force values and associated bone strains measured on the cortical surface in two different-sized animals. To facilitate comparison, like measurements from two monkeys at a given bite point have been paired, with the values obtained from the smaller monkey always listed to the left. Bite forces in the smaller monkeys are consistently less; The magnitude of difference in every case but one equals or exceeds the relative differences in body weight. In the exceptional instance (at the right second permanent molars), the force generated by the smaller animal is 49% of that generated by the larger animal.
Bone strain analysis Graphic representations of bone strain measurements on the left zygoma are depicted in Figs. 4 to 10. Strains observed in the outer cortical surface of the zygoma are predominantly tensile and relatively low. There is no clear relation between bite force magnitudes and bone strain measurements, regardless of size. The largest principal strains recorded on the zygoma do not occur exclusively in association with a particular bite point. Strains associated with incisal loading some-
times exceed and sometimes are less than those measured when posterior teeth are loaded. In accordance with the experimental protocol (strain gauges unilaterally placed on the left side), maximum principal strains on the zygoma differ significantly, depending on the side of loading. The largest principal strains occur when teeth on the right side are loaded, causing the rosette on the left side to read balancingside strains. An important quality of strain measurements is their directionality. As we explained under Methods, strain direction is reported in this study as the principal angle derived from the calculation of cumulative values of strains obtained from a rosette and expressed relative to the long axis (a) of a given gauge (Fig. 2). When a rosette strain gauge was implanted in the zygomatic region, the a axis was oriented superoinferiorly along the frontal process of the zygomatic bone, roughly parallel to the lateral orbital margin. This orientation was chosen to approximate the trajectory used in the pillarand-beam model. Thus, a maximum principal strain, with an angular measurement at or near zero, is oriented more or less along the trajectory proposed by the model.
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Am. J. Orthod. Dentofac. Orthop. April 1991
Oyen and Tsay
Rt.M2
t ? I'-,., 2 Bite Position
Principal Strains
Principal Ang]e
Lt M2
189/- 59
23
Lt M1
145/- 54
17
Lt Pm4
141/- 61
17
I
178/-125
25
Rt Pm4
200/-127
23
Rt M1
233/-136
23
Rt M2
272/-157
23
Fig. 6. Monkey 012, body weight 7.0 kg. Principal strains and angles, with vectors for loading at the incisor and right and left second permanent molars.
Bite Position
Principal Strains
Principal Angle
Lt M2
84/- 15
-40
Lt MI
0/- 56
-82
22/- 45
18
Lt dm2 I
186/
0
-85
Rt M1
154/-100
-12
Rt M2
121/- 89
9
Fig. 7. Monkey 016, body weight 3.6 kg. Principal strains and angles, with vectors for loading at the incisor and right and left second permanent motars.
a
t~hlme 99 Number4
Biochemical analysis of bite force Bite Position
Principal Strains
305
Principal Angle dl
Lt HI
38/-41
2
Lt dm2
51/-45
- 4
dl
97/-91
6
Rt dm2
85/-85
13
Rt MI
81/-94
17
Fig. 8. Monkey 593, body weight 1.7 kg. Principal strains and angles, with vectors for loading at the deciduous incisor and right and left first permanent molars.
By convention, a negative reading denotes clockwise rotation from the a axis. The angles of maximum principal strains seen in the figures vary somewhat with the apparent vertical axis of the lateral orbital margin. The angles are generally aligned anteriorly or posteriorly to the a axis and mn superiorly. The direction of principal strain changes as the position of the bite point moves. There is no clear relation, however, in the variation of principal angles from the a axis and the position of loading. The principal angles also differ according to which side of the face has been loaded. The angles generally shift in a counterclockwise fashion as the load changes from the left side to the right side. The relationships between magnitude of bite force measured at the left second permanent molar and zygomatic bone strain in monkey 16 are reported in Fig. 11. In this instance electrical stimulation was manipulated so that different states of contraction of the jaw elevator muscles were induced to generate different magnitudes of bite force. The results represented in this figure are from an animal with occluding second permanent molars and a body weight of 3.6 kg. Bone strain was measured on the same side as the occlusal loading. In this example, bite forces show more than a fivefold increase between the lowest and highest values, with changes taking place in a somewhat orderly incremental fashion. In contrast, differences in bone strains associated with the smallest and largest bite forces are less than twofold. From the lowest to the highest bite force measurements and their associated strains, the principal angles showed a counterclockwise rotation of some 10°. Again, the angles of the maximum
principal strains do not appear to be in alignment with the apparent vertical axis of the lateral orbital margin. Fig. 3 shows a side-by-side comparison of bone strains and princip~il angles in two monkeys with different body weights. Because of the difficulty involved in positioning the rosette gauge at identical locations in every animal, the position of the a axis is not exactly the same in these two monkeys. Therefore, the readings concerning principal angles are not directly comparable. However, in the graphic representation, the angles are correctly related to anatomic structures. A reasonable comparison of the orientation of maximum strains is thus possible. The directions of strains in these two monkeys were both upward, with a more posterior orientation for the larger monkey. The most significant difference between these monkeys is the apparently minor change in the direction of maximum strains when the loads are placed on the different teeth in the larger monkey. DISCUSSION
The bite force measurements presented in this report are consistent with findirigs obtained from similar research. ~2 Relatively large forces are generated when posterior teeth are brought to occlusion. These forces decrease when the bite point is moved anteriorly. There is also a proportional relationship between bite force and body weight in the growing animals. Our in vivo results show that the maximum principal strain measured on the cortical surface in the zygomatic area is tensile rather than compressive. From observation of the pillar-and-beam model, one might expect compression in the zygomatic "pillar" when the force
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Am. J. Orthod. Dentofac. Orthop. April 1991
Oyen and Tsay
Rt.M1
Bite Position
Principal Strains
Principal Angle
Lt HI
43/
49
44
Lt dm2
54/- 47
35
dl
220/-137
18
Rt dm2
321/-123
4
Rt Hi
214/-118
10
a
Fig. 9. Monkey 594, body weight 1.17 kg. Principal strains and angles, with vectors for loading at the deciduous incisor and right and left first permanent molars.
generated in occlusion is transmitted to this area. Several explanations seem likely for this situation: First, the architectural arrangement of the skeleton may show compression or tension under load, depending on the point of measurement. When a curved structure is subject to compressive force, the convex surface tends to become more convex and therefore translates increased elastic deformation into tensile strain on the outer surface. The inner, concave side might thus show compression when force is applied. Second, when force is generated through mastication on one side, the attachments of the masticatory muscles on the countralateral side also contract and generate a pulling force that may act across the skull, 's Thus tensile forces generated on the unloaded side of the face could counteract the compressive effect measured on the contralateral side in response to dental loads and, therefore, d e c r e a s e - - o r even reverse--the compressive force caused by biting. On the frontal process of the zygoma, the highest tensile strains usually occurred during contralateral loading (i.e., when the gauge and bite point were on opposite sides). These findings are difficult to explain on the basis of the beam-and-pillar model, which essentially links conduction of dentally transmitted, presumably compressive bite force, to the final form of the facial skeleton. Our finding that there is no clear correlation between
the magnitude of bite force and bone strain seems to indicate that dentally transmitted bite force is not the sole factor that determines bone strains in the zygomatic region. One must also consider the effects of the forces conducted to the skull by the muscles of mastication through the bones. It can also be argued that forces generated by the simultaneous contraction of jaw elevator muscles on the opposite side and isometric contraction of muscles that maintain head posture also influence the bone strain measured on the biting side. To date, these factors have never really been given adequate consideration, especially through in vivo tests. This picture becomes even more complex when one considers the interindividual and intraindividual variations of principal angles. Nonetheless, our findings indicate that dentally transmitted bite force per se seems to play a minor role in bone strain determination, at least in the zygomatic area. If conventional wisdom concerning bone strain is adhered to, the evidence given in this report and that presented by Hylander and his colleagues ~6 might lead one to conclude that growth in the zygomatic region is not related in any meaningful way to masticatory function and that other explanatory models are called for. This concept has already been argued forcefully by a variety of investigators, the most notable of whom probably has been Moss. 6 However, there are several good
Vohmte 99 Number 4
Biochemical analysis of bite force
Bite Position
Principal Strains
307
Principal Angle
Lt M1
55/
5
45
Lt dm2
70/-25
29
Lt dml
66/-27
34
dl
88/-30
-36
Rt dml
95/-43
-22
Rt dm2
87/-42
-20
Rt M1
82/-37
-22
Fig. 1().,Monkey 606, body weight 1.3 kg. Principal strains and angles, with vectors for loading at the deciduous incisor and right and left first permanent molars.
Bite Force
Principal Strains
Principal Angle ~axo
2
61/-29
-16
4
98/-60
-13
6
101/-69
-13
7
105/-80
-10
8
105/-86
- 8
9
105/-86
- 8
10
101/-85
5
Fig. 11. Monkey 016. Principal strains and angles shown for differing magnitudes of bite force at the same bite point (incisors); only the strains and angles for the largest (Max.) and smallest (Min.) bite forces have been vectored.
reasons for exercising due caution before using strain magnitudes as the sole basis for casting aside a model of growth that posits a close, but not exclusive, relationship between masticatory function and the middle and upper parts of the facial skeleton. First, virtually all of our ideas about bone strain have been derived exclusively from studies of adult long bones that consist almost entirely of lamellar bone tissue. In our study, only nonadults have been considered, and it has been well established that in a wide variety
of species the zygomatic region of the primate facial skeleton in both adults and nonadults initially comprises largely nonlamellar bone tissue. ~9-2j Moreover, the physical properties of these nonlamellar tissues are very poorly understood, and experimental data on their strain characteristics are virtually nonexistent. 2-''23 Second, in the postcranial skeleton, the line of action of a given muscle tends to be along the vertical axis of the involved skeletal component(s), something that is easily determined in "long" bones. One of the challenging aspects
308
Oyen and Tsay
o f interpreting bone strain data in the zygomatic region is its geometric complexity. Bone-muscle relationships in this area do not closely resemble and, therefore, cannot easily be modeled on the relationships between long bones and muscles. Third, conventional studies of bone strain tend to focus on considerations o f the "safety factor" that enables a bone, usually in an adult, to resist strains up to a certain level without experiencing failure. The role played by strain during normal growth o f a bone remains to be determined; we have a sense about the conditions that are involved when a bone breaks, but we know surprisingly little about the conditions that prevail during growth. It is likely that the principles governing the growth and remodeling changes in the facial skeleton vary from those derived from studies o t adult long bones. Wholesale transfer o f conclusions obtained from studies of long bones to the phenomena o f facial growth may be misleading, even erroneous. Further research in the basic areas o f stress/strain relations o f facial bones as well as the physical properties of the tissues involved seems indicated. One may conclude that the hypothesis tested in this study is correct. The force/remodeling relationship is site-specific and may differ from long bones to facial bones. Moreover, tensile strain seems to be predominant. It must be borne in mind, however, that the electrically induced tetanic contractions o f the masticatory muscles must differ from the recruitment patterns that actually occur during a normal chewing cycle. In a sense, the data on bite forces and bone strain reportect here more closely resemble the outcomes that would prevail during isometric forceful occlusion, as during extreme clenching. It must also be remembered that the bone strain obtained in this experiment results from force transmitted to the zygomatic region with no or little decrease in m a g n i t u d e - - i . e . , an isometric contraction. In efficient physiologic mastication, a significant part o f the impact generated by chewing is absorbed by food itself while the j a w closes, thereby reducing the amount o f force actually transmitted to the facial skeleton. It is o f interest to note that, in a preliminary report, Hylander and his colleagues '6 have described similar results in adult monkeys o f another species under more physiologic conditions. In this study, a body of in vivo bite force and facial bone strain data from a population o f growing monkeys has been described and analyzed. Observations on the functional implications of these data are made with the precaution that methodologic constraints color our resuits and that current understanding o f strains and bone
Am. J. Orthod. Dentofac. Orthop. April 1991
growth in general is rather meager. For now, it seems that the immediate value o f our research stems from its demonstration of some o f the advantages as well as some o f the dangers involved in attempts to use such phenomena as bite force and bone strain in the testing and construction o f explanatory models for biologic structures. These results and analyses also should serve to remind us that due caution must be used in the application o f seductively logical models whose validity has never really been verified through in vivo testing. REFERENCES 1. Benninghoff A. Spaltlinien am Knochen; eine Methode zur Ermittlung der Architektur platter Knochen. Verh Anat Anz 1925;60:189-206. 2. Sicher H, Tandler J. Anatomie fllr Zahnarzte. Wien: Verlag yon Springer, 1928:298. 3. Graber TM. Orthodontics: principles and practice. 3rd ed. Philadelphia: WB Saunders, 1972:133. 4. SchumacherGH. Anatomic furStomatlogenLehrbuchundAtlas. Vol 1. Leipzig: Barth, 1984:147, 165. 171. 5. DuBrul EL. Sicher's oral anatomy: 8th ed. St. Louis: Ishiyaku EuroAmerican, 1988:56-60. 6. Nloss NIL, Young RW. A functional approach to craniology. Am J Phys Anthropol 1960;57:904-8. 7. Cowin SC. Mechanical modeling of !he stress and adaptation process in bone. Calcif Tissue Int 1984;36:$98-Si03. 8. Endo B. Experimental studies on the mechanical significanceof the form of the human facial skeleton. J Fac Sci Univ Tokyo, Sect V, Anthropology 1966;3:1-106. 9. Endo B. Mechanical analysis of the form of the human facial skeleton. Vll Congr Int Sci Anthrop Ethol 1967;2:346-53. 10. Endo B. Analysis of stresses around the orbit due to masseter and temporalis muscles. J Anthropol SOCNippon 1970;78:25166. 11. Hy!ander WL. Mandibular function in Galago crassicaudatus and Macacafascicularis: an in vivo approach to stress analysis of the mandible. J Morphol 1979;159:253-96. 12. Dechow P, Carlson DS. A method of bite force measurement in primate. J Biomech 1983;16:797-802. 13. Weijs WA, deJongh HJ. Strain in mandibular alveolar bone during mastication in the rabbit. Arch Oral Biol 1971;22:667-775. 14. Hylander WL. In vivo bone strain in the mandible of Galago crassicaudatus. Am J Phys Anthropol 1977;46:309-26. 15. Hylander WL. Bone strain in the mandibular symphysis of Macacafascicularis. J Dent Res (Spec Issue B) 1977;56:344. 16. Hylander WL, Picq PG, Johnson KR. A preliminary stress analysis of the supraorbital region in Macacafascicularis. Am Phys Anthropol. 1987;72:214. 17. Beckwith TG, Buck NL. Marangoni RD. Mechanical measurements. Reading: Addison-Wesley, 1982:388. 18. Behrents RG. Carlson DS, Abdelnour T. In vivo analysis of bone strain about the sagittal suture in Macaca mulatta during masticatory movements. J Dent Res 1978;57:904-8. 19. Oyen OJ, Walker AC, Rice R. Craniofacial growth in the olive baboons (Papio cynocephalus anubis): browridge formation. Growth 1979;43:174-87. 20. Oyen OJ, Rice RW, Enlow DH. Cortical surface patterns in human and nonhuman primates. Am J Phys Anthropol 1981;54:415-9.
Biochemical analysis of bite force
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21. Oyen OJ. Masticatory function and histogenesis of the middle and upper face in chimpanzees (P. troglodytes). In: Dixon AR, Sarnat BG, eds. Factors and mechanisms influencing bone growth: progress in clinical and biological research. Vol 101. New York: Liss, 1982:559-68. 22. Evans FG. Mechanical properties of bone. Springfield: Charles C Thomas, 1973. 23. Currey JD. Rigid Material. In: Wainwright SA, Biggs WD, Cur-
309
rey JD, Gosline JM, eds. Mechanical design in organisms. Princeton: Princeton University Press, 1976:144-240.
Reprint requests to: Dr. Ordean J. Oyen Office of Research Administration Case Western Reserve University Cleveland, OH 44106
AAO MEETING CALENDAR
1991--Seattle, Wash., May 11 to 15, Seattle Convention Center 1992--St. Louis, Mo., May 10 to 13, St. Louis Convention Center 1993--Toronto, Canada, May 16 to 19, Metropolitan Toronto Convention Center 1994--Orlando, Fla., May 1 to 4, Orange County Convention and Civic Center 1995--San Francisco, Calif., May 7 to 10, Moscone Convention Center 1996--Denver, Colo., May 12-15, Colorado Convention Center
O n e of the structural responsibilities of the skeleton is to withstand and distribute the loads engendered during physiologic movements. The design of the human facial skeleton is also expected to serve the function of distributing masticatory forces without endangering the integrity of facial structures. Following on the work of Benninghoff, t Sicher and Tandler2 proposed a "beam" hypothesis, suggesting the transmission of masticatory force through several "routes" along the facial skeleton (Fig. 1). This view persists essentially unchanged in several textbooks. 3-5 In this model, force generated in the molar area when the jaw closes is said to be transmitted through the key ridge and along the zygomatic bone and lateral border of orbit until it is finally dissipated over the skull. The forces referred to in this model apparently are universally compressive in nature, at least insofar as the cranium is concerned. (Force transmission in the mandible is more problematic. Even though it is not of concern in this discussion, it should be noted that, according to the model, the compressive "dental trajectory" is the most important route of the mandible because it conducts masticatory pressure to the skull.) Forces emanating from the molar region are also transmitted through the maxillary tuberosity along the posterior border of the maxilla and "pterygoid buttress" upward and dissipated over the base of skull. In the premaxillary area, bite force is said to be transmitted through the canine root eminence From Case Western Reserve University School of Dentistry. Supported by National Science Foundation Grants BNS 8217034 and 8520078, O.l. Oyen, P.I.; by National Institutes of Health Grant NIDR DE07182, M.F. Teaford, P.I.; and R.I. Reynolds Company. *Assistant Director. Office of Research Administration; Associate Professor of Orthodontics, Oral Biology, and Anthropology. **Assistant Professor and Vice Chairman, Department of Orthodontics.
298
Fig. 1. Stress trajectories, or "routes," that masticatory forces dissipate in the middle face and cranium. (From Sicher H, Tandler J. Anatomie for Zahnarzte. Wien, Verlag von Springer, 1929.)
and along the Idteral border of the piriform aperture and nasal bone, to be dissipated over the skull. The concepts just described are logical inferences drawn from static analyses of the masticatory apparatus. Moreover, this explanatory model is based on the premise that any impact generated by chewing is not drastically diminished when food is crushed between teeth. Since the architectural design of the skeleton also serves a very important function in providing stimulation to facial growth in growing persons and maintaining homeostasis of facial structure in adults, the pillar-andbeam model can have a profound influence on attempts
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Biochemical analysis of bite force 299
T a b l e I. Bite force measurements (kg) Monkeys with mixed dentition
Monkeys with permanent dentition Monkey Sex Body
weight Lt M2 Lt MI Lt dm2 L(dml Lt Pm4 dl I
Rt Pro4 Rt dml Rt dm2 Rt MI Rt M2
003 M 4.0 (kg)
006 M 3.7 (kg)
012 M 7.0 (kg)
016 M 3.6 (kg)
593 F 1.7 (kg)
594 M 1.7 (kg)
606 F 1.3 (kg)
27.9 23.9
19.5 15.3
28.5 23.4
20.3 19.1 14.3
8.2 6.7
8.6 7.5
6.4 6.0 5.2
20.6
14.3
21.3 6.0
5.3
3.7
9.8
7.8 14.1
11.4
7.5 8.3
7.5 10.5
5.2 6.0 6.7
24.9 28.1
15.2 17.2
9.6
25.5 28.3 35.4
18.0 21.3
Lt = Left; Rt = right; M I I M 2 = permanent first/second molar; Pro4 = permanent fourth premolar; 1 = permanent incisor; dl = deciduous incisor; d m l l d m 2 = deciduous first/second molar.
to apply the functional matrix concept 6 for the purpose of understanding the mechanisms that regulate and maintain facial harmony. Investigators have shown that tensile forces may be more critical than compressive forces in evoking nontraumatic remodeling changes in long bone. ~ If this concept of tensile forces is correct and can be transferred to the facial skeleton, we are left with the problem of explaining how the pillar-andbeam model works if it relies solely on the predominance of compressive forces. This analysis was designed to examine the nature of the forces transmitted to the lateral orbital margin of the facial skeleton during maximum contraction of masticatory muscles, thereby providing some insights into the validity of the pillar-and-beam model. In this study we tested the hypothesis that the force/remodeling relationship is site-specific and is predominantly tensile in nature. In contrast to earlier studies, which used dry skulls of adults more than two decades ago, ~~° this analysis used in vivo bite force and bone strain data obtained from growing animals. MATERIALS AND METHODS Experimental animals
In this report, results obtained from seven growing African green monkeys (Cercopithecus aethiops) are considered. The animals ranged from those with deciduous teeth and occluding first permanent molars to animals with occluding second permanent molars and erupting third molars. Additional information about each monkey is provided in Table I.
Bite force measurement
Masticatory bite force data were collected through a bite force transducer and according to protocols established by Hylander n and Dechow and CarlsonJ 2 The bite force transducer consists of a 6 x 1.5 × 0.2 cm aluminum beam sandwiched between two other beams of the same width (1.5 cm) but 10 cm in length. Each 10 cm beam has two single-element strain gauges mounted in series on its free inner surface. Leads from the strain gauges pass along the long axis of the instrument through channels milled in the surface of the aluminum spacer beam and exit at the nonworking end, where they are connected with leads to a strain amplifier. Compressive forces acting to bring the 10 cm working beams closer to each other are recorded by t h e strain gauges as the beams are bent. The researcher calibrated the transducer by applying known amounts of force to the working beams and recording the strain output. The strain gauges were calibrated before and after each laboratory recording session. The system is relatively small and easily manipulated, thereby enabling the operator to position it for biting at specific tooth positions. The transducer resists the amount of deformation that would bring the working beams into contact with each other, yet it is precise enough to record even low-level strain. The arrangement of the two gauges in series per beam reduces both variability in bite force data caused by the position of the transducer relative to the tooth row and variability in the direction of bite force. Also, because the strain gauges are loaded on the inner surfaces of the working
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Oyen and Tsay
bite force transducer was then placed between maxillary and mandibular teeth at selected points. Attainment of full tetany, or maximum isometric closure of the mandible, as demonstrated by a plateau in bite force level, was recorded and verified through use of the transducer. It should be noted that in all cases this method of stimulation of the muscles yields forces in excess of those obtained through "natural stimuli" (i.e., normal motor innervation). If no other measurements were required, the animal was then allowed to recover from the anesthesia. Because of the nature of the stimulus, as well as the mildness of the anesthesia, the monkeys usually recovered within 20 to 30 minutes and began to eat immediately upon recovery. Bite force measurements were repeated approximately every 6 months. The bite forceeiectrostimulation procedures were used in conjunction with bone strain measurement techniques described below.
a
a,b,c depict o r i e n t a t i o n ofelementsfirst, second, and t h i r d gauges of a rosette.
Forr~ula f o r detefi~ining Maximum P r i n c i p a l S t r a i n [Ca+Co
"L
~ ' 'V ~ 2 ( , . - -
Cb)Z+2(¢.,
--
Cc) 2] J
¢a,b.c - s t r a i n s measured a t r e s p e c t i v e gauges Formula f o r d e t e r m i n i n g Angle o f Raxinxim P r i n c i p a l
Strain
Bone strain measurement }tan - I [
z%
C 8
(% * --
co)
E c
Fig. 2. Diagrammatic representation of the arrangement of three strain gauges in a rosette and the formula used to derive the maximum principal strain and the principal angle.
beams and coated with water-repellent materials, the instrument effectively withstands strenuous handling in the laboratory. The following procedure was used to obtain maximum unilateral bite force: The monkeys were anesthetized with subcutaneous injections of 5 to 7 mg/kg of Ketaset (Ketamine HCI, Bristol, Syracuse, N.Y.) and 1 to 2 mg/kg of Rompun (Xylazine, Mobay, Syracuse, N.Y.). Unipolar platinum needle electrodes (Grass Instruments E28 subdermal electrodes, Quincy, Mass.) were inserted into the right and left masseter and temporalis muscles through the skin. The electrodes were then attached to a stimulator (Grass Instruments Model 55) and electric current was applied. On the basis of an earlier study of macaques by Dechow and Carlson'-" and on our own work with the vervets, three levels of stimulation were used: 60, 70, and 80 volts (all at 0.8 milliseconds, 60 hertz) during dental loading. In animals with smaller body weights, maximum tetany was attainable with lower stimulation (i.e., 60 or 70 volts). Each level of stimulation is applied for 0.5 to 1.0 second, with 5 to 7 seconds separating episodes of stimulation. This procedure has consistently achieved full tetany of the jaw elevator muscles, presumably including the pterygoids by volume conduction. The
Mechanical (engineering) strain is the deformation of a specimen caused by an external force; it is measured in terms of change in overall dimension per unit dimension (e = 1/1o, where e = strain, 1 = change in specimen length, 1o = original length). Strain is thus a dimensionless unit referring to the ratio of change (elastic deformation) to some basic size in response to applied force. A strain gauge allows measurement, both quantitatively and qualitatively, of this deformation when the specific geometry and resistance of its wire grid are modified by deformation of the solid to ~,vhich the gauge is attached. The strain gauge measures strain in only one direction, along the length of its grid wires, in the plane of the gauge. The sensitivity of a gauge to transverse forces can be adjusted for, and in this study a gauge type that minimized sensitivity to such transverse forces was selected. At the onset of the study, the principal axis of in vivo strain in the circumorbital region was unknown. Thus, rosettes of three identical gauges stacked one upon another, and two gauges oriented 45 ° to'the primary gauge were used to determine maximum and minimum strains and the principal axis of strain. The actual strain calculations are described below and in Fig. 2. Short-term implantable strain gauge techniques were used to measure in vivo bone strains in the facial skeleton in each monkey. The methods used were patterned after studies by Weijs and deJongh '3 and Hylander t~~6 and were developed in direct cooperation with Hylander. Strain gauge implantation. Rosette strain gauges
Volume 99 Number 4
Biochemical analysis of bite force 301 Figs. 3 to 11. Principal strain values and graphic (vectored) representations of maximum principal strains and angles for the seven monkeys reported in this study. For clarity, only vectors of maximum principal strains associated with selected bite points have been drawn. Abbreviations are defined in Table I. i~Rt. M2 I I
I~ I I
II II II
Bite Force
Bite
Point 006
012
Principa] Strains
006
006
012
Lt M2
20
29
35
189/- 59
-65
23
Lt MI
15
23
86/- 46
145/- 54
20
17
Lt Pm4
14
21
56/-
141/- 61
53
17
8
11
261/-118
178/°125
1
25
Rt Pm4
14
26
294/-135
200/-127
3
23
Rt MI
15
28
281/-125
233/-136
2
23
Rt M2
17
35
264/-111
272/-157
0
23
I
1!81
012
Principal Angle
6
II iJ
II| |
.t.M2
ii 11 ||
II Lt,M2
s ~"
Fig. 3. comparison of bite force and bone strains from monkeys 006 (sofid line) and 012 (broken line).
(WA-p6-030WR-120, Measurements Group, Inc., Raleigh, N.C.) were implanted on a short-term basis (several hours) on the frontal process of the zygoma. The position and orientation of each implanted gauge were standardized to allow collection of comparable data about bone strain patterns from different persons. When implanted, each rosette was positioned approximately at the midpoint along the lateral border of the orbit anteroposteriorly and superoinferiorly. One element of the rosette was oriented parallel to the lateral orbital rim; the second element was approximately perpendicular to the axis of the first and parallel with the orbital rim, and the third element of the rosette was oriented 45 ° from the other two elements. The axis of intersection of the rosettes was directed medially. The actual strain gauge bonding procedure was as follows: After the animals were anesthetized by means of the procedure described above, a 3 cm incision was made along the lateral orbital margin (under aseptic conditions) parallel to and approximately I cm from the orbital rim. The soft tissues, including the periosteum, were de-
flected and hemostasis was achieved. The bonding site on the exposed bone was degreased and dehydrated with acetone. The bonding site was then flooded with surface activator and a rosette strain gauge, which had been previously treated with a moisture-resistant coating (M-coat A, Micro-Measurements, Raleigh, N.C.), was bonded to the cortical surface with a cyanoacrylate adhesive (Perma-Bond 910, Micro-Measurements). Before closure of the surgical incision, the strain gauge was temporarily used to form one ann of a Wheatstone bridge by being connected to a strain gauge amplifier, and the functioning of the gauge was confirmed. To prevent lead wire movements that would affect gauge readings, during the installation process the wires were cemented to the cortical bone surface for a distance of at least 5 mm beyond the rosette. The effectiveness of this preventive measure was tested in every instance by tugging on the wires with the gauges activated. Once it was confirmed that good anchorage had been obtained, the free components of the leads were then tagged to the overlying tissue with a single silk stitch
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Am, J. Orthod. Dentofac. Orthop. April t991
Oyen and Tsay
Rt.M2
Bite Position
Principal Strains
Principal Angle
Lt M2
145/- 25
41
Lt M1
99/- 20
62
Lt Pm4
76/- 21
89
I
156/-102
4
Rt M1
213/-139
9
Rt M2
211/-134
- 7
L t . M2
a
Fig. 4. Monkey 003, body weight 4.0 kg. Principal strains and angles, with vectors for loading at the incisor and right and left second permanent molars.
and a cadaver needle was used to pass the leads under the skin and out at a point in the region of the right dorsal quadrant of the neck. Strain recording. The anesthetized monkeys, with strain gauges in place, were subjected to the bite forceelectrostimulation procedures described above. With the strain gauge connected to the amplifier, the bite force transducer was placed at a given location between the upper and lower teeth. An electric stimulus was applied to the jaw elevator musculature and simultaneous recordings of bite force and bone strain were obtained. This procedure was repeated with the bite force transducer placed between the incisors and then between the molars. Following bone strain recordings, the strain rosette was removed and the wound was closed. The monkeys were treated with antibiotics, allowed to recover from the anesthesia, and returned to their quarters. Maximum and minimum principal strains and principal angles were algebraically derived from the values of the strains measured at each of the single foil gauges in a stacked rosette (Fig. 2). Maximum principal strain characterizes the maximum deformation that occurs in a material under given loading conditions. The specific orientation of a maximum principal strain in relation to the a axis is referred to as the principal angle. Minimum principal strain is an algebraically derived value of the
strain that occurs perpendicular to the line of maximum principal strain. Both maximum and minimum principal strains can be either tensile or compressive. Because these values are algebraically derived, the absolute value of the minimum principal strain can exceed that of the maximum principal strain. ~7 RESULTS Maximum bite force
Data from the seven monkeys are reported in Table I. The data are arranged into two subgroups--one of monkeys with permanent teeth except third molars and another group of monkeys with mixed dentition. In the table, bite forces in the mixed-dentition group are always less than those in the other group. When the location of the bite point shifts anteriorly from the most posterior bite point (i.e., the molars), the bite force consistently decreases, with the values at the first molars approximately 102% greater than those at the incisors. At the second deciduous molars, the bite force exceeds incisor loads by 40.5%. Bilateral symmetry in maximum bite force is seen, but symmetrical distributions are less apparent in larger animals. A relative difference of some 20% between the "weak" and "strong" sides occurs in posterior bite forces in the larger monkeys (data not shown). Fig. 3 and its table allow a direct comparison of
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Biochemical analysis of bite force 303
I
Bite Position
Principal Strains
Et M2
118/
Principal Angle
34
-65
Lt Ml
861- 46
20
Lt Pm4
56/-
6
53
I
261/-118
1
Rt Pm4
294/-135
3
Rt MI
281/-125
2
Rt M2
264/-111
0
\ ,,.M2
Fig. 5. Monkey 006, body weight 3.7 kg. Principal strains and angles, with vectors for loading at the incisor and right and left second permanent molars.
bite force values and associated bone strains measured on the cortical surface in two different-sized animals. To facilitate comparison, like measurements from two monkeys at a given bite point have been paired, with the values obtained from the smaller monkey always listed to the left. Bite forces in the smaller monkeys are consistently less; The magnitude of difference in every case but one equals or exceeds the relative differences in body weight. In the exceptional instance (at the right second permanent molars), the force generated by the smaller animal is 49% of that generated by the larger animal.
Bone strain analysis Graphic representations of bone strain measurements on the left zygoma are depicted in Figs. 4 to 10. Strains observed in the outer cortical surface of the zygoma are predominantly tensile and relatively low. There is no clear relation between bite force magnitudes and bone strain measurements, regardless of size. The largest principal strains recorded on the zygoma do not occur exclusively in association with a particular bite point. Strains associated with incisal loading some-
times exceed and sometimes are less than those measured when posterior teeth are loaded. In accordance with the experimental protocol (strain gauges unilaterally placed on the left side), maximum principal strains on the zygoma differ significantly, depending on the side of loading. The largest principal strains occur when teeth on the right side are loaded, causing the rosette on the left side to read balancingside strains. An important quality of strain measurements is their directionality. As we explained under Methods, strain direction is reported in this study as the principal angle derived from the calculation of cumulative values of strains obtained from a rosette and expressed relative to the long axis (a) of a given gauge (Fig. 2). When a rosette strain gauge was implanted in the zygomatic region, the a axis was oriented superoinferiorly along the frontal process of the zygomatic bone, roughly parallel to the lateral orbital margin. This orientation was chosen to approximate the trajectory used in the pillarand-beam model. Thus, a maximum principal strain, with an angular measurement at or near zero, is oriented more or less along the trajectory proposed by the model.
304
Am. J. Orthod. Dentofac. Orthop. April 1991
Oyen and Tsay
Rt.M2
t ? I'-,., 2 Bite Position
Principal Strains
Principal Ang]e
Lt M2
189/- 59
23
Lt M1
145/- 54
17
Lt Pm4
141/- 61
17
I
178/-125
25
Rt Pm4
200/-127
23
Rt M1
233/-136
23
Rt M2
272/-157
23
Fig. 6. Monkey 012, body weight 7.0 kg. Principal strains and angles, with vectors for loading at the incisor and right and left second permanent molars.
Bite Position
Principal Strains
Principal Angle
Lt M2
84/- 15
-40
Lt MI
0/- 56
-82
22/- 45
18
Lt dm2 I
186/
0
-85
Rt M1
154/-100
-12
Rt M2
121/- 89
9
Fig. 7. Monkey 016, body weight 3.6 kg. Principal strains and angles, with vectors for loading at the incisor and right and left second permanent motars.
a
t~hlme 99 Number4
Biochemical analysis of bite force Bite Position
Principal Strains
305
Principal Angle dl
Lt HI
38/-41
2
Lt dm2
51/-45
- 4
dl
97/-91
6
Rt dm2
85/-85
13
Rt MI
81/-94
17
Fig. 8. Monkey 593, body weight 1.7 kg. Principal strains and angles, with vectors for loading at the deciduous incisor and right and left first permanent molars.
By convention, a negative reading denotes clockwise rotation from the a axis. The angles of maximum principal strains seen in the figures vary somewhat with the apparent vertical axis of the lateral orbital margin. The angles are generally aligned anteriorly or posteriorly to the a axis and mn superiorly. The direction of principal strain changes as the position of the bite point moves. There is no clear relation, however, in the variation of principal angles from the a axis and the position of loading. The principal angles also differ according to which side of the face has been loaded. The angles generally shift in a counterclockwise fashion as the load changes from the left side to the right side. The relationships between magnitude of bite force measured at the left second permanent molar and zygomatic bone strain in monkey 16 are reported in Fig. 11. In this instance electrical stimulation was manipulated so that different states of contraction of the jaw elevator muscles were induced to generate different magnitudes of bite force. The results represented in this figure are from an animal with occluding second permanent molars and a body weight of 3.6 kg. Bone strain was measured on the same side as the occlusal loading. In this example, bite forces show more than a fivefold increase between the lowest and highest values, with changes taking place in a somewhat orderly incremental fashion. In contrast, differences in bone strains associated with the smallest and largest bite forces are less than twofold. From the lowest to the highest bite force measurements and their associated strains, the principal angles showed a counterclockwise rotation of some 10°. Again, the angles of the maximum
principal strains do not appear to be in alignment with the apparent vertical axis of the lateral orbital margin. Fig. 3 shows a side-by-side comparison of bone strains and princip~il angles in two monkeys with different body weights. Because of the difficulty involved in positioning the rosette gauge at identical locations in every animal, the position of the a axis is not exactly the same in these two monkeys. Therefore, the readings concerning principal angles are not directly comparable. However, in the graphic representation, the angles are correctly related to anatomic structures. A reasonable comparison of the orientation of maximum strains is thus possible. The directions of strains in these two monkeys were both upward, with a more posterior orientation for the larger monkey. The most significant difference between these monkeys is the apparently minor change in the direction of maximum strains when the loads are placed on the different teeth in the larger monkey. DISCUSSION
The bite force measurements presented in this report are consistent with findirigs obtained from similar research. ~2 Relatively large forces are generated when posterior teeth are brought to occlusion. These forces decrease when the bite point is moved anteriorly. There is also a proportional relationship between bite force and body weight in the growing animals. Our in vivo results show that the maximum principal strain measured on the cortical surface in the zygomatic area is tensile rather than compressive. From observation of the pillar-and-beam model, one might expect compression in the zygomatic "pillar" when the force
306
Am. J. Orthod. Dentofac. Orthop. April 1991
Oyen and Tsay
Rt.M1
Bite Position
Principal Strains
Principal Angle
Lt HI
43/
49
44
Lt dm2
54/- 47
35
dl
220/-137
18
Rt dm2
321/-123
4
Rt Hi
214/-118
10
a
Fig. 9. Monkey 594, body weight 1.17 kg. Principal strains and angles, with vectors for loading at the deciduous incisor and right and left first permanent molars.
generated in occlusion is transmitted to this area. Several explanations seem likely for this situation: First, the architectural arrangement of the skeleton may show compression or tension under load, depending on the point of measurement. When a curved structure is subject to compressive force, the convex surface tends to become more convex and therefore translates increased elastic deformation into tensile strain on the outer surface. The inner, concave side might thus show compression when force is applied. Second, when force is generated through mastication on one side, the attachments of the masticatory muscles on the countralateral side also contract and generate a pulling force that may act across the skull, 's Thus tensile forces generated on the unloaded side of the face could counteract the compressive effect measured on the contralateral side in response to dental loads and, therefore, d e c r e a s e - - o r even reverse--the compressive force caused by biting. On the frontal process of the zygoma, the highest tensile strains usually occurred during contralateral loading (i.e., when the gauge and bite point were on opposite sides). These findings are difficult to explain on the basis of the beam-and-pillar model, which essentially links conduction of dentally transmitted, presumably compressive bite force, to the final form of the facial skeleton. Our finding that there is no clear correlation between
the magnitude of bite force and bone strain seems to indicate that dentally transmitted bite force is not the sole factor that determines bone strains in the zygomatic region. One must also consider the effects of the forces conducted to the skull by the muscles of mastication through the bones. It can also be argued that forces generated by the simultaneous contraction of jaw elevator muscles on the opposite side and isometric contraction of muscles that maintain head posture also influence the bone strain measured on the biting side. To date, these factors have never really been given adequate consideration, especially through in vivo tests. This picture becomes even more complex when one considers the interindividual and intraindividual variations of principal angles. Nonetheless, our findings indicate that dentally transmitted bite force per se seems to play a minor role in bone strain determination, at least in the zygomatic area. If conventional wisdom concerning bone strain is adhered to, the evidence given in this report and that presented by Hylander and his colleagues ~6 might lead one to conclude that growth in the zygomatic region is not related in any meaningful way to masticatory function and that other explanatory models are called for. This concept has already been argued forcefully by a variety of investigators, the most notable of whom probably has been Moss. 6 However, there are several good
Vohmte 99 Number 4
Biochemical analysis of bite force
Bite Position
Principal Strains
307
Principal Angle
Lt M1
55/
5
45
Lt dm2
70/-25
29
Lt dml
66/-27
34
dl
88/-30
-36
Rt dml
95/-43
-22
Rt dm2
87/-42
-20
Rt M1
82/-37
-22
Fig. 1().,Monkey 606, body weight 1.3 kg. Principal strains and angles, with vectors for loading at the deciduous incisor and right and left first permanent molars.
Bite Force
Principal Strains
Principal Angle ~axo
2
61/-29
-16
4
98/-60
-13
6
101/-69
-13
7
105/-80
-10
8
105/-86
- 8
9
105/-86
- 8
10
101/-85
5
Fig. 11. Monkey 016. Principal strains and angles shown for differing magnitudes of bite force at the same bite point (incisors); only the strains and angles for the largest (Max.) and smallest (Min.) bite forces have been vectored.
reasons for exercising due caution before using strain magnitudes as the sole basis for casting aside a model of growth that posits a close, but not exclusive, relationship between masticatory function and the middle and upper parts of the facial skeleton. First, virtually all of our ideas about bone strain have been derived exclusively from studies of adult long bones that consist almost entirely of lamellar bone tissue. In our study, only nonadults have been considered, and it has been well established that in a wide variety
of species the zygomatic region of the primate facial skeleton in both adults and nonadults initially comprises largely nonlamellar bone tissue. ~9-2j Moreover, the physical properties of these nonlamellar tissues are very poorly understood, and experimental data on their strain characteristics are virtually nonexistent. 2-''23 Second, in the postcranial skeleton, the line of action of a given muscle tends to be along the vertical axis of the involved skeletal component(s), something that is easily determined in "long" bones. One of the challenging aspects
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Oyen and Tsay
o f interpreting bone strain data in the zygomatic region is its geometric complexity. Bone-muscle relationships in this area do not closely resemble and, therefore, cannot easily be modeled on the relationships between long bones and muscles. Third, conventional studies of bone strain tend to focus on considerations o f the "safety factor" that enables a bone, usually in an adult, to resist strains up to a certain level without experiencing failure. The role played by strain during normal growth o f a bone remains to be determined; we have a sense about the conditions that are involved when a bone breaks, but we know surprisingly little about the conditions that prevail during growth. It is likely that the principles governing the growth and remodeling changes in the facial skeleton vary from those derived from studies o t adult long bones. Wholesale transfer o f conclusions obtained from studies of long bones to the phenomena o f facial growth may be misleading, even erroneous. Further research in the basic areas o f stress/strain relations o f facial bones as well as the physical properties of the tissues involved seems indicated. One may conclude that the hypothesis tested in this study is correct. The force/remodeling relationship is site-specific and may differ from long bones to facial bones. Moreover, tensile strain seems to be predominant. It must be borne in mind, however, that the electrically induced tetanic contractions o f the masticatory muscles must differ from the recruitment patterns that actually occur during a normal chewing cycle. In a sense, the data on bite forces and bone strain reportect here more closely resemble the outcomes that would prevail during isometric forceful occlusion, as during extreme clenching. It must also be remembered that the bone strain obtained in this experiment results from force transmitted to the zygomatic region with no or little decrease in m a g n i t u d e - - i . e . , an isometric contraction. In efficient physiologic mastication, a significant part o f the impact generated by chewing is absorbed by food itself while the j a w closes, thereby reducing the amount o f force actually transmitted to the facial skeleton. It is o f interest to note that, in a preliminary report, Hylander and his colleagues '6 have described similar results in adult monkeys o f another species under more physiologic conditions. In this study, a body of in vivo bite force and facial bone strain data from a population o f growing monkeys has been described and analyzed. Observations on the functional implications of these data are made with the precaution that methodologic constraints color our resuits and that current understanding o f strains and bone
Am. J. Orthod. Dentofac. Orthop. April 1991
growth in general is rather meager. For now, it seems that the immediate value o f our research stems from its demonstration of some o f the advantages as well as some o f the dangers involved in attempts to use such phenomena as bite force and bone strain in the testing and construction o f explanatory models for biologic structures. These results and analyses also should serve to remind us that due caution must be used in the application o f seductively logical models whose validity has never really been verified through in vivo testing. REFERENCES 1. Benninghoff A. Spaltlinien am Knochen; eine Methode zur Ermittlung der Architektur platter Knochen. Verh Anat Anz 1925;60:189-206. 2. Sicher H, Tandler J. Anatomie fllr Zahnarzte. Wien: Verlag yon Springer, 1928:298. 3. Graber TM. Orthodontics: principles and practice. 3rd ed. Philadelphia: WB Saunders, 1972:133. 4. SchumacherGH. Anatomic furStomatlogenLehrbuchundAtlas. Vol 1. Leipzig: Barth, 1984:147, 165. 171. 5. DuBrul EL. Sicher's oral anatomy: 8th ed. St. Louis: Ishiyaku EuroAmerican, 1988:56-60. 6. Nloss NIL, Young RW. A functional approach to craniology. Am J Phys Anthropol 1960;57:904-8. 7. Cowin SC. Mechanical modeling of !he stress and adaptation process in bone. Calcif Tissue Int 1984;36:$98-Si03. 8. Endo B. Experimental studies on the mechanical significanceof the form of the human facial skeleton. J Fac Sci Univ Tokyo, Sect V, Anthropology 1966;3:1-106. 9. Endo B. Mechanical analysis of the form of the human facial skeleton. Vll Congr Int Sci Anthrop Ethol 1967;2:346-53. 10. Endo B. Analysis of stresses around the orbit due to masseter and temporalis muscles. J Anthropol SOCNippon 1970;78:25166. 11. Hy!ander WL. Mandibular function in Galago crassicaudatus and Macacafascicularis: an in vivo approach to stress analysis of the mandible. J Morphol 1979;159:253-96. 12. Dechow P, Carlson DS. A method of bite force measurement in primate. J Biomech 1983;16:797-802. 13. Weijs WA, deJongh HJ. Strain in mandibular alveolar bone during mastication in the rabbit. Arch Oral Biol 1971;22:667-775. 14. Hylander WL. In vivo bone strain in the mandible of Galago crassicaudatus. Am J Phys Anthropol 1977;46:309-26. 15. Hylander WL. Bone strain in the mandibular symphysis of Macacafascicularis. J Dent Res (Spec Issue B) 1977;56:344. 16. Hylander WL, Picq PG, Johnson KR. A preliminary stress analysis of the supraorbital region in Macacafascicularis. Am Phys Anthropol. 1987;72:214. 17. Beckwith TG, Buck NL. Marangoni RD. Mechanical measurements. Reading: Addison-Wesley, 1982:388. 18. Behrents RG. Carlson DS, Abdelnour T. In vivo analysis of bone strain about the sagittal suture in Macaca mulatta during masticatory movements. J Dent Res 1978;57:904-8. 19. Oyen OJ, Walker AC, Rice R. Craniofacial growth in the olive baboons (Papio cynocephalus anubis): browridge formation. Growth 1979;43:174-87. 20. Oyen OJ, Rice RW, Enlow DH. Cortical surface patterns in human and nonhuman primates. Am J Phys Anthropol 1981;54:415-9.
Biochemical analysis of bite force
Volume 99 Number 4
21. Oyen OJ. Masticatory function and histogenesis of the middle and upper face in chimpanzees (P. troglodytes). In: Dixon AR, Sarnat BG, eds. Factors and mechanisms influencing bone growth: progress in clinical and biological research. Vol 101. New York: Liss, 1982:559-68. 22. Evans FG. Mechanical properties of bone. Springfield: Charles C Thomas, 1973. 23. Currey JD. Rigid Material. In: Wainwright SA, Biggs WD, Cur-
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rey JD, Gosline JM, eds. Mechanical design in organisms. Princeton: Princeton University Press, 1976:144-240.
Reprint requests to: Dr. Ordean J. Oyen Office of Research Administration Case Western Reserve University Cleveland, OH 44106
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