Elastic Properties and Masticatory Bone Stressin the Macaque Mandible
PAUL C. DECHOW1* AND WILLIAM L. HYLANDER2
1Department of Biomedical Sciences, Baylor College of Dentistry, Dallas,Texas 752462Department of Biological Anthropology and Anatomy, Duke UniversityMedical Center, Durham, North Carolina 27710
KEY WORDS biomechanics; skeletal function; bone strain; cranio-facial biology; bone adaptation
ABSTRACT One important limitation of mechanical analyses withstrain gages is the difficulty in directly estimating patterns of stress orloading in skeletal elements from strain measurements. Because of theinherent anisotropy in cortical bone, orientation of principal strains andstresses do not necessarily coincide, and it has been demonstrated theoreti-cally that such differences may be as great as 45° (Cowin and Hart, 1990).Likewise, relative proportions of stress and strain magnitudes may differ.This investigation measured the elastic properties of a region of cortical boneon both the buccal and lingual surfaces of the lower border of the macaquemandible. The elastic property data was then combined with macaque man-dibular strain data from published and a new in vivo strain gage experimentto determine directions and magnitudes of maximum and minimum principalstresses. The goal was to compare the stresses and strains and assess thedifferences in orientation and relative magnitude between them. The mainquestion was whether these differences might lead to different interpreta-tions of mandibular function. Elastic and shear moduli, and Poisson’s ratioswere measured using an ultrasonic technique from buccal and lingual corticalsurfaces in 12 macaque mandibles. Mandibular strain gage data were takenfrom a published set of experiments (Hylander, 1979), and from a newexperiment in which rosette strain gauges were fixed to the buccal andlingual cortices of the mandibular corpus of an adult female Macaca fascicu-laris, after which bone strain was recorded during mastication. Averagedelastic properties were combined with strain data to calculate an estimate ofstresses in the mandibular corpus. The elastic properties were similar tothose of the human mandibular cortex. Near its lower border, the macaquemandible was most stiff in a longitudinal direction, less stiff in an inferosu-perior direction, and least stiff in a direction normal to the bone’s surface. Thelingual aspect of the mandible was slightly stiffer than the buccal aspect.Magnitudes of stresses calculated from average strains ranged from a com-pressive stress of 216.00 GPa to a tensile stress of 8.84 GPa. The orientationof the principal stresses depended on whether the strain gage site was onthe working or balancing side. On the balancing side of the mandibles,
Grant sponsor: National Institute of Dental Research Merit Award; grant number DE04532; Grant sponsor: National Institute ofDental Research; Grant number: DE07761; Grant sponsor: National Science Foundation; Grant number: BNS-8711842.
*Correspondence to: Dr. Paul C. Dechow, Department of Biomedical Sciences, Baylor College of Dentistry, 3302 Gaston Avenue,Dallas, Texas 75246.Email: [email protected] or [email protected]
Received 19 June 1998; accepted 23 June 1999.
AMERICAN JOURNAL OF PHYSICAL ANTHROPOLOGY 112:553–574 (2000)
One of the most productive methods fordetermining the functional properties of theskeleton is strain gage technology. Straingages can directly measure skeletal defor-mation. This information can be coupledwith data on morphology to better under-stand how skeletal elements function, whatsorts of loading patterns result from diverseloads induced by muscles and externalforces, and how function affects skeletalmodeling and remodeling. Yet mechanicalanalyses with strain gages have several lim-itations; most notable is the difficulty in di-rectly estimating patterns of stress or load-ing in skeletal elements from strainmeasurements.
Another approach to mechanical analysisof the skeleton is to study the material prop-erties of the bone itself (Dechow et al.,1993). Such studies, which determine fea-tures such as cortical thickness, bone den-sity, and elastic properties, tell us about thestructure of the skeleton but do little to re-veal how skeletal elements may actuallyfunction. Indeed, much of the literature offunctional morphology seeks to determinethe relationship between the form andstructure of tissue and its possible func-tional adaptation. The often apparent real-
ity is that form and function do not appearto correspond in the skeletal system in aconsistent way. Such discrepancies as theapparent differences in adaptation betweenthe cranial vault and the midcortex ofbones, such as the femur or mandible, leadto considerable speculation about mecha-nisms that have led to the development andmaintenance of skeletal adaptations in dif-ferent parts of the skeleton.
Because the material properties of thebone do not consistently correlate with thefunction of individual skeletal elements,there is a potential danger in making func-tional inferences based on strain gage stud-ies alone. A series of studies have pointedout the possible theoretical discrepanciesbetween bone strain and stress, if boneproperties are regarded as isotropic (Carter,1978; Cowin and Hart, 1990). One of thelargest dangers is due to the misalignmentof the principal axes of strain and stress inanisotropic materials. If functional inter-pretations rely on a correspondence of thedirections of these axes, as they do in isotro-pic materials, the potential discrepanciesbetween them may result in misinterpreta-tions of strain data. While the theoreticalstudies have shown that discrepancies in
554 P.C. DECHOW AND W.L. HYLANDER
axis orientation in bone may be as large as45° (Cowin and Hart, 1990), the degree ofdifferences actually depend on the degree ofanisotropy of the skeletal element understudy and the pattern of loading (Ricos etal., 1996).
In a series of studies, one of us (WLH) hasused strain gage techniques to define pat-terns of loading and function in the cranio-facial skeleton of several species of primates(Hylander, 1979, 1981, 1984, 1985, 1986,1987; Hylander and Johnson, 1989, 1997;Hylander et al., 1991). Likewise, one of us(PCD) has conducted a series of studies todefine the material properties of the facialskeleton in humans (Dechow et al., 1992,1993; Schwartz-Dabney and Dechow, 1997).In this investigation, we combined ap-proaches to study the relationship betweenpatterns of stress and strain in the mandi-ble of macaque monkeys during function.Specifically, we asked (1) what are the elas-tic properties of the mandibular corpus, (2)what are the magnitudes and directions ofstress in the macaque mandible duringfunction, (3) how well do directions and rel-ative magnitudes of principal stresses andstrains correspond, and (4) do differencesbetween these axes result in any reinterpre-tation of our understanding of mandibularfunction in macaques. Our hypothesis wasthat although there are significant differ-ences by direction in the elastic properties ofthe mandibular corpus in macaques, as inthe human mandible, the impact of thesedifferences was small compared to the fullrange of theoretical differences, resulting inminor reinterpretations of studies of func-tion of the mandible based on strain gagetechniques.
Several approaches are taken to this re-search. First, elastic properties of the cor-pus of the macaque mandible are deter-mined. Second, these data are used withpublished data on strains in the macaquemandible during function to determine di-rections and magnitudes of stress. Thesevalues are compared with directions andmagnitudes of strain. Third, elastic prop-erty data are applied to the results of anexperiment that measured mandibular bonestrain on both the facial and lingual aspectsof an adult female macaque during function.
As in the second experimental approach, theprincipal directions and magnitudes ofstrain and the calculated values of stressare compared. Possible differences in inter-pretation of the data with and without theinclusion of the information on bone elasticproperties are considered.
Dechow et al. (1993) showed that the hu-man mandible is about 40% stiffer in thelongitudinal direction than in the inferosu-perior direction. As the discussion of straingage experiments in the mandible of ma-caques (Hylander, 1979, 1981) did not takethis inherent anisotropy into consideration,it is possible that reexamination of resultsmight lead to additional insights and rein-terpretation. Dechow et al. (1993:300) spec-ulated that the combination of elastic prop-erty and strain data would “strengthen theassessment of the importance of bendingalong the lower border of the corpus, andde-emphasize the importance of torsion dur-ing mastication and incision.” The straingage experiment described in this paperwas meant to address this question directlyby looking at strain on both the lingual andbuccal aspects of the mandible. As will besubsequently described, predictable pat-terns should be found simultaneously on thebuccal and lingual aspects of the mandibledepending on the pattern of loading (twist-ing, bending, or some combination thereof)during function.
MATERIALS AND METHODS
Measurement of elastic properties
Cortical bone samples from the mandiblesof 12 adult female rhesus monkeys (Macacamulatta) were used to measure elastic prop-erties. All monkeys had third molars in oc-clusion prior to death. Mandibles were ob-tained from monkeys sacrificed for researchprojects unrelated to the current investiga-tion; no animals were known to have beenexposed to any medication or treatmentwith recognized effects on bone structure. Inlife, all animals had been fed a diet of hardmonkey chow supplemented with fruit.Mandibles were obtained fresh at sacrifice.They were dissected free of surrounding tis-sues, tightly wrapped in cloth and plastic to
prevent desiccation, and stored in a freezerat 220°F.
Bone samples were removed from the fa-cial and lingual corpora below the secondmolar in the mandibles. After the mandibleswere thawed, low-speed dental drills wereused to remove the bone in cubes of 5 3 5mm with a thickness of 1.5–2.5 mm. A Uni-mat miniature lathe was used to grind spec-imens where necessary to make sure thatthe opposite sides of the cubes were parallel.Specimens were cooled with water duringgrinding. In the initial three specimens,bone cubes were only removed on the facialside prior to discarding the mandibles. Thusthe sample size consisted of 12 facial sam-ples and 9 lingual samples.
Studies on the effects of storing bone sam-ples in preservative media such as formalinsuggested that such media altered the col-lagen fibers comprising the organic matrixof bone affecting the elastic properties of thebone (Reilly and Burstein, 1974). Likewise,work in our laboratory suggested that pres-ervation in formalin decreased bone stiff-ness (Dechow and Huynh, 1994). Accord-ingly, samples were stored in a solutionconsisting of 95% ethanol and isotonic sa-line in equal proportions; this mediummaintained the elastic properties of corticalbone for extended periods (Ashman et al.,1984, Dechow and Huynh, 1994).
Bone specimens were prepared for testingfrom each of the following locations (Fig. 1):(1) on the facial aspect of the mandibularcorpus, 1–2 mm above the lower border, andinferior to the second molar, and (2) on thelingual aspect on the mandibular corpus ina similar position as the first sample. Bonespecimens were labeled with an arrow toindicate orientation. For each sample, den-sities were determined according toArchimedes principle of buoyancy (Ashman,1989) using a Mettler PM 460 balanceequipped with a densitometry kit.
Samples were tested with an ultrasonicpulse transmission technique in three mu-tually perpendicular directions, using meth-ods described by Ashman et al. (1984) forpostcranial cortical bone and modified byDechow et al. (1993) for use in bone samplesfrom the cortex of human mandibles. Theultrasonic waves were generated by piezo-electric transducers resonating at 2.25MHz. Directions were labeled on each sam-ple such that 1 represented a direction nor-mal (radial) to the bone surface, 2 was in-ferosuperior to the bone surface, and 3 (thereference axis) was parallel to the longitu-dinal axis of the mandible (Fig. 1). Pretestsusing histological sections and longitudinalultrasonic waves confirmed that, like hu-man mandibles (Dechow et al., 1993), ma-caque mandibles can be modeled as ortho-tropic with their stiffest axis oriented alongthe long axis of the bone. In macaque man-dibles, Haversian canals and most collagenfibrils are oriented parallel to the long axis(Bromage, 1993). In human mandibles, theapatite crystals are also primarily orientedin this direction in the corpus (Bacon et al.,1980); this is most likely also true for ma-caque mandibles.
Ultrasonic measurements were made byusing two mounted piezoelectric transduc-ers to propagate longitudinal and trans-verse ultrasonic waves through the bonesamples in the directions under test. Thetime delay of wave propagation was readfrom an oscilloscope connected to the trans-ducer. The time delay and width of the spec-imen were used to calculate ultrasonic ve-locities. These velocities and data on thedensity of the bone samples were used togenerate a matrix of elastic coefficients, or
Fig. 1. Area and directions for bone sample site.Bone samples, approximately 5 3 5 mm and the thick-ness of the cortical plate (1.5–2.5 mm), were taken frommacaque mandibles on both the lingual and facial cor-tices at the site indicated. The 1 direction was approx-imately mediolaterally oriented or normal to the surfaceof the bone; this direction is not shown in the illustra-tion. The 2 direction was inferosuperior along the bonesurface. The 3 direction was oriented along the long axisof the lower border of the mandible (longitudinal).
“C” matrix, defined by Hooke’s law. Techni-cal elastic constants were calculated fromthe matrix. The computational techniquesare more fully described in the literature(Ashman, 1982; Ashman et al., 1984; Ash-man and Van Buskirk, 1987; Carter, 1989).The technical elastic constants included theelastic modulus, shear modulus, and Pois-son’s ratio.
Directions in technical constants were in-dicated with the following convention, asdefined in Figure 1. Elastic moduli E arefollowed by a subscript indicating direction.Shear moduli are followed by a double sub-script indicating the plane of shear. Pois-son’s ratios are followed by a double sub-script in which the first number indicatesthe direction of the primary strain and thesecond number indicates the direction of thesecondary strain (for further explanations,see Ashman et al., 1984, Cowin, 1989a, b, orMartin and Burr, 1989).
One-way analysis of variance was used totest for significant differences in bone den-sity among locations. Two-way analysis ofvariance was used to test for significant dif-ferences between directions and locationsfor the elastic moduli, shear moduli, andPoisson’s ratios. Significant differences be-tween individual cells were determinedwith post hoc Tukey tests.
Calculation of stress inmacaque mandibles
Mean elastic properties of the macaquemandibular corpus, as presented in Tables2–4, were combined with macaque bonestrain data to calculate the magnitude anddirection of principal stresses in the ma-caque mandible during function. As a sam-ple of macaque mandibular strain values,data were taken from Hylander (1979). Thedata consisted of mean balancing and work-ing side strains during transducer biting(Table 3 and Fig. 8 in Hylander, 1979) andduring mastication of apples (Table 8 andFig. 13 in Hylander, 1979).
Several computational steps were neededto calculate the magnitude and direction ofstress from these data. First, it was neces-sary to compute the magnitude of bonestrain in the direction of the primary axes ofstiffness of the mandibular corpus, namely
the directions shown in Figure 1. These di-rections were along the longitudinal axis ofthe mandibular corpus (3 direction) and at90o to this in the inferosuperior direction (2direction). Equations to transform strainvalues from maximum and minimumstrains (as given in Hylander, 1979) to thosealong these designated axes were:
e2 5 ep 3 sin (ar)2 1 eq 3 cos (ar)2
e3 5 ep 3 cos (ar)2 1 eq 3 sin (ar)2
t 5 2 3 cos (ar) 3 sin (ar) 3 (ep 1 eq),
where jp and jq were maximum and mini-mum principal strains; j2 and j3 werestrains in the 2 (inferosuperior) and 3 (lon-gitudinal) directions; ar was the angle be-tween the 3 (longitudinal) direction and thedirection of the maximum principal strain;and t was the shear strain.
Given the strains along orthotropic axes(directions 2 and 3), stresses in these direc-tions were calculated from the followingequations:
s3 5E3
1 2 v32 3 v233 (e3 1 v23 3 e2)
s2 5E2
1 2 v32 3 v233 (e2 1 v23 3 e3)
g 5 t 3 G32
where s2 and s3 were normal stresses in the2 and 3 directions respectively; E2 andE3 were elastic moduli of the cortical bone inthe 2 and 3 directions; G32 was the shearmodulus in the plane formed by the 2 and 3directions; n23 and n32were the Poisson’s ra-tios in the directions indicated by their re-spective subscripts; and g was shear stress.
Given the normal stresses in the 2 and 3directions and the shear stress in thatplane, maximum and minimum principalstresses and their orientations were calcu-lated as follows:
where sp and sq were the maximum andminimum principal (normal) stresses; andFs was the angle of the maximum normalstress.
From these data, the ratio of the maxi-mum to the minimum principal strain (jq/jp)was compared with that of the maximum tothe minimum principal stress (sq/sp). Alsocompared was the orientation or angle ofthe maximum principal strain (Fj) with themaximum principal stress (Fs).
Strain gage experiment
One adult female macaque (Macaca fas-cicularis) served as a subject for this exper-iment. This animal had a Class I molar re-lationship and full adult dentition with allmolars in occlusion. Two rosette straingages were bonded on the right corpus of themandible inferior to the second molar andseveral millimeters above the inferior bor-der. One strain gage was bonded on thefacial (buccal) surface, while the other wasbonded on the lingual surface. The align-ment of the rosettes was determined fromradiographs taken following the bondingprocedure.
The two strain gages were miniature 120-ohm; stacked rosettes (SA-06–030WY-120,Micro-Measurements, Raleigh, NC). Theywere bonded to the cortical bone with a cy-anoacrylate adhesive. The details of thisprocedure have been previously described(Hylander 1984, 1986; Hylander and John-son, 1989). Strain gages were attached withthe animal heavily sedated with aceproma-zine and ketamine (Connolly and Quimby,1978). A local anesthetic (lidocaine HCl)containing epinephrine (1:1000,000) infil-trated the surgical site prior to strain gagebonding for hemostasis and additional an-esthesia. A unique aspect of this procedurewas the lingual placement of one straingage. Surgical protocol for this placementrequired an incision along the lower borderof the mandible. A small part of the anteriorportion of the digastric muscle was dis-placed medially to allow access to the lin-gual side of the inferior border of the man-dible. The strain gage site was prepared
inferior to the attachment of the mylohyoidmuscle on the mandible (mylohyoid line).The site for the other strain gage was easilyprepared using the same surgical approachbut with dissection on the facial aspect ofthe mandible without a need for an addi-tional surgical incision. Lead wires wererouted out through the surgical incision,which was closed with suture.
Each of the three strain-gauge elementsin both rosettes formed one arm of a Wheat-stone bridge. For each element, bridge exci-tation was 1 V. Conditioning and amplifica-tion of the voltage output was accomplishedthrough the use of the Vishay 2100 System(Vishay Instruments, Raleigh, NC). Voltageoutput was recorded at 15 inches/sec with a14-channel FM tape recorder (Bell andHowell CPR4020A, Datatape Division, Pas-adena, CA). A record of whether the subjectchewed on the right or left side was alsomade on the voice track of the tape recorder.Additional details of the recording proce-dure are described elsewhere (Hylander etal., 1991; Hylander and Johnson, 1997).
The monkey was placed in a primate re-straining chair prior to recovery from seda-tion. The chair permitted normal head,neck, and jaw movements during mastica-tion. After a 5-hour period, the animal wasfully alert and was fed popcorn kernels, ahard food item for which the animal had apreference. Here we report on the results of39 right side (working strain) chews and 46left side (balancing strain) chews.
The zero level of strain was determined asthe monkey sat at rest with no clenching ormasticatory movements. Then the animalwas fed for a period of time until she refusedto eat additional food. At the end of therecording session, the monkey was sedated,strain gages were removed, surgical inci-sions were sutured, antibiotics were admin-istered, and the animal was returned to hercage. Recovery and healing were uneventfuland proceeded as normal.
Analysis of the bone strain recording wasaccomplished by first examining the signalsby outputting the data on a six-channelchart recorder (Brush 260, Gould Inc.,Cleveland, OH). Several complete chewingsequences were selected for analysis, in-cluding right- and left-sided chewing se-
558 P.C. DECHOW AND W.L. HYLANDER
quences. Through the use of a 16-channelanalog-to-digital converter (Model NB-MIO-16H-9, 12-bit resolution, National Instru-ments Corporation, Austin, TX), the rawstrains of the selected chewing cycles on FMtape were digitized at a rate of 500 Hz. witha channel separation time of 0.123 msec.The digitized values were stored on a com-puter hard disk for further processing andanalysis with LabView 2 graphical pro-gramming system (National InstrumentsCorporation). The digitized raw strain val-ues were filtered at 40 Hz. through the useof a digital low-pass Butterworth filter.Peak shear strain (gmax) was used as thedefining factor for peak strain as it was theabsolute value of the difference between themaximum and minimum principal strains(jp and jq). At gmax for each cycle, jp, jq, andthe angle (ar) of jp relative to the direction ofE3 were calculated. From these data, maxi-mum and minimum normal stress values(sp and (sq), and the angle of the maximumnormal stress (Fs) relative to the directionof E3 were calculated according to the pro-cedures discussed in the preceding section(Fig.2).
RESULTS
Elastic properties of macaquemandibular bone
No significant differences in density werefound between cortical bone samples fromthe lingual aspect of the macaque mandiblecompared to the samples from the buccalaspect (Table 1). Mandibular bone on thebuccal aspect averaged 2.003 g/cm3 com-pared to 2.056 g/cm3 on the lingual aspect.
Elastic moduli differed significantly (Ta-ble 2) between directions and between thetwo sites on the mandible. The cortical bonein the longitudinal direction (3 direction)was the most stiff, averaging 21.0 GPa onthe buccal aspect of the mandible and 23.9GPa on the lingual aspect. In the inferosu-perior direction (2 direction), values of elas-tic moduli of cortical bone averaged about75% of that in the longitudinal direction.Values in the direction normal to the bone (1direction) were about 40% of that in thelongitudinal direction. In all directions, cor-tical bone was slightly stiffer on the lingual
aspect of the mandible than on the buccalaspect.
Shear moduli differed significantly (Table3) between planes and between the two siteson the mandible. Cortical bone was mostresistant to deformation by shear forces inthe plane formed by the inferosuperior andlongitudinal (2 and 3) directions. On aver-age, this modulus was greater on the lingualside (8.2 GPa) than on the buccal side (7.0GPa). On both sides, the bone was moreresistant to shear in the plane made up ofthe normal and longitudinal (1 and 3) direc-tions than in the plane made up of the nor-mal and inferosuperior (1 and 2) directions.This difference was small, and shear modulifor these later two planes were considerablyless than in the 2 and 3 plane. Shear moduliin the 1 and 3 plane were about 60% that inthe 2 and 3 plane; and in the 1 and 2 plane,about half than in the 2 and 3 plane. In allplanes, cortical bone was slightly more re-sistant to shear on the lingual aspect of themandible than on the buccal aspect.
Significant differences were found be-tween directions and between sites in Pois-son’s ratio (Table 4). At both sites, v31 hadthe largest average values, followed by v32.v12 had the smallest average ratios on bothsides. The remaining values were interme-diate and fairly similar to each other. Therelative rankings of the Poisson’s ratioswere approximately as expected given therelationships between the elastic moduli inthe different directions. Poisson’s ratioswere higher in every direction at the buccalmandibular site than at the lingual site.The calculations of Poisson’s ratios by ultra-sonic measurements are the most derived ofall the technical elastic constants and thushave more error, as was evident from therelatively high standard deviations. Fewerconclusions can be drawn from these ratiosthan from elastic and shear moduli. How-ever, several of these values were needed forstress estimates. Values here were similarto those we have found at some sites inhuman bone, particularly at the symphysis(Dechow et al., 1992). For subsequent calcu-lations, we used values of 0.184 for v23 and0.214 for v32.
BONE STRESS IN THE MACAQUE MANDIBLE 559
Stress in macaque mandibles
The magnitude and orientations of themaximum and minimum principal strainsduring unilateral molar biting and duringmastication have been described by Hy-lander (1979). Here they are presented tocontrast them with the corresponding prin-
TABLE 1. Density1
Buccal mandible Lingual mandibleMean SD Mean SD
2.003 0.116 2.056 0.1281 Means are not significantly different. All values are in grams/cm3.
Fig. 2. Working-side (above)and balancing-side (below) plots ofbone strain vs. time during masti-cation of popcorn kernels. Maxi-mum and minimum principalstrains are illustrated for straingages positioned on both the buc-cal and lingual sides of the mandi-ble. In this figure only, j1 and j2are maximum (tensile) and mini-mum (compressive) principalstrains following the conventionused by Hylander (1979) and arethe same as jpand jq, respectively,as used elsewhere in this paper.
560 P.C. DECHOW AND W.L. HYLANDER
cipal stresses (Tables 5–8 and Figs. 3 and4). Overall, the principal stresses were ori-ented more closely to the orthotropic axes ofthe cortical bone than the principal strains.Likewise, compressive stresses tended to belarger in absolute magnitude relative to ten-sile stresses than compressive strains rela-tive to tensile strains. The one exceptionwas during transducer biting on the work-ing side, where the relative values of com-pressive and tensile stresses compared to
compressive and tensile strains tended to besimilar.
On the working side during unilateral bit-ing (Table 5), mean tensile (maximum prin-cipal) strains tended to be slightly higher inabsolute magnitude than mean compressive(minimum principal) strains. This was alsotrue for stresses, although tensile stresseswere slightly larger than compressivestresses compared to strains, with the ex-ceptions of Macaque 1, Experiment 1 andMacaque 6, Experiment 7. In these experi-ments, compressive stresses were abso-lutely larger than tensile stresses, and theratio sq/sp was equal to or larger than jq/jp.
On the balancing side during unilateralbiting, mean compressive and tensilestrains were similar; the values were within10% of each other in four out of six cases.However, compressive stresses were largerthan tensile stresses for all six means withsq/sp ranging from 1.04 to 1.81.
On the working side during mastication(Table 7), compressive stresses were largerthan tensile stresses for five out of eightmeans. In all five of these cases, sq/sp (range:1.10–2.86) was larger than jq/jp (range:0.96–1.76). In the other three cases, jq/jpwas larger than sq/sp, but on average by asmaller amount of difference, e.g., 0.88 vs.0.86, 0.65 vs. 0.47, and 1.02 vs. 0.87.
On the balancing side during mastication(Table 8), mean compressive strains andstresses were uniformly larger than meantensile strains and stresses. Likewise, sq/sp(range: 1.37–11.97) was always larger thanjq/jp (range: 1.03–11.09).
The direction of changes (greater orlesser) in the ratio of mean compressive andtensile strains (jq/jp) compared to stresses(sq/sp) related to the orientation of thestrains relative to the axes of orthotropy orsymmetry (E2 and E3) of the bone (see Dis-cussion). This can be more easily visualizedwhen considering changes in the orientationof the maximum principal stresses (Fs)compared to corresponding strains (Fj)(Figs. 3 and 4). The principal stresses al-ways became oriented more closely to theaxes of orthotropy or symmetry. The directionof change in the ratio sq/sp compared to jq/jpgenerally related to whether the shift inorientation of the maximum principal stress
TABLE 2. Elastic modulus1
Buccal mandible Lingual mandibleMean SD Mean SD
E1 9.0 1.8 9.3 1.6E2 15.9 4.0 17.6 3.1E3 21.0 3.2 23.9 3.21 Analysis of variance indicated significant differences amongbone directions (F 5 102.6, P , 0.001) and between buccal andlingual aspects of the mandible (F 5 4.7, P , 0.035); interactiveeffects were not significant. E1 is the elastic modulus in the 1 ormediolateral direction (normal) to the surface of the bone; E2 isthe elastic modulus in the 2 or inferosuperior direction along thebone surface; and E3 is the elastic modulus in the 3 or longitu-dinal direction along the bone surface. All values are in gigapas-cals (GPa).
TABLE 3. Shear modulus1
Buccal mandible Lingual mandibleX SD X SD
G12 3.8 1.1 4.3 0.9G13 4.4 1.1 5.1 1.1G23 7.0 1.7 8.2 1.01 Analysis of variance indicated significant differences amongbone directions (F 5 51.2, P , 0.001) and between buccal andlingual aspects of the mandible (F 5 6.5, P , 0.03); interactiveeffects were not significant. G values are shear moduli in planesindicated by their subscripts. Directions indicated by subscriptsare given in the notes concerning elastic moduli following Table2. All values are in GPa.
TABLE 4. Poisson’s ratio1
Buccal mandible Lingual mandibleX SD X SD
v12 0.075 0.071 0.055 0.069v13 0.206 0.090 0.135 0.085v21 0.131 0.114 0.107 0.158v23 0.184 0.079 0.130 0.079v31 0.450 0.183 0.325 0.231v32 0.214 0.095 0.173 0.1061 Analysis of variance indicated significant differences betweenbone directions (F 5 15.8, P , 0.001), and between buccal andlingual aspects of the mandible (F 5 7.2, P , 0.01; interactiveeffects were not significant. Directions indicated by subscriptsare given in the notes concerning elastic moduli following Table2. The first subscript denotes the direction of the normal strain,while the second subscript denotes the direction of the Poisson’sstrain. Note that Poisson’s ratio is dimensionless, i.e., it does nothave a unit of measurement.
BONE STRESS IN THE MACAQUE MANDIBLE 561
compared to strain was toward the orienta-tion of E2 or E3.
The difference in orientation or angle(DF) of the maximum principal stress (Fs)compared to the angle of the maximumprincipal strain (Fj) was low for all means.DF ranges from a minimum value of 0.5° toa high value of 12.0°.
Strain gage experiment
Our new experiment suggested that dur-ing mastication, the magnitude of bonestrain and stress was larger on the buccalthan on the lingual side of the mandibularcorpus. Also, as expected from previousstudies (Hylander, 1979), working side bonestrain was on average larger than balancing
side strain. These relationships held truefor both average strains and peak strains(Table 9). Similar relationships were alsofound for stress (Table 10).
Ratios of compressive strain relative totensile strain (jq/jp) compared to the similarstress ratio (sq/sp) showed that on the buc-cal aspect of the working side, compressivestress and strain were similar in magnitudeto tensile stress and strain, respectively. Onthe lingual aspect of the working side, ten-sile strain was twice that of compressivestrain. This relationship was more exagger-ated for stress; tensile stress was more thanthree times compressive stress. On the buc-cal and lingual aspects of the balancing side,compressive strain and stress were abso-
TABLE 5. Mean strain and stress during transducer biting on the working side1
Animal andexperiment number ep eq sp sq eq/ep sq/sp Fe Fs DF
Macaque 1, experiment 1 491 2448 7.24 25.97 0.91 0.82 40.8 35.3 5.5Macaque 1, experiment 2 476 2443 6.49 26.68 0.93 1.03 59.1 69.9 10.8Macaque 2, experiment 3 534 2458 8.19 25.89 0.86 0.72 37.3 28.4 8.9Macaque 2, experiment 5 343 2263 5.07 23.40 0.77 0.67 48.1 50.2 2.1Macaque 3, experiment 6 364 2240 5.41 23.03 0.66 0.56 54.7 62.3 7.6Macaque 3, experiment 7 453 2505 6.16 27.25 1.12 1.12 43.7 42.8 0.91 ep and eq are the maximum and minimum principal strains; sp and sq are the maximum and minimum principal stresses; Fe andFs are the angles of the maximum principal strain and stress expressed relative to the orientation of E3 in a counterclockwisedirection, and DF is the difference between the angles of the maximum principal strain and stress. All strains are in microstrain (me).All stresses are in megapascals (MPa). All angles are in degrees.
TABLE 6. Mean strain and stress during transducer biting on the balancing side1
Animal andexperiment number ep eq sp sq eq/ep sq/sp Fe Fs DF
Macaque 1, experiment 1 184 2194 2.47 22.86 1.05 1.16 50.6 57.2 6.6Macaque 1, experiment 2 327 2318 4.39 25.19 0.97 1.18 67.9 78.2 10.3Macaque 2, experiment 3 707 2894 8.84 216.00 1.26 1.81 73.5 82.1 8.6Macaque 2, experiment 5 247 2238 3.37 23.49 0.96 1.04 54.1 63.0 8.9Macaque 3, experiment 6 160 2146 2.18 22.26 0.91 1.04 63.3 74.3 11.0Macaque 3, experiment 7 225 2263 2.91 23.99 1.17 1.37 50.9 58.4 7.51 Key to symbols is given under Table 5. All strains are in microstrain (me). All stresses are in megapascals (MPa). All angles are indegrees.
TABLE 7. Mean strain and stress during mastication on the working side1
Animal andexperiment number ep eq sp sq eq/ep sq/sp Fe Fs DF
lutely larger than comparable tensile strainand stress. Likewise, sq/sp was more than50% greater than jq/jp on both buccal andlingual sides.
The orientation of the maximum principalstrains varied by buccal or lingual aspect ofthe mandible and functional location (Table10 and Fig. 5). On the buccal aspect of theworking side, the maximum principal strainangled upward and backward at 35.3° clock-wise to the orientation of E3. This was incontrast to the lingual aspect of the workingside where the maximum principal strainangled upward and forward. On the lingualaspect, the maximum principal strain wasoriented 58.2° off-axis from the maximumprincipal strain on the buccal aspect.
On the buccal aspect of the balancingside, the maximum principal strain angledupward and backward at 80.7° clockwise tothe orientation of E3. The maximum princi-pal strain on the lingual aspect was alsooriented upward and backward and differedin direction from the buccal aspect of themandible by 11.5°.
As described in the previous section, theprincipal stresses always became orientedmore closely to the axes of orthotropy orsymmetry compared to the correspondingprincipal strains (Fig. 5). The orientation ofthe stresses differed from that of the strainsby values ranging from 5.2° to 11.6°.
DISCUSSION
The relevance of studies of the elasticproperties of bone relates to both the basicbiology of bone structure, function, growth,and adaptation, and to an adequate assess-ment of the biomechanics of functioningskeletal structures (Dechow et al., 1993).
Processes of bone adaptation in response toaltered function and bone growth have beenwidely studied. Yet many basic features ofchanges in cortical bone architecture result-ing from growth and adaptation remain elu-sive. Perhaps most elusive is the relation-ship between bone ultrastructure andmaterial properties, and the effect of mod-eling and remodeling on this relationship.Recent studies suggest correlations betweenspecific bone microstructure and variationsin strain mode (tensile or compressive)(Skedros et al., 1996, 1997), and functionaladaptations in directional differences(anisotropies) in cortical bone (Kohles et al.,1996, 1997). Such differences may reflectuncorrelated anisotropies in the mineral-ized and collagenous components of corticalbone (Takano et al., 1996).
Studies of collagen orientation in the la-mella of osteons suggest a “rotated plywood”model (Wagner and Weiner, 1992) for os-teonal bone that alludes to deviations fromorthotropy in cortical bone elastic properties(Turner et al., 1995). The implications ofdeviations from orthotropy for lamella inthe walls of single osteons is not clear forlarger structural regions of bones like themandible, where the cortex is constructed ofcomplex combinations of primary and sec-ondary bone, including osteons of unde-scribed overall shape, and interstitial bone.Although empirical data of ultrasound ve-locities in different directions suggest thatorthotropy is a reasonable simplification formandibular cortical bone structure (Dechowet al., 1993), how well this assumption ac-tually fits requires further experimentation.
The relevance of studies of the elasticproperties of bone for an adequate assess-
TABLE 8. Mean strain and stress during mastication on the balancing side1
Animal andexperiment number ep eq sp sq eq/ep sq/sp Fe Fs DF
ment of the biomechanics of functioningskeletal structures was the primary focus ofthe current investigation. The mechanics of
Fig. 3. Results of stress analysis applied to straingauge experiments in which macaques bit unilaterallyon a bite force transducer (strain data is from Table 3and Fig. 8 in Hylander, 1979). All experiments are la-beled as in Hylander (1979). For each experiment, theblack dot indicates the position of the rosette straingage. E3 is the orientation of the longitudinal axis or 3direction along which peak values of elastic moduli are
found. The arrows indicate the direction of the maxi-mum principal strain on the working side (jw),the maximum principal stress on the working side (sw),the maximum principal strain on the balancing side(jb), and the maximum principal stress on the balancingside (sb). Note that the arrows are not vectors; theirlengths do not show the magnitude of stress or strain.For further discussion, see the text.
Fig. 4. Results of stress analysis applied to straingage experiments in which macaques masticated apples(strain data is from Table 8 and Fig. 13 in Hylander,1979). For further explanation and a key to the symbols,see Figure 3 and the text.
564 P.C. DECHOW AND W.L. HYLANDER
Fig. 4.
skeletal structures are dependent on thephysical characteristics of the bone, includ-
ing bone shape, size, structure, and orienta-tion of trabecular bone, thickness of the cor-tical plate in various regions of the bone,and the details of applied loads on the struc-ture. However, often overlooked are the ma-terial properties of the cortical bone itself.Despite the fact that directional differencesin elastic properties can result in discor-dance between the primary directions ofloading or stress in a structure (Carter,1978; Cowin and Hart, 1990; Cowin et al.,1991; Ricos et al., 1996), and those inferredfrom strain gage studies (orientation of themaximum and minimum principal strains),elastic properties of bone are hardly everconsidered in studies using bone strain asan indicator of skeletal loading patterns.The aim of this study was to assess theimpact of anisotropies in cortical bone onthe interpretation of bone strain in the func-tioning mandible.
Elastic properties of themacaque mandible
The first goal of this investigation was todocument the elastic properties of the ma-caque mandibular corpus, specifically inthose regions where strain gages were at-tached in previous studies and in the cur-rent investigation. We will review the newinformation on the elastic properties of themacaque mandible and compare these re-
Fig. 5. Results of strain gauge experiment andstress analysis in which rosette strain gages were ap-plied to the buccal and lingual surfaces of a macaquemandibular corpus. For further explanation and a keyto the symbols, see Figure 3 and the text. The linemarked “X” indicates the alignment of the A element ofthe rosette.
TABLE 9. Bone strain on the facial and lingual sides of the macaque mandibleduring mastication of popcorn kernels1
Rosettelocation
Functionallocation N
epmean
epSD
eplargestvalue
eqmean
eqSD
eqlargestvalue
Buccal side Working side 39 388 96 661 2410 81 2612Buccal side Balancing side 44 291 120 601 2414 174 2939Lingual side Working side 39 200 69 362 2100 38 2195Lingual side Balancing side 44 122 31 199 2250 76 24311 ep and eq are the maximum and minimum principal strains. All strains are in microstrain (me).
TABLE 10. Strain and stress in the macaque experiment1
Rosettelocation
Functionallocation ep eq sp sq eq/ep sq/sp Fe Fs DF
Buccal side Working side 388 2410 5.65 25.63 1.06 1.00 35.3 26.7 8.6Buccal side Balancing side 291 2414 3.53 27.78 1.42 2.20 80.7 84.8 5.2Lingual side Working side 200 2100 4.24 21.26 0.50 0.30 157.1 168.7 11.6Lingual side Balancing side 122 2250 1.53 25.37 2.05 3.52 69.2 79.1 9.91 Key to symbols is given under Table 5. All strains are in microstrain (me). All stresses are in megapascals (MPa). All angles are indegrees. The angles of the maximum principal strain and stress is expressed relative to the orientation of E3 in a clockwise directionon the buccal aspect and in a counterclockwise direction on the lingual aspect—see Figure 5 to visualize this.
566 P.C. DECHOW AND W.L. HYLANDER
sults with available information on elasticproperties in other mammalian species.
There are few comparable studies of theelastic properties of the mandible in anymammalian species with which to comparethe data collected from the macaque mandi-ble. Available studies include data fromdogs (Ashman et al., 1985), and smallersamples from humans (Ashman and VanBuskirk, 1987; Carter, 1989; Arendts andSigolotto, 1989, 1990; Rho, 1991). All thesestudies had small sample sizes, a low num-ber of measured sites, or included function-ally compromised individuals, such as bonefrom edentulous mandibles.
One problem with our investigation isthat the elastic properties were measuredon mandibles of a different macaque species(Macaca mulatta) than the species on whichthe strain gage studies were conducted (Ma-caca fascicularis). However, several studiesfrom our laboratory have documented theelastic properties of primate and mamma-lian mandibles in more detail, includingmeasurements from humans (Dechow et al.,1992, 1993; Schwartz-Dabney and Dechow,1997), baboons (Dechow and Huynh, 1996),and pigs (Shinedling and Dechow, 1996).These studies showed similarities in theelastic properties of mandibular corticalbone between more distantly related taxa.Because of these similarities, the discrep-ancy between animal samples in the currentstudy was not thought to be a significantproblem. Especially, since rhesus and long-tailed macaques have great similarity incraniofacial structure with a minimal differ-ence in size.
Humans, baboons, and macaques all showa similar amount of anisotropy in corticalbone from the mandibular corpus with bonebeing absolutely the most stiff along thelong axis of the bone, less stiff in the infero-superior direction, and least stiff in a direc-tion normal to the surface of the bone. Thispattern can also be found in the cortices ofshafts of long bones, although the relativeproportions of the elastic properties in thethree perpendicular directions may differ.
Another common feature may be the in-creased stiffness of the bone on the lingualcortex compared to the buccal cortex. In hu-man mandibles, there was a general trend
in all measured regions, from the symphysisto the condylar neck, to have stiffer corticalbone on the lingual side of the mandible,and some of these differences were statisti-cally significant (Dechow et al., 1992;Schwartz-Dabney and Dechow, 1997). How-ever, relationships of stiffness and densityversus location in human mandibular corti-cal bone were actually more complex withsignificant variations found anteroposteri-orly and inferosuperiorly in the mandible,and in the muscular processes of the man-dible.
Function and patterns of bone strainand stress in the macaque mandible
The second and primary goal of this studywas to compare patterns of stress and strainin the macaque mandible using strain datafrom a previously published study (Hy-lander, 1979) and a new experiment. Weasked: how different were the patterns ofstress and strain, and do these differencesresult in any reinterpretation of our under-standing of mandibular function in ma-caques.
Loading and expected patterns ofstress.
When comparing patterns of stress andstrain, we compared two important fea-tures: (1) the orientation of the maximumprincipal strain (Fj) and stress (Fs), and (2)the ratio of the absolute values of the mini-mum and maximum principal strain (jq/jp)and the minimum and maximum principalstress (sq/sp). We suggested previously (Hy-lander, 1979; Dechow et al., 1993) that thesefactors were significant when analyzingstrain patterns near the buccal surface ofthe lower border of the mandibular corpusbecause distinct patterns will result de-pending on whether the mandible was ei-ther parasagittal bent or twisted about itslong axis. Because of the anisotropy in man-dibular cortical bone, these relationshipswill hold true for stress but not for strain,although these expectations were originallypresented for strain data (Hylander, 1979,Dechow et al., 1993). Strain data will showsome deviation from calculated stressesgiven the anisotropic structure of mandibu-lar cortical bone.
BONE STRESS IN THE MACAQUE MANDIBLE 567
If the mandible is bent during biting ormastication and if the lower border of thecorpus is compressed longitudinally, it isexpected that at the lower border (1) FjandFs will be perpendicular to the long axis ofthe mandible, while the orientation of theminimum principal or compressive strainand stress will be parallel to the lower bor-der of the mandible, and (2) the absolutemagnitude of jq and sq will be larger than jpand sp respectively, and jq/jpand sq/sp willbe greater than 1.0. This pattern of bendingwith the lower border of the mandible incompression and the alveolar border in ten-sion about their long axes is generally trueon the balancing side of the mandible. How-ever, on the working side, the pattern ismore complex. Parasaggittal bending, littleor no bending (Hylander, 1979), or even re-verse patterns of parasagittal bending maybe found. These variations presumably de-pend on the position of the bite point andthe region of the corpus under study (Demeset al., 1984). Theoretically, regions of themandible on the working side may undergoprimarily torsion and/or direct shear withlittle bending, or have regions where thelower border of the corpus is experiencingtension and the alveolar border compressionalong their longitudinal axes (reverse para-sagittal bending).
If the mandible is twisted about its longaxis during biting or mastication, a charac-teristic pattern of stress and strain wouldresult. Torsion results in eversion of thelower border of the mandible. Near thelower border of the buccal mandibular cor-pus beneath the premolars or molars, (1) Fj
and Fs would be oriented upward and back-ward at about 45° to the lower border on thebuccal cortex, and (2) the absolute magni-tude of jq would be similar to jp, and sq/spwould be about equal to 1.0. As when con-sidering bending, this pattern may be morecomplex on the working side of the mandibledepending on the mediolateral position ofthe bite point relative to the neutral axis ofthe mandible (Hylander, 1979).
Another consideration on the workingside is the direct shear associated with mo-lar occlusal forces. On the buccal cortex ofthe mandible, the result of direct shearwould be a pattern similar to that for tor-
sion. The combination of torsion and directshear would be additive on the buccal cortexof the working side, resulting in greaterstress and strain than would result fromeither torsion or direct shear alone. On thelingual cortex, the effect would be the oppo-site. Principal stresses along the lingual re-sulting from torsion would theoretically ro-tate 90° relative to their orientation on thebuccal cortex, while stresses resulting fromdirect shear would have the same orienta-tion on the buccal and lingual cortices.Thus, stresses resulting from torsion anddirect shear would be subtractive on thelingual cortex of the mandible, resulting inlower lingual stress (Demes et al., 1984;Daegling and Hylander, 1998). For purposesof the work described in this paper, thesepredicted differences in stress pattern pro-vided further tests of the interpretation ofloading patterns from strain gage studies.In the mastication experiments reexaminedfrom Hylander (1979), it was not possible todistinguish on the working side betweentorsion and direct shear. However, in ournew experiment, one of the following pat-terns should reveal details about the load-ing regimen in the mandible during masti-cation:
1. Fjand Fs will be oriented upward andbackward at about 45° to the lower bor-der on both the buccal and lingual cortexof the mandible. The absolute magni-tude of jq will be similar to jp, and sq/spwill be about equal to 1.0. This patternsuggests direct shear as the primarypattern of loading.
2. Fj and Fs will be perpendicular to thelong axis of the mandible on both thebuccal and lingual cortex. The absolutemagnitude of jq and sq will be largerthan jp and sp, respectively, and jq/jpand sq/sp will be much greater than 1.0.This pattern suggests parasagittalbending as the primary pattern of load-ing.
3. Fj and Fs will be oriented upward andbackward at about 45° to the lower bor-der on the buccal cortex of the mandible,while Fj and Fs will be oriented upwardand forward at about 45° to the lowerborder on the lingual cortex of the man-
568 P.C. DECHOW AND W.L. HYLANDER
dible. The absolute magnitude of jq willbe similar to jp, and sq/sp will be aboutequal to 1.0. This pattern suggests tor-sion as the primary pattern of loading.
The most likely pattern was some combina-tion of the above possibilities. For instance,superimposition of bending and torsion willresult in deviations of stresses from 45° tothe lower border of the mandible. sq will bemore closely aligned with the lower borderof the mandible. Likewise, the absolutemagnitude of sq will be greater than sp. Ifdirect shear and torsion were superimposed,we would expect reduced strains on the lin-gual cortex compared to the buccal cortex.As before, patterns can be inferred fromboth strain and stress data. The questionwas whether the interpretations based onstrains compared to stresses differed signif-icantly or if they were similar.
Differences between patterns of bonestress and strain and their significance.Comparison of bone stress and strain nearthe lower border of the mandibular corpus(Tables 5–9 and Figs. 3–5) led to severalobservations. (1) The anisotropy of the man-dibular corpus resulted in consistent pat-terns of differences between the orienta-tions of the principal stresses and strains.(2) The differences in the orientations of theprincipal stresses and strains in most caseswere relatively small. (3) Changes in theratio sq/sp compared to jq/jp were not al-ways predictable but generally related towhether the shift in orientation of the max-imum principal stress compared to strainwas toward the orientation of E2 or E3. If theorientation shifted toward E2, sq/sp wasusually less than jq/jp. If the orientationshifted toward E3, sq/sp was usually greaterthan jq/jp. There were several exceptions,mostly at values of sq/sp close to 1.0. (4) Thedifferences between the ratios sq/sp andjq/jp were negligible in some cases and largein others varying, respectively, from no dif-ference to a maximum difference of 2.66 ver-sus 6.49.
Based on the loading models presentedabove, the consistent differences betweenthe orientation of stress and strain slightlyoveremphasized the importance of torsion
or direct shear. Inspection of each result inTables 5–8 and 10 (also Figs. 3–5) showedthat sp was always oriented closer to theorientation of E2 (inferosuperior) or E3 (lon-gitudinal) than was jp. If Fj , 45°, than Fs
, Fj, placing the orientation of sp closer tothat of E3 than jp was to E3. If Fj , 45°,then Fs . Fj, placing the orientation of spcloser to that of E2 than jp was to E2. Be-cause our loading models suggested that ori-entation of the principal stresses close to 45°indicated torsion or direct shear, and in allcases the orientation of jp was closer to 45°than was the orientation of sp, the result ofmandibular anisotropy was to overempha-size the relative importance of torsion ordirect shear compared to bending. However,the magnitude of overestimation was notlarge, as the angular differences varied be-tween a minimum difference of less than adegree to a maximum difference of 12.0°.
Differences between the orientation andrelative magnitudes of principal stressesand strains were consistent on the balanc-ing side of the mandible. Hylander (1979)found that strain patterns on the balancingside of the mandible indicated that the cor-pus was primarily bent during both masti-cation and transducer biting. Orientationsof principal strains were closer to 45° duringtransducer biting than mastication, indicat-ing a relatively greater amount of torsion.Principal stresses (Tables 6 and 8) sug-gested similar conclusions, and resulted in asmall de-emphasis in the importance of tor-sion during transducer biting, althoughmore torsion was still indicated than thatfound during mastication. In all cases, spwas oriented closer to E2 than jp was to E2.All values of sq/sp were greater than corre-sponding values for jq/jp and were largerthan 1.0. In contrast to expectations, somevalues of jq/jp were less than 1.0. Compari-son with sq/sp, showed that these low val-ues for jq/jp were a consequence of mandib-ular anisotropy, and not relatively lowcompressive stress longitudinally or rela-tively high tensile stress inferosuperiorly.
Interpretations of the differences betweenprincipal stresses and strains and the deter-mination of corresponding loading patternswas more problematic on the working sideof the mandible (Tables 5 and 7). Overall,
BONE STRESS IN THE MACAQUE MANDIBLE 569
differences between the orientation and rel-ative magnitudes of stresses and strainsgenerally underemphasized variability inmechanically relevant variables. Orienta-tions of sp were more variable than jp. Fortransducer biting and mastication com-bined, Fj ranged from 28.2° to 60.6°, whilethe corresponding range of Fs was 17.0° to71.7°. This was because values of Fj below45° had lower values for Fs, while values ofFj above 45° had higher values for Fs. Like-wise, values of jq/jp ranged from 0.65 to1.76, while values of sq/sp ranged from 0.47to 2.86. Interpretation of these stresses andcorresponding strains suggested either thepresence of torsion or direct shear of themandibular corpus, as originally suggestedby Hylander (1979). However, the wide de-viations of Fs from 45° and values of sq/splarger and smaller than 1.0 in some exper-iments suggested the superimposition oftorsion or direct shear and other patterns ofloading. The importance and range of theseother superimposed loading patterns wasless pronounced when considering strainvalues alone.
What other loading patterns might be su-perimposed on torsion or direct shear on theworking side? Possibilities included some ofthose patterns suggested earlier in this pa-per (cf. Hylander, 1979). Data for macaque1-experiment 2 during transducer biting(Table 5) and macaque 1-experiment 2, ma-caque 2-experiments 3–4, and macaque3-experiment 7 during mastication (Table 7)indicated parasagittal bending with thelower border of the mandible in compressionand the alveolar border in tension. In theseexperiments, sq . 45°and sq/sp . 1.0. Datafrom several other experiments, such as ma-caque 1-experiment 1, and macaque 2-ex-periment 3 during transducer biting (Table5) and macaque 3-experiment 6 during mas-tication (Table 7), indicated reverse para-sagittal bending with the lower border ofthe mandible in tension and the alveolarborder in compression. In these experi-ments, sq , 45° and sq/sp , 1.0. Data fromsome of the other experiments in Tables 5and 7 did not readily fit any of the loadingpatterns described previously.
It was important to realize that loadingpatterns in the mandibular corpus below
the bite point may be difficult to interpretbecause of stress concentrations and associ-ated stress gradients associated with theforce application at the bite point or region.Interpretation was made more difficult inthis case because of lack of knowledge of theexact location of the bite point relative tothe position of the strain gauge in each ex-periment. Furthermore, data considered inthis study were mean data taken from Hy-lander (1979) and did not include resultsfrom individual trials; since stress gradientswere expected over small regions of corticalbone inferior to the bite point, individualdata may vary and lead to incorrect inter-pretations when averaged. In any case, fur-ther investigation is needed to investigatethe complexity of patterns of strains andstresses in the working side mandibular cor-pus, inferior to the bite point.
Bone stress and strain on the lingualsurface compared to the buccal surfaceof the mandible. Strains and associatedstresses from both the buccal and lingualcortices of the mandible (as reported in Ta-bles 9 and 10 and Fig. 5) suggested that (1)the mandible was primarily bent parasagi-tally on the balancing side during mastica-tion, as described by Hylander (1979), and(2) the mandible experienced torsion on theworking side coupled with other possible su-perimposed patterns of loading. On the bal-ancing side, Fs on both the buccal and lin-gual cortices was very much greater than45°. A small deviation from 90° suggested aminor amount of torsion. sq/sp was also sub-stantially greater than 1.0 on both buccaland lingual cortices, as expected when theinferior border of the mandible was in com-pression. Interestingly, stresses were rela-tively more similar in magnitude betweenbuccal and lingual cortices than werestrains. This was because the elastic modu-lus was stiffer on the lingual cortex.
The meaning of strains and stresses wasagain more problematic on the working sideof the mandible. However, some interpreta-tions could be suggested. The angle of prin-cipal stress differed by 142° between corti-ces such that the orientation of the principalstrains and stresses was upward and poste-rior on the buccal cortex and upward and
570 P.C. DECHOW AND W.L. HYLANDER
anterior on the lingual cortex. This patternconfirmed the suggestion (Hylander, 1979)that during the power stroke of mastication,the working side was primarily twistedabout its long axis with the lower bordereverted and the alveolar border inverted.
These data did not suggest that directshear was superimposed on torsion on theworking side. The expectation of lowerstrains and stresses on the lingual com-pared to the buccal cortex on the workingside was found. However, strains andstresses were equally dissimilar to eachother between buccal and lingual cortices onthe balancing side as on the working side.Bending should result in similar stressmagnitudes on both cortices of the corpus ofthe mandible. Thus, this difference may be aresult of experimental error, as considerablevariations in strain magnitude may resultdepending on the quality of the bonding ofthe strain gage to bone. Additional experi-ments are needed to confirm these results.
These results did not mean that directshear, which is unavoidable and must bethere and torsion were never superimposedin the suggested pattern on the workingside. This pattern may only result in specificregions of the working side when the biteforce was appropriately placed. As sug-gested above, more detailed study of loadingpatterns during individual bites with morespecific information on exact regions of load-ing are needed to sort out complex strainpatterns in the mandible inferior to the re-gion of biting on the working side.
Arguments could be made for other super-imposed loading patterns on the workingside of the mandible. Here, the orientation(Fs) of the maximum stress was closer tothe mandibular long axis than the mini-mum stress on both buccal and lingual cor-tices. Likewise, the value of sq/sp on thelingual side was low. These data indicatedthat the lower border of the mandible was intension as would be found in reverse para-sagittal bending. Further, the differences instrain between buccal and lingual cortices,if confirmed by further experiments, mightsuggest wishboning or transverse bendingof the mandible, which would increase com-pression on the buccal cortex and increasetension on the lingual cortex.
The effects of considering the anisotropiesof the mandible in the analysis of this ex-periment were much the same as those de-scribed above in the reinterpretation of datafrom Hylander (1979). On the buccal aspect,the results from this experiment were par-allel to those found in the previous investi-gation.
Empirical results and theoreticalpredictions of misalignment between
strain and stress
Given the small number of studies of bothlocal variations in skeletal material proper-ties and in vivo strain gage studies, it wasnot surprising that there were few empiricalestimates of bone stress. Carter (1978) de-scribed methods to calculate bone stressesfrom strains in bone if the material proper-ties were known. He determined bonestresses in the anteromedial (bare area) of ahuman tibia during walking from an exper-iment by Lanyon and colleagues (1975). Thedifferences between strain and stress in thetibial example were similar to those foundhere in the macaque mandible.
Cowin and Hart (1990) created a generalmodel for determining errors of orientationin the principal stress axes in bone, if thebone was modeled as isotropic when it wasactually orthotropic or anisotropic. Theseerrors were equivalent to differences be-tween the orientations of principal strainsand stresses, because their orientationswould coincide in an isotropic material.Cowin and Hart demonstrated that thesedifferences could be as large as 45°. Theyalso stated that while most errors were notthat large, a typical error did represent asignificant difference. However, their oneexample from the human femur had an er-ror or difference of 8.69° between the twoaxes. It was not clear from Cowin and Hart’sstudy what specific strain patterns wouldresult in larger errors in orientation, or howthese strain patterns might have interactedwith the known range of material propertiesin cortical bone in producing errors. It wasinteresting that their example fell withinthe range of errors noted in our macaquestudies. The question of what magnitude oferror in orientation is significant is debat-able. An error of 8° is huge in any precision
BONE STRESS IN THE MACAQUE MANDIBLE 571
instrument, but in measurements of biolog-ical systems, such errors may be small tomoderate, and depend primarily on the na-ture of the measurement and its intendedpurpose. Cowin and Hart did not discusspossible shifts in the relative proportions ofminimum and maximum principal strainsand stresses.
Empirical studies of in vivo deformationin bone using strain gages are limited by thetechnology to relatively few sites. Loadingregimes can be suggested that comply withthe data collected at these sites. Finite ele-ment analysis (FEA) provides a usefulmethod for extending the work of straingage studies. FEA produces computer mod-els, which after validation through experi-mental work, can be extended to studylarger overall patterns of stress and straindistributions in skeletal elements. A recentstudy by Ricos and colleagues (1996) dem-onstrated that modeling bones using aglobal simplified constitutive characteriza-tion such as isotropy can lead to somemarked differences in computed stress andstrain distributions. However, the degree ofdifference in modeled turkey ulnas de-pended on the type of loading; results fromtorsional loading simulations were more in-fluenced than axial loading simulations. Al-though several mandibular models havebeen created with FEA (Hart et al., 1992;Korioth et al., 1992), these have not ad-dresses the question of the influence ofchanges in material properties on stress andstrain patterns under different loading con-ditions. We would expect similar differencesas those found in the turkey ulna by Ricosand colleagues (1996).
CONCLUSIONS
In mechanical studies of the skeleton, cor-tical bone strain can be measured and usedas an approximation for bone stress in in-ferring in vivo loading patterns. If bonewere isotropic, principal strains andstresses would coincide in orientation; alsomagnitudes of stress and strain would beproportional in different directions. How-ever, cortical bone was anisotropic leadingto differences between stress and strain.
In this study, we measured the elasticproperties of a region of the lower border of
the macaque mandible on its buccal andlingual cortices, and used these data alongwith the results of several in vivo straingage experiments (Hylander, 1979 and thecurrent investigation) to assess the magni-tude and significance of differences betweenthe principal stresses and strains. Specifi-cally, we asked four questions:
1. What are the elastic properties ofthe mandibular corpus?
Our measurement of elastic properties in-dicated similar values to those found in hu-man mandibles. Near its lower border, ma-caque mandibles were most stiff in alongitudinal direction, less stiff in an infero-superior direction, and least stiff in a direc-tion normal to the surface of the bone. Theregion measured on the lingual aspect of themandible was found to be slightly stifferthan the region on the buccal aspect.
2. What are the magnitudes anddirections of stress in the macaque
mandible during function?
The largest values of calculated stressesnear the lower border of the corpus of themacaque mandible during function rangedfrom a compressive stress of 216.00 GPa toa tensile stress of the 8.84 GPa. Since thesevalues were derived from averaged strains,individual stresses would be greater in mag-nitude. The orientation of the principalstresses depended on specific activities. Onthe balancing side of the mandibles, maxi-mum principal stresses were orientednearly perpendicular to the lower border.On the working side of the mandibles, theorientation of the maximum principalstresses was more variable than on the bal-ancing side, indicating a larger range of pos-sible mechanisms of loading.
3. How well do directions and relativemagnitudes of principal stresses
and strains correspond?
Near the lower border of the mandible,differences between the orientation ofstresses and strains were 12° or less. Thesedifferences were considerably smaller thanthe maximum theoretical differences of 45°(Cowin and Hart, 1990). Ratios between
572 P.C. DECHOW AND W.L. HYLANDER
maximum and minimum stresses (sq/sp)were generally more extreme (further awayfrom a ratio of 1.0) than ratios betweenmaximum and minimum strains (jq/jp). Dif-ferences between sq/sp and jq/jp rangedfrom no difference to a maximum differenceof 6.49 compared to 2.66.
4. Do differences between these axesresult in any reinterpretation of our
understanding of mandibularfunction in macaques?
While our results did not provide any ma-jor reinterpretations of our understandingof mandibular function in macaques, it wasequally important to address the impact ofstudies of skeletal material properties onthe interpretation of strain gage experi-ments in general. Our null hypothesis wasthat although there were significant differ-ences by direction in the elastic properties ofthe mandibular corpus in macaques, as inthe human mandible, the impact of thesedifferences was small compared to the fullrange of theoretical differences, resulting inminor reinterpretations of studies of func-tion of the mandible based on strain gagetechniques. Did the results support this hy-pothesis? Unfortunately, the answer wasequivocal. The significance of differences be-tween the orientations and relative magni-tudes of stresses and strains must be ad-dressed on a case by case basis. Thedifferences between stresses and strains onthe balancing side of the mandible generallysupported the view that the mandible wasbent and twisted slightly both during mas-tication and transducer biting. The calcu-lated stresses also served to de-emphasizeslightly the relative importance of torsion.On the working side, the greater range ofvariability in the stress analysis comparedto the strain analysis suggested that a moredetailed examination of loadings and stresspatterns in each individual experimentwould be useful to interpret the results. Tor-sion was evident on the working side, but ina number of experiments, further informa-tion was needed to interpret other superim-posed regional loading patterns, includingbut not limited to parasagittal, reverseparasagittal, and transverse bending in sep-arate experiments.
ACKNOWLEDGMENTS
This investigation was supported byMerit Award DE04531 to WLH and re-search grant DE07761 to PCD from the Na-tional Institute of Dental Research, andBNS-8711842 to WLH from the NationalScience Foundation. We thank Dr. DavidDaegling for a critical reading of the manu-script.
LITERATURE CITED
Arendts FJ, Sigolotto C. 1989. Standardabmessungen,Elastizitätskennwerte und Festigkeitsverhalten desHuman-Unterkiefers, ein Beitrag zur Darstellung derBiomechanik der Unterkiefer—Teil I. Biomed Tech-nik 24:248–255.
Arendts FJ, Sigolotto C. 1990. Mechanische Kennwertedes Human-Unterkiefers und Untersuchung zum »invivo«-Verhalten des kompakten Knochengewebes, einBeitrag zur Darstellung der Biomechanik des Unter-kiefers—Teil II. Biomed Technik 25:123–130.
Ashman RB. 1982. Ultrasonic determination of the elas-tic properties of cortical bone: Techniques and limita-tions. Ph.D. Dissertation, Tulane University, U.M.I.Dissertation Services [8311363.
Ashman RB. 1989. Experimental techniques. In: CowinSC, editor. Bone mechanics. Boca Raton, FL: CRCPress. p 76–95.
Ashman RB, Van Buskirk WC. 1987. The elastic prop-erties of a human mandible. Adv Dent Res 1:64–67.
Ashman RB, Cowin SC, Van Buskirk WC, Rice JC.1984. A continuous wave technique for measurementof the elastic properties of cortical bone. J Biomech17:349–361.
Ashman RB, Rosinia G, Cowin SC, Fontenot MG. 1985.The tissue of the canine mandible is elastically iso-tropic. J. Biomech 18:717–721.
Bacon GE, Bacon PJ, Griffiths RK. 1980. Orientation ofapatite crystals in relation to muscle attachment inthe mandible. J Biomech 13:725–729.
Bromage TG. 1993. Preferential intracortical remodel-ing and growth of the macaque mandible: develop-mental constraints on growth and adaptation of bone.Proceedings of the VIII International Symposium onDental Morphology, Jerusalem, Israel. p 1–69.
Carter DR. 1978. Anisotropic analysis of strain rosetteinformation from cortical bone. J Biomech 11:199–202.
Carter R. 1989. The elastic properties of the humanmandible. Ph.D. Dissertation, Tulane University,U.M.I. Dissertation Services [9008726.
Connolly R, Quimby FW. 1978. Acepromazine-ketamineanesthesia in the Rhesus monkey (Macaca mulatta).Lab Anim Sci 28:72–74.
Cowin SC. 1989a. The mechanical properties of corticalbone tissue. In: Cowin SC, editor. Bone mechanics.Boca Raton, FL: CRC Press. p 97–127.
Cowin SC. 1989b. Mechanics of materials. In: CowinSC, editor. Bone mechanics. Boca Raton, FL: CRCPress. p 15–42.
Cowin SC, Hart RT. 1990. Errors in the orientation ofthe principal stress axes if bone tissue is modeled asisotropic. J Biomech 23:349–352.
Cowin SC, Sadegh AM, Luo GM. 1991. Correction for-mulae for the misalignment of axes in the measure-ment of the orthotropic elastic constants. J Biomech24:637–641.
BONE STRESS IN THE MACAQUE MANDIBLE 573
Daegling DJ, Hylander WL. 1998. Biomechanics of tor-sion in the human mandible. Am J Phys Anthropol105:73–87.
Dechow PC, Huynh T. 1994. Effects of preservation onthe anisotropic elastic properties of mandibular cor-tical bone [abstract]. J Morph 220: 339.
Dechow PC, Huynh T. 1996. Elastic properties and bi-omechanics of the baboon mandible [abstract]. Am JPhys Anthropol Suppl 22:94–95.
Dechow PC, Schwartz-Dabney CL, Ashman R. 1992.Elastic properties of the human mandibular corpus.In: Goldstein SA, Carlson DS, editors. Bone biody-namics in orthodontic and orthopedic treatment, Vol27, Craniofacial growth series. Ann Arbor, MI: Centerfor Human Growth and Development, The Universityof Michigan. p 299–314.
Dechow PC, Nail GA, Schwartz-Dabney CL, AshmanRB. 1993. Elastic properties of human supraorbitaland mandibular bone. Am J Phys Anthropol 90:291–306.
Demes B, Preuschoft H, Wolff JEA. 1984. Stress-strength relationships in the mandibles of hominoids.In: Chivers DJ, Wood BA, Bilsborough A, editors.Food acquisition and processing in primates. NewYork: Plenum. p 369–390.
Hart RT, Hennebel VV, Thongpreda N, Van BuskirkWC, Anderson RC. 1992. Modeling the biomechanicsof the mandible: a three-dimensional finite elementstudy. J Biomech 25:261–286.
Hylander WL. 1979. Mandibular function in Galagocrassicaudatus and Macaca fascicularis: An in vivoapproach to stress analysis of the mandible. J Mor-phol 159:253–296.
Hylander WL. 1981. Patterns of stress and strain in themacaque mandible. In: Carlson DS, editor. Craniofa-cial biology, Vol10. Craniofacial growth series. AnnArbor, MI: Center for Human Growth and Develop-ment, The University of Michigan. p 1–37.
Hylander WL. 1984. Stress and strain in the mandibu-lar symphysis of primates: A test of competing hy-potheses. Am J Phys Anthropol 64:1–46.
Hylander WL. 1985. Mandibular function and biome-chanical stress and scaling. Am Zool 25:315–330.
Hylander WL. 1986. In-vivo bone strain as an indicatorof masticatory bite force in Macaca fascicularis. ArchOral Biol 31:149–158.
Hylander WL. 1987. Loading patterns and jaw move-ments during mastication in Macaca fascicularis: Abone-strain, electromyographic, and cineradiographicanalysis Am J Phys Anthropol 72:287–314
Hylander WL, Johnson KR. 1989. The relationship be-tween masseter force and masseter electromyogramduring mastication in the monkey Macaca fascicu-laris. Arch Oral Biol 34:713–722.
Hylander WL, Johnson KR. 1997. In vivo bone strainpatterns in the zygomatic arch of macaques and thesignificance of these patterns for functional interpre-tations of craniofacial form. Am J Phys Anthropol102:203–232.
Hylander WL, Picq PG, Johnson KR. 1991. Masticatory-stress hypotheses and the supraorbital region or pri-mates. Am J Phys Anthropol 86:1–36.
Kohles SS, Cartee GD, Vanderby RJ. 1996. Corticalelasticity in aging rats with and without growth hor-mone treatments. J Med Eng Technol 20:157–163.
Kohles SS, Martinez DA, Bowers JR, Vailas AC,Vanderby RJ. 1997. Effect of a growth hormone treat-ment on bone orthotropic elasticity in dwarf rats. AnnBiomed Eng 25:77–85.
Korioth TWP, Romilly DP, Hannam AG. 1992. Three-dimensional finite element stress analysis of the den-tate human mandible. Am J Phys Anthropol 88:69–96.
Lanyon LE, Hampson WG, Goodship AE, Shah JS.1975. Bone deformation recorded in vivo from straingauges attached to the human tibial shaft. Acta Or-thop Scand 46:256–268.
Martin RB, Burr DB. 1989. Structure, function, andadaptation of compact bone. New York: Raven Press.
Reilly DT, Burstein AH. 1974. The mechanical proper-ties of cortical bone. J Bone Joint Surg 56A:1001–1022.
Rho JY. 1991. Mechanical properties of human corticaland cancellous bone. Ph.D. dissertation, The Univer-sity of Texas Southwestern Medical Center at Dallas,Dallas, Texas.
Ricos V, Pedersen DR, Brown TD, Ashman RB, RubinCT, Brand RA. 1996. Effects of anisotropy and mate-rial axis registration on computed stress and straindistributions in the turkey ulna. J Biomech 29:261–267.
Schwartz-Dabney CL, Dechow PC. 1997. Variation incortical material properties from throughout the hu-man mandible. J Dent Res 76SI:Abstract 1882.
Shinedling EA, Dechow PC. 1996. Elastic properties ofmandibular cortical bone in neonatal pigs. J Dent Res75SI:Abstract 798.
Skedros JG, Mason MW, Nelson MC, Bloebaum RD.1996. Evidence of structural and material adaptationto specific strain features in cortical bone. Anat Rec246:47–63.
Skedros, JG, Su SC, Bloebaum RD. 1997. Biomechani-cal implications of mineral content and microstruc-tural variations in cortical bone of horse, elk, andsheep calcanei. Anat Rec 249:297–316.
Takano Y, Turner CH, Burr DB. 1996. Mineral anisot-ropy in mineralized tissues is similar among speciesand mineral growth occurs independently of collagenorientation in rats: Results from acoustic velocitymeasurements. J Bone Miner Res 11:1292–1301.
Turner CH, Chandran A, Pidaparti RMV. 1995. Theanisotropy of osteonal bone and its ultrastructuralimplications. Bone 17:85–89.
Wagner HD, Weiner S. 1992. On the relationship be-tween the microstructure of bone and its mechanicalstiffness. J Biomech 25:1311–1320.
