Masticatory loading and bone adaptation in the ... - Wiley Online Library

Download PDF
45 downloads 0 Views 272KB Size Report
Comment
Dec 2, 2008 - 6School of Anatomy and Human Biology and Forensic Science ... primates; biomechanics; finite element analysis; muscle physiological cross- ...
AMERICAN JOURNAL OF PHYSICAL ANTHROPOLOGY 139:193–203 (2009)

Masticatory Loading and Bone Adaptation in the Supraorbital Torus of Developing Macaques K. Kupczik,1,2* C.A. Dobson,3 R.H. Crompton,4 R. Phillips,5 C.E. Oxnard,2,6 M.J. Fagan,3 and P. O’Higgins2 1

Department of Human Evolution, Max Planck Institute for Evolutionary Anthropology, Leipzig, Germany Hull York Medical School, The University of York, Heslington, UK 3 Department of Engineering, University of Hull, Hull, UK 4 Division of Human Anatomy and Cell Biology, School of Biomedical Sciences, University of Liverpool, Liverpool, UK 5 Department of Computer Science, University of Hull, Hull, UK 6 School of Anatomy and Human Biology and Forensic Science Center, The University of Western Australia, Crawley, WA, Australia 2

KEY WORDS area

primates; biomechanics; finite element analysis; muscle physiological cross-sectional

ABSTRACT Research on the evolution and adaptive significance of primate craniofacial morphologies has focused on adult, fully developed individuals. Here, we investigate the possible relationship between the local stress environment arising from masticatory loadings and the emergence of the supraorbital torus in the developing face of the crab-eating macaque Macaca fascicularis. By using finite element analysis (FEA), we are able to evaluate the hypothesis that strain energy density (SED) magnitudes are high in subadult individuals with resulting bone growth in the supraorbital torus. We developed three micro-CT-based FEA models of M. fascicularis skulls ranging in dental age from deciduous to permanent dentitions and validated them against published experimental data. Applied masticatory muscle forces were estimated from physiological cross-sectional areas of macaque cadaveric

specimens. The models were sequentially constrained at each working side tooth to simulate the variation of the bite point applied during masticatory function. Custom FEA software was used to solve the voxel-based models and SED and principal strains were computed. A physiological superposition SED map throughout the face was created by allocating to each element the maximum SED value from each of the load cases. SED values were found to be low in the supraorbital torus region throughout ontogeny, while they were consistently high in the zygomatic arch and infraorbital region. Thus, if the supraorbital torus arises to resist masticatory loads, it is either already adapted in each of our subadult models so that we do not observe high SED or a lower site-specific bone deposition threshold must apply. Am J Phys Anthropol 139:193–203, 2009. V 2008 Wiley-Liss, Inc.

There has been continuous debate as to the evolution and functional significance of features of form in the craniofacial skeleton of living and fossil primates (e.g., Hylander et al., 1991; Lieberman, 2000; Ravosa et al., 2000; Ross, 2001). The growth and development of bone structures is regulated by both intrinsic biological (e.g., genes, hormones) and mechanobiological (e.g., stress and strain magnitudes, strain rates) signals (see reviews in Pearson and Lieberman, 2004; Rubin et al., 2006; Ruff et al., 2006). Since adult bone is already largely adapted to external mechanical stimuli (Ruff et al., 2006), one approach to understanding the evolution and phenotypic variation of features of form in the adult primate craniofacial complex is to examine the relationship between the ontogenetic history of masticatory loadings and facial bone adaptation (Moss, 1973; Oyen et al., 1979; Oyen and Rice, 1980; Dechow and Carlson, 1990; Bouvier and Hylander, 1996; Lieberman, 1997; Pearson and Lieberman, 2004; Ruff et al., 2006). Most studies addressing questions pertaining to adult primate craniofacial and dental biomechanics have relied on morphometric approaches as well as in vitro and in vivo experimentation. These have been complemented increasingly by simulation and modeling techniques such as finite element analysis (FEA) and multibody dynamics analysis, because they allow for the prediction of stress/strain pat-

terns and other mechanical parameters of complex geometries under specific loading conditions (Chen and Chen, 1998; McConnell and Crompton, 2001; Witzel and Preuschoft, 2002; Preuschoft and Witzel, 2004; Sellers and Crompton, 2004; Witzel et al. 2004; Macho et al., 2005; Marinescu et al., 2005; Richmond et al., 2005; Ross et al., 2005; Strait et al., 2005, 2007; Kupczik et al., 2007; Wroe et al., 2007; Curtis et al., 2008). In this study, we investigate the possible relationship between the local stress/strain environment arising from masticatory loadings and the emergence of the supraorbital torus or brow ridge in the developing craniofacial skele-

C 2008 V

WILEY-LISS, INC.

C

Grant sponsor: The Leverhulme Trust, Grant number: F/00 224/I; Grant sponsors: BBSRC, Australian Research Council, Max-PlanckGesellschaft. *Correspondence to: Dr. Kornelius Kupczik, Department of Human Evolution, Max Planck Institute for Evolutionary Anthropology, Leipzig, Germany. E-mail: [email protected] Received 7 May 2008; accepted 14 October 2008 DOI 10.1002/ajpa.20972 Published online 2 December 2008 in Wiley InterScience (www.interscience.wiley.com).

194

K. KUPCZIK ET AL.

ton of the crab-eating macaque Macaca fascicularis. We carry out this analysis using novel software that allows us to both build and test models more efficiently than is the case with standard mechanical engineering tools and readily evaluate the net effect of multiple loading scenarios in the same structure.

Bone modeling and remodeling The skeleton of the developing primate face undergoes changes in size and shape through a combination of sutural bone deposition and surface bone deposition and resorption. This change in bone morphology is referred to as modeling as opposed to Haversian remodeling, which is in fact bone turnover (Frost, 1990a,b; Pearson and Lieberman, 2004). Numerous authors have devised models of bone modeling and remodeling in relation to systemic and nonsystemic factors (see reviews in Martin et al., 1998; Carter and Beaupre´, 2001; Pearson and Lieberman, 2004). Proponents of so-called ‘‘equilibrium models’’ (Pearson and Lieberman, 2004) have suggested in one way or another that mechanical stimuli such as stress, strain, strain rate, or strain energy density (SED) above a certain maximum threshold induce bone deposition, while mechanical stimuli below a minimum threshold cause resorption (e.g., Frost, 1987, 1990a,b; Huiskes et al., 1987; Carter et al., 1996; Carter and Beaupre´, 2001). Thus, between these thresholds, there is a neutral or equilibrium zone in which loadings elicit neither deposition nor resorption. It is likely that both the range of the neutral zone and the threshold levels differ according to age, individual, and location within the skeleton (Beaupre´ et al., 1990; Carter et al., 1996; Gross et al., 1997; Cowin, 2001; Hsieh et al., 2001; Pearson and Lieberman, 2004). For instance, since the skeleton of juveniles is particularly susceptible to changes in mechanical environment, responses of cortical bone to masticatory loading occur primarily in individuals prior to their sexual maturity (Bouvier and Hylander, 1996; Pearson and Lieberman, 2004; Ruff et al., 2006). Thus, in subadult M. fascicularis, secondary osteon density, indicating remodeling, was found to be higher in highstrain regions in the face compared to low-strain regions and the mandible unlike the case in adult individuals where the densities were similar in high- and low-strain regions (Bouvier and Hylander, 1996).

low because the morphology is already optimized for resisting a specific masticatory loading regime. In subadults, however, one might expect relatively higher strains in this region. These will result in bone deposition until strains come to lie within the neutral zone. The state of knowledge of the function and ontogeny of brow ridges is covered in some detail by Lieberman (2000). Here, in view of the debate regarding the ontogeny of brow ridges in relation to masticatory stresses, and the paucity of experimental strain data for these structures in subadults, we use an FEA approach to investigate the extent to which masticatory stress in the brow ridge varies ontogenetically in M. fascicularis. To this end, we test the hypothesis that masticatory loading of the brow ridge is high in sexually immature individuals. We evaluate this hypothesis using the parameter of strain energy density (SED) as the mechanical signal that controls bone adaptation. Unlike direct stress or strain, SED incorporates effects from all direct and shear components into a single value. It thus reflects the general state of stress and strain at a point and has previously been used as the mechanical variable in models of bone remodeling that determines bone shape and density (Huiskes et al., 1987, 2000; Ruimerman et al., 2005). We estimate masticatory loads using a novel technique that evaluates peak SED within the face in a range of different bites in both juvenile and adult M. fascicularis. To take the biomechanical differences between juvenile and adult individuals into account, we build FE models with additional complexities such as developing versus fully erupted permanent dentitions and craniofacial sutures.

MATERIALS AND METHODS Materials Three cadaveric heads of M. fascicularis were used for this study (Table 1), ranging in dental age from deciduous to permanent dentitions. The sample represents individuals both prior to and after reaching sexual maturity. The specimens had previously been used in dental caries experiments unrelated to the present study (Smith and Beighton, 1986, 1987). One of the M. fascicularis specimens was also used in a previous study by Kupczik et al. (2007). The craniofacial sutures in the specimens were still patent.

Bone adaptation and craniofacial morphology Several features of developing and adult primate faces have been attributed to mechanical adaptation, including the paranasal sinuses (O’Higgins et al., 2006) and circumorbital structures. In particular, it has been argued that the form, function, and evolution of the supraorbital torus and its associated structures occurring in many extant and extinct primates are determined by masticatory loading regimes; in other words, these massively built structures may constitute an adaptation to a highstrain regime (Endo, 1966; Greaves, 1985; Russell, 1985; Hilloowala and Trent, 1988a,b; Bookstein et al., 1999). Yet, several in vivo strain gauge studies on adult anthropoids and strepsirrhines have found strains to be very low in this region, compared for example to those in the infraorbital region or the zygomatic arch (Hylander et al., 1991; Hylander and Johnson, 1992; Ross and Hylander, 1996; Ravosa et al., 2000). It is conceivable that the low supraorbital strains in adult individuals simply reflect ontogenetic adaptation; that is, strains are American Journal of Physical Anthropology

Methods Computed tomography and 3D model generation Computed tomography (CT) scans of the specimens were taken using either an X-Tek HMX 160 (X-Tek Systems, Tring, UK), a BIR ACTIS 300/225 (Bio-Imaging Research, Lincolnshire, IL), or a Philips Mx8000 clinical CT scanner (Hull Royal Infirmary, UK) (Table 2). The CT datasets were processed in Amira v.3.1 (Mercury Computer Systems, Chelmsford, MA) and cortical and cancellous bone and teeth (in the case of the subadult specimens both deciduous and permanent teeth) were segmented using a semiautomatic threshold approach with subsequent manual editing (see Fig. 1). Since the resolution of the CT images did not allow for segmentation of individual trabeculae, cancellous bone was segmented as a bulk material. In addition, the periodontal ligament (PDL), which connects the tooth to the alveolar bone, was segmented as a layer of one to two voxels around the tooth roots of each specimen. We also seg-

195

BONE ADAPTATION IN THE DEVELOPING MACAQUE CRANIOFACIAL SKELETON TABLE 1. Sex and dental age of M. fascicularis specimens used Specimen

Sex

Age (years)

Comments

Mac01 Mac02 Mac14

unknown unknown M

1–2 2–3 [7

Deciduous dentition in occlusion; M1 erupted but not in occlusion Deciduous dentition and M1 in occlusion; M2 crown developed Complete permanent dentition except M3 congenitally missing

TABLE 2. CT-scanning parameters Specimen

Scanner

Voltage (kV)

Current

Filter

Voxel size (mm)

Mac01 Mac02 Mac14

X-Tek BIR Philips

117 85 120

89 lA 55 lA 228 mA

0.1 mm Cu – –

0.22 0.2 0.23

Fig. 1. Frontal and lateral views of subadult M. fascicularis finite element model showing the locations from which strain energy density, principal strain, and maximum shear strain values were sampled. Inset showing coronal section through FE model with cortical and cancellous bone, teeth, and craniofacial sutures (indicated by black lines). W 5 working-side; B 5 balancing side; 1 5 dorsal interorbital; 2/3 5 W/B dorsal orbital; 4/5 5 W/B infraorbital; 6/7 5 W/B midzygomatic; 8 5 W postorbital; 9 5 dorsal rostrum; 10/11 5 W/B lateral rostum; 12/13 5 W/B posterior zygomatic.

mented the developing permanent tooth germs in the subadult specimens, including a one- to two-voxel-thick layer to prevent contact between the teeth and bone. The craniofacial sutures (zygomatico-temporal, internasal, naso-maxillary, median and transverse palatine, interpalatine, maxillo-premaxillary, maxillo-zygomatic, fronto-zygomatic) were also segmented ranging in thickness between two and four voxels (see Fig. 1). The segmented images were exported as a stack of bitmap (*.bmp) images and each dataset was converted into an FE mesh file consisting of between two and four million (depending on specimen size) eight-noded cubic elements using custom software. Finite element modeling Material properties. Each finite element (FE) mesh file was imported into VOX-FE, our custom FE preprocessing software. We assigned isotropic, linear elastic properties to the five materials involved (cortical and cancellous bone, teeth, sutures, PDL), since our software currently does not support anisotropic elastic properties. We assigned a Young’s modulus (E) of 17 GPa to cortical bone and teeth (cf. Strait et al., 2005). The craniofacial sutures and PDL were assigned an E of 0.0012 GPa

[based on results for rabbit zygomatico-temporal sutures from Radhakrishnan and Mao (2004)]. For cancellous bone, there is a plethora of elasticity values published for human and bovine postcranial elements ranging from less than 0.05 to 20.7 GPa (reviewed in Athanasiou et al., 2000 and Currey, 2002), but data for cranial bone are lacking. Since it has been argued that E values less than 6 GPa may be too low (Currey, 2002), we therefore decided to treat cancellous bone as a bulk tissue with E 5 10GPa. The Poisson’s ratio (v) was set to 0.3 for all materials. Boundary conditions. The models were constrained at the glenoid fossae and sequentially at each maxillary working side tooth (both left and right incisors were constrained simultaneously) to simulate the changes in location of bite points used during masticatory function over a period of time (Fig. 2A). The occlusal surface of each tooth was constrained in the superior–inferior direction only, while the glenoid fossae were constrained in all three directions. The models were loaded by selecting surface nodes on the working and balancing sides to represent the four main masticatory muscles: the superficial and deep masseters, the medial pterygoid, and the anterior tempoAmerican Journal of Physical Anthropology

196

K. KUPCZIK ET AL.

Fig. 2. (A) Voxel-based finite element model of an adult M. fascicularis cranium with craniofacial sutures and periodontal ligament (in green) showing boundary conditions and applied loads. The model was constrained sequentially at each working-side (model’s left side) tooth (left and right incisors were constrained simultaneously). For illustrative purposes, only three tooth positions are shown (black arrows). Gray arrows indicate masticatory muscle forces (F) applied. (B) Strain energy density (SED) contour plots for the three single-bite load cases. (C) Physiological superposition map of the peak SED summarizing all load cases. See text for details.

ralis (Fig. 2A). The latter is defined here as the anterior vertical section of the temporal muscle adjacent to the postorbital bar and septum (cf. Ross, 1995). This portion includes the zygomatico-temporalis. The selection of surface nodes was informed by dissections of the masticatory muscles of each of the M. fascicularis specimens. The muscle forces for each of the masticatory muscles were estimated from physiological cross-sectional areas (PCSA) of the three M. fascicularis cadaveric specimens following the protocol in Anapol and Barry (1996) (Table 3). The muscle forces for each working and balancing side muscle were calculated as F 5 (PCSA) 3 (300 kN/ m2) 3 (% of peak activity 20 ms prior to peak corpus strain) (Strait et al., 2005) (Table 3). The percentage of peak activity was calculated based on data for M. mulatta soft food feeding (apple with skin) given in Ross et al. (2005) and Strait et al. (2007). Since the PCSA of the superficial masseter in Mac02 yielded a relatively high muscle force similar to that in much larger adults

Fig. 3. SED contour plots of juvenile and adult M. fascicularis. (A) Mac01, (B) Mac02, (C) Mac14. The working side is on the models’ left side. All plots are scaled to the same peak SED range (models are not to scale). Note the supraorbital brow ridge region in all models show relatively low SED values, while they are relatively high in the zygomatic arch region.

American Journal of Physical Anthropology

BONE ADAPTATION IN THE DEVELOPING MACAQUE CRANIOFACIAL SKELETON

197

TABLE 3. Estimated physiological cross-sectional area (PSCA) and applied masticatory muscle forces Mac01

Mac02

Mac14

Musclea

Scaling factorb

PCSA (cm2)

Force (N)

PCSA (cm2)

Force (N)

PCSA (cm2)

Force (N)

Sup mass WS Sup mass BS Deep mass WS Deep mass BS Med pteryg WS Med pteryg BS Ant temp WS Ant temp BS

0.701 0.344 0.579 0.211 0.547 0.109 0.753 0.312

1.31

27.61 13.56 5.50 2.00 29.78 5.91 32.73 13.55

1.76

37.06 18.20 11.37 4.13 18.21 3.61 28.93 11.98

2.09

41.73 20.49 24.35 8.85 42.84 8.50 42.83 17.73

0.32 1.81 1.45

0.65 1.11 1.28

1.40 2.61 1.90

Sup/deep mass 5 superficial/deep masseter, med pteryg 5 medial pterygoid, ant temp 5 anterior temporalis, WS 5 working side, BS 5 balancing side. b Muscle peak activity 20 ms prior to peak corpus strain (Strait et al., unpublished data for M. mulatta). a

(Table 3), we also used an adjusted superficial masseter force equivalent to that of Mac01 (working side 27.61 N; balancing side 13.56 N) because of the possibility that subadult muscle has a lower intrinsic strength. The rationale behind this is presented in the Discussion. In all FE models, the loadings of the working and balancing side muscles were unbalanced (i.e., Fworking [ Fbalancing; ratio based on Strait et al., 2005) when ‘‘biting’’ on the canine and postcanine teeth but balanced (i.e., Fworking 5 Fbalancing) when biting on the incisors. Solution and validation. Custom finite element software (VOX-FE) was used to solve the voxel-based models. To test for the effects of a model consisting of cortical bone with or without a cancellous bone core and the implications of using sutures and PDL on the results, we devised three sets of analyses for each of the three macaque models. Since a maximum of two different materials per model can be processed with our FE solver, the first set consisted of cortical and cancellous bone without sutures or PDL (cortical/cancellous model). In the second set, we removed the cancellous bone and used cortical bone and sutures/PDL (hollow model). The third set was a solid model with cortical bone throughout the model and sutures/PDL. The solid and hollow models reflect the upper and lower margin of published elastic property variation in cancellous bone (see above). In other words, the solid model represents cancellous bone with an E of cortical bone, whereas the hollow model reflects to some extent an exceptionally low cancellous bone E. The maximum (e1) and minimum principal strains (e3) as well as the orientation of e1 and the maximum shear strain (cmax) were computed for Mac02 and Mac14 constrained at the first permanent molar and for Mac01 constrained at the second deciduous molar. The average cmax and e1 orientation values of 20 adjacent surface elements (4 mm2) taken at eight locations in the models (Fig. 1; locations 1–8) were compared with experimental strain gauge data from subadult (Hylander and Johnson, 1997) and adult macaques [unpublished and published data collated by Strait et al. (2007) in Table 2 of their article]. The overall difference between the cmax obtained experimentally and those obtained in the FEAs was expressed as the Euclidean distance calculated for each of the models. In Mac14, all eight locations were taken into account, while this was limited to the midzygomatic arch on the working and balancing sides in Mac01 and Mac02, because no comparative data for the other locations are given in Hylander and Johnson (1997). The Euclidean distance was computed as the square root of the sum of squared differences between experiment and model. The

minimum Euclidean distance values obtained identify the models that best fit the experimental results. Following the above analyses, the best fit FE model was selected and up to six models per individual were analyzed depending on the number of constrained teeth, and strain energy density (SED) values were computed (Fig. 2B). Strain energy density is a scalar parameter with units in J/m3 or N/m2. Subsequently, a quasidynamic, physiological-superposition map of the peak SED environment throughout the face was created by allocating to each element the maximum SED value from each of the load cases (Fig. 2C).

RESULTS The average ratio of maximum-to-minimum principal strains and maximum shear strain values at eight locations in the three model sets (cortical/cancellous, hollow, solid) of Mac01, Mac02, and Mac14 are shown in Table 4. For Mac02, the results of the analysis with the reduced superficial masseter force are also tabulated. Ratios of e1/e3 are comparable with the experimentally derived data of Hylander and Johnson (1997) in the working and balancing side zygomatic arch, although they are somewhat higher in the subadults than in Mac14 (Table 4). For macaques, grand means in adults have been reported to be 0.7 and 0.6 for WMZ and BMZ, respectively, while values for subadults are 0.8 and 0.6 (Hylander and Johnson, 1997). Our ratios for the dorsal interorbital region are within the range of in vivo data (Hylander et al., 1991), but exceed in vivo ratios in the dorsal orbital region (particularly in Mac02; Table 4). The cmax values for Mac14 correspond well with published and unpublished in vivo strain gauge data (Strait et al., 2007) in five out of eight locations (Table 4). Strains in the dorsal orbital regions (WDO, BDO) and the balancing side mid-zygomatic region (BMZ) fall below the range of experimental data. In the subadult Mac01, the simulated cmax values are within the range of the experimental data for adults with the exception of the working and balancing side dorsal orbital region (Table 4). Compared to experimental data for subadults reported by Hylander and Johnson (1997), the simulated midzygomatic arch strains are higher on the working side, but fall within the range on the balancing side. In Mac02, the FEAs yielded cmax values that are in agreement with adult experimental data at six locations (DIO, WDO, WIO, BIO, BMZ, WPB) and in two out of four analyses at the working side midzygomatic arch (both solid models). Compared to the experimental data in the midzygomatic of subadults, our cmax results are markAmerican Journal of Physical Anthropology

American Journal of Physical Anthropology 2.9 2.8 2.9 2.8 1.6 0.8 1.7 0.3–0.9

48

67 47 43

69

89 56

29–356

39–161

53 21

23

68 56 51

57

28 18

47 33

35

62 36 32

38

35 22

22

cmax

76–207

BDO

1.6–1.2

1.0 2.5

2.3

2.2 2.8 2.8

2.7

1.0 1.2

1.1

e1/e3

230 136

174

479 286 217

304

116 105

100

cmax

52–869

WIO

0.1–1.4

1.2 1.9

1.7

1.5 1.9 2.0

1.7

1.9 2.7

2.7

e1/e3

121 83

110

62 36 32

38

97 78

79

cmax

32–529

BIO

2.2–2.4

1.1 1.1

1.1

2.2 2.8 2.8

2.7

1.5 1.3

1.4

e1/e3

146–1,217 194–602

458 322

242

1,515 1,220 998

1,340

741 646

675

cmax

WMZ

0.6–1.0 0.8

1.0 0.8

0.7

1.1 1.1 1.1

1.1

1.2 1.1

1.2

e1/e3

84 61

93

696 646 522

643

313 284

300

cmax

114–790 34–613

BMZ

0.5–0.9 0.6

0.5 0.5

0.5

0.9 1.0 1.0

1.0

0.8 0.8

0.8

e1/e3

0.5–1.5

1.6 1.7

1.7

1.0 0.9 0.6

0.9

1.1 1.0

1.0

167 159

158

41 43 49

40

84 87

80

cmax

3–391

WPB e1/e3

392 521

511

1,196 904 652

1,014

348 251

281

EDc

a Average of 20 elements (4mm2) per location. W 5 working-side, B 5 balancing side, DIO 5 dorsal interorbital, WDO/BDO 5 dorsal orbital, WIO/BIO 5 infraorbital, WMZ/ BMZ 5 midzygomatic, WPB 5 postorbital bar. b Single tooth is constrained (Mac02, Mac14 5 M1; Mac01 5 dm2). c Euclidean distance between mean experimental and simulated cmax (Mac14, all locations; Mac01 and 02, WMZ and BMZ only). d Same superficial masseter force as in Mac01. e Ranges of in vivo maximum shear strains and principal strain ratios encompassing all of the means 6 2SD for adult Macaca (reported in Strait et al., 2005, 2007) and subadult M. fascicularis (Hylander and Johnson, 1997).

1.2 1.5

18

cmax

WDO

69 53

e1/e3 1.4

cmax

55

DIO

MAC01 Cortical/ 1.8 cancellous Hollow 1.2 Solid 2.1 MAC02 Cortical/ 2.8 cancellous Hollow 2.3 Solid 2.7 2.8 Solid (red. force)d MAC14 Cortical/ 2.7 cancellous Hollow 1.9 Solid 2.7 e Experimental data Adults 1.1–4.6 Subadults

e1/e3

TABLE 4. Mean ratio of maximum-to-minimum principal strains (e1/e3 ) and maximum shear strain (cmax, in le) at eight locationsa in the FE modelsb

198 K. KUPCZIK ET AL.

Values represent direction cosines. x-direction is positive to the left (working) side; y-direction is positive superiorly; z-direction is positive anteriorly. Single tooth is constrained (Mac02, Mac14 5 M1; Mac01 5 dm2). b

a

WPB BMZ

0.25, 0.77, 0.49 0.12, 0.66, 0.72 20.07, 0.71, 0.19 20.10, 0.76, 0.62 0.27, 20.33, 20.27 20.05, 0.87, 0.45

WMZ BIO

0.83, 20.05, 0.54 0.73, 0.38, 0.54 0.71, 0.43, 0.53 0.70, 20.34, 20.60 0.54, 20.26, 20.35 0.63, 20.15, 20.40

WIO BDO

0.82, 0.49, 20.24 0.94, 0.26, 0.12 0.70, 20.07, 20.51

WDO

0.79, 20.39, 0.09 0.92, 20.22, 20.05 0.64, 0.12, 0.70

DIO

0.97, 20.13, 0.03 0.98, 20.15, 0.12 0.87, 20.08, 0.24 Mac01 Mac02 Mac14

TABLE 5. Orientation of maximum principal straina at eight locations in the solid (Mac01, Mac02) and hollow (Mac14) FE modelsb

20.16, 0.60, 0.30 0.45, 0.32, 0.25 20.36, 0.88, 0.06

BONE ADAPTATION IN THE DEVELOPING MACAQUE CRANIOFACIAL SKELETON

199

edly higher in the working side, but only fall slightly outside the range in the balancing side. The difference between experimental and simulated cmax means in all FEA sets is expressed as the Euclidean distance (ED, Table 4). While all eight locations in Mac14 were taken into account, the comparison for the two subadults is limited to the working and balancing side midzygomatic arch. However, when the eight adult experimental values are compared to strains computed by FEA in the subadults, the relative differences between the models are the same with the solid model fitting best (data not presented). In Mac14, the hollow model with sutures and PDL yields the best results followed by the solid model. In both Mac01 and Mac02, the results of the solid models fit best with experimental cmax values. Among the analyses for Mac02, the model with reduced superficial masseter force results in the smallest Euclidean distance. The results for the orientation of the maximum principal strain in the solid (Mac01, Mac02) and hollow models (Mac14) are presented in Table 5 (in terms of direction cosines). The strain orientations in the supraorbital region (x-axis; DIO, WDO, BDO) are in agreement with data ranges derived from strain gauge experiments (Hylander et al., 1991; Hylander and Johnson, 1997; Strait et al., 2007). In the zygomatic arch, the anteriorly oriented maximum principal strains (z-axis) concur with experimentally observed values (Hylander and Johnson, 1997; Strait et al., 2007) in all models except for Mac02 where the working side strains are oriented posteriorly (Hylander and Johnson, 1997; Strait et al., 2007). Moreover, the orientation of e1 in the working side postorbital bar and infraorbital region (y-axes) correspond well with published values, while they fall slightly outside the range on the balancing side in Mac02 and Mac14. The quasi-dynamic FEAs were conducted with the best-fit FE models resulting from the above validation study, i.e., for Mac01 and Mac02 (with reduced superficial masseter muscle force) the solid models and for Mac14 the hollow model were used. Table 6 lists mean peak SED magnitudes computed at 13 loci in the three solid FE models (see Fig. 1; locations 1–13). Strain energy density contour plots of the M. fascicularis models are shown in Figure 3. The plots are all scaled to a range of between 0 and 2,000 N/m2, thus highlighting the regions with peak SED values in the craniofacial region, in particular the mid- and posterior zygomatic arch regions. In both Mac01 and Mac02, the lateral aspects of the dorsal rostral (upper nasal) region are also markedly strained (Fig. 3A,B), while SED in the posterior zygomatic on the balancing side of Mac14 is very high (Table 6). Compared to the other models, Mac02 has the absolutely highest SED values in the working and balancing side mid- and posterior zygomatic regions overall (Table 6). In the working side zygomatic arch of all models, there is a gradient of high to low SED values between the midzygomatic and the posterior zygomatic regions (Table 6). The same gradient exists in the balancing-side zygomatic arch of Mac01 and Mac02 but it is reversed in Mac14. The supraorbital torus region (DIO, WDO and BDO; Table 6, Fig. 3) consistently shows the lowest values of peak SED in all three specimens.

DISCUSSION This study attempts to relate changes in the local SED environment to the emergence of brow ridges in the American Journal of Physical Anthropology

200

K. KUPCZIK ET AL. 2

TABLE 6. Mean maximum SED values (in N/m ) at 13 locationsa in the solid (Mac01, Mac02) and hollow (Mac14) FE modelsb Specimen

DIO

WDO

BDO

WIO

BIO

WMZ

BMZ

WPB

DR

WLR

BLR

WPZ

BPZ

Mac01 Mac02 Mac14

36 25 132

2 15 26

5 9 23

174 490 213

210 324 319

2,214 5,288 762

1,151 4,808 190

82 95 224

221 336 96

404 328 103

37 94 51

596 1,707 394

924 2,095 1,210

a Average of 20 elements per location. DR 5 dorsal rostrum; WLR/BLR 5 lateral rostrum; WPZ/BPZ 5 posterior zygomatic; all other abbreviations as in Table 4. b Models were sequentially constrained at each working side tooth (incisors were constrained simultaneously). Data presented are the maximum SED values per location of all load cases taken together.

developing craniofacial skeleton of M. fascicularis. To this end, we have applied a novel quasi-dynamic FEA approach reflecting the differences in muscle and bone geometry and physiology arising from both intraindividual variation in the feeding cycle and ontogenetic changes in facial size and shape. In addition, our three FE models include craniofacial sutures, permanent teeth, and tooth germs as well as the periodontal ligament, since they are important for primate craniofacial function (Marinescu et al., 2005; Wang et al., 2006; Kupczik et al., 2007). This approach therefore constitutes an extension of previous FEA studies on the biomechanics of the primate craniofacial skeleton, which have exclusively focused on adult morphologies (Ross et al., 2005; Strait et al., 2005, 2007; Kupczik et al., 2007; Wroe et al., 2007). A number of previous studies have examined the accuracy of voxel-based modeling (Camacho et al., 1997; Guldberg et al., 1998; Ulrich et al., 1998; Charras and Guldberg, 2000; Yeni et al., 2005; Verhulp et al., 2006) and demonstrated that, with sufficient numbers of elements, it can produce very accurate answers. The three skulls considered here were scanned with a minimum resolution of 230 lm and thus defined with at least 4 voxels/mm. In Camacho’s study of the meshing a human skull, he showed that at least five voxels were needed through the bone’s thickness to produce reasonable results in very thin structures (Camacho et al., 1997). Since visual examination of the CT data used in this current study shows that the bone structures in the supraorbital region, zygomatic arch and much of the rest of the face are defined by at least this number of voxels, we can be confident in the convergence and mathematical accuracy of the FE calculations performed here as evidenced by the validation results. We devised three FE models for each of our three individuals to assess the sensitivity of the results to the presence or absence of cancellous bone and craniofacial sutures and PDL. These results were validated against published data obtained in in vivo strain gauge studies of macaques (Hylander et al., 1991; Hylander and Johnson, 1997; Strait et al., 2007). We found good correspondence between the simulated and published experimental data in terms of maximum shear strain and the orientation of maximum principal strain (Table 4). While none of the three model types (cortical/cancellous, hollow, solid) could be unambiguously identified as the best matching model for all macaques, the hollow (Mac14) or solid models (Mac01, Mac02) with craniofacial sutures and PDL most closely replicated experimental results. This may be due to the fact that subadult skulls have less well developed sinuses and other spaces within the skull than do adults. Somewhat conspicuous are the high maximum shear strain and SED values observed in the zygomatic and infraorbital regions of two of the American Journal of Physical Anthropology

Mac02 models (Tables 4 and 6). These exceed mean and peak maximum shear strain data for subadult and adult M. fascicularis and M. mulatta reported in the literature (cf. Ross and Metzger, 2004; Strait et al., 2007). The relatively small size of the zygomatic arch and the less flaring zygoma of Mac02 compared to the adult model Mac14 and the subadult Mac01 (see Fig. 3) as well as the presence of the developing permanent dentition and concomitantly an internal network of thin bone struts in the face may have resulted in higher strains in this juvenile model. The application of the masticatory muscle forces could also be a confounding factor. Our muscle force calculation was based on the estimation of the PCSA of the four main masticatory muscles and assumed an intrinsic muscle strength of 300 kN/m2 for both juveniles and adults. We obtained higher values for the adult male Mac14 compared to superficial and deep masseter and medial pterygoid PCSAs of adult female M. fascicularis published by Anto´n (1999, 2000). This sexual dimorphism in muscle force generation needs to be taken into account in FEA studies. The generally high strains noted in the models of the juvenile individuals (Mac01, Mac02) may be the result of an overestimate of the force generated by the superficial masseter. Dechow and Carlson (1990) estimated temporalis and combined masseter and medial pterygoid muscle forces for incisor and molar biting in juvenile and adult M. mulatta using a biomechanical model and bite force data. Their data show that adults can potentially generate up to 2–2.6 times higher masticatory muscle force than juveniles of comparable dental ages to Mac01 and Mac02. In contrast, our PCSA calculations give force ratios between adults and juveniles of superficial masseter of 1.2–1.5, although the ratios for the other muscles agree more closely (Table 3). It is possible that the assumption of the intrinsic strength of 300 kN/m2 for subadult muscle is too high, although there are no systematic data on masticatory muscle strength among different age groups. To take into account differences in muscle activity pattern, we used a scaling factor based on M. mulatta EMG data (Ross et al., 2005; Strait et al., 2005). Since M. mulatta has larger masticatory muscles than M. fascicularis (Anto´n, 1999, 2000), the latter actually may require comparatively greater muscle activity when chewing the same food items (Strait, personal communications). Thus, our applied forces may be an underestimate of the actual M. fascicularis muscle force potential. However, an independent test using Mac14 with M. mulatta muscle force resulted in a larger difference between simulated and experimental strain data (data not shown here).

Bone adaptation and supraorbital structures The supraorbital torus apparently arises from differential growth of the inner and outer table of the frontal

BONE ADAPTATION IN THE DEVELOPING MACAQUE CRANIOFACIAL SKELETON bone as the face projects forwards (Duterloo and Enlow, 1970; Ravosa, 1991b; Lieberman, 2000). The methodological issues raised above notwithstanding, our data support the notion that the growth of the supraorbital torus region is not a result of a high-strain loading regime and thus that its presence and morphology in adult fossil hominins is unrelated to mastication (cf. Hylander et al., 1991; Hylander and Johnson, 1992; Ravosa et al., 2000). In agreement with in vivo strain gauge studies on adult macaques (Hylander et al., 1991; Hylander and Johnson, 1992), in the present study the SED magnitudes measured at the three supraorbital torus locations (DIO, WDO, BDO; Tables 4 and 6) are consistently low among the juvenile and adult individuals. Strain levels may be expected to be higher in juvenile individuals, since cortical bone elasticity levels are apparently lower when compared to adults, which have been shown for human femoral cortical bone ranging in age from 2 to 48 years (Currey and Butler, 1975). However, if the bone adaptation threshold levels for bone modeling are equal throughout the face, then it is not very likely that the relatively low mechanical signal (SED) in the brow ridge would elicit bone deposition. The present findings would refute the hypothesis that masticatory loading of the brow ridge is high in sexually immature individuals. There is a problem, however, in attempting to relate cranial bone deposition to the mechanical environment, since it has been shown previously (Hylander et al., 1991; Hylander and Johnson, 1992; Ross and Hylander, 1996; Ravosa et al., 2000) and again here, in an ontogenetic series, that despite the high strains in the zygomatic region it grows relatively slowly compared to the brow ridges, which manifest much lower strains. Structurally, the zygoma in humans is characterized by relatively thin and less dense cortical bone in conjunction with a relatively dense cancellous bone core compared to the parietal and the frontal including the supraorbital torus (Hylander and Johnson, 1997; Peterson and Dechow, 2003). Moreover, it has been demonstrated that bone deposition/resorption thresholds in the skeleton are age- and site-specific (Carter et al., 1996; Gross et al., 1997; Hsieh et al., 2001). For instance, it has been argued that the strain thresholds are higher in those regions of the skeleton where the mechanical strain signal is high (Turner, 1999). In fact, significant strain gradients are present within and between the bones of the cranium across several tetrapod taxa (Hylander and Johnson, 1992, 1997; Lieberman et al., 2003; Ross and Metzger, 2004). Thus, with regard to the supraorbital torus, it is conceivable that the strain threshold for deposition is very low, i.e., strains of a relatively low magnitude induce bone formation, while the zygomatic arch and the infraorbital regions, which constantly have to withstand high feeding forces, require high magnitude strains to trigger bone deposition. It could also be maintained that bone in the brow ridge region adapts so rapidly that we never observe high SED. However, since several experimental studies have rejected hypotheses that the supraorbital torus behaves as a bending beam or exists to limit twisting between the face and neurocranium during incision and mastication (Hylander et al., 1991; Hylander and Johnson, 1992; Ross, 2001), brow ridges might be optimized for demands other than mastication (Ross and Metzger, 2004) and they manifest low strains attributable to masticatory loading throughout postnatal ontogeny. This renders it unlikely that they arise to resist masticatory loads (cf. Hylander et al., 1991;

201

Hylander and Johnson, 1992). This conclusion merits further testing through future simulation studies in which the effects of varying brow ridge morphology are tested. For example, under the same loading conditions, models of hypothetical juvenile and adult macaque with absent or reduced brow ridges might be expected to yield increased levels of SED compared to that of a normal and/or hyperrobust brow ridge morphology. From the current results, however, it would appear to be more likely that the spatial relationship between the orbits and the anterior cranial fossa and/or allometric effects of overall cranial and facial size account for brow ridge formation and size (Moss and Young, 1960; Ravosa, 1991a,b; Lieberman, 2000).

ACKNOWLEDGMENTS We would like to thank Lee Page and Jia Liu for programming Vox-FE and Sue Taft for technical assistance. We are also grateful to Andrea Cardini, Sam Cobb, John Currey, Neil Curtis, Laura Fitton, Flora Gro¨ning, Callum Ross, Amanda Smith, David Strait, and Ulrich Witzel as well as Chris Ruff, the Associate Editor, and anonymous reviewers for very helpful and stimulating comments and discussions on the project design and the manuscript. David Strait and Amanda Smith are thanked for providing muscle activity data and helping with strain orientation calculations.

LITERATURE CITED Anapol F, Barry K. 1996. Fiber architecture of the extensors of the hindlimb in semiterrestrial and arboreal guenons. Am J Phys Anthropol 99:429–447. Anto´n SC. 1999. Macaque masseter muscle: internal architecture, fiber length and cross-sectional area. Int J Primatol 20:441–462. Anto´n SC. 2000. Macaque pterygoid muscles: internal architecture, fiber length, and cross-sectional area. Int J Primatol 21:131–156. Athanasiou KA, Zhu C-F, Lanctot DR, Agrawal CM, Wang X. 2000. Fundamentals of biomechanics in tissue engineering of bone. Tissue Eng 6:361–381. Beaupre´ GS, Orr TE, Carter DR. 1990. An approach for time-dependent bone modeling and remodeling—theoretical development. J Orthop Res 8:651–661. Bookstein F, Scha¨fer K, Prossinger H, Seidler H, Fieder M, Stringer C, Weber GW, Arsuaga JL, Slice DE, Rohlf FJ, Recheis W, Mariam AJ, Marcus LF. 1999. Comparing frontal cranial profiles in archaic and modern Homo by morphometric analysis. Anat Rec 257:217–224. Bouvier M, Hylander WL. 1996. The mechanical or metabolic function of secondary osteonal bone in the monkey Macaca fascicularis. Arch Oral Biol 41:941–950. Camacho DLA, Hopper RH, Lin GM, Myers BS. 1997. An improved method for finite element mesh generation of geometrically complex structures with application to the skull base. J Biomech 30:1067–1070. Carter DR, Beaupre´ GS. 2001. Skeletal function and form: mechanobiology of skeletal development, aging, and regeneration. Cambridge: Cambridge University Press. Carter DR, Van der Meulen MCH, Beaupre´ GS. 1996. Skeletal development: mechanical consequences of growth, aging and disease. In: Feldman MR, Kelsey J, editors. Osteoporosis. San Diego: Academic Press. p 333–350. Charras GT, Guldberg RE. 2000. Improving the local solution accuracy of large-scale digital image-based finite element analyses. J Biomech 33:255–259. Chen XB, Chen H. 1998. The influence of alveolar structures on the torsional strain field in a gorilla corporeal cross-section. J Hum Evol 35:611–633.

American Journal of Physical Anthropology

202

K. KUPCZIK ET AL.

Cowin SC. 2001. Bone modeling and remodeling: theories and computation. In: Cowin SC, editor. Bone mechanics handbook, 2nd ed. Boca Raton, FL: CRC Press. p 1–42. Currey JD. 2002. Bones: structure and mechanics. Princeton: Princeton University Press. Currey JD, Butler G. 1975. The mechanical properties of bone tissue in children. J Bone Joint Surg Am 57:810–814. Curtis N, Kupczik K, O’Higgins P, Moazen M, Fagan MJ. 2008. Predicting skull loading: applying multibody dynamics analysis to a macaque skull. Anat Rec (Hoboken) 291:491–501. Dechow PC, Carlson DS. 1990. Occlusal force and craniofacial biomechanics during growth in rhesus monkeys. Am J Phys Anthropol 83:219–237. Duterloo HS, Enlow DE. 1970. A comparative study of cranial growth in Homo and Macaca. Am J Anat 127:357–368. Endo B. 1966. Experimental studies on the mechanical significance of the form of the human facial skeleton. J Fac Sci Univ Tokyo 8:1–106. Frost HM. 1987. Bone mass and the mechanostat—a proposal. Anat Rec 219:1–9. Frost HM. 1990a. Skeletal structural adaptations to mechanical usage (SATMU): 1. Redefining Wolff ’s law: the bone modeling problem. Anat Rec 226:403–413. Frost HM. 1990b. Skeletal structural adaptations to mechanical usage (SATMU): 2. Redefining Wolff ’s law: the remodeling problem. Anat Rec 226:414–422. Greaves WS. 1985. The mammalian postorbital bar as a torsionresisting helical strut. J Zool (Lond) 207:125–136. Gross TS, Edwards JL, McLeod KJ, Rubin CT. 1997. Strain gradients correlate with sites of periosteal bone formation. J Bone Miner Res 12:982–988. Guldberg RE, Hollister SJ, Travers GT. 1998. The accuracy of digital image-based finite element models. J Biomech Eng 120: 289–295. Hilloowala RA, Trent RB. 1988a. Supraorbital ridge and masticatory apparatus 1: primates. Hum Evol 3:343–350. Hilloowala RA, Trent RB. 1988b. Supraorbital ridge and masticatory apparatus 2: humans (Eskimos). Hum Evol 3:351–356. Hsieh YF, Robling AG, Ambrosius WT, Burr DB, Turner CH. 2001. Mechanical loading of diaphyseal bone in vivo: the strain threshold for an osteogenic response varies with location. J Bone Miner Res 16:2291–2297. Huiskes R, Ruimerman R, Van Lenthe GH, Janssen JD. 2000. Effects of mechanical forces on maintenance and adaptation of form in trabecular bone. Nature 405:704–706. Huiskes R, Weinans H, Grootenboer HJ, Dalstra M, Fudala B, Slooff TJ. 1987. Adaptive bone-remodeling theory applied to prosthetic-design analysis. J Biomech 20:1135–1150. Hylander WL, Johnson KR. 1992. Strain gradients in the craniofacial region of primates. In: Davidovitch Z, editor. The biological mechanisms of tooth movement and craniofacial adaptation. Columbus: Ohio State University College of Dentistry. p 559–569. Hylander WL, Johnson KR. 1997. In vivo bone strain patterns in the zygomatic arch of macaques and the significance of these patterns for functional interpretations of craniofacial form. Am J Phys Anthropol 102:203–232. Hylander WL, Picq PG, Johnson KR. 1991. Masticatory-stress hypotheses and the supraorbital region of primates. Am J Phys Anthropol 86:1–36. Kupczik K, Dobson CA, Fagan MJ, Crompton RH, Oxnard CE, O’Higgins P. 2007. Assessing mechanical function of the zygomatic region in macaques: validation and sensitivity testing of finite element models. J Anat 210:41–53. Lieberman DE. 1997. Making behavioral and phylogenetic inferences from hominid fossils: considering the developmental influence of mechanical forces. Annu Rev Anthropol 26:185–210. Lieberman DE. 2000. Ontogeny, homology, and phylogeny in the hominid craniofacial skeleton: the problem of the browridge. In: O’Higgins P, Cohn M, editors. Development, growth and evolution: implications for the study of hominid skeletal evolution. London: Academic Press. p 85–122. Lieberman DE, Pearson OM, Polk JD, Demes B, Crompton AW. 2003. Optimization of bone growth and remodeling in

American Journal of Physical Anthropology

response to loading in tapered mammalian limbs. J Exp Biol 206:3125–3138. Macho GA, Shimizu D, Jiang Y, Spears LR. 2005. Australopithecus anamensis: a finite element approach to studying the functional adaptations of extinct hominins. Anat Rec A Discov Mol Cell Evol Biol 283:310–318. Marinescu R, Daegling DJ, Rapoff AJ. 2005. Finite-element modeling of the anthropoid mandible: the effects of altered boundary conditions. Anat Rec A Discov Mol Cell Evol Biol 283:300–309. Martin RB, Burr DB, Sharkey NA. 1998. Skeletal tissue mechanics. Berlin: Springer. McConnell CJ, Crompton RH. 2001. Finite element stress analysis of food–tooth interactions in primates. In: Middleton J, Jones ML, Shrive NG, Pande GN, editors. Computer methods in biomechanics and biomedical engineering. Amsterdam: Gordon and Breach. p 673–678. Moss ML. 1973. A functional analysis of primate craniofacial growth. In: Zingeser MR, editor. Symposium of the IVth International Congress on Primatology. Vol 3. Basel: Karger. p 191– 208. Moss ML, Young RW. 1960. A functional approach to craniology. Am J Phys Anthropol 18:281–292. O’Higgins P, Bastir M, Kupczik K. 2006. Shaping the human face. Int Congr Ser 1296:55–73. Oyen OJ, Rice RW. 1980. Supraorbital development in chimpanzees, macaques and baboons. J Med Primatol 9:161–168. Oyen OJ, Walker AC, Rice RW. 1979. Craniofacial growth in olive baboons (Papio cynocephalus): browridge formation. Growth 43:174–187. Pearson OM, Lieberman DE. 2004. The aging of Wolff ’s ‘‘law’’: ontogeny and responses to mechanical loading in cortical bone. Yearb Phys Anthropol 47:63–99. Peterson J, Dechow PC. 2003. Material properties of the human cranial vault and zygoma. Anat Rec A Discov Mol Cell Evol Biol 274:785–797. Preuschoft H, Witzel U. 2004. Functional structure of the skull in hominoidea. Folia Primatol 75:219–252. Radhakrishnan P, Mao JJ. 2004. Nanomechanical properties of facial sutures and sutural mineralization front. J Dent Res 83:470–475. Ravosa MJ. 1991a. Ontogenetic perspective on mechanical and nonmechanical models of primate circumorbital morphology. Am J Phys Anthropol 85:85–112. Ravosa MJ. 1991b. Interspecific perspective on mechanical and non-mechanical models of primate circumorbital morphology. Am J Phys Anthropol 86:369–396. Ravosa MJ, Noble VE, Hylander WL, Johnson KR, Kowalski EM. 2000. Masticatory stress, orbital orientation and the evolution of the primate postorbital bar. J Hum Evol 38:667–693. Richmond BG, Wright BW, Grosse L, Dechow PC, Ross CF, Spencer MA, Strait DS. 2005. Finite element analysis in functional morphology. Anat Rec A Discov Mol Cell Evol Biol 283:259–274. Ross C. 2001. In vivo function of the craniofacial haft: the interorbital ‘‘pillar’’. Am J Phys Anthropol 116:108–139. Ross CF. 1995. Muscular and osseous anatomy of the primate anterior temporal fossa and the functions of the postorbital septum. Am J Phys Anthropol 98:275–306. Ross C, Metzger KA. 2004. Bone strain gradients and optimization in vertebrate skulls. Ann Anat 186:387–396. Ross CF, Hylander WL. 1996. In vivo and in vitro bone strain in the owl monkey circumorbital region and the function of the postorbital septum. Am J Phys Anthropol 101:183–215. Ross CF, Patel BA, Slice DE, Strait DS, Dechow PC, Richmond BG, Spencer MA. 2005. Modeling masticatory muscle force in finite element analysis: sensitivity analysis using principal coordinates analysis. Anat Rec A Discov Mol Cell Evol Biol 283:288–299. Rubin J, Rubin C, Jacobs CR. 2006. Molecular pathways mediating mechanical signaling in bone. Gene 367:1–16. Ruff C, Holt B, Trinkaus E. 2006. Who’s afraid of the big bad Wolff? ‘‘Wolff ’s law’’ and bone functional adaptation. Am J Phys Anthropol 129:484–498.

BONE ADAPTATION IN THE DEVELOPING MACAQUE CRANIOFACIAL SKELETON Ruimerman R, van Rietbergen B, Hilbers P, Huiskes R. 2005. The effects of trabecular-bone loading variables on the surface signaling potential for bone remodeling and adaptation. Ann Biomed Eng 33:71–78. Russell MD. 1985. The supraorbital torus—a most remarkable peculiarity. Curr Anthropol 26:337–360. Sellers WI, Crompton RH. 2004. Using sensitivity analysis to validate the predictions of a biomechanical model of bite forces. Ann Anat 186:89–95. Smith K, Beighton D. 1986. The effects of the availability of diet on the levels of exoglycosidases in the supragingival plaque of macaque monkeys. J Dent Res 65:1349–1352. Smith K, Beighton D. 1987. Proteolytic activities in the supragingival plaque of monkeys (Macaca fascicularis). Arch Oral Biol 32:473–476. Strait DS, Richmond BG, Spencer MA, Ross CF, Dechow PC, Wood BA. 2007. Masticatory biomechanics and its relevance to early hominid phylogeny: an examination of palatal thickness using finite-element analysis. J Hum Evol 52:585–599. Strait DS, Wang Q, Dechow PC, Ross CF, Richmond BG, Spencer MA, Patel BA. 2005. Modeling elastic properties in finite element analysis: how much precision is needed to produce an accurate model? Anat Rec A Discov Mol Cell Evol Biol 283:275–287.

203

Turner CH. 1999. Toward a mathematical description of bone biology: the principle of cellular accommodation. Calcif Tissue Int 65:466–471. Ulrich D, van Rietbergen B, Weinans H, Ru¨egsegger P. 1998. Finite element analysis of trabecular bone structure: a comparison of image-based meshing techniques. J Biomech 31:1187–1192. Verhulp E, van Rietbergen B, Huiskes R. 2006. Comparison of micro-level and continuum-level voxel models of the proximal femur. J Biomech 39:2951–2957. Wang Q, Strait DS, Dechow PC. 2006. Fusion patterns of craniofacial sutures in rhesus monkey skulls of known age and sex from Cayo Santiago. Am J Phys Anthropol 131:469–485. Witzel U, Preuschoft H. 2002. Function-dependent shape characteristics of the human skull. Anthropol Anz 60:113–135. Witzel U, Preuschoft H, Sick H. 2004. The role of the zygomatic arch in the statics of the skull and its adaptive shape. Folia Primatol 75:202–218. Wroe S, Moreno K, Clausen P, McHenry C, Curnoe D. 2007. High-resolution three-dimensional computer simulation of hominid cranial mechanics. Anat Rec (Hoboken) 290:1248–1255. Yeni YN, Christophersin GT, Dong XN, Kim D-G, Fyhrie DP. 2005. Effect of microcomputed tomography voxel size on the finite element model accuracy for human cancellous bone. J Biomech Eng 127:1–8.

American Journal of Physical Anthropology