Assessing mechanical function of the zygomatic region in macaques: validation and sensitivity...

J. Anat.

(2007)

210

, pp41–53 doi: 10.1111/j.1469-7580.2006.00662.x

© 2006 The Authors Journal compilation © 2006 Anatomical Society of Great Britain and Ireland

Blackwell Publishing Ltd

Assessing mechanical function of the zygomatic region in macaques: validation and sensitivity testing of finite element models

K. Kupczik,

1

C. A. Dobson,

2

M. J. Fagan,

2

R. H. Crompton,

3

C. E. Oxnard

1,4

and P. O’Higgins

1

1

Hull York Medical School, The University of York, UK

2

Centre for Medical Engineering and Technology, Department of Engineering, University of Hull, UK

3

Department of Human Anatomy & Cell Biology, University of Liverpool, UK

4

School of Anatomy and Human Biology, The University of Western Australia, Australia

Abstract

Crucial to the interpretation of the results of any finite element analysis of a skeletal system is a test of the validity

of the results and an assessment of the sensitivity of the model parameters. We have therefore developed finite

element models of two crania of

Macaca fascicularis

and investigated their sensitivity to variations in bone material

properties, the zygomatico-temporal suture and the loading regimen applied to the zygomatic arch. Maximum

principal strains were validated against data derived from

ex vivo

strain gauge experiments using non-physiological

loads applied to the macaque zygomatic arch. Elastic properties of the zygomatic arch bone and the zygomatico-

temporal suture obtained by nanoindentation resulted in a high degree of congruence between experimental and

simulated strains. The findings also indicated that the presence of a zygomatico-temporal suture in the model pro-

duced strains more similar to experimental values than a completely separated or fused arch. Strains were distinctly

higher when the load was applied through the modelled superficial masseter compared with loading an array of

nodes on the arch. This study demonstrates the importance of the accurate selection of the material properties

involved in predicting strains in a finite element model. Furthermore, our findings strongly highlight the influence

of the presence of craniofacial sutures on strains experienced in the face. This has implications when investigating

craniofacial growth and masticatory function but should generally be taken into account in functional analyses of

the craniofacial system of both extant and extinct species.

Key words

cranial sutures; elastic properties; experimental strain analysis; finite element analysis; primates; sensi-

tivity; skull; validation.

Introduction

Here we present a validation study of finite element

models (FEMs) of two macaque crania and assess the

sensitivity of these models to elastic properties of bone,

the presence or absence of a suture and the mode of

load application.

A major prerequisite of the study of the evolution of

the primate craniofacial complex is to develop an

understanding of how mechanical factors influence

facial growth and adult morphology (e.g. Moss, 1973;

Oyen et al. 1979; Dechow & Carlson, 1990). This issue

can be approached in several ways, but that adopted in

this paper is to develop FEMs of macaque faces at

different stages during growth and to explore how

stresses and strains experienced during static loading

are related to bone modelling. Finite element analysis

(FEA) is increasingly being used to test hypotheses per-

taining to the functional morphology of the primate

craniodental system (Spears & Crompton, 1996; Daegling

& Hylander, 1997, 2000; Chen & Chen, 1998; Spears &

Macho, 1998; Macho & Spears, 1999; McConnell &

Crompton, 2001; Witzel & Preuschoft, 2002; Preuschoft

& Witzel, 2004; Witzel et al. 2004; Macho et al. 2005;

Correspondence

Dr Kornelius Kupczik, Department of Human Evolution, Max Planck Institute for Evolutionary Anthropology, Deutscher Platz 6, 04103 Leipzig, Germany. T: +49 (341) 3550 756; F: +49 (341) 3550 399; E: [email protected]

Accepted for publication

18 September 2006

FEM of the macaque zygomatic region, K. Kupczik et al.

© 2006 The AuthorsJournal compilation © 2006 Anatomical Society of Great Britain and Ireland

42

Marinescu et al. 2005; Richmond et al. 2005; Ross et al.

2005; Strait et al. 2005). The reliability of models ought

to be tested against real-world data before they can be

employed confidently (Richmond et al. 2005). Several

authors have recognized this need; thus, Fagan et al.

(2002) carried out sensitivity studies of FEMs of inter-

vertebral discs, and Sellers & Crompton (2004) and

Wang et al. (2004) undertook both validation and

sensitivity studies to dynamic models of the masticatory

and locomotor systems. Those cranial FEA studies that

do take the need for verification and sensitivity into

account have done so, for example, by comparing the

FEM with known muscle physiological data (Ross et al.

2005) or by referring to material properties of bone

obtained by mechanical testing (Strait et al. 2005).

Additionally,

in vitro

experimental strain analyses have

enabled validation of FEMs (e.g. Marinescu et al. 2005).

The latter approach offers the particular advantage of

a better control of the loads and boundary conditions,

model geometry and elastic properties of the materials

defined in the model. Moreover, the strain gauge loca-

tions in the experimental specimens can be precisely

recorded, allowing an accurate comparison between

experimental and simulated strain results.

In this study we aim to validate and investigate the

sensitivity of FEMs of two crania of the crab-eating

macaque

Macaca fascicularis

focusing on the infraorbital

region and the zygomatic arch. We are particularly

concerned with the effects of (1) the variation of bone

material properties, (2) the complexity of the morphology

involved (i.e. the presence or absence of representation

of morphological features such as sutures in the FEM)

and (3) the nature of loading of the zygomatic arch on

the predicted strain magnitudes observed in the FEM

both locally within the zygomatic arch and the infra-

orbital region and globally throughout the cranium. The

results of the FEA are validated against data derived from

ex vivo

strain gauge experiments using non-physiological

loads applied to the macaque zygomatic arch.

It has been observed that the specification of the

material properties (i.e. magnitude, direction, spatial

variation) in the model has significant implications on

the results of an FEA (Marinescu et al. 2005; Richmond

et al. 2005; Strait et al. 2005). Although solving an FEM

with heterogeneous, orthotropic elastic properties pre-

dicts the most congruent strain results when compared

with experimental data (Marinescu et al. 2005; Strait

et al. 2005), for the sake of simplicity the materials

involved in the present FEA are modelled with homo-

geneous, isotropic and linear elastic properties. In order

to enable the validation of the FEA strain results, elastic

properties of selected regions in the bone of the zygo-

matic arch were obtained using a nanoindention tech-

nique (see below). Moreover, the effect of changes in

bone stiffness on the distribution of strains in the zygo-

matic arch and the circumorbital region are investigated

by sequential alteration in the FEA of the experiment-

ally determined Young’s modulus of elasticity (

E

, GPa)

of bone and these effects are compared with our strain

gauge data.

The zygomatic arch has been chosen as it represents

a discrete morphological region of the cranium of

importance in terms of investigating craniofacial bio-

logy and as a key component in the FEM (e.g. Hylander

& Johnson, 1997; Rafferty et al. 2000; Witzel et al.

2004). The attachment areas of the superficial and

deep heads of the masseter muscle are easily identifiable

and the arrangement and orientation of the fibres

makes this muscle easier to model than, for instance,

the temporalis muscle – attaching as it does to the

curved parietal bone. Moreover, the presence of the

zygomatico-temporal suture is of interest from both a

functional and a developmental point of view (Herring,

1972; Jaslow, 1990; Hylander & Johnson, 1997; Mao,

2002; Mao et al. 2003; Rafferty et al. 2003; Rayfield,

2005).

In vivo

strain gauge experiments have shown

that the zygomatic arch of

M. fascicularis

experiences a

strain gradient, the largest strains occurring at the

anterior end of the arch (Hylander & Johnson, 1997). As

the superficial masseter muscle attaches along the

anterior portion of the zygomatic arch anterior to the

zygomatico-temporal suture, the force will be concen-

trated anteriorly and hence strains are expected to be

larger in this region.

The zygomatic arch resembles to some extent a beam

with fixed ends, to which a uniform but off-centre load

has been applied (Hylander & Johnson, 1997). Under

this model bending moments are consequently largest

in the anterior portion of the arch, resulting in relatively

larger strains in this region and lower strains towards

the posterior arch (Hylander & Johnson, 1997). How-

ever, as these authors also noted such a beam model

would not take into account the zygomatico-temporal

suture connecting the zygomatic processes of the zygo-

matic and temporal bones. It is known from research

on miniature pigs that flexible cranial sutures are sub-

jected to large deformations and limit the strains that

can develop in the delicate bones of the face during



43

dynamic loading (Herring & Teng, 2000; Rafferty et al.

2003). Flexible sutures are also said to act as shock-

absorbers, being able to absorb more impact energy

than bone (Buckland-Wright, 1978; Jaslow, 1990). More-

over, Sun et al. (2004) showed that the magnitude and

polarity of strains in some cranial sutures of pigs

change with increasing age. This is particularly relevant

to solving FEMs of juvenile vs. adult macaques. In terms

of bending moments and induced stresses and strains

in the zygomatic arch our model is like a beam with a

built-in (cantilevered) constraint at one end and a flex-

ible joint at the other. In immature individuals with a

patent suture the bending moment of the anterior

zygomatic arch will be higher than in older individuals

with more mineralized and thus stiffer sutures. It is thus

hypothesized that strains in the anterior zygomatic

arch in particular decrease with gradual obliteration of

the suture. This is tested by comparing experimental

strain values with those computed from FEMs with

zygomatic arches that are (1) disconnected, (2) fully

fused and (3) connected by a zygomatico-temporal

suture of varying elastic properties.

A further issue to be addressed here is the modelling

of the muscle forces involved. Commonly, force vectors

of a certain magnitude and direction are simply

applied to the surface nodes of the FEM. The selection

of these nodes should reflect the attachment site and

the distribution and the concentration of the muscle

fibres (Richmond et al. 2005; Ross et al. 2005). One

question of interest is how the strain field is influenced

by the distribution of the applied forces. It can be

hypothesized that the more focussed, centralised appli-

cation of loads, the more complex and potentially larger

the loading and induced stresses and strains experienced

by the bone will be. We investigate this by conducting

FEAs with varying arrangements of distributed load

while keeping the total force applied to the zygomatic

arch constant. An alternative approach is to incorpor-

ate the muscle itself into the FEM and load the zygo-

matic arch indirectly via the modelled muscle. This has

the advantage of capturing the exact geometry of the

muscle and might be expected to result in predicted

strains that are more congruent with experimental data.

Material and methods

We selected whole cadaveric heads of two adult male

M. fascicularis

for this study. The study animals (referred

to here as MAC-14 and MAC-17) had been used previ-

ously in dental caries experiments unrelated to the

present study (Smith & Beighton, 1986, 1987). The exact

history of preservation of the cadaveric heads is un-

certain, although it is known that they have been kept

in formaldehyde, 70% industrial methylated spirit and

other aqueous solutions at various times. MAC-14 is a

relatively small specimen with the third molars congenit-

ally missing, while MAC-17 is a large adult with a com-

plete dentition. The zygomatico-temporal suture is

clearly defined and unfused in MAC-14, whereas in the

more mature MAC-17 specimen the suture is less visible

and appears more mineralised.

Experimental strain analysis

In both specimens the skin and the underlying soft tissue

were removed to reveal the bone and the masticatory

muscles. The superficial masseter was dissected on one

side of each of the heads (MAC-14: left-hand side;

MAC-17: right-hand side) and detached from its inser-

tion site on the mandible sufficiently to permit in-

dependence when loads were applied to it. Dehydration

was minimized by applying a glycerine/water solution

onto the soft tissue and bone and by keeping the speci-

mens in a sealed container in a fridge when not under

experimental employment. Prior to the strain gauging

experiments the exposed bone was degreased with

isopropanol (M-Line GC-6 Degreaser, Vishay Measure-

ments Group, Basingstoke, UK) and abraded with pumice

powder. Six 120

±

0.5-

Ω

rosette strain gauges wired in

a three-wire quarter-bridge circuit (TML FRA-1–11,

Tokyo Sokki Kenkyujo, Tokyo, Japan) were bonded with

cyanoacrylate along the zygomatic arch of each speci-

men, from the infra-orbital region to the posterior

zygomatic arch (gauges IO and ZA1–ZA5), three gauges

being placed anterior to the suture and two posterior

to it (Fig. 1). The strain gauges were connected to a

Vishay 5100B Wheatstone bridge amplifier with an

excitation voltage of 0.5 V (Vishay Micro-Measurements).

The heads were then placed on a specially constructed

test rig and constrained by means of a rubber plug

fixing the foramen magnum. The second molars and

the first molars of MAC-17 and MAC-14, respectively,

rested on a rubber-coated bar. Each of the dissected

superficial masseters (working side) and the gonion

region of the mandible on the balancing side were per-

forated to allow passage and attachment of nylon-coated

strings (1 mm diameter, Berkley Outdoor Technologies

Group, Spirit Lake, IA, USA). We conducted the loading



44

via the strings in line with the orientation of the super-

ficial masseters, by manually placing weights at the ends

of the strings up to a maximum of 15 N for the smaller

MAC-14 specimen and 20 N for the MAC-17 specimen.

Simultaneously, in each of the specimens an equal load

was applied to the string on the balancing side jaw also

in line with the orientation of the superficial masseter.

We recorded the orientation of the working side mas-

seter by taking three-dimensional (3D) coordinates with

a MicroScribe GTX digitizing system (Immersion Corpo-

ration, San Jose, CA, USA) in order to derive the force

vectors for the FEA. Maximum principal strains (expressed

as microstrain

µε

) under static loads were recorded as

the strain most readily comparable with the FE results.

Five consecutive strain readings at the strain peak were

taken per loading, and loadings were repeated four

times within 15 min of the experiment to minimize the

effects of dehydration and atmospheric change.

Nanoindentation of zygomatic arch cortical bone and

zygomatico-temporal suture

Although the fixation history of the specimens is

unknown it is likely to have had an effect on mechanical

properties. Thus, to establish the elastic properties of

the cortical bone and the zygomatico-temporal suture

of the fixed specimens we investigated the mechanical

properties of the bone using an instrumented nano-

indenter. Following the strain gauge experiments, the

zygomatic arch from the balancing side of each specimen

was cut both at the anterior (zygomatic) end and at the

posterior (temporal) end of the arch. Subsequently, the

isolated bones were sectioned with an Isomet 5000

linear precision saw (Buehler Ltd, Lake Bluff, IL, USA) at

two locations along the arch of MAC-14 (anteriorly and

through the zygomatico-temporal suture) and three

locations along the arch of MAC-17 (anteriorly, through

the zygomatico-temporal suture and posteriorly). The

three samples were then embedded in epoxy cold-

mounting resin (Epothin, Buehler Ltd) before the

surfaces were ground (Phoenix Beta Vector, Buehler Ltd)

and polished (ChemoMat synthetic polishing pad and

Mastermet silica polishing suspension, Buehler Ltd).

Using a nano-hardness tester with a Berkovitch diamond

indenter (CSM Instruments S.A., Peseux, Switzerland),

we measured the Young’s elastic modulus at 16 loca-

tions along the perimeter of each cross-sectional sample,

using a load of 100 mN applied for 5 s. In addition, four

nanoindentation measurements were taken through

the zygomatico-temporal suture of the two specimens.

The mean of the

E

of bone and suture for each of the

sections of MAC-14 and MAC-17 are summarized in

Table 1. The grand mean for bone is 9.1

±

2.8 GPa

(MAC-14) and 11.0

±

3.0 GPa (MAC-17), while it is

1.9

±

1.7 and 7.7

±

3.4 GPa for the suture of MAC-14

and MAC-17, respectively.

CT scanning and 3D reconstruction

Coronal computed tomography (CT) scans were taken

of MAC-14 on a Philips Mx8000 scanner (helical mode,

Fig. 1 Three-dimensional reconstructions and finite element mesh of (A) MAC-14 with zygomatico-temporal suture (dashed line) and (B) MAC-17 with right superficial masseter muscle (dark grey). Nodes highlighted correspond to strain gauge locations on the zygomatic arch and the infraorbital region in the specimens used in the loading experiments (three nodes represent one location; see text for details). Numbers refer to strain gauge positions (1 = infraorbital region; 2–6 = zygomatic arch locations). Open arrows indicate load point on M1 (MAC-14) and M2 (MAC-17); thin arrows indicate line of action of muscle loaded.

Table 1 Mean, standard deviation (SD) and maximum and minimum Young’s elastic moduli (in GPa) for cortical bone of the zygomatic arch (MAC-14: two sections, MAC-17: three sections) and for the zygomatico-temporal suture in MAC-14 and MAC-17. The values are based on 16 nanoindentation measurements for each of the bone sections (anterior, suture and posterior) and four and five for the suture tissue of MAC-14 and MAC-17, respectively

Anterior section

Suture section

Posterior section

Grand mean

Zygomatico-temporal suture

MAC-14Mean 9.8 8.3 – 9.1 1.9SD 2.9 2.7 – 2.8 1.7Min. 4.0 1.0 – 0.8Max. 13.3 12.0 – 4.5

MAC-17Mean 11.1 11.5 10.3 11.0 7.7SD 2.5 2.4 4.1 3.0 3.4Min. 5.2 7.1 2.2 4.3Max. 16.8 15.7 14.9 12.1



45

0.3 mm slice thickness, 120 kV, 228 mA). MAC-17 was

scanned on an X-Tek HMX 160 scanner (X-Tek Systems

Ltd, Tring, UK) at 123 kV, 87

µ

A and with a 0.2-mm Cu

filter. The voxel size was 0.23 mm. Prior to scanning,

the specimen MAC-17 was deliberately dehydrated for

14 days at room temperature in order to assist in the

visualization of the masticatory muscles. We sub-

sequently used the visualization software Amira (Mercury

Computer Systems, Inc., San Diego, CA, USA) to segment

the bone and teeth (treating enamel and dentine as a

single material) and, by extracting the surfaces, re-

constructed these materials in three dimensions. The

components of the periodontal ligament were not taken

into account as the limited resolution of the CT scans

did not allow for an accurate reconstruction. In MAC-

14 a clearly defined zygomatico-temporal suture was

also segmented as a discrete object, thus separating

the zygomatic from the temporal bone (Fig. 1A). In

MAC-17 this suture was partly fused and hence only

weakly indicated in the segmentation. Moreover, in

MAC-17 the superficial masseter was segmented and

reconstructed in three dimensions (Fig. 1B). Both surface

models were then converted into a volumetric tetrahedral

grid to be imported into ANSYS Mechanical (ANSYS,

Inc., Canonsburg, PA, USA).

Finite element modelling

The FEMs derived from the CT data used quadratic,

tetrahedral elements (ANSYS type SOLID 92). The MAC-14

model consists of 178 427 elements, while the larger

MAC-17 model including the superficial masseter com-

prises 232 564 elements. Given the size difference, this

resulted in a similar mesh density for the two samples.

All materials (i.e. bone, teeth, muscle and suture) were

modelled as linear elastic and isotropic (see

E

values for

each of the materials used below) with a Poisson’s ratio

of 0.3 in all cases.

In both models we modelled the boundary condi-

tions for the foramen magnum and occlusal surfaces of

the relevant molars by fully constraining the corre-

sponding nodes in these areas. In MAC-14, ten nodes

on the inferior border of the left zygomatic arch were

selected and a total load of 15 N applied. The loading

conditions of the zygomatic arch of MAC-17 are

described in detail below. In addition, the equivalent

surface nodes on the opposite zygomatic arch were

fully constrained. This idealization of the balancing

side forces was considered justifiable as it was remote

from the primary region of interest. Three series of

finite element analyses were conducted by varying:

(1) the

E

of the bone material (both models); (2) the

presence, absence and

E

of the zygomatico-temporal

suture (MAC-14 only); and (3) the method of load appli-

cation (MAC-17 only). The sensitivity of the FEMs to these

parameters was assessed and the parameters which

resulted in predicted strains concurring with those

measured experimentally were identified.

(1) Variation of bone elastic properties

We varied the Young’s modulus of the bone material

using values measured from the nanoindentation

study of the bone (see Table 1). A range of values were

noted and the highest, lowest and average value were

used for the modelling, with further fine adjustment to

identify the value that produced results similar to those

recorded experimentally. The teeth were assigned an

elastic modulus

E

of 70 GPa based on a mean of pub-

lished values for enamel and dentine (Cuy et al. 2002;

Kinney et al. 2003).

(2) Variations of the zygomatico-temporal suture

The defined zygomatico-temporal suture in the MAC-

14 specimen consisted of 420 tetrahedral elements.

Modelling was initially conducted to represent the two

extremes of fusion and complete disconnection. We

modelled the suture either with the same properties as

the surrounding bone (

E

= 9.1GPa) or omitted it from

the model completely, thus separating the zygomatic

and temporal portions of the zygomatic arch. We sub-

sequently modelled the suture with

E

-values derived

from the literature (1.20

±

0.20 MPa in 8-week-old

rabbits; Radhakrishnan & Mao, 2004) and also from the

nanoindentation results (see Table 1), with further

variation conducted to provide agreement with the

experimental results.

(3) Variation of load application

In MAC-17 we modelled the zygomatic arch loading

either by direct application of the load vectors to nodes

along the zygomatic arch or by application of the load

vectors to the modelled superficial masseter muscle.

Where direct loading was used, the load of 20 N was

uniformly distributed between 10, 20 and 41 nodes

along the superficial masseter bone scar on the zygomatic



46

arch (Fig. 2). These loading conditions represented a

linear distribution (ten nodes) to an area distribution

covering the full attachment site of the muscle (41

nodes).

In the case of the muscle loading in the MAC-17

model, the load was applied to attempt to replicate the

experimental load conditions in a number of ways. In

the absence of a literature value for the bulk elastic

modulus of the superficial masseter, we experimented

by varying

E

and Poisson’s ratio. A value for

E

of 1 GPa

and Poisson’s ratio of 0.3 was found to deviate least

from the experimentally determined values. Thus, in

loading scenarios 1–3 the load of 20 N was distributed

between all the nodes of a cross-section of the muscle

through inferior, central and superior parts of the mus-

cle (Fig. 3). In loading scenario 4, a closer replication of

experimental conditions was attempted by loading a

line of nodes through the depth of the muscle at the

approximate location where the loading string pene-

trated the muscle (Fig. 3).

We compared the results from the finite element

modelling in each case to the experimental results. This

was done by calculating the mean maximum principal

strain of three superficial nodes in the model coincid-

ing with each of the six strain gauge locations on the

skulls (see Fig. 1). The overall difference between the

strains obtained experimentally at all six locations and

those obtained in the FEA was expressed as the Eucli-

dean distance calculated for each of the models. This

was computed as the square root of the sum of squared

differences between experiment and model. The

minimum Euclidean distance values obtained identi-

fied the modelling parameters which best fit the experi-

mental results. No statistical treatment of sensitivity

beyond this was feasible given the small number of

models solved.

Results

Variation of bone elastic properties

Figure 4(A,B) compares the mean maximum principal

strains recorded for five strain gauges (MAC-14 – with

the suture modelled using optimum

E

from the studies

of Fig. 5, see below) and six strain gauges (MAC-17) in

the loading experiments with the results of the FE

modelling while taking into account a range of bone

E

values. The strain gauge ZAL3 for MAC-14 turned out

to be faulty, and hence the results were excluded from

the subsequent analyses. In MAC-14, at all bone stiff-

ness levels the largest maximum principal strains occur

in the anterior zygomatic arch (ZAL1) with rapidly

decreasing strains posteriorly (Fig. 4A; except ZAL4,

E

= 4.0 GPa). Both the experimental and the modelled

strains in MAC-17 are more uniformly distributed and

peak in the middle of the anterior zygomatic arch for

E

= 11–17 GPa (ZAR-2, Fig. 4B).

Fig. 2 Variation of load application. Basal view of right zygomatic arch of MAC-17 with (A) 10, (B) 20 and (C) 41 nodes selected for loading. The area covered by the selected nodes reflects the attachment site of the superficial masseter (grey shaded area).

Fig. 3 Variation of loading of the right superficial masseter in MAC-17. 1, 2, 3: inferior, central and superior part of muscle loaded; 4: line of nodes loaded through the depth of the muscle (see text for details). Arrow indicates load point on M2.



47

In general, the strains decrease with an increase in the

stiffness of bone in both models. The Euclidean distances

for MAC-14 indicate that the difference between experi-

mental and FE strains is lowest when modelled with the

mean

E

of bone derived from nanoindentation (9.1 GPa).

By contrast, for MAC-17 it was found that

E

= 14 GPa yields

a lower Euclidean distance than the average value obtained

by nanoindentation (11.0 GPa). The largest discrepancy

between the strains in the FEM and in the experiments

in MAC-17 is found for location IOR (

c

. 75

µε

see Fig. 4B).

Fig. 4 Effect of variation of bone material properties on maximum principal strains in FEA compared with experimental strain values (Exp, mean and standard deviation). (A) MAC-14; 15 N load application (please note that no experimental strain value is given for ZAL 3 due to gauge malfunction). Ebone ranges from 4 to 13.3 GPa with a mean of 9.1 GPa with Esuture = 0.0025 GPa constant (Poisson’s ratio is 0.3 throughout). (B) MAC-17; a load of 20 N was uniformly distributed between ten nodes on the zygomatic arch. Ebone ranges from 2.2 to 13 GPa with a mean of 11 GPa. ED = Euclidean distances (expressing the difference between the experimental and simulated strains; see text for details). IOL/R = infraorbital, left/right; ZAL/R1 to ZAL/R5 = zygomatic arch, left/right.

Fig. 5 Presence, absence and elastic properties variation of zygomatico-temporal suture in MAC-14 (Ebone = 9.1 GPa, Poisson’s ratio = 0.3). (A) Maximum principal strains along zygomatic arch with arch completely separated, fused (Esuture = Ebone) and suture with E = 0.0025 GPa (Poisson’s ratio = 0.3). (B) Effects of varying elastic properties of zygomatico-temporal suture on maximum principal strains in zygomatic arch. Esuture ranges from 0.001 to 1.9 GPa. Abbreviations as in Fig. 4.



48

Variations of the zygomatico-temporal suture

Figure 5(A) illustrates the effects on the maximum prin-

cipal strains in MAC-14 when the zygomatic arch is fully

fused (i.e. the

E

of the zygomatico-temporal suture

equals that of bone), completely disconnected and

connected by a zygomatico-temporal suture. The bone

elastic modulus is kept constant in all three models

(

E

= 9.1 GPa). If the arch is separated, the strains are

markedly higher in the infraorbital region and on the

anterior portion of the zygomatic arch, whilst a decrease

is observed at these sites when the arch is completely

fused. The Euclidean distance shows that modelling the

zygomatic arch with a suture with

E

= 0.0025 GPa results

in strain values that are most similar to the experimen-

tal ones. If the stiffness of the suture is either increased

(

E

= 1.9 GPa; the mean obtained by our nanoindentation

study) or decreased (

E

= 0.0012 GPa; Radhakrishnan &

Mao, 2004) the differences in strain magnitude between

the model and the experiments become larger (Fig. 5B).

It is worth noting that the difference in Euclidean

distance between complete arch fusion (

E

= 9.1 GPa,

Fig. 5A),

E

= 1.9 GPa and

E

= 0.8 GPa (minimum value

from nanoindentation) is negligible.

Variation of load application to the zygomatic arch

Figure 6 shows the strain magnitudes in the six loca-

tions of MAC-17 when the zygomatic arch is loaded

either through the superficial masseter muscle or by

directly loading 10, 20 or 41 nodes of the zygomatic

arch. The zygomatic arch experiences relatively higher

strains when loaded through the superficial masseter

muscle as opposed to being loaded directly, although

the variation of strains between both types of loading

is less obvious in the infraorbital region (IOR). Among

the muscle-loaded models it is the loading at the most

superior level of the masseter muscle that is associated

with the relatively lowest strains. If the zygomatic arch

is loaded directly, the strains generally decrease with

an increase in the number of selected nodes (10–41)

although at gauge locations IOR and ZAR1 the model

with 41 nodes exhibits slightly higher strains than do

the other two models. As already shown in Fig. 4(B), the

difference between the modelled and experimental

strains is largest for IOR.

Local vs. global effects of strain distribution

Figure 7 illustrates the effects of the presence or

absence of the zygomatic suture in MAC-14 and Fig. 8

shows the effects of the mode of load application on

the global strain distribution in the skull. In the case of

a fused zygomatic arch, strains of high magnitude

Fig. 7 Distribution of maximum principal strain in specimen MAC-14. (A) Zygomatic arch fused in model (Esuture/Ebone = 7.2 GPa) and (B) zygomatico-temporal suture present (Ebone = 7.2 GPa, Esuture = 0.0025 GPa). Please note that the scale bar is capped at 182 µε in both figures in order to emphasize the overall differences in strain distribution.

Fig. 6 Effect of mode of loading on distribution of maximum principal strains in zygomatic arch of MAC-17 (Ebone is 14 GPa, Poisson’s ratio of 0.3). Direct loading: a load of 20 N is distributed over ten, 20 or 41 nodes. Muscle loading: the load is distributed between all the nodes of a cross-section of the muscle through inferior (Minf), central (Mcent) and superior (Msup) parts of the muscle. In addition, the muscle is loaded via a line of nodes through the depth of the muscle (Mline). All other abbreviations as in Fig. 4.



49

(i.e. > 164

µε

) are only present in the anterior end of

the zygomatic process and at the base of the zygomatic

process of the temporal (Fig. 7A). By contrast, if the

zygomatic arch is modelled with the suture present,

the relatively highest maximum principal strains are

observed in the zygoma covering parts of the infra-

orbital region and extending into the lateral orbital

margin (Fig. 7B). In MAC-17, the variation of the loading

conditions has less of an impact on regions in the face

adjacent to the zygomatic arch (Fig. 8A,B). The relatively

highest strains (> 273

µε

) are limited to the anterior

portion of the zygomatic process when the arch is

loaded directly (Fig. 8A). By contrast, when the arch is

loaded via the superficial masseter, these peak strains

occur both in the zygomatic arch and in the root of the

zygomatic process (Fig. 8B).

Discussion

The main objective of this study is to validate and assess

the sensitivity of FEMs of the macaque cranium to

variations in bone material properties, the presence or

absence of the zygomatico-temporal suture and the

loading regimen applied to the zygomatic arch.

To this end we carried out three studies to assess the

sensitivity of the principal strain distribution to varia-

tions in these parameters. The first examined the effects

of varying the material properties of the bone and was

carried out in conjunction with direct measurement of

the material properties of the experimental specimens.

The second examined the effects of presence or absence

and varying material properties of the zygomatico-

temporal suture. This aimed to test the hypothesis that

strains in the zygomatic arch decrease with gradual

obliteration of the suture. The third investigated the

effects of varying the ways in which loads are applied

to the zygomatic arch. The influence of the distribution

of the applied force on the predicted strain magnitudes

in the model was ascertained. It was hypothesised that a

more focussed, centralised application of loads on the

zygomatic arch would result in a larger bending moment

and hence maximum principal strains. Additionally, we

experimented with applying loads through a simplified

(i.e. isotropic, linear elastic) model of the superficial

masseter in order to see whether this led to strains that

are more congruent with experimental data. Finally,

we plotted strain maps in order to evaluate local vs.

global effects of the above experiments. The validity of

the different models was evaluated by examining

maximum principal strains in the infraorbital region and

the zygomatic arch and comparing values measured by

experimental strain gauge analysis with those obtained

through FEA simulation.

Variation of bone elastic properties

The results of Fig. 4 indicate that variations in

E

have

marked effects on the observed magnitudes of the

maximum principal strain as measured at each strain

gauge site. Unfortunately, our experiments suffered

from a strain gauge malfunction (ZAL3, MAC-14). This

gave extraordinarily high strain readings, which we

were able to demonstrate were erroneous in sub-

sequent experiments with a replacement gauge that gave

much better agreement with the modelling results.

However, because of uncertainties about alterations to

bone material properties due to dehydration in the

intervening period we have omitted the data obtained

for this site.

The Euclidean distances between successive experi-

ments indicate that using values of

E

close to experi-

mentally determined values results in a high degree of

congruence between experiment and model. The result

in MAC-14 was optimal when using the experimentally

obtained value (

E

= 9.1 GPa) while that in MAC-17 was

very close (using the experimentally determined value

of 11 GPa), but an iteratively determined value of

E

=

14 GPa provided an even closer match. In MAC-17 very

Fig. 8 Distribution of maximum principal strain in specimen MAC-17. (A) Zygomatic arch loaded directly through 20 nodes (Ebone = 11.3 GPa) and (B) zygomatic arch loaded via superficial masseter (Ebone = 11.3 GPa, Emasseter = 1 GPa; muscle not shown here). Please note that the scale bar is capped at 303 µε in both figures in order to emphasize the overall difference in the strain distribution.



50

close agreement between experimental and modelled

strains is obtained at this value for E at all locations

except IOR (c. 75 µε discrepancy; see Fig. 4B). In this

specimen this gauge was placed on the maxilla with the

zygomatico-maxillary suture between it and the load

while in MAC-14 the equivalent gauge was on the

zygomatic. Thus, in MAC-17 it is highly likely that the

omission of this suture from the model underlies this

result (see below).

Irrespective of the bone Young’s modulus used, maxi-

mum principal strains peak in the anterior portion of

the zygomatic arch and then fall off sharply towards

the posterior end (MAC-14; Fig. 4A). These findings

confirm results of in vivo experiments of adult macaques

by Hylander & Johnson (1997), who also described a

steep strain gradient in the zygomatic arch. The situa-

tion is somewhat different in both the experimental

and the modelling results of MAC-17 where such a

strain gradient is less pronounced (Fig. 4B). This can

probably be attributed to the fact that the zygomatico-

temporal suture was more fused in this specimen and

hence not clearly defined in our FEM (see also below).

The mean E values of the zygomatic arch obtained by

the nanoindentation study do not compare well with

those used in previous FE studies of the macaque cra-

nium. Strait et al. (2005, their table 2) used an E value

of 12.5 GPa for the posterior zygomatic arch (based on

unpublished data for Macaca mulatta by Wang &

Dechow), whilst E = 20.8 GPa was used for the anterior

zygomatic arch. This lack of correspondence between

our measurements of E (see Table 1) and those of other

workers is little surprising given the uncertain preser-

vation history of our material. Several studies have sug-

gested that formalin fixation changes, to some extent,

the material properties of bone (Reilly & Burstein,

1974; Zioupos et al. 2000). In particular, it was shown

that fixation results in a decrease in bone stiffness of

pigs after 2 weeks of preservation (Dechow & Huynh,

1994), although Currey et al. (1995) showed that fixing

bone from an 18-month-old bovine in a 10% formalin

mixture for 3 h and subsequent buffering for 3 days

has only a limited effect on the elastic modulus in ten-

sion. While FEA should be accompanied by mechanical

testing of the materials involved, the anisotropic and

heterogeneous behaviour of bone as well as the type

(cortical or cancellous), the provenance (i.e. species and

anatomical region) and the preservation should ideally

be considered as well (Dechow & Hylander, 2000; Zioupos

et al. 2000; Peterson & Dechow, 2003; Schwartz-Dabney

& Dechow, 2003; Marinescu et al. 2005; Strait et al.

2005). For example, Peterson & Dechow (2003) found

that the zygomatic process of the temporal bone has

the highest anisotropy of all sites. We did not take this

into account in this study because of the complexity

and size of the model and yet obtained a remarkably

close match between experimental and modelling

results. It will be of interest in future studies further to

explore the sensitivity of FEMs to variations in the

direction and spatial variation of material properties

over a more substantial anatomical area.

Variations of the zygomatico-temporal suture

As noted in the introduction, the zygomatic arch has

been likened to a beam with fixed ends that is sub-

jected to an off-centre but uniform load, although the

zygomatico-temporal suture is likely to modulate the

ways in which loads are borne (Hylander & Johnson,

1997). Consequently, in our FEMs we introduced the

zygomatico-temporal suture such that the zygomatic arch

possessed a built-in constraint at one end and a flexible

joint at the other. The effects on the maximum principal

strains in MAC-14 of variations in the zygomatico-

temporal suture were therefore examined in order to

investigate the role of this suture in the FEM.

In these experiments the zygomatic arch is either

fully fused, disconnected or connected by a suture (with

E = 0.0025 GPa). Our results (Fig. 5A) indicate that when

the arch is fused the strains are markedly lower in the

infraorbital region (IOL) and on the anterior portion of

the zygomatic arch (ZAL1), whereas strains increase

when the arch is completely disconnected. By contrast,

introducing a suture into the model results in predicted

strains most similar to experimental values.

A second set of experiments examined the effects of

varying the stiffness of the suture (between E = 1.9 GPa

and E = 0.0012 GPa). The results (Fig. 5B) indicate that

a value of 0.0025 GPa, close to that reported in the

literature, gives the best overall fit to the experimentally

determined zygomatic and facial strains. This is not

consistent with the estimate of E = 1.9 GPa from

nanoindentation and serves to illustrate the difficulties

we experienced in sectioning the bone and suture

while maintaining low temperatures to avoid drying

out of the material.

Our study supports the view that sutures are decisive

for the accuracy of skeletal FEMs, at least with respect

to the cranium (Rayfield, 2005; Wang et al. 2006) and



51

that the elastic properties of the suture have profound

effects on estimated strain magnitudes. This is consist-

ent with experimental findings, which show that the

strains in facial bones are limited while the interposed

sutures experience large deformations (Herring et al.

1996; Herring & Teng, 2000). Clearly this issue is most

significant when dealing with subadult material as

sutures tend to fuse gradually with age in larger mam-

mals (Sun et al. 2004). Under parasagittal bending the

infant/juvenile zygomatic arch with a relatively un-

mineralized suture will initially experience a relatively steep

anterior–posterior strain gradient due to large bending

moments at the anterior end (cf. Fig. 5B; E = 0.001 GPa).

With a gradual fusion of the suture the arch will resemble

more of a beam with two built-in ends and consequently

the bending moments and hence strains decrease ante-

riorly (cf. Fig. 5B; E = 1.9 GPa).

The material properties of sutures are highly variable

within a single cranium and between species. Thus, the

cranial sutures of neonate and young rats and pigs have

Young’s moduli ranging between 0.64 and 171.5 MPa

(Margulies & Thibault, 2000; McLaughlin et al. 2000;

Tanaka et al. 2000). This might have implications for

primate FEMs if the FE model uses sutural elastic pro-

perties taken from non-primate material. However, the

estimation of the material properties of sutures is not

straightforward as our attempt has shown. Therefore,

it might be reasonable where experimental data are

available to estimate the Young’s modulus iteratively

from the FE model – as indeed we have done in this

study. This approach is, however, only applicable in

limited situations and would not be possible for fossils.

In any case our findings underline the importance of

sutures and their mechanical properties in building

FEMs of crania.

Variation of load application to the zygomatic arch

A further experiment examined the effects of different

approaches to loading of the zygomatic arch. In the

first approach we applied loads to the arch directly,

varying the distribution of the loads however by select-

ing varying numbers of model nodes for their applica-

tion. In the second approach loads were applied via a

simplified model of the superficial masseter. The results

indicate that direct loadings consistently produce results

that are closer to the experimentally determined values.

Interestingly, loading the arch through a linear array of

ten nodes shows the best agreement with experimental

strains, although differences compared with the models

with a higher number of selected nodes are relatively

small. The findings also corroborate the hypothesis that

a more centralized load application results in relatively

larger maximum principal strains in the zygomatic arch

(Fig. 6).

The effect on the model’s results of loading the zygo-

matic arch through the masseter muscle is very surpris-

ing, particularly as the magnitude of the predicted

strains is significantly higher (Fig. 6) when the muscle is

included. It is not clear why this is the case. Possibly the

muscle is providing an additional torsional load to the

arch and it might also add leverage if the force vectors

are not exactly in line with the long axis of the muscle,

as suggested by an anonymous reviewer. Alternatively,

it may indicate that the superficial masseter transfers

forces to the zygomatic arch via a limited number of

tendinous connections, most like the arrangement of

loads in Fig. 2(A). The failure of the muscle loading simu-

lations to achieve results close to experimental values

likewise indicates the inadequacy of modelling muscle

as an isotropic linear elastic material. In future models,

if muscles are to be used to apply loads it will be necessary

to include more accurate information on the muscle’s

elasticity as well as anisotropies and non-linearities to

account for true muscle architecture.

Local vs. global effects of strain distribution

Finally we examined the full FEM of each macaque

cranium under varying loadings and conditions as in

the preceding experiments. FEA has the advantage of

allowing strain maps of the whole to be estimated and

visualized although, as we have shown here, there are

many variables that can undermine the accuracy of the

FEM. In producing these maps our aim is to evaluate

local vs. global effects of the above experiments.

From Figs 7 and 8 it is clear that the effects we

describe above in relation to the areas local to strain

gauges obtain more generally. Thus, the presence of a

zygomatico-temporal suture affects the strains experi-

enced over a wide area (Fig. 7A vs. Fig. 7B) including

the anterior part of the zygomatic and infraorbital

regions. The effect of direct vs. ‘muscle’ loading of the

zygomatic arch (Fig. 8A vs. Fig. 8B) is more confined to

within the zygomatic region. However, within this

region the effects are substantial.

In detail, the effects of varying these diverse para-

meters are significant in that estimates of absolute



52

values of strain at specific loci are markedly affected.

However, in general all loading regimens show that

the zygomatic arch manifests relatively large strains,

most concentrated anteriorly and falling away in mag-

nitude with distance. Whether this level of generality is

acceptable is entirely dependent on the question at

hand; but our data indicate that reasonable approxi-

mations of how loads are handled in the cranium might

be obtained for regions not amenable to strain gauging

in living species and in fossil material as long as atten-

tion is paid to the modelling of sutures and muscle

attachments. If accuracy is required then the details of

suture morphology, muscle attachment, applied loads

and mechanical properties become of too great signi-

ficance to be ignored.

Acknowledgements

We gratefully acknowledge the financial support of

the Leverhulme Trust (F/00224/I). We also thank Sue

Taft, Neil Curtis, Lee Page, Andrea Cardini, Sam Cobb,

Callum Ross, Fred Spoor, Chris Dean and staff at Hull

Royal Infirmary for their advice and assistance. We are

also grateful to Daniel Lieberman and three anony-

mous reviewers for their helpful comments during the

preparation of the manuscript.

References

Buckland-Wright JC (1978) Bone structure and the patterns offorce transmission in the cat skull (Felis catus). J Morph 155,35–62.

Chen XB, Chen H (1998) The influence of alveolar structures onthe torsional strain field in a gorilla corporeal cross-section.J Hum Evol 35, 611–633.

Currey JD, Brear K, Zioupos P, Reilly GC (1995) Effect offormaldehyde fixation on some mechanical properties ofbovine bone. Biomaterials 16, 1267–1271.

Cuy JL, Mann AB, Livi KJ, Teaford MF, Weihs TP (2002) Nano-indentation mapping of the mechanical properties of humanmolar tooth enamel. Arch Oral Biol 47, 281–291.

Daegling DJ, Hylander WL (1997) Occlusal forces and mandibularbone strain: is the primate jaw ‘overdesigned’? J Hum Evol33, 705–717.

Daegling DJ, Hylander WL (2000) Experimental observation,theoretical models, and biomechanical inference in the studyof mandibular form. Am J Phys Anthropol 112, 541–551.

Dechow PC, Carlson DS (1990) Occlusal force and craniofacialbiomechanics during growth in rhesus monkeys. Am J PhysAnthropol 83, 219–237.

Dechow PC, Huynh T (1994) Elastic properties and biomechanicsof the baboon mandible [abstract]. Am J Phys AnthropolSuppl 22, 94–95.

Dechow PC, Hylander WL (2000) Elastic properties and masti-catory bone stress in the macaque mandible. Am J PhysAnthropol 112, 553–574.

Fagan MJ, Julian S, Siddall DJ, Mohsen A (2002) Patient-specificspine models – Part 1: finite element analysis of the lumbarintervertebral disc – a material sensitivity study. Proc IME HJ Eng Med 216, 299–314.

Herring SW (1972) Sutures – a tool in functional cranial analysis.Acta Anat 83, 222–247.

Herring SW, Teng SY (2000) Strain in the braincase and itssutures during function. Am J Phys Anthropol 112, 575–593.

Herring SW, Teng SY, Huang XF, Mucci RJ, Freeman J (1996)Patterns of bone strain in the zygomatic arch. Anat Rec 246,446–457.

Hylander WL, Johnson KR (1997) In vivo bone strain patternsin the zygomatic arch of macaques and the significance ofthese patterns for functional interpretations of craniofacialform. Am J Phys Anthropol 102, 203–232.

Jaslow CR (1990) Mechanical properties of cranial sutures. JBiomech 23, 313–321.

Kinney JH, Marshall SJ, Marshall GW (2003) The mechanicalproperties of human dentin: a critical review and re-evaluationof the dental literature. Crit Rev Oral Biol M 14, 13–29.

Macho GA, Spears IR (1999) Effects of loading on the bio-mechanical behavior of molars of Homo, Pan, and Pongo.Am J Phys Anthropol 109, 211–227.

Macho GA, Shimizu D, Jiang Y, Spears LR (2005) Austra-lopithecus anamensis: a finite element approach to studyingthe functional adaptations of extinct hominins. Anat RecPart A 283A, 310–318.

Mao JJ (2002) Mechanobiology of craniofacial sutures. J DentRes 81, 810–816.

Mao JJ, Wang X, Kopher RA (2003) Biomechanics of craniofacialsutures: orthopedic implications. Angle Orthod 73, 128–135.

Margulies SS, Thibault KH (2000) Infant skull and suture pro-perties: measurements and implications for mechanismsof pediatric brain injury. J Biomech Eng-T Asme 122, 364–371.

Marinescu R, Daegling DJ, Rapoff AJ (2005) Finite-elementmodeling of the anthropoid mandible: the effects of alteredboundary conditions. Anat Rec Part A 283A, 300–309.

McConnell CJ, Crompton RH (2001) Finite element stressanalysis of food–tooth interactions in primates. In ComputerMethods in Biomechanics and Biomedical Engineering 3(eds Middleton J, Jones ML, Shrive NG, Pande GN), pp. 673–678. Amsterdam: Gordon and Breach.

McLaughlin E, Zhang Y, Pashley D, Borke J, Yu J (2000) Theload-displacement characteristics of neonatal rat cranialsutures. Cleft Palate-Cran J 37, 590–595.

Moss ML (1973) A functional cranial analysis of primatecraniofacial growth. In Symposium IVth International Con-gress on Primatology: Craniofacial Biology of the Primates 3(ed. Zingeser MR), pp. 191–208. Basel: Karger.

Oyen OJ, Walker AC, Rice RW (1979) Craniofacial growth inolive baboons (Papio cynocephalus): browridge formation.Growth 43, 174–187.

Peterson J, Dechow PC (2003) Material properties of thehuman cranial vault and zygoma. Anat Rec 274A, 785–797.

Preuschoft H, Witzel U (2004) Functional structure of the skullin hominoidea. Folia Primatol 75, 219–252.



53

Radhakrishnan P, Mao JJ (2004) Nanomechanical properties offacial sutures and sutural mineralization front. J Dent Res83, 470–475.

Rafferty KL, Herring SW, Artese F (2000) Three-dimensionalloading and growth of the zygomatic arch. J Exp Biol 203,2093–2104.

Rafferty KL, Herring SW, Marshall CD (2003) Biomechanics ofthe rostrum and the role of facial sutures. J Morph 257, 33–44.

Rayfield EJ (2005) Using finite-element analysis to investigatesuture morphology: a case study using large carnivorousdinosaurs. Anat Rec Part A 283A, 349–365.

Reilly DT, Burstein AH (1974) The mechanical properties ofcortical bone. J Bone Joint Surg 56A, 1001–1022.

Richmond BG, Wright BW, Grosse L, et al. (2005) Finite elementanalysis in functional morphology. Anat Rec Part A 283A,259–274.

Ross CF, Patel BA, Slice DE, et al. (2005) Modeling masticatorymuscle force in finite element analysis: Sensitivity analysis usingprincipal coordinates analysis. Anat Rec Part A 283A, 288–299.

Schwartz-Dabney CL, Dechow PC (2003) Variations in corticalmaterial properties throughout the human dentate mandi-ble. Am J Phys Anthropol 120, 252–277.

Sellers WI, Crompton RH (2004) Using sensitivity analysis tovalidate the predictions of a biomechanical model of biteforces. Ann Anat 186, 89–95.

Smith K, Beighton D (1986) The effects of the availability ofdiet on the levels of exoglycosidases in the supragingivalplaque of macaque monkeys. J Dent Res 65, 1349–1352.

Smith K, Beighton D (1987) Proteolytic activities in the suprag-ingival plaque of monkeys (Macaca fascicularis). Arch OralBiol 32, 473–476.

Spears IR, Crompton RH (1996) The mechanical significance ofthe occlusal geometry of great ape molars in food break-down. J Hum Evol 31, 517–535.

Spears IR, Macho GA (1998) Biomechanical behaviour ofmodern human molars: implications for interpreting thefossil record. Am J Phys Anthropol 106, 467–482.

Strait DS, Wang Q, Dechow PC, et al. (2005) Modeling elasticproperties in finite element analysis: how much precision isneeded to produce an accurate model? Anat Rec Part A283A, 275–287.

Sun ZY, Lee E, Herring SW (2004) Cranial sutures and bones:growth and fusion in relation to masticatory strain. AnatRec Part A 276A, 150–161.

Tanaka E, Miyawaki Y, del Pozo R, Tanne K (2000) Changes inthe biomechanical properties of the rat interparietal sutureincident to continuous tensile force application. Arch OralBiol 45, 1059–1064.

Wang Q, Dechow PC, Richmond B, et al. (2006) Fusion ofcraniofacial sutures in monkey skulls with special referenceto the Finite Element Analysis. Am J Phys Anthrop Suppl129, 184–185.

Wang WJ, Crompton RH, Carey TS, et al. (2004) Comparisonof inverse-dynamics musculo-skeletal models of AL 288-1Australopithecus afarensis and KNM-WT 15000 Homoergaster to modern humans, with implications for theevolution of bipedalism. J Hum Evol 47, 453–478.

Witzel U, Preuschoft H (2002) Function-dependent shapecharacteristics of the human skull. Anthropol Anz 60,113–135.

Witzel U, Preuschoft H, Sick H (2004) The role of the zygomaticarch in the statics of the skull and its adaptive shape. FoliaPrimatol 75, 202–218.

Zioupos P, Smith CW, An YH (2000) Factors affecting mechan-ical properties of bone. In Mechanical Testing of Bone andthe Bone–Implant Interface (eds An YH, Draughn RA),pp. 65–85. New York: CRC Press.

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