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High-Resolution Three-Dimensional Computer Simulation of Hominid Cranial Mechanics.

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THE ANATOMICAL RECORD 290:1248–1255 (2007)
High-Resolution Three-Dimensional
Computer Simulation of Hominid
Cranial Mechanics
STEPHEN WROE,1* KAREN MORENO,1 PHILIP CLAUSEN,2 COLIN MCHENRY,1–3
4
AND DARREN CURNOE
1
School of Biological Earth and Environmental Sciences, University of New South Wales,
NSW, Australia
2
School of Engineering, University of Newcastle, NSW, Australia
3
School of Environmental and Life Sciences, University of Newcastle, NSW, Australia
4
School of Medical Sciences, University of New South Wales, NSW, Australia
ABSTRACT
In vivo data demonstrates that strain is not distributed uniformly on
the surface of the primate skull during feeding. However, in vivo studies
are unable to identify or track changes in stress and strain throughout
the whole structure. Finite element (FE) analysis, a powerful engineering
tool long used to predict the performance of man-made devices, has the
capacity to track stress/strain in three dimensions (3-D) and, despite the
time-consuming nature of model generation, FE has become an increasingly popular analytical device among biomechanists. Here, we apply the
finite element method using sophisticated computer models to examine
whether 3-D stress and strain distributions are nonuniform throughout
the primate skull, as has been strongly suggested by 2-D in vivo strain
analyses. Our simulations document steep internal stress/strain gradients, using models comprising up to three million tetrahedral finite elements and 3-D reconstructions of jaw adducting musculature with both
cranium and mandible in correct anatomical position. Results are in
broad concurrence with the suggestion that few regions of the hominid
cranium are clearly optimized for routine feeding and also show that
external stress/strain does not necessarily reflect internal distributions.
Findings further suggest that the complex heterogeneity of bone in the
skull may act to dissipate stress, but that consequently higher strain
must be offset by additional strain energy. We hypothesize that, despite
energetic costs, this system may lend adaptive advantage through
enhancing the organism’s ability to modify its behavior before reaching
catastrophic failure in bony or dental structures. Anat Rec, 290:1248–
1255, 2007. Ó 2007 Wiley-Liss, Inc.
Key words: finite element analysis; cranial morphology; Hominidae; computer-modeling
In vivo studies of the primate skull have demonstrated
strong strain gradients in the surface of the primate cranium during feeding, leading to the conclusion that the
skull may not be strongly optimized for mastication
(Hylander et al., 1991; Hylander, 1997). However, in
vivo analyses cannot directly address the question of
whether, or to what degree, similarly nonuniform distriÓ 2007 WILEY-LISS, INC.
*Correspondence to: Stephen Wroe, School of Biological Earth
and Environmental Sciences, University of New South Wales,
NSW, Australia, 2052. E-mail: s.wroe@unsw.edu.au
Received 6 April 2007; Accepted 26 June 2007
DOI 10.1002/ar.20594
Published online in Wiley InterScience (www.interscience.wiley.
com).
SIMULATION OF HOMINID CRANIAL MECHANICS
butions of stress/strain may occur within the structure,
and the number of gauges that can be applied within a
given area can be limiting, even with respect to the documentation of external strain (Dumont et al., 2005; Rayfield, 2007). As an alternative, beam theory, although applicable to materially homogeneous structures, such as
the midshaft cortex of long bones, cannot accurately predict mechanical behavior in more complex heterogeneous
structures that incorporate both cortical and cancellous
bone (Thomason, 1995), as is found in the crania and
mandibles of primates and many other vertebrates.
Finite element (FE) analysis is routinely used to predict the mechanical behavior of man-made structures. In
the life sciences, the ability of FE to facilitate nondestructive analyses of mechanical behavior under controlled and easily replicated conditions lends it promise
as a valuable source of data to researchers in fields
ranging from the prediction of feeding ecology in living
and fossil species, to the optimization of prosthetic
devises. FE allows the investigator to map stress/strain
distributions throughout three-dimensional structures
(Thomason, 1995). However, despite very notable advances (Rayfield et al., 2001; Rayfield, 2004, 2007; Dumont
et al., 2005; Strait et al., 2005; Tizzard et al., 2005;
McHenry et al., 2006), the considerable potential of FE
analysis in biology has been constrained by the timeconsuming nature of model generation (Rayfield, 2007).
Achieving sufficient resolution to incorporate the variable material properties of bone (Dumont et al., 2005;
Rayfield, 2007) has also been problematic, yet investigations involving FE modeling of the cranium of Macaca
fascicularis have shown that allowance for differences in
bone properties might strongly impact on the accuracy
of results (Strait et al., 2005). However, in this instance
properties were assigned manually, and sudden shifts
between regional boundaries may not have been realistic
(Strait et al., 2005). Three-dimensional reconstruction of
muscle remains another challenge, with crania and
mandibles typically treated separately and forces reduced
to single vectors, producing high point loads that can confound interpretation of results (Dumont et al., 2005).
Our aim in the present study has been to investigate
internal stress/strain gradients in the primate skull and
compare differences between simulations that assume a
single uniform material property (homogeneous), and
models that incorporate multiple material properties for
cortical and cancellous bone (heterogeneous). An additional objective has been to develop protocols that
improve model realism while reducing assembly time.
Models presented here comprise two to three million 3-D
‘‘brick’’ finite elements, produced using a relatively rapid
and largely automated method that allows the assignment of variable material properties for cortical and cancellous bone, as well as tooth enamel. Further advances
over previous models include treatment of the skull and
mandible as a single articulated mechanism, and more
accurate simulation of the 3-D architecture of jaw
Fig. 1. The 3,877,678 heterogeneous brick element model of Pan
troglodytes. A,B: Comparison of a computer assisted tomography
slice (A) with a slice through same region of finite element model (B).
C: Model before addition of musculature. D: Areas for muscle origins
and insertions for major jaw adductors and placement of trusses used
to simulate muscle actions.
1249
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WROE ET AL.
Fig. 2. A–H: Stress (Von Mises) distributions in frontal views top
row (A–D) and cross-sectional views bottom row (E–H) in four simulations of maximal static bites in Pan troglodytes: bilateral bite at the
second molars in homogeneous model (A,E), bilateral bite at the sec-
ond molars in heterogeneous model (B,F), bilateral bite at the second
incisors in heterogeneous model (C,G), and unilateral bite at the second molars in heterogeneous model (D,H). MPa, mega pascals.
adducting musculature, spreading loads across muscle
origin/insertion points and minimizing the confounding
influence of point loads. These simulations are based on
computer assisted tomography (CT) from a common
chimpanzee, Pan troglodytes, (Fig. 1A,B), long recognized as our closest living relative together with Pan
paniscus, the bonobo (Begun, 1992).
angle edge lengths were kept at a 1:3 ratio (0.1 geometric error) to minimize differences between triangle
dimensions, which can lead to major discrepancies in
brick element size in the final solid and thereby introduce artifacts. Solid meshing was performed with
Strand7 Finite Element software (Vers. 2.3). Models
were assembled using 3-D low-order four-noded tetrahedral ‘‘brick’’ elements (tet4). Tet4 based models can produce less accurate results than those built from higher
order elements; however, differences diminish with
increasing brick element number. Differences of around
10% have been recorded in comparisons between tet4
and higher order ten-noded (tet10) models of <252,000
brick elements (Dumont et al., 2005). It is likely that
our use of tet4 elements is to some degree mitigated by
the use of high brick element numbers and associated
increases in geometric accuracy.
MATERIALS AND METHODS
Both homogeneous (single material property) and heterogeneous models (seven material properties) were constructed using CT data for a common chimpanzee cranium and mandible comprising 478 transaxial slices
separated by 0.5-mm intervals from the University of
Austin Digital Morphology Web site (digimorph.org). In
the original surface mesh, maximum and minimum tri-
SIMULATION OF HOMINID CRANIAL MECHANICS
1251
Fig. 3. A–H: Strain (Von Mises) distributions in frontal views top
row (A–D) and cross-sectional views bottom row (E–H) in four simulations of maximal static bites in Pan troglodytes: bilateral bite at the
second molars in homogeneous model (A,E), bilateral bite at the sec-
ond molars in heterogeneous model (B,F), bilateral bite at the second
incisors in heterogeneous model (C,G), and unilateral bite at the second molars in heterogeneous model (D,H).
For the simulation of bilateral loads (i.e., boundary
conditions and, hence, the distribution of stress and
strain identical on both sides of the skull), we used half
skull and mandible models that comprised 1,938,839
brick elements. All nodes at the midline were fixed relative to the transverse axis. In unilateral biting, boundary conditions differ between the two sides of the skull
and distributions of stress and strain are asymmetrical.
Consequently, we used a full skull model to simulate
unilateral biting through mirroring the heterogeneous
half skull and lower jaw. Total 3-D brick number in this
instance (3,877,678) exceeded the current computational
limits of the software. The mandible was removed giving
a brick element total of 3,023,365 with the trusses simulating jaw musculature (see below) retained and fixed in
the position of insertion, thereby allowing bite simulation for the cranium. We modeled the temporomandibular joint using a hinged beam linked to both upper and
lower jaws.
Simulations of bilateral bites at the upper and lower
second molars and second incisors, and unilateral bites
at the second molars were performed (Figs. 2, 3). For
bilateral bites, two half models inclusive of both upper
and lower jaws were used and a half model was mirrored to simulate a unilateral bite. The first of the half
models was homogeneous, wherein it was assumed that
the entire skull comprised cortical bone only. Remaining
simulations were heterogeneous, with seven material
properties applied (Fig. 1A). Mean brick element stress
and strain were compared in five regions of interest; the
brow-ridge, postorbital bar, zygomatic arch, cranium,
and mandible (Table 1).
For the homogeneous model, all brick elements were
assigned a single set of material properties for cortical
bone (Young’s modulus of Elasticity [Y] 5 27.0 GPa;
Poisson’s ratio 5 0.4; density 5 2,190 Kg/m3). For heterogeneous models, six additional material properties were
assigned on the basis of density values (Rho et al., 1995;
1252
WROE ET AL.
TABLE 1. Mean von Mises brick element stresses and strains for regions of interest
in four static bite simulations in the skull of Pan troglodytesa
Cranial brick stress (VM)
Mandibular brick stress (VM)
Brow-ridge brick stress (VM)
Brow-ridge brick stress R (VM)
Brow-ridge brick stress L (VM)
Postorbital bar brick stress (VM)
Postorbital bar brick stress R (VM)
Postorbital bar brick stress L (VM)
Zygomatic arch brick stress (VM)
Zygomatic arch brick stress R (VM)
Zygomatic arch brick stress L (VM)
Cranial brick strain (VM)
Mandibular brick strain (VM)
Brow-ridge brick strain (VM)
Brow-ridge brick strain R (VM)
Brow-ridge brick strain L (VM)
Postorbital bar brick strain (VM)
Postorbital bar brick strain R (VM)
Postorbital bar brick strain L (VM)
Zygomatic arch brick strain (VM)
Zygomatic arch brick strain R (VM)
Zygomatic arch brick strain L (VM)
Ho Bilat M2
He Bilat M2
He Bilat I2
He Unilat M2
3.969E201
1.489E100
2.614E201
N/A
N/A
6.336E201
N/A
N/A
7.999E100
N/A
N/A
2.052E205
7.699E205
1.351E205
N/A
N/A
3.273E205
N/A
N/A
4.135E204
N/A
N/A
3.738E201
1.155E100
2.169E201
N/A
N/A
6.180E201
N/A
N/A
5.342E100
N/A
N/A
9.899E205
1.824E204
2.587E205
N/A
N/A
6.587E205
N/A
N/A
8.297E204
N/A
N/A
7.070E201
1.545E100
6.679E201
N/A
N/A
8.082E201
N/A
N/A
5.594E100
N/A
N/A
1.319E204
2.169E204
1.218E204
N/A
N/A
8.432E205
N/A
N/A
8.684E204
N/A
N/A
5.062E201
N/A
2.238E201
1.901E201
2.575E201
7.681E201
6.841E201
8.511E201
5.890E100
5.885E100
5.894E100
1.212E204
N/A
2.706E205
2.324E205
3.088E205
5.291E205
5.080E205
5.502E205
6.111E204
6.108E204
6.114E204
a
Ho, homogeneous model; He, heterogeneous model; Bilat, bilateral bite; Unilat, unilateral bite; M2, second molars; I2, second incisors; N, Newtons; VM, Von Mises; R, right; L, left; N/A, not applicable.
Schnider et al., 1996; Fig.. 1A,B). These ranged from
property 1 (lowest density), with values intermediate
between free spaces and low-density tissue (Y 5 1.5 GPa;
Poisson’s ratio 5 0.4; density 5 250 Kg/m3), to property
7, simulating enamel (Y 5 38.6 GPa; Poisson’s ratio 5
0.4; density 5 2,860 Kg/m3).
Calculations of muscle forces were based on a dry
skull method using estimates for cross-sectional area
(Thomason, 1991; Wroe et al., 2005; Christiansen and
Wroe, 2007) adjusted for application to hominids (O’Conner
et al., 2005). In each simulation, the 3-D architecture and
actions of the musculature were approximated using
pretensioned trusses, beam finite elements that carry
axial loads only (Fig. 1C). The number and diameters of
the truss elements assigned to each muscle group were
determined on the basis of muscle origin and insertion
areas (Fig. 1C). Pretension values for each truss were
adjusted accordingly. These were 6.5 N, 18.7 N, and
2.9 N, respectively, for each of 29 temporalis, 10 masseter, and 5 medial pterygoid trusses. Although the effect
of the lateral pterygoid with respect to the power stroke
is negligible, an additional four unloaded trusses were
inserted to simulate its potential stabilizing influence.
Regions of particular interest with respect to feeding
mechanics in the hominid skull include the zygomatic
arches, supraorbital torus (brow-ridge) and orbital bar
(Hylander et al., 1991; Hylander, 1997; O’Conner et al.,
2005). These regions were selected within the models
and analyzed statistically using a program written in
RGui by K. Moreno.
RESULTS
Estimated unilateral muscle forces for the primary
jaw adductors (temporalis, masseteric, and medial pterygoid) were 189, 187, and 15 Newtons (N), respectively.
Total maximal bilateral muscle force was 782 N.
Comparison of the homogeneous and heterogeneous
models biting at the second molars reveals broadly similar distributions of von Mises stress and strain (Figs. 2,
3). In both homogeneous and heterogeneous simulations,
mean brick element stresses and strains within the
brow-ridge (Table 1) are considerably less than means
for the cranium as a whole (67% and 27%, respectively)
and tiny relative to those in the zygomatic arch (<4%).
However, although broad surface distributions are
similar, the distributions of stress and strain through
cross-sections of these two models demonstrate strong
internal gradients, and furthermore, that correspondence between internal and external distributions of
stress and strain are not necessarily tight. For example,
high internal brick element von Mises stresses of up to
5.3 MPa evident in cross-sections of the heterogeneous
model (Fig. 2) at the anteromedial aspect of the face are
much higher than in overlaying external elements (2.7–
3.1 MPa).
Evaluation of the homogeneous and heterogeneous
models further shows that, for each region of interest,
mean and maximum stresses were higher in the homogeneous model (comprising cortical bone only), while
mean and maximum strains were higher in the heterogeneous structure (Figs. 2, 3; Table 1). Distinctions
between the two are best exemplified in comparison of
displacements, which are much higher in the heterogeneous model (see Fig. 4).
Simulation of bilateral incisive biting demonstrates
differences with respect to the distribution of stresses
and strains relative to biting at the second molars. In
the heterogeneous models of these behaviors, cross-sections show that internal stresses are relatively high
anteromedial to the orbit in an incisive bite (Fig. 2).
However, as with bilateral biting at the molars, mean
stresses and strains in the brow-ridge remain well below
those of the cranium as a whole (Table 1). In unilateral
SIMULATION OF HOMINID CRANIAL MECHANICS
1253
Fig. 4. A–L: Von Mises stress (A–D), strain (E–H), and displacement
(I–L) in lateral views in four simulations of maximal static bites in Pan
troglodytes. A,E,I: The bilateral bite at the second molars in a homogeneous model. B,F,J: The bilateral bite at the second molars in a
heterogeneous model. C,G,K: The bilateral bite at the second incisors
in a heterogeneous model. D,H,L: Unilateral bite at the second molars
in heterogeneous model.
molar biting, we found that stress and strain were
slightly higher in the balancing than working side (Figs.
2, 3; Table 1).
2000; Ross and Metzger, 2004). There is further correspondence in that our models reveal an increasing gradient of stress anteriorly for the zygomatic arch (Hylander,
1997).
Our finding that, in unilateral molar biting, stress
and strain were slightly higher in the balancing than
working side, is contrary to empirically derived results.
This is likely because our model assumes that maximal
bite forces are applied on both sides, whereas empirical
data demonstrate that the working-side masseter usually exerts more force than does that of the balancing-
DISCUSSION
Surface strain patterns correspond qualitatively with
external in vivo data taken from other primate species,
which have suggested that, when biting, strain is minimal in the brow-ridge and highest in the zygomatic
arches and lower jaws (Hylander, 1997; Ravosa et al.,
1254
WROE ET AL.
side during the power stroke (Hylander, 1997). Our
interpretation is further supported by in vivo evidence
attesting to a reduction in the discrepancy between the
two sides as increasingly tough foods are chewed
(Hylander, 1997).
Our results demonstrate the potential value of 3-D FE
studies that incorporate the variable material properties
of bone, strongly suggesting that internal stress/strain
distributions are nonuniform and moreover, that the
external distributions of surface stress/strain do not necessarily reflect internal distributions. We conclude that
externally derived data may not accurately reflect distributions throughout the entire skull, and these findings
offer empirical support for the argument of Thomason
(1995), that is, that FE analyses are required to fully
investigate the behavior of structures that incorporate
cancellous bone.
These findings remain in general agreement with the
proposal that much of the facial anatomy of primates
may not be strongly influenced by its role in routine
food processing (Hylander, 1997). Cranially, the most informative regions with respect to feeding mechanics are
the zygomatic arches. Overall, our finding that the mandible appears more clearly optimized for feeding than
the cranium is in agreement with the conclusions of Preuschoft and Witzel (2002) and Ross and Metzger (2004).
However, we note that to date only jaw adducting
(intrinsic) musculature has been considered in either in
vivo or FE studies of stress/strain during feeding in the
primate skull. It has been shown that extrinsic forces
generated by cervical musculature can be relatively high
in predatory mammals in the dispatch of small prey
(Preuschoft and Witzel, 2005; Wroe et al., In Press) and
Pan troglodytes is known to kill and eat other vertebrates (Anderson and Kitchener, 1983; Boesch, 1994).
Our finding that strain and displacement were considerably greater in the heterogeneous as opposed to the
homogeneous models may have important implications.
Mean brick element strain energy stored in the heterogeneous mandible was 7.2 times higher than that stored
in the homogeneous simulation. Historically, it has been
argued that the advantage of incorporating lighter cancellous bone centers on mass reduction and consequent
energy savings to the organism. However, our results
show that additional work is required to achieve the
same ends in the more realistic model accommodating
cancellous as well as cortical bone. This additional
energy must be generated by muscle.
The storage and appropriate release of energy has
been well demonstrated in other biological systems, particularly with respect to tendons in locomotion, where
90% or more of strain energy can be recovered in passive
elastic recoil within the power stroke (Alexander, 1984;
Bullimore and Burn, 2005). Our results suggest that
cancellous bone may also play some role in storage and
release of energy for long bones in locomotion. However,
there is little obvious advantage to such energy storage
in biting because there is no means to recoup such
energy from the bone for another power stroke in closing
the jaws, and opening the jaws is largely accomplished
by gravity (Turnbull, 1970).
Results suggest that cancellous bone may assist in dissipating stress, as has been proposed for sutures (Rayfield, 2007). However, our results indicate that weight
savings gained through the use of lighter cancellous
bone are to some degree offset by the requirement for
additional, energetically expensive musculature. Considered holistically, the primary advantages associated with
heterogeneous construction may not simply be direct
optimization to produce a minimal mass of bone tissue,
rather, there may be a trade-off between the materials
and energy invested in the bony and muscular components of the system.
Structures constructed entirely of compact bone are
stiffer with higher yield points. They are, however, also
more brittle, and less deformation over a shorter time
span will presage ultimate failure (Currey, 2004). Theoretically, the greater elasticity imparted through the
incorporation of cancellous bone translates into a lower
yield point, but also a less brittle structure that permits
greater deformation over a longer period before reaching
ultimate failure. Moreover, tooth breakage is common in
primates (Cuozzo and Yamashita, 2006), and greater
elasticity in surrounding bone may reduce the likelihood
of tooth failure following accidental occlusion with hard
materials.
Mechanoreceptors within the periodontal ligament are
known to inhibit jaw adductors and trigger a jaw opening response as reactions to biting on unexpectedly
resistant, potentially damaging foods (Anderson et al.,
1970; Dessem et al., 1988). We suggest that a system
that experiences higher displacements and strains will
facilitate greater opportunity for feedback through the
nervous system and, hence, a greater capacity for the
organism to modify behavior and avoid catastrophic failure in bones and teeth. This line of reasoning might also
apply to sutures.
Whether a chimpanzee could develop sufficient bite
force to seriously damage parts of its own cranium or
mandible remains untested. That primates can generate
sufficient force to damage their own teeth appears more
certain. More broadly, the mechanism described here
may be of greater importance in dissipating stress and
facilitating modulation of behavior among carnivorous
species. Structural damage is relatively common in predators, where powerful killing bites to soft tissue in prey
can result in unexpected contact with bone (Van Valkenburgh, 1988).
We believe that the approaches and models described
here represent several steps forward in computer simulation of the vertebrate skull. These include (1) a relatively rapid method for the incorporation of variable
properties for bone, which allows for more realistic modeling of structural behavior; (2) the addition of a temporomandibular joint that facilitates more accurate reconstruction of the 3-D architecture of muscle and collation
of data from both cranium and mandible in correct
anatomical relationship to one another, and minimizes
the introduction of artifacts through point loading; (3) a
program to compute mean brick stress and strain in
regions of interest for very large models that permits
statistical comparisons; and (4) overall, our protocols
allow rapid assembly and solution of models on standard
desktop computers. The solid mesh used here was generated in 1 day, and the complete model assembled from
CT data within a week.
There are, however, many areas in which further
improvements can be made. Validation, based on investigations of both specimens in vivo and using materials
testing systems is required to fully assess the material
SIMULATION OF HOMINID CRANIAL MECHANICS
properties of both cortical and cancellous bone. Our joint
reconstructions are rigid and do not account for elastic
properties of connective soft tissue, and, although our
muscle simulations better describe 3-D architecture and
allow for distribution of forces across relevant structures,
they do not fully account for the influence of muscle pennation. Our loadings are further simplifications of actual
chewing behavior in that all muscles are maximally activated in unison. In reality, muscle recruitment can be
variable within and between working and balancing sides
(Ross and Metzger, 2004). Sutures may also influence the
distribution of stress/strain (Rayfield, 2005; Kupczik
et al., 2007). In the few FE analyses that have addressed
this issue, sutures have been introduced manually into
homogeneous models, either as breaks in the mesh, or by
assignment of different material properties to bricks along
sutures (Rayfield, 2004; Kupczik et al., 2007). In the models presented here, the role of sutures is not strictly
addressed. However, some well-defined sutures visible in
the CT data, are partially captured in our FE models as
incompletely defined regions comprising brick elements
assigned high elasticity. Relatively minor additional
increases in brick element number for heterogeneous FE
meshes such as these may facilitate accurate modeling of
the role of suture morphology.
Work is under way to improve modeling in each of
these areas. With the development of methodologies and
procedures allowing relatively rapid generation of more
realistic skull models, it will be possible to simulate and
compare a wide range of hominid material, fossil and
extant, facilitating further detailed mechanically based
investigations into relationships between anatomy and
behavior. These techniques may also have practical
potential in biomedical fields, including prosthetics, orthodontics, and the design of safety equipment.
ACKNOWLEDGMENTS
We thank A. Pendharkar, D. Wroe and T. Rowe (DigiMorph) for access to CT data. This work was funded by
ARC Discovery, ARC QE2 Research Fellowship and
UNSW Strategic Research Initiatives grants to S.W.,
and an Internal Grant (University of Newcastle) to P.C.
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