We designed loads and restraints in our FE simulations to model a range of feeding behaviours. Our objective was to address levels of convergence in biomechanical performance, respective limitations on potential feeding behaviour and the potential for niche overlap in T. cynocephalus and C. l. dingo.
The dingo's skull was smaller than that of the thylacine (basal condylar length of 166
mm as opposed to 219
mm) and we estimate that body mass in the placental was approximately 60% that of the marsupial (see below). We did not rescale models to approximate equivalent dimensions in both. All our analyses were linear static, and increasing or decreasing model sizes will not affect stress distributions or magnitudes of stress for individual ‘brick’ elements, i.e. mechanical behaviour of these models will remain constant regardless of scale. In reality, there would be some allometric variation with size. For example, Wroe et al. (2005)
found negative allometry regarding the estimated bite force and body mass among mammalian carnivores and allometry has also been demonstrated with respect to endocranial volume (Jerison 1973
; Wroe & Milne 2007
). In the absence of CT data from specimens of similar size, we do not control for allometry in this study. Given the gross geometric disparity between the marsupial and placental, we consider it probable that allometry will play a relatively minor role in explaining any differences in mechanical behaviour between these two specimens. It is also important to note that a lack of validated data for material properties dictates that our models cannot yet be used to deduce absolute performance limits and results of FE analyses were interpreted following a comparative approach (Dumont et al. 2005
; McHenry et al. 2006
We assessed mechanical behaviour on the basis of visual output of the post-processing software () and mean brick element stress for selected regions (). Mean stress was used rather than maximal stress following Dumont et al. (2005)
. Although maximal stress is potentially informative, the interpretation of maximal stress values is currently problematic in FE analyses of complex biological structures. This is because such FE models are likely to contain a number of irregular elements that register artefactually high values (Snively & Russell 2002
Figure 2 Stress (Von Mises) distributions in lateral views of FE models of (a)–(d) C. l. dingo and (e–h) T. cynocephalus under four load cases: (a,e) bilateral bite at canines, (b,f) bilateral bite at carnassials, (c, g) dorsoventral head depression (more ...)
Figure 3 Stress (Von Mises) distributions in left and right lateral views of FE models of (a–d) C. l. dingo and (e–h)T. cynocephalus under two load cases: (a,e) unilateral bite at canines (left), (b,f) unilateral bite at canines (right), (c,g) (more ...)
Stress (Von Mises) distributions in lateral views of FE models of (a–c) C. l. dingo and (e–g) T. cynocephalus under two load cases: (a,d) lateral shake (left), (b,e) lateral shake (right) and (c,f) axial twist. MPa, mega pascals.
Mean brick element stresses (von Mises) for selected regions in solved FE models of C. l. dingo and T. cynocephalus under four load cases. (cran, cranium; rost, rostrum; ant o, anterior orbit; zygo, zygomatic arch; mand, mandible.)
Our heterogeneous models (eight material properties) were constructed using data from computer tomography (CT) for two skulls held in the Australian Museum: T. cynocephalus
(AM 1821) and C. l. dingo
(AM 38587). Scans comprised 293 and 228 transaxial slices, respectively. Slices were separated by 0.8
mm intervals. For surface meshes, maximum and minimum triangle edge lengths were kept at a 1
3 ratio (0.1 geometric error). Minimizing differences between dimensions of triangles within models reduces the probable incidence of artefacts. Solid meshing was performed with the Strand7
(v. 2.3) FE program.
Material properties were assigned on the basis of density values (Rho et al. 1995
; Schneider et al. 1996
). These ranged from Young's modulus of elasticity, E
GPa, Poisson's ratio, ν
=0.4 and density, ρ
=0.4 and ρ
. DICOM files include X-ray attenuation data as Hounsfield Units (HU). For each scan, the total range of HUs was divided to give the eight material property types. We used the mean HU value for each type to calculate its average density. The relationship between HU and density is nonlinear, and equations derived from data presented by Rho et al
. (1995) and Schneider et al. (1996)
were applied to convert HU values into average density values. Values for density were converted to Young's modulus (E
) using data from Rho et al
Very high resolution was required with respect to brick element number in order to produce simulations that realistically accommodated differences between bone densities. Models comprised 1
216 (T. cynocephalus
) and 887
281 (C. l. dingo
) three-dimensional four-noded tetrahedral brick elements.
Theoretically, models based on four-noded elements (tet4) produce less accurate results than those built from higher-order elements, however, with increasing brick element number models converge on identical results. Dumont et al. (2005)
found differences of approximately 10% between tet4 and 10-noded (tet10) based models of less than 252
000 brick elements. Since our models contain at least 3.5 times as many brick elements, our results should be well within 10% of those that might be drawn from tet10 models of the same resolution.
We modelled the temporomandibular joint using a hinged beam connected to both upper and lower jaws by rigid links. The two pivot beams were released to allow rotation.
Eight loading cases were applied, four ‘intrinsic’ (bite transmitted) and four ‘extrinsic’ (neck transmitted). The four intrinsic cases simulated bites driven solely by skull musculature with maximal bite force assumed in each instance. These were: (i) a bilateral bite at the canines, (ii) a unilateral bite at the left canine, (iii) a bilateral bite at the carnassial notch, and (iv) a unilateral bite at the left carnassial notch. Rigid links connecting the four canine teeth were arranged in an H-shaped configuration with forces or moment applied to a central node in the two cross links. Loads comprised: (i) a lateral ‘shake’, (ii) an axial twist wherein moment was applied around the long axis of the skull, (iii) a dorsoventral force, and (iv) a pull back/simulating prey pulling away from the predator.
To prevent free body motion, FE models must be sufficiently restrained. Inappropriate point constraints (restricted to single nodes) can produce pronounced artefacts and inaccurate results (McHenry et al. 2006
). Here we have applied more realistic constraints using frameworks of rigid links at the occipital condyle as well as at tooth bite points to more broadly distribute forces.
Mean brick element stresses were compared in six regions of interest for loading cases that produced symmetrical stress distributions, the whole skull, the cranium (i.e. here treated as that part of the skull inclusive of the facial skeleton excluding the mandible), the rostrum (from the antorbital fenestra to the anteriormost tip of the cranium), anterior orbit (from anterior margin of the orbit to antorbital fenestra), zygomatic arch and mandible (). For simulations that produced asymmetrical loadings, these regions were further divided into left and right volumes.
All data were calculated in terms of von Mises stress. Von Mises is a uniaxial tensile stress which is a good predictor of failure in relatively ductile materials such as bone and proportional to the strain energy of distortion (Dumont et al. 2005
). For statistical analyses, element number was too great to be accommodated by standard software packages and comparison of these large datasets was facilitated using a program written in RGui
(by K. Moreno).
We calculated unilateral maximal contractile muscle forces using estimates for cross-sectional area (see Thomason (1991)
and Wroe et al. (2005)
for details). Muscle forces were 1320.1
N for T. cynocephalus
N for the smaller Canis l. dingo
. The three-dimensional architectures of the muscles were approximated using pre-tensioned trusses, beam elements that carry axial loads only (see Wroe et al. in press
The number of truss elements and their diameters with respect to each major muscle subdivision were determined assuming that their force contributions were relative to muscle mass. Relative masses of muscle subdivisions for our dingo and thylacine models were taken from published data for C. l. dingo
) and Didelphis virginiana
). While overall forces for each muscle subdivision were computed on the basis of muscle mass, the number of trusses was calculated on the basis of muscle origin and insertion areas in order to spread forces appropriately. Pretension values for each truss were then calculated by dividing total force for the muscle subdivision by the number of trusses for that division.
In the T. cynocephalus
model, the number of beams and their pretension values as applied to each muscle subdivision were: 42×22.7
N (temporalis profunda); 24×22.8
N (temporalis superficialis); 12×21.5
N (masseter profunda); 18×22.1
N (masseter superficialis); 10×24.7
N (zygomaticomandibularis); and 8×21.5
N (pterygoideus internus).
In our model of C. l. dingo
, the number of beams and pretension values were: 38×16
N (temporalis profunda); 18×14.8
N (temporalis superficialis); 8×16
N (masseter profunda); 12×16.5
N (masseter superficialis); 8×15.9
N (masseter profunda); 8×14.2
N (zygomaticomandibularis); and 8×14.2
N (pterygoideus internus). The effect of the pterygoideus externus is negligible with respect to the power stroke, but additional unloaded beams were inserted in both models to simulate its potential stabilizing influence.
Four extrinsic loading cases simulated the influence of unrestrained prey (or cervically generated forces by the predator itself). These were calculated as directly proportional to body mass for both models. On the basis of predictive equations for craniodental dimensions in dasyuromorphian marsupials (Myers 2001
) and canids (Van Valkenburgh 1990
), estimated body masses were 23.5 and 13.8
kg for the T. cynocephalus
and C. l. lupus
, respectively. Forces for most extrinsic loadings were 500
N (T. cynocephalus
) and 295
N (dingo). The exception here was for the axial loading case, which was applied as a moment (5000 and 295
As demonstrated by Preuschoft & Witzel (2004)
, extrinsic forces developed in the handling of even relatively small prey by a domestic dog are within the same order of magnitude as intrinsic bite forces. Thus, in shaking a 2
kg rabbit, accelerating the rostrum and overcoming mass moment of inertia will require an extrinsic muscle force of approximately 284
N and allowing for head and prey weight will bring total condylar force to 485
N. The extrinsic forces used in the present study are somewhat arbitrary, but are not unreasonable estimates for what might be expected in the dispatch and processing of relatively small prey in light of the findings of Preuschoft & Witzel (2004)