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:
[email protected] 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.
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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
