Biomechanics of the macaque postorbital septum investigated using finite element analysis: implications for anthropoid evolution

Does the model reflect the system? When two-dimensional biomechanics is not 'good enough'

Models are mathematical representations of systems, processes or phenomena. In biomechanics, finite-element modelling (FEM) can be a powerful tool, allowing biologists to test form-function relationships in silico, replacing or extending results of in vivo experimentation. Although modelling simplifications and assumptions are necessary, as a minimum modelling requirement the results of the simplified model must reflect the biomechanics of the modelled system. In cases where the three-dimensional mechanics of a structure are important determinants of its performance, simplified two-dimensional modelling approaches are likely to produce inaccurate results. The vertebrate mandible is one among many three-dimensional anatomical structures routinely modelled using two-dimensional FE analysis. We thus compare the stress regimes of our published three-dimensional model of the chimpanzee mandible with a published two-dimensional model of the chimpanzee mandible and identify several fundamental differences. We then present a series of two-dimensional and three-dimensional FE modelling experiments that demonstrate how three key modelling parameters, (i) dimensionality, (ii) symmetric geometry, and (iii) constraints, affect deformation and strain regimes of the models. Our results confirm that, in the case of the primate mandible (at least), two-dimensional FEM fails to meet this minimum modelling requirement and should not be used to draw functional, ecological or evolutionary conclusions.

Comparative cranial biomechanics in two lizard species: impact of variation in cranial design

Cranial morphology in lepidosaurs is highly disparate and characterised by the frequent loss or reduction of bony elements. In varanids and geckos, the loss of the postorbital bar is associated with changes in skull shape, but the mechanical principles underlying this variation remain poorly understood. Here, we sought to determine how the overall cranial architecture and the presence of the postorbital bar relate to the loading and deformation of the cranial bones during biting in lepidosaurs. Using computer-based simulation techniques, we compared cranial biomechanics in the varanid Varanus niloticus and the teiid Salvator merianae, two large, active foragers. The overall strain magnitude and distribution across the cranium were similar in the two species, despite lower strain gradients in V. niloticus. In S. merianae, the postorbital bar is important for resistance of the cranium to feeding loads. The postorbital ligament, which in varanids partially replaces the postorbital bar, does not affect bone strain. Our results suggest that the reduction of the postorbital bar impaired neither biting performance nor the structural resistance of the cranium to feeding loads in V. niloticus. Differences in bone strain between the two species might reflect demands imposed by feeding and non-feeding functions on cranial shape. Beyond variation in cranial bone strain related to species-specific morphological differences, our results reveal that similar mechanical behaviour is shared by lizards with distinct cranial shapes. Contrary to the situation in mammals, the morphology of the circumorbital region, calvaria and palate appears to be important for withstanding high feeding loads in these lizards.

Summary:In vivo measurements and computer-based simulations of the cranial mechanics of two large lizards indicate that similar mechanical behaviour is shared by lizards with distinct cranial architecture, and show the importance of the postorbital bar in resisting the feeding loads.

Human rather than ape-like orbital morphology allows much greater lateral visual field expansion with eye abduction

While convergent, the human orbit differs from that of non-human apes in that its lateral orbital margin is significantly more rearward. This rearward position does not obstruct the additional visual field gained through eye motion. This additional visual field is therefore considered to be wider in humans than in non-human apes. A mathematical model was designed to quantify this difference. The mathematical model is based on published computed tomography data in the human neuro-ocular plane (NOP) and on additional anatomical data from 100 human skulls and 120 non-human ape skulls (30 gibbons; 30 chimpanzees / bonobos; 30 orangutans; 30 gorillas). It is used to calculate temporal visual field eccentricity values in the NOP first in the primary position of gaze then for any eyeball rotation value in abduction up to 45° and any lateral orbital margin position between 85° and 115° relative to the sagittal plane. By varying the lateral orbital margin position, the human orbit can be made "non-human ape-like". In the Pan-like orbit, the orbital margin position (98.7°) was closest to the human orbit (107.1°). This modest 8.4° difference resulted in a large 21.1° difference in maximum lateral visual field eccentricity with eyeball abduction (Pan-like: 115°; human: 136.1°).

Unique human orbital morphology compared with that of apes

Humans' and apes' convergent (front-facing) orbits allow a large overlap of monocular visual fields but are considered to limit the lateral visual field extent. However, humans can greatly expand their lateral visual fields using eye motion. This study aimed to assess whether the human orbital morphology was unique compared with that of apes in avoiding lateral visual field obstruction. The orbits of 100 human skulls and 120 ape skulls (30 gibbons; 30 orangutans; 30 gorillas; 30 chimpanzees and bonobos) were analyzed. The orbital width/height ratio was calculated. Two orbital angles representing orbital convergence and rearward position of the orbital margin respectively were recorded using a protractor and laser levels. Humans have the largest orbital width/height ratio (1.19; p < 0.001). Humans and gibbons have orbits which are significantly less convergent than those of chimpanzees/bonobos, gorillas and orangutans (p < 0.001). These elements suggest a morphology favoring lateral vision in humans. More specifically, the human orbit has a uniquely rearward temporal orbital margin (107.1°; p < 0.001), suitable for avoiding visual obstruction and promoting lateral visual field expansion through eye motion. Such an orbital morphology may have evolved mainly as an adaptation to open-country habitat and bipedal locomotion.

The feeding biomechanics and dietary ecology of Paranthropus boisei

The African Plio-Pleistocene hominins known as australopiths evolved derived craniodental features frequently interpreted as adaptations for feeding on either hard, or compliant/tough foods. Among australopiths, Paranthropus boisei is the most robust form, exhibiting traits traditionally hypothesized to produce high bite forces efficiently and strengthen the face against feeding stresses. However, recent mechanical analyses imply that P. boisei may not have been an efficient producer of bite force and that robust morphology in primates is not necessarily strong. Here we use an engineering method, finite element analysis, to show that the facial skeleton of P. boisei is structurally strong, exhibits a strain pattern different from that in chimpanzees (Pan troglodytes) and Australopithecus africanus, and efficiently produces high bite force. It has been suggested that P. boisei consumed a diet of compliant/tough foods like grass blades and sedge pith. However, the blunt occlusal topography of this and other species suggests that australopiths are adapted to consume hard foods, perhaps including grass and sedge seeds. A consideration of evolutionary trends in morphology relating to feeding mechanics suggests that food processing behaviors in gracile australopiths evidently were disrupted by environmental change, perhaps contributing to the eventual evolution of Homo and Paranthropus.

Biomechanical implications of intraspecific shape variation in chimpanzee crania: moving toward an integration of geometric morphometrics and finite element analysis

In a broad range of evolutionary studies, an understanding of intraspecific variation is needed in order to contextualize and interpret the meaning of variation between species. However, mechanical analyses of primate crania using experimental or modeling methods typically encounter logistical constraints that force them to rely on data gathered from only one or a few individuals. This results in a lack of knowledge concerning the mechanical significance of intraspecific shape variation that limits our ability to infer the significance of interspecific differences. This study uses geometric morphometric methods (GM) and finite element analysis (FEA) to examine the biomechanical implications of shape variation in chimpanzee crania, thereby providing a comparative context in which to interpret shape-related mechanical variation between hominin species. Six finite element models (FEMs) of chimpanzee crania were constructed from CT scans following shape-space Principal Component Analysis (PCA) of a matrix of 709 Procrustes coordinates (digitized onto 21 specimens) to identify the individuals at the extremes of the first three principal components. The FEMs were assigned the material properties of bone and were loaded and constrained to simulate maximal bites on the P(3) and M(2) . Resulting strains indicate that intraspecific cranial variation in morphology is associated with quantitatively high levels of variation in strain magnitudes, but qualitatively little variation in the distribution of strain concentrations. Thus, interspecific comparisons should include considerations of the spatial patterning of strains rather than focus only on their magnitudes.

The morphology of the mouse masticatory musculature

The mouse has been the dominant model organism in studies on the development, genetics and evolution of the mammalian skull and associated soft-tissue for decades. There is the potential to take advantage of this well studied model and the range of mutant, knockin and knockout organisms with diverse craniofacial phenotypes to investigate the functional significance of variation and the role of mechanical forces on the development of the integrated craniofacial skeleton and musculature by using computational mechanical modelling methods (e.g. finite element and multibody dynamic modelling). Currently, there are no detailed published data of the mouse masticatory musculature available. Here, using a combination of micro-dissection and non-invasive segmentation of iodine-enhanced micro-computed tomography, we document the anatomy, architecture and proportions of the mouse masticatory muscles. We report on the superficial masseter (muscle, tendon and pars reflecta), deep masseter, zygomaticomandibularis (anterior, posterior, infraorbital and tendinous parts), temporalis (lateral and medial parts), external and internal pterygoid muscles. Additionally, we report a lateral expansion of the attachment of the temporalis onto the zygomatic arch, which may play a role in stabilising this bone during downwards loading. The data presented in this paper now provide a detailed reference for phenotypic comparison in mouse models and allow the mouse to be used as a model organism in biomechanical and functional modelling and simulation studies of the craniofacial skeleton and particularly the masticatory system.

Finite element analysis of a micromechanical model of bone and a new 3D approach to validation

Finite Element Analysis (FEA) is now widely used to analyse the mechanical behaviour of bone structures. Ideally, simulations are validated against experimental data. To date, validation of Finite Element Models (FEMs) has been 2 Dimensional (2D) only, being based on comparison with surface-mounted strain gauge readings. In this study we present a novel 3-Dimensional (3D) approach to validation that allows comparison of modelled with experimental results between any two points in 3D space throughout the structure, providing magnitude and direction data for comparison, internally and externally. Specifically, we validate a FEM of a rat tibia, including trabecular network geometry, using a material testing stage housed within a microCT scanner. We further apply novel landmark based morphometric approaches to more effectively compare modelled and experimental results. 542 landmark points on the cortical and trabecular bone surfaces of the model were selected and validated in 3D against experimental data. This approach may hold considerable potential in fields wherein a better understanding of the mechanical behaviour of trabecular networks is important, e.g., the studies of osteoporosis and trabecular loss after orthopaedic implant insertion.

Sensitivity and ex vivo validation of finite element models of the domestic pig cranium

A finite element (FE) validation and sensitivity study was undertaken on a modern domestic pig cranium. Bone strain data were collected ex vivo from strain gauges, and compared with results from specimen-specific FE models. An isotropic, homogeneous model was created, then input parameters were altered to investigate model sensitivity. Heterogeneous, isotropic models investigated the effects of a constant-thickness, stiffer outer layer (representing cortical bone) atop a more compliant interior (representing cancellous bone). Loading direction and placement of strain gauges were also varied, and the use of 2D membrane elements at strain gauge locations as a method of projecting 3D model strains into the plane of the gauge was investigated. The models correctly estimate the loading conditions of the experiment, yet at some locations fail to reproduce correct principal strain magnitudes, and hence strain ratios. Principal strain orientations are predicted well. The initial model was too stiff by approximately an order of magnitude. Introducing a compliant interior reported strain magnitudes more similar to the ex vivo results without notably affecting strain orientations, ratios or contour patterns, suggesting that this simple heterogeneity was the equivalent of reducing the overall stiffness of the model. Models were generally insensitive to moderate changes in loading direction or strain gauge placement, except in the squamosal portion of the zygomatic arch. The use of membrane elements made negligible differences to the reported strains. The models therefore seem most sensitive to changes in material properties, and suggest that failure to model local heterogeneity in material properties and structure of the bone may be responsible for discrepancies between the experimental and model results. This is partially attributable to a lack of resolution in the CT scans from which the model was built, and partially due to an absence of detailed material properties data for pig cranial bone. Thus, caution is advised when using FE models to estimate absolute numerical values of breaking stress and bite force unless detailed input parameters are available. However, if the objective is to compare relative differences between models, the fact that the strain environment is replicated well means that such investigations can be robust.

Mastication and the postorbital ligament: dynamic strain in soft tissues

Although the FEED database focuses on muscle activity patterns, it is equally suitable for other physiological recording and especially for synthesizing different types of information. The present contribution addresses the interaction between muscle activity and ligamentary stretch during mastication. The postorbital ligament is the thickened edge of a septum dividing the orbital contents from the temporal fossa and is continuous with the temporal fascia. As a tensile element, this fascial complex could support the zygomatic arch against the pull of the masseter muscle. An ossified postorbital bar has evolved repeatedly in mammals, enabling resistance to compression and shear in addition to tension. Although such ossification clearly reinforces the skull against muscle pull, the most accepted explanation is that it helps isolate the orbital contents from contractions of the temporalis muscle. However, it has never been demonstrated that the contraction of jaw muscles deforms the unossified ligament. We examined linear deformation of the postorbital ligament in minipigs, Sus scrofa, along with electromyography of the jaw muscles and an assessment of changes in pressure and shape in the temporalis. During chewing, the ligament elongated (average 0.9%, maximum 2.8%) in synchrony with the contraction of the elevator muscles of the jaw. Although the temporalis bulged outward and created substantial pressure against the braincase, the superficial fibers usually retracted caudally, away from the postorbital ligament. In anesthetized animals, stimulating either the temporalis or the masseter muscle in isolation usually elongated the ligament (average 0.4-0.7%). These results confirm that contraction of the masticatory muscles can potentially distort the orbital contents and further suggest that the postorbital ligament does function as a tension member resisting the pull of the masseter on the zygomatic arch.