Jen A. Bright

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.

The Response of Cranial Biomechanical Finite Element Models to Variations in Mesh Density

Finite element (FE) models provide discrete solutions to continuous problems. Therefore, to arrive at the correct solution, it is vital to ensure that FE models contain a sufficient number of elements to fully resolve all the detail encountered in a continuum structure. Mesh convergence testing is the process of comparing successively finer meshes to identify the point of diminishing returns; where increasing resolution has marginal effects on results and further detail would become costly and unnecessary. Historically, convergence has not been considered in most CT‐based biomechanical reconstructions involving complex geometries like the skull, as generating such models has been prohibitively time‐consuming. To assess how mesh convergence influences results, 18 increasingly refined CT‐based models of a domestic pig skull were compared to identify the point of convergence for strain and displacement, using both linear and quadratic tetrahedral elements. Not all regions of the skull converged at the same rate, and unexpectedly, areas of high strain converged faster than low‐strain regions. Linear models were slightly stiffer than their quadratic counterparts, but did not converge less rapidly. As expected, insufficiently dense models underestimated strain and displacement, and failed to resolve strain “hot‐spots” notable in contour plots. In addition to quantitative differences, visual assessments of such plots often inform conclusions drawn in many comparative studies, highlighting that mesh convergence should be performed on all finite element models before further analysis takes place. Anat Rec, 2011.

Digital dissection – using contrast-enhanced computed tomography scanning to elucidate hard- and soft-tissue anatomy in the Common Buzzard Buteo buteo

Gross dissection has a long history as a tool for the study of human or animal soft‐ and hard‐tissue anatomy. However, apart from being a time‐consuming and invasive method, dissection is often unsuitable for very small specimens and often cannot capture spatial relationships of the individual soft‐tissue structures. The handful of comprehensive studies on avian anatomy using traditional dissection techniques focus nearly exclusively on domestic birds, whereas raptorial birds, and in particular their cranial soft tissues, are essentially absent from the literature. Here, we digitally dissect, identify, and document the soft‐tissue anatomy of the Common Buzzard (Buteo buteo) in detail, using the new approach of contrast‐enhanced computed tomography using Lugols iodine. The architecture of different muscle systems (adductor, depressor, ocular, hyoid, neck musculature), neurovascular, and other soft‐tissue structures is three‐dimensionally visualised and described in unprecedented detail. The three‐dimensional model is further presented as an interactive PDF to facilitate the dissemination and accessibility of anatomical data. Due to the digital nature of the data derived from the computed tomography scanning and segmentation processes, these methods hold the potential for further computational analyses beyond descriptive and illustrative proposes.

Mega-evolutionary dynamics of the adaptive radiation of birds

The origin and expansion of biological diversity is regulated by both developmental trajectories and limits on available ecological niches. As lineages diversify, an early and often rapid phase of species and trait proliferation gives way to evolutionary slow-downs as new species pack into ever more densely occupied regions of ecological niche space. Small clades such as Darwin’s finches demonstrate that natural selection is the driving force of adaptive radiations, but how microevolutionary processes scale up to shape the expansion of phenotypic diversity over much longer evolutionary timescales is unclear. Here we address this problem on a global scale by analysing a crowdsourced dataset of three-dimensional scanned bill morphology from more than 2,000 species. We find that bill diversity expanded early in extant avian evolutionary history, before transitioning to a phase dominated by packing of morphological space. However, this early phenotypic diversification is decoupled from temporal variation in evolutionary rate: rates of bill evolution vary among lineages but are comparatively stable through time. We find that rare, but major, discontinuities in phenotype emerge from rapid increases in rate along single branches, sometimes leading to depauperate clades with unusual bill morphologies. Despite these jumps between groups, the major axes of within-group bill-shape evolution are remarkably consistent across birds. We reveal that macroevolutionary processes underlying global-scale adaptive radiations support Darwinian and Simpsonian ideas of microevolution within adaptive zones and accelerated evolution between distinct adaptive peaks.

The shapes of bird beaks are highly controlled by nondietary factors

Significance We show that beak and skull shapes in birds of prey (“raptors”) are strongly coupled and largely controlled by size. This relationship means that, rather than being able to respond independently to natural selection, beak shapes are highly constrained to evolve in a particular way. The main aspects of shape variation seem to correspond with specific genes active during development. Because raptors are not each other’s closest relatives, similar shape constraints may therefore have been present in the ancestors of all modern songbirds, including Darwin’s finches, the classic example of explosive evolution in birds. If this hypothesis is true, then such classic examples may be unusual, needing first to break a genetic lock before their beaks could evolve new shapes. Bird beaks are textbook examples of ecological adaptation to diet, but their shapes are also controlled by genetic and developmental histories. To test the effects of these factors on the avian craniofacial skeleton, we conducted morphometric analyses on raptors, a polyphyletic group at the base of the landbird radiation. Despite common perception, we find that the beak is not an independently targeted module for selection. Instead, the beak and skull are highly integrated structures strongly regulated by size, with axes of shape change linked to the actions of recently identified regulatory genes. Together, size and integration account for almost 80% of the shape variation seen between different species to the exclusion of morphological dietary adaptation. Instead, birds of prey use size as a mechanism to modify their feeding ecology. The extent to which shape variation is confined to a few major axes may provide an advantage in that it facilitates rapid morphological evolution via changes in body size, but may also make raptors especially vulnerable when selection pressures act against these axes. The phylogenetic position of raptors suggests that this constraint is prevalent in all landbirds and that breaking the developmental correspondence between beak and braincase may be the key novelty in classic passerine adaptive radiations.

A review of paleontological finite element models and their validity

Abstract Finite element analysis (FEA) is a powerful quantitative tool that models mechanical performance in virtual reconstructions of complex structures, such as animal skeletons. The unique potential of FEA to elucidate the function, performance, and ecological roles of extinct taxa is an alluring prospect to paleontologists, and the technique has gained significant attention over recent years. However, as with all modeling approaches, FE models are highly sensitive to the information that is used to construct them. Given the imperfect quality of the fossil record, paleontologists are unlikely to ever know precisely which numbers to feed into their models, and it is therefore imperative that we understand how variation in FEA inputs directly affects FEA results. This is achieved through sensitivity and validation studies, which assess how inputs influence outputs, and compare these outputs to experimental data obtained from extant species. Although these studies are restricted largely to primates at present, they highlight both the power and the limitations of FEA. Reassuringly, FE models seem capable of reliably reproducing patterns of stresses and strains even with limited input data, but the magnitudes of these outputs are often in error. Paleontologists are therefore cautioned not to over-interpret their results. Crucially, validations show that without knowledge of skeletal material properties, which are unknowable from fossilized tissues, absolute performance values such as breaking stresses cannot be accurately determined. The true power of paleontological FEA therefore lies in the ability to manipulate virtual representations of morphology, to make relative comparisons between models, and to quantitatively assess how evolutionary changes of shape result in functional adaptations.

Strain accommodation in the zygomatic arch of the pig: A validation study using digital speckle pattern interferometry and finite element analysis

It has been repeatedly suggested that mammalian cranial sutures act not only to allow growth but also to reduce the levels of strain experienced by the skull during feeding. However, because of the added complexity they introduce, sutures are rarely included in finite element (FE) models, despite their potential to influence strain results. Because sutures present different morphologies and with differing degrees of internal fusion, many different methods of modeling may be necessary to accurately measure strain environments. Alternatively, these variables may exert very little influence on the scale of a whole‐skull model. To validate suture modeling methods, four alternative ways of including a suture in 3D FE models of the pig zygomatic arch were considered and compared with ex vivo experimental data from digital speckle pattern interferometry (DSPI). The use of DSPI rather than traditional strain gauge techniques allows strain gradients around the suture as well as the motions of the two bones to be observed. Results show that the introduction of 3D elements assigned more compliant material properties than the surrounding bone, is the most effective way of modeling both morphologies of suture, both in tension and compression. However, models containing no suture are almost indistinguishable from these compliant suture models, beyond the high strain gradient immediately adjacent to the suture. Conversely, modeling the suture as an open break in the mesh, or with spring elements assigned suture properties, fails to reproduce the experiment. Thus, although a solid but flexible model of sutures is preferred, the similarity between these models and those without sutures tentatively suggests that such extra detail may be unnecessary in pigs if the behavior of the whole skull is of interest. J. Morphol., 2011.

The importance of craniofacial sutures in biomechanical finite element models of the domestic pig

Craniofacial sutures are a ubiquitous feature of the vertebrate skull. Previous experimental work has shown that bone strain magnitudes and orientations often vary when moving from one bone to another, across a craniofacial suture. This has led to the hypothesis that craniofacial sutures act to modify the strain environment of the skull, possibly as a mode of dissipating high stresses generated during feeding or impact. This study tests the hypothesis that the introduction of craniofacial sutures into finite element (FE) models of a modern domestic pig skull would improve model accuracy compared to a model without sutures. This allowed the mechanical effects of sutures to be assessed in isolation from other confounding variables. These models were also validated against strain gauge data collected from the same specimen ex vivo. The experimental strain data showed notable strain differences between adjacent bones, but this effect was generally not observed in either model. It was found that the inclusion of sutures in finite element models affected strain magnitudes, ratios, orientations and contour patterns, yet contrary to expectations, this did not improve the fit of the model to the experimental data, but resulted in a model that was less accurate. It is demonstrated that the presence or absence of sutures alone is not responsible for the inaccuracies in model strain, and is suggested that variations in local bone material properties, which were not accounted for by the FE models, could instead be responsible for the pattern of results.

Models in palaeontological functional analysis

Models are a principal tool of modern science. By definition, and in practice, models are not literal representations of reality but provide simplifications or substitutes of the events, scenarios or behaviours that are being studied or predicted. All models make assumptions, and palaeontological models in particular require additional assumptions to study unobservable events in deep time. In the case of functional analysis, the degree of missing data associated with reconstructing musculoskeletal anatomy and neuronal control in extinct organisms has, in the eyes of some scientists, rendered detailed functional analysis of fossils intractable. Such a prognosis may indeed be realized if palaeontologists attempt to recreate elaborate biomechanical models based on missing data and loosely justified assumptions. Yet multiple enabling methodologies and techniques now exist: tools for bracketing boundaries of reality; more rigorous consideration of soft tissues and missing data and methods drawing on physical principles that all organisms must adhere to. As with many aspects of science, the utility of such biomechanical models depends on the questions they seek to address, and the accuracy and validity of the models themselves.

Validation experiments on finite element models of an ostrich (Struthio camelus) cranium

The first finite element (FE) validation of a complete avian cranium was performed on an extant palaeognath, the ostrich (Struthio camelus). Ex-vivo strains were collected from the cranial bone and rhamphotheca. These experimental strains were then compared to convergence tested, specimen-specific finite element (FE) models. The FE models contained segmented cortical and trabecular bone, sutures and the keratinous rhamphotheca as identified from micro-CT scan data. Each of these individual materials was assigned isotropic material properties either from the literature or from nanoindentation, and the FE models compared to the ex-vivo results. The FE models generally replicate the location of peak strains and reflect the correct mode of deformation in the rostral region. The models are too stiff in regions of experimentally recorded high strain and too elastic in regions of low experimentally recorded low strain. The mode of deformation in the low strain neurocranial region is not replicated by the FE models, and although the models replicate strain orientations to within 10° in some regions, in most regions the correlation is not strong. Cranial sutures, as has previously been found in other taxa, are important for modifying both strain magnitude and strain patterns across the entire skull, but especially between opposing the sutural junctions. Experimentally, we find that the strains on the surface of the rhamphotheca are much lower than those found on nearby bone. The FE models produce much higher principal strains despite similar strain ratios across the entirety of the rhamphotheca. This study emphasises the importance of attempting to validate FE models, modelling sutures and rhamphothecae in birds, and shows that whilst location of peak strain and patterns of deformation can be modelled, replicating experimental data in digital models of avian crania remains problematic.