RETRACTED: Modelling subcortical bone in finite element analyses: A validation and sensitivity study in the macaque mandible

Influences of geometrical and mechanical properties of bone tissues in mandible behaviour - experimental and numerical predictions

The properties and geometry of bone in the mandible play a key role in mandible behaviour during a person's lifetime, and attention needs to be paid to the influence of bone properties. We analysed the effect of bone geometry, size and bone properties in mandible behaviour, experimenting on cadaveric mandibles and FE models. The study was developed using the geometry of a cadaveric mandible without teeth. Three models of cadaveric condyles were experimentally tested with instrumented with four rosettes, and a condyle reaction of 300 N. Four finite element models were considered to validate the experiments and analyse mandible behaviour. One numeric model was simulated with 10 muscles in a quasi-static condition. The experimental results present different condyle stiffness's, of 448, 215 and 254 N/mm. The values presented in the rosettes are influenced by bone geometry and bone thickness; maximum value was -600 με in rosette #4, and the maximum strain difference between mandibles was 111%. The numerical results show that bone density decreases and strain distribution increases in the thinner mandible regions. Nevertheless, the global behaviour of the structure remains similar, but presents different strain magnitudes. The study shows the need to take into account bone characteristics and their evolutions in order to improve implant design and fixation throughout the patient life. The change in bone stiffness promotes a change in maximum strain distribution with same global behaviour.

Protuberance or fossa on the lateral surface of the mandible in primates

In order to clarify the morphological characteristics and function of the protuberance and/or fossa on the lateral surface of the mandible, we examined 778 mandibles of 9 genera, 19 species of non-human primates. Both protuberance and fossa were found in Macaca, Chlorocebus, and Cercocebus at frequencies ranging from 0% to 60%. The protuberance was composed of compact bone and was similar to the mandibular torus in humans. A well-developed protuberance extended from the fourth premolar to third molar region, and was situated at the central part of the mandibular body, or continued on the oblique line. Sometimes the protuberance localized on the mandibular base. A deep and large fossa was found in all individuals of Papio, Theropithecus, and Mandrillus, and the bone width was thin in the center of the fossa. The fossa extended from the third premolar to the second molar region, and the deepest area was the first molar region. In Macaca, Chlorocebus, and Cercocebus, the curvature of the external table of the mandible created a fossa. In Colobus, and Hylobates, the external surface of the mandible looked concave because of the thickened mandibular base. These concavo-convex structures have some biological functions and represent an adaptive change for mastication.

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.

Biomechanics of the canine mandible during bone transport distraction osteogenesis

This study compared biomechanical patterns between finite element models (FEMs) and a fresh dog mandible tested under molar and incisal physiological loads in order to clarify the effect of the bone transport distraction osteogenesis (BTDO) surgical process. Three FEMs of dog mandibles were built in order to evaluate the effects of BTDO. The first model evaluated the mandibular response under two physiological loads resembling bite processes. In the second model, a 5.0 cm bone defect was bridged with a bone transport reconstruction plate (BTRP). In the third model, new regenerated bony tissue was incorporated within the defect to mimic the surgical process without the presence of the device. Complementarily, a mandible of a male American foxhound dog was mechanically tested in the laboratory both in the presence and absence of a BTRP, and mechanical responses were measured by attaching rosettes to the bone surface of the mandible to validate the FEM predictions. The relationship between real and predicted values indicates that the stress patterns calculated using FEM are a valid predictor of the biomechanics of the BTDO procedures. The present study provides an interesting correlation between the stiffness of the device and the biomechanical response of the mandible affected for bone transport.

Beware the black box: investigating the sensitivity of FEA simulations to modelling factors in comparative biomechanics

Finite element analysis (FEA) is a computational technique of growing popularity in the field of comparative biomechanics, and is an easily accessible platform for form-function analyses of biological structures. However, its rapid evolution in recent years from a novel approach to common practice demands some scrutiny in regards to the validity of results and the appropriateness of assumptions inherent in setting up simulations. Both validation and sensitivity analyses remain unexplored in many comparative analyses, and assumptions considered to be ‘reasonable’ are often assumed to have little influence on the results and their interpretation.

Here we report an extensive sensitivity analysis where high resolution finite element (FE) models of mandibles from seven species of crocodile were analysed under loads typical for comparative analysis: biting, shaking, and twisting. Simulations explored the effect on both the absolute response and the interspecies pattern of results to variations in commonly used input parameters. Our sensitivity analysis focuses on assumptions relating to the selection of material properties (heterogeneous or homogeneous), scaling (standardising volume, surface area, or length), tooth position (front, mid, or back tooth engagement), and linear load case (type of loading for each feeding type).

Our findings show that in a comparative context, FE models are far less sensitive to the selection of material property values and scaling to either volume or surface area than they are to those assumptions relating to the functional aspects of the simulation, such as tooth position and linear load case. Results show a complex interaction between simulation assumptions, depending on the combination of assumptions and the overall shape of each specimen. Keeping assumptions consistent between models in an analysis does not ensure that results can be generalised beyond the specific set of assumptions used. Logically, different comparative datasets would also be sensitive to identical simulation assumptions; hence, modelling assumptions should undergo rigorous selection. The accuracy of input data is paramount, and simulations should focus on taking biological context into account. Ideally, validation of simulations should be addressed; however, where validation is impossible or unfeasible, sensitivity analyses should be performed to identify which assumptions have the greatest influence upon the results.

In vivo bone strain and finite element modeling of the mandible of Alligator mississippiensis

Forces experienced during feeding are thought to strongly influence the morphology of the vertebrate mandible; in vivo strain data are the most direct evidence for deformation of the mandible induced by these loading regimes. Although many studies have documented bone strains in the mammalian mandible, no information is available on strain magnitudes, orientations or patterns in the sauropsid lower jaw during feeding. Furthermore, strain gage experiments record the mechanical response of bone at a few locations, not across the entire mandible. In this paper, we present bone strain data recorded at various sites on the lower jaw of Alligator mississippiensis during in vivo feeding experiments. These data are used to understand how changes in loading regime associated with changes in bite location are related to changes in strain regime on the working and balancing sides of the mandible. Our results suggest that the working side mandible is bent dorsoventrally and twisted about its long-axis during biting, and the balancing side experiences primarily dorsoventral bending. Strain orientations are more variable on the working side than on the balancing side with changes in bite point and between experiments; the balancing side exhibits higher strain magnitudes. In the second part of this paper, we use principal strain orientations and magnitudes recorded in vivo to evaluate a finite element model of the alligator mandible. Our comparison demonstrates that strain orientations and mandibular deformation predicted by the model closely match in vivo results; however, absolute strain magnitudes are lower in the finite element model.

Masticatory loadings and cranial deformation in Macaca fascicularis: a finite element analysis sensitivity study

Biomechanical analyses are commonly conducted to investigate how craniofacial form relates to function, particularly in relation to dietary adaptations. However, in the absence of corresponding muscle activation patterns, incomplete muscle data recorded experimentally for different individuals during different feeding tasks are frequently substituted. This study uses finite element analysis (FEA) to examine the sensitivity of the mechanical response of a Macaca fascicularis cranium to varying muscle activation patterns predicted via multibody dynamic analysis. Relative to the effects of varying bite location, the consequences of simulated variations in muscle activation patterns and of the inclusion/exclusion of whole muscle groups were investigated. The resulting cranial deformations were compared using two approaches; strain maps and geometric morphometric analyses. The results indicate that, with bite force magnitude controlled, the variations among the mechanical responses of the cranium to bite location far outweigh those observed as a consequence of varying muscle activations. However, zygomatic deformation was an exception, with the activation levels of superficial masseter being most influential in this regard. The anterior portion of temporalis deforms the cranial vault, but the remaining muscles have less profound effects. This study for the first time systematically quantifies the sensitivity of an FEA model of a primate skull to widely varying masticatory muscle activations and finds that, with the exception of the zygomatic arch, reasonable variants of muscle loading for a second molar bite have considerably less effect on cranial deformation and the resulting strain map than does varying molar bite point. The implication is that FEA models of biting crania will generally produce acceptable estimates of deformation under load as long as muscle activations and forces are reasonably approximated. In any one FEA study, the biological significance of the error in applied muscle forces is best judged against the magnitude of the effect that is being investigated.

Multi-layered bird beaks: a finite-element approach towards the role of keratin in stress dissipation

Bird beaks are layered structures, which contain a bony core and an outer keratin layer. The elastic moduli of this bone and keratin were obtained in a previous study. However, the mechanical role and interaction of both materials in stress dissipation during seed crushing remain unknown. In this paper, a multi-layered finite-element (FE) model of the Java finch's upper beak (Padda oryzivora) is established. Validation measurements are conducted using in vivo bite forces and by comparing the displacements with those obtained by digital speckle pattern interferometry. Next, the Young modulus of bone and keratin in this FE model was optimized in order to obtain the smallest peak von Mises stress in the upper beak. To do so, we created a surrogate model, which also allows us to study the impact of changing material properties of both tissues on the peak stresses. The theoretically best values for both moduli in the Java finch are retrieved and correspond well with previous experimentally obtained values, suggesting that material properties are tuned to the mechanical demands imposed during seed crushing.

Determination and validation of the elastic moduli of small and complex biological samples: bone and keratin in bird beaks

In recent years, there has been a surge in the development of finite-element (FE) models aimed at testing biological hypotheses. For example, recent modelling efforts suggested that the beak in Darwin's finches probably evolved in response to fracture avoidance. However, knowledge of the material properties of the structures involved is crucial for any model. For many biological structures, these data are not available and may be difficult to obtain experimentally given the complex nature of biological structures. Beaks are interesting as they appear to be highly optimized in some cases. In order to understand the biomechanics of this small and complex structure, we have been developing FE models that take into account the bilayered structure of the beak consisting of bone and keratin. Here, we present the results of efforts related to the determination and validation of the elastic modulus of bone and keratin in bird beaks. The elastic moduli of fresh and dried samples were obtained using a novel double-indentation technique and through an inverse analysis. A bending experiment is used for the inverse analysis and the validation of the measurements. The out-of-plane displacements during loading are measured using digital speckle pattern interferometry.

Left Atrial Wall Stress Distribution and Its Relationship to Electrophysiologic Remodeling in Persistent Atrial Fibrillation

Background—

Atrial stretch causes remodeling that predisposes to atrial fibrillation. We tested the hypothesis that peaks in left atrial (LA) wall stress are associated with focal remodeling.

Methods and Results—

Nineteen patients underwent LA mapping before catheter ablation for persistent atrial fibrillation. Finite Element Analysis was used to predict wall stress distribution based on LA geometry from CT. The relationship was assessed between wall stress and (1) electrogram voltage and (2) complex fractionated atrial electrograms (CFAE), using CFAE mean (the mean interval between deflections). Wall stress varied widely within atria and between subjects (median, 36 kPa; interquartile range, 26–51 kP). Peaks in wall stress (≥90th percentile) were common at the pulmonary vein (PV) ostia (93%), the appendage ridge (100%), the high posterior wall (84%), and the anterior wall and septal regions (42–84%). Electrogram voltage showed an inverse relationship across quartiles for wall stress (19% difference across quartiles, P =0.016). There was no effect on CFAE mean across quartiles of wall stress. Receiver operating characteristic analysis showed high wall stress was associated with low voltage (ie, <0.5 mV) and electrical scar (ie, <0.05 mV; both P <0.0001) and with absence of CFAE (ie, CFAE mean <120 ms; P <0.0001). However, peaks in wall stress and CFAE were found at 88% of PV ostia.

Conclusions—

Peaks in wall stress were associated with areas of low voltage, suggestive of focal remodeling. Although peaks in wall stress were not associated with LA CFAE, the PV ostia may respond differently.

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.

What makes an accurate and reliable subject-specific finite element model? A case study of an elephant femur

Finite element modelling is well entrenched in comparative vertebrate biomechanics as a tool to assess the mechanical design of skeletal structures and to better comprehend the complex interaction of their form-function relationships. But what makes a reliable subject-specific finite element model? To approach this question, we here present a set of convergence and sensitivity analyses and a validation study as an example, for finite element analysis (FEA) in general, of ways to ensure a reliable model. We detail how choices of element size, type and material properties in FEA influence the results of simulations. We also present an empirical model for estimating heterogeneous material properties throughout an elephant femur (but of broad applicability to FEA). We then use an ex vivo experimental validation test of a cadaveric femur to check our FEA results and find that the heterogeneous model matches the experimental results extremely well, and far better than the homogeneous model. We emphasize how considering heterogeneous material properties in FEA may be critical, so this should become standard practice in comparative FEA studies along with convergence analyses, consideration of element size, type and experimental validation. These steps may be required to obtain accurate models and derive reliable conclusions from them.

The mechanical significance of morphological variation in the macaque mandibular symphysis during mastication

Catarrhine symphyseal morphology displays considerable variation. Although this has been related to dentition, phylogeny, sexual dimorphism, and facial orientation, most emphasis has been given to the functional significance of the symphysis to mechanical loading during mastication. The current state of knowledge regarding the mechanical significance of the symphysis is based on a combination of in vivo experimental and comparative studies on Macaca fascicularis. These approaches have provided considerable insight into the stereotypical patterns of loading in the symphyseal region during chewing and hypotheses related to the associated symphyseal morphologies. Finite element analysis (FEA) was used to assess how in silico manipulation translates into the mechanical loading hypotheses previously proposed experimentally. In particular, this study tests the form-function relationship of the symphysis of an adult M. fascicularis mandible during lateral transverse bending and dorsoventral shear of the mandibular symphysis, and a series of modified hypothetical morphologies including absence/presence of tori and variation in the inclination and depth of the symphysis. FEA results of this study support previous findings that stresses associated with lateral transverse bending and dorsoventral shear of the mandibular symphysis can be minimized via an increased labio-lingual thickness in the superior transverse torus, an oblique symphyseal inclination, and/or an increased symphyseal depth. The finding that reduction of strains related to lateral transverse bending and dorsoventral shear can be achieved through a number of different morphologies contributes to our understanding of the influence of morphological and/or developmental constraints, such as dental development, on symphyseal form.

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.

Allometry in the distribution of material properties and geometry of the felid skull: why larger species may need to change and how they may achieve it

Extant members of the cat family (Felidae) have been considered behaviourally and morphologically conservative, i.e., despite great differences in size, there is relatively little variation in either the shape of the felid skull and dentition across species, or in the way in which these structures are used to kill and dismember prey. Consequently felids have been considered an appropriate focus for a number of investigations into the influence of allometry on craniomandibular mechanics and morphology. However, although previous treatments have considered the role of shape, they have not investigated the influence of differences in the distribution of relatively stiff cortical and more compliant cancellous bone on performance. Here, using models that incorporate material properties for both cortical and cancellous bone, we apply three-dimensional (3D) finite element analysis (FEA) to models representing the skulls of seven extant felid species. Our objectives being to determine allometric trends regarding both overall geometry and the relative distributions of cortical and cancellous bone tissue. We also more comprehensively assess variation in the efficiency with which muscular force is converted to bite force and the capacity to resist associated stresses. Our results show that the cheetah (Acinonyx jubatus) may be exceptional regarding both the efficiency with which muscular force is converted to bite force and the distribution of stress. We found a negative allometric trend between cortical bone volume and total skull bone volume, and positive allometry between the total skull bone volume and skull surface area. Results gained from mathematical modelling of beam analogies suggest that these trends reflect a need for larger species to respond to physical challenges associated with increased size, and, that changes in skull shape, bone composition, or a combination of both may be required to accommodate these challenges. With geometrical scaling stress increases by the same factor, and displacement by the same factor squared, but the ultimate failure stress of the material is invariant. We find that as species become larger, overall skull bone volume relative to surface area increases by adding a higher proportion of less dense and more compliant cancellous bone. This results in an increased cross-sectional area and second moment of inertia, which acts to reduce the overall stresses. An overall saving in mass is a likely additional consequence. Although we do find evidence that skull stiffness does diminish with size, we also argue that this is at least in part mitigated through the influence of these allometric trends. We further suggest that these trends and the explanations for them may be universal for vertebrates.

Balancing the spatial demands of the developing dentition with the mechanical demands of the catarrhine mandibular symphysis

The superior transverse torus of the catarrhine mandible has been shown to effectively reduce bending at the symphysis during unilateral postcanine biting. While the adult superior transverse torus contains trabecular bone, the juvenile one is almost entirely filled by developing permanent incisors until their eruption. This study uses finite elements analysis (FEA) to investigate whether the presence of developing incisors in the juvenile symphysis increases strains on the superior transverse torus. Two FE models of a juvenile Macaca fascicularis mandible were created: one included all the developing teeth; the second was modified to remove the incisor tooth crypts by filling them with trabecular bone. The models were loaded identically to simulate static physiological unilateral biting on dp(4) and strain magnitudes, patterns and distributions of the two FE models were compared. The FEA results show a notable increase in strain magnitudes by up to 40% when the developing incisors are present. The results indicate that, in order to maintain the same symphyseal strain magnitudes during chewing, the presence of the incisors in the symphysis necessitates a larger superior transverse torus in the juvenile than would be required if the superior transverse torus did not house the developing incisors. These results highlight the adaptational balance of the symphyseal morphology throughout ontogeny between biomechanics and the spatial demands of the developing dentition. Based on the findings we therefore propose that the spatial requirements of the developing incisors during ontogeny can act as a constraint on the functional adaptation and subsequent adult morphology observed in the catarrhine mandibular symphysis.

The mechanical function of the periodontal ligament in the macaque mandible: a validation and sensitivity study using finite element analysis

Whilst the periodontal ligament (PDL) acts as an attachment tissue between bone and tooth, hypotheses regarding the role of the PDL as a hydrodynamic damping mechanism during intraoral food processing have highlighted its potential importance in finite element (FE) analysis. Although experimental and constitutive models have correlated the mechanical function of the PDL tissue with its anisotropic, heterogeneous, viscoelastic and non-linear elastic nature, in many FE simulations the PDL is either present or absent, and when present is variably modelled. In addition, the small space the PDL occupies and the inability to visualize the PDL tissue using μCT scans poses issues during FE model construction and so protocols for the PDL thickness also vary. In this paper we initially test and validate the sensitivity of an FE model of a macaque mandible to variations in the Young's modulus and the thickness of the PDL tissue. We then tested the validity of the FE models by carrying out experimental strain measurements on the same mandible in the laboratory using laser speckle interferometry. These strain measurements matched the FE predictions very closely, providing confidence that material properties and PDL thickness were suitably defined. The FE strain results across the mandible are generally insensitive to the absence and variably modelled PDL tissue. Differences are only found in the alveolar region adjacent to the socket of the loaded tooth. The results indicate that the effect of the PDL on strain distribution and/or absorption is restricted locally to the alveolar bone surrounding the teeth and does not affect other regions of the mandible.

The global impact of sutures assessed in a finite element model of a macaque cranium

The biomechanical significance of cranial sutures in primates is an open question because their global impact is unclear, and their material properties are difficult to measure. In this study, eight suture-bone functional units representing eight facial sutures were created in a finite element model of a monkey cranium. All the sutures were assumed to have identical isotropic linear elastic material behavior that varied in different modeling experiments, representing either fused or unfused sutures. The values of elastic moduli employed in these trials ranged over several orders of magnitude. Each model was evaluated under incisor, premolar, and molar biting conditions. Results demonstrate that skulls with unfused sutures permitted more deformations and experienced higher total strain energy. However, strain patterns remained relatively unaffected away from the suture sites, and bite reaction force was likewise barely affected. These findings suggest that suture elasticity does not substantially alter load paths through the macaque skull or its underlying rigid body kinematics. An implication is that, for the purposes of finite element analysis, omitting or fusing sutures is a reasonable modeling approximation for skulls with small suture volume fraction if the research objective is to observe general patterns of craniofacial biomechanics under static loading conditions. The manner in which suture morphology and ossification affect the mechanical integrity of skulls and their ontogeny and evolution awaits further investigation, and their viscoelastic properties call for dynamic simulations.

Combining geometric morphometrics and functional simulation: an emerging toolkit for virtual functional analyses

The development of virtual methods for anatomical reconstruction and functional simulation of skeletal structures offers great promise in evolutionary and ontogenetic investigations of form-function relationships. Key developments reviewed here include geometric morphometric methods for the analysis and visualization of variations in form (size and shape), finite element methods for the prediction of mechanical performance of skeletal structures under load and multibody dynamics methods for the simulation and prediction of musculoskeletal function. These techniques are all used in studies of form and function in biology, but only recently have they been combined in novel ways to facilitate biomechanical modelling that takes account of variations in form, can statistically compare performance, and relate performance to form and its covariates. Here we provide several examples that illustrate how these approaches can be combined and we highlight areas that require further investigation and development before we can claim a mature theory and toolkit for a statistical biomechanical framework that unites these methods.

Strain in the ostrich mandible during simulated pecking and validation of specimen-specific finite element models

Finite element (FE) analysis is becoming a frequently used tool for exploring the craniofacial biomechanics of extant and extinct vertebrates. Crucial to the application of the FE analysis is the knowledge of how well FE results replicate reality. Here I present a study investigating how accurately FE models can predict experimentally derived strain in the mandible of the ostrich Struthio camelus, when both the model and the jaw are subject to identical conditions in an in-vitro loading environment. Three isolated ostrich mandibles were loaded hydraulically at the beak tip with forces similar to those measured during force transducer pecking experiments. Strains were recorded at four gauge sites at the dorsal and ventral dentary, and medial and lateral surangular. Specimen-specific FE models were created from computed tomography scans of each ostrich and loaded in an identical fashion as in the in-vitro test. The results show that the strain magnitudes, orientation, patterns and maximum : minimum principal strain ratios are predicted very closely at the dentary gauge sites, even though the FE models have isotropic and homogeneous material properties and solid internal geometry. Although the strain magnitudes are predicted at the postdentary sites, the strain orientations and ratios are inaccurate. This mismatch between the dentary and postdentary predictions may be due to the presence of intramandibular sutures or the greater amount of cancellous bone present in the postdentary region of the mandible and requires further study. This study highlights the predictive potential of even simple FE models for studies in extant and extinct vertebrates, but also emphasizes the importance of geometry and sutures. It raises the question of whether different parameters are of lesser or greater importance to FE validation for different taxonomic groups.