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

Cranial functional specialisation for strength precedes morphological evolution in Oviraptorosauria

Oviraptorosaurians were a theropod dinosaur group that reached high diversity in the Late Cretaceous. Within oviraptorosaurians, the later diverging oviraptorids evolved distinctive crania which were extensively pneumatised, short and tall, and had a robust toothless beak, interpreted as providing a powerful bite for their herbivorous to omnivorous diet. The present study explores the ability of oviraptorid crania to resist large mechanical stresses compared with other theropods and where this adaptation originated within oviraptorosaurians. Digital 3D cranial models were constructed for the earliest diverging oviraptorosaurian, Incisivosaurus gauthieri, and three oviraptorids, Citipati osmolskae, Conchoraptor gracilis, and Khaan mckennai. Finite element analyses indicate oviraptorosaurian crania were stronger than those of other herbivorous theropods (Erlikosaurus and Ornithomimus) and were more comparable to the large, carnivorous Allosaurus. The cranial biomechanics of Incisivosaurus align with oviraptorids, indicating an early establishment of distinctive strengthened cranial biomechanics in Oviraptorosauria, even before the highly modified oviraptorid cranial morphology. Bite modelling, using estimated muscle forces, suggests oviraptorid crania may have functioned closer to structural safety limits. Low mechanical stresses around the beaks of oviraptorids suggest a convergently evolved, functionally distinct rhamphotheca, serving as a cropping/feeding tool rather than for stress reduction, when compared with other herbivorous theropods.

Effect of carbon-fiber-reinforced polyetheretherketone on stress distribution in a redesigned tumor-type knee prosthesis: a finite element analysis

Background: Surgery for bone tumors around the knee often involves extensive resection, making the subsequent prosthetic reconstruction challenging. While carbon fiber-reinforced polyetheretherketone (CF-PEEK) has been widely used in orthopedic implants, its application in tumor-type prosthesis is limited. This study aims to evaluate the feasibility of using 30wt% and 60wt% carbon fiber-reinforced polyetheretherketone (CF30-PEEK and CF60-PEEK) as materials for a redesigned tumor-type knee prosthesis through numerical analysis. Methods: A knee joint model based on CT data was created, and the resection and prosthetic reconstruction were simulated. Three finite element models of the prostheses, representing the initial and updated designs with CoCrMo and CFR-PEEK components, were constructed. Loading conditions during standing and squatting were simulated with forces of 700 N and 2800 N, respectively. Finite element analysis was used to analyze the von Mises stress and stability of all components for each prosthesis type. Results: After improvements in both material and design, the new Type 3 prosthesis showed significantly lower overall stress with stress being evenly distributed. Compared with the initial design, the maximum von Mises stress in Type 3 was reduced by 53.9% during standing and 74.2% during squatting. In the standing position, the maximum stress in the CF30-PEEK femoral component decreased by 57.3% compared with the initial design which was composed of CoCrMo, while the stress in the CF60-PEEK cardan shaft remained consistent. In the squatting position, the maximum stress in the femoral component decreased by 81.9%, and the stress in the cardan shaft decreased by 46.5%. Conclusion: The incorporation of CF30-PEEK effectively transmits forces and reduces stress concentration on the femoral component, while CF60-PEEK in the redesigned cardan shaft significantly reduces stress while maintaining stiffness. The redesigned prosthesis effectively conducts loading force and demonstrates favorable biomechanical characteristics, indicating the promising potential of utilizing CF30-PEEK and CF60-PEEK materials for tumor-type knee prostheses. The findings of this study could provide novel insights for the design and development of tumor-type knee prostheses.

Assessment of the mechanical role of cranial sutures in the mammalian skull: Computational biomechanical modelling of the rat skull

Cranial sutures are fibrocellular joints between the skull bones that are progressively replaced with bone throughout ontogeny, facilitating growth and cranial shape change. This transition from soft tissue to bone is reflected in the biomechanical properties of the craniofacial complex. However, the mechanical significance of cranial sutures has only been explored at a few localised areas within the mammalian skull, and as such our understanding of suture function in overall skull biomechanics is still limited. Here, we sought to determine how the overall strain environment is affected by the complex network of cranial sutures in the mammal skull. We combined two computational biomechanical methods, multibody dynamics analysis and finite element analysis, to simulate biting in a rat skull and compared models with and without cranial sutures. Our results show that including complex sutures in the rat model does not substantially change overall strain gradients across the cranium, particularly strain magnitudes in the bones overlying the brain. However, local variations in strain magnitudes and patterns can be observed in areas close to the sutures. These results show that, during feeding, sutures may be more important in some regions than others. Sutures should therefore be included in models that require accurate local strain magnitudes and patterns of cranial strain, particularly if models are developed for analysis of specific regions, such as the temporomandibular joint or zygomatic arch. Our results suggest that, for mammalian skulls, cranial sutures might be more important for allowing brain expansion during growth than redistributing biting loads across the cranium in adults.

Stress distributions of the short stem and the tapered wedge stem at different alignments: a finite element analysis study

BACKGROUND

The mechanical effects of stem length reduction and stem alignment on the surrounding femur remain unknown. This study directly compared the stress distribution on the surrounding femur of existing tapered wedge stems and short stems and examined the properties of stress distribution at different stem alignments in three dimensions.

METHODS

Finite element analysis was conducted for standing and walking. The cementless stem was appropriately sized to ensure adequate contact with the medial cortical bone line that contours the medullary cavity. The stem neck axis was aligned with the femoral neck axis in the mid-position and placed in 2° of the varus and valgus, 3° of flexion and extension, and 10° and 40° of anteversion.

RESULTS

Regardless of stem length, the trend of stress distribution was similar. The short stem generated less stress around the stem than the tapered wedge stem. In the coronal plane, the effect of varus and valgus deflection was small. In the sagittal plane, the stress generated around the stem was higher in the extended position than in the flexed position. In the horizontal plane, the stress generated around the stem was higher when the stem anteversion was smaller.

CONCLUSIONS

Depending on the design, short stems can reduce the stress on the surrounding bone, compared to a longer tapered wedge with similar stress distribution. Additionally, a short stem can reduce the effect of the varus position. Stems should be placed to achieve stable initial fixation while noting that stresses increase with extension and reduced anteversion.

Dietary niche partitioning in Early Jurassic ichthyosaurs from Strawberry Bank

Jurassic ichthyosaurs dominated upper trophic levels of marine ecosystems. Many species coexisted alongside each another, and it is uncertain whether they competed for the same array of food or divided dietary resources, each specializing in different kinds of prey. Here, we test whether feeding differences existed between species, applying finite element analysis to ichthyosaurs for the first time. We examine two juvenile ichthyosaur specimens, referred to Hauffiopteryx typicus and Stenopterygius triscissus, from the Strawberry Bank Lagerstätte, a shallow marine environment from the Early Jurassic of southern England (Toarcian, ~183 Ma). Snout and cranial robusticity differ between the species, with S. triscissus having a more robust snout and cranium and specializing in slow biting of hard prey, and H. typicus with its slender snout specializing in fast, but weaker bites on fast-moving, but soft prey. The two species did not differ in muscle forces, but stress distributions varied in the nasal area, reflecting differences when biting at different points along the tooth row: the more robustly snouted Stenopterygius resisted increases or shifts in stress distribution when the bite point was shifted from the posterior to the mid-point of the tooth row, but the slender-snouted Hauffiopteryx showed shifts and increases in stress distributions between these two bite points. The differences in cranial morphology, dentition and inferred stresses between the two species suggest adaptations for dietary niche partitioning.

Softening the steps to gigantism in sauropod dinosaurs through the evolution of a pedal pad

How sauropod dinosaurs were able to withstand the forces associated with their immense size represents one of the most challenging biomechanical scenarios in the evolution of terrestrial tetrapods, but also one lacking robust biomechanical testing. Here, we use finite element analyses to quantify the biomechanical effects of foot skeletal postures with and without the presence of a soft tissue pad in sauropodomorphs. We find that none of the models can maintain bone stresses that fall within optimal bone safety factors in the absence of a soft tissue pad. Our findings suggest that a soft tissue pad in sauropods would have reduced bone stresses by combining the mechanical advantages of a functionally plantigrade foot with the plesiomorphic skeletally digitigrade saurischian condition. The acquisition of a developed soft tissue pad by the Late Triassic-Early Jurassic may represent one of the key adaptations for the evolution of gigantism that has become emblematic of these dinosaurs.

Modeling tooth enamel in FEA comparisons of skulls: Comparing common simplifications with biologically realistic models

Palaeontologists often use finite element analyses, in which forces propagate through objects with specific material properties, to investigate feeding biomechanics. Teeth are usually modeled with uniform properties (all bone or all enamel). In reality, most teeth are composed of pulp, dentine, and enamel. We tested how simplified teeth compare to more realistic models using mandible models of three reptiles. For each, we created models representing enamel thicknesses found in extant taxa, as well as simplified models (bone, dentine or enamel). Our results suggest that general comparisons of stress distribution among distantly related taxa do not require representation of dental tissues, as there was no noticeable effect on heatmap representations of stress. However, we find that representation of dental tissues impacts bite force estimates, although magnitude of these effects may differ depending on constraints. Thus, as others have shown, the detail necessary in a biomechanical model relates to the questions being examined.

Evaluation of Mesh and Sensor Resolution for Finite Element Modeling of Non-Invasive Fetal ECG Signals

Non-invasive fetal electrocardiography (NI-FECG) is an emerging tool with novel diagnostic potential for monitoring fetal wellbeing using electrical signals acquired from the maternal abdomen. However, variations in the geometric structure and conductivity of maternal-fetal tissues have been shown to affect the reliability of NI-FECG signals. Previous studies have utilized detailed finite element models to simulate these impacts, however this approach is computationally expensive. In this study, we investigate a range of mesh and sensor resolutions to determine an optimal trade-off between computational cost and modeling accuracy for simulating NI-FECG signals. Our results demonstrate that an optimal refinement of mesh resolution provides comparable accuracy to a detailed reference solution while requiring approximately 12 times less computation time and one-third of the memory usage. Furthermore, positioning simulated sensors at a 20 mm grid spacing provides a sufficient representation of abdominal surface potentials. These findings represent default parameters to be used in future simulations of NI-FECG signals. Code for the model utilized in this work is available under an open-source GPL license as part of the fecgsyn toolbox.Clinical Relevance- Simulating NI-FECG signals provides the opportunity to study the effects of sensor placement and maternal-fetal anatomic variations in a controlled setting. This work has relevance in determining default parameters for efficiently performing these simulations.

Computational biomechanical modelling of the rabbit cranium during mastication

Although a functional relationship between bone structure and mastication has been shown in some regions of the rabbit skull, the biomechanics of the whole cranium during mastication have yet to be fully explored. In terms of cranial biomechanics, the rabbit is a particularly interesting species due to its uniquely fenestrated rostrum, the mechanical function of which is debated. In addition, the rabbit processes food through incisor and molar biting within a single bite cycle, and the potential influence of these bite modes on skull biomechanics remains unknown. This study combined the in silico methods of multi-body dynamics and finite element analysis to compute musculoskeletal forces associated with a range of incisor and molar biting, and to predict the associated strains. The results show that the majority of the cranium, including the fenestrated rostrum, transmits masticatory strains. The peak strains generated over all bites were found to be attributed to both incisor and molar biting. This could be a consequence of a skull shape adapted to promote an even strain distribution for a combination of infrequent incisor bites and cyclic molar bites. However, some regions, such as the supraorbital process, experienced low peak strain for all masticatory loads considered, suggesting such regions are not designed to resist masticatory forces.

QCT-FE modeling of the proximal tibia: Effect of mapping strategy on convergence time and model accuracy

Quantitative computed tomography (QCT) based finite element (FE) modeling, referred to as QCT-FE, has seen rapid growth and application for modeling bone mechanics. With this approach, varying bone material properties are set via experimentally-derived density-modulus equations. One challenge though associated with QCT-FE is to identify the appropriate mapping strategy for assigning elastic moduli to elements. The goal of this study was to evaluate different QCT-FE mapping strategies to identify the optimum approach with fastest convergence rate and highest accuracy. Four proximal tibial medial compartments were imaged using QCT and experimentally tested to characterize proximal tibial subchondral bone stiffness at four surface points, resulting in a total of 16 indentation measures. Three material mapping methods were analyzed: (1) constant-E where an average elastic modulus was assigned to each element; (2) node-based where the material properties were first mapped on nodes then interpolated to Gaussian integration points; and (3) element-based in which the material properties were directly assigned to Gaussian integration points. Different element sizes were assessed with edge-lengths ranging from 0.9 to 3 mm. Results indicated that all converged models showed similar coefficient-of-determination (R²) and normalized root-mean-square errors (RMSE%). Though, the constant-E and node-based methods converged with the element edge-length of 1.5 mm (prediction error of 4.8% and 2.5%, respectively) whereas the element-based method converged with a larger element having an edge-length 2.5 mm (error = 4.9%). In conclusion, the element-based method, with a larger element size, resulted in similar predictive accuracy, faster convergence and shorter run-times relative to the constant-E and node-based approaches. As such, we recommend the element-based method for future subject-specific QCT-FE modeling.

Potential of zebrafish as a model to characterise MicroRNA profiles in mechanically mediated joint degeneration

Mechanically mediated joint degeneration and cartilage dyshomeostasis is implicated in highly prevalent diseases such as osteoarthritis. Increasingly, MicroRNAs are being associated with maintaining the normal state of cartilage, making them an exciting and potentially key contributor to joint health and disease onset. Here, we present a summary of current in vitro and in vivo models which can be used to study the role of mechanical load and MicroRNAs in joint degeneration, including: non-invasive murine models of PTOA, surgical models which involve ligament transection, and unloading models based around immobilisation of joints or removal of load from the joint through suspension. We also discuss how zebrafish could be used to advance this field, namely through the availability of transgenic lines relevant to cartilage homeostasis and the ability to accurately map strain through the cartilage, enabling the response of downstream MicroRNA targets to be followed dynamically at a cellular level in areas of high and low strain.

Biomechanical comparison of implantation approaches for the treatment of mandibular total edentulism

Applying four anterior implants placed vertically or tilted in the mandible is considered to provide clinically reasonable results in the treatment of mandibular posterior edentulism. It is also reported that a combination of four anterior and two short posterior implants can be an alternative approach for the rehabilitation of severe atrophy cases. In this study, we aimed to evaluate the biomechanical responses of three different implant placement configurations, which represent the clinical options for the treatment of mandibular edentulism. Three-dimensional models of the mandible, prosthetic bar, dental implant, abutment, and screw were created. Finite element models of the three implant configurations (Protocol 1: Four anterior implants, Protocol 2: Four anterior and two short posterior implants, Protocol 3: Two anterior and two tilted posterior implants: All-on-4™ concept) were generated for 10 patients and analyzed under different loading conditions including chewing, biting, and impact forces. Protocol 2 led to the lowest stress concentrations over the mandible among the three protocols (p < 0.016). Protocol 2 resulted in significantly lower stresses than Protocol 3 and Protocol 1 over prosthetic bars under chewing forces (p < 0.016). None of the implant placement protocols consistently exhibited the lowest stress distribution over abutments. The lowest stresses over dental implants under the chewing, biting, and impact forces were obtained in Protocol 1, Protocol 2, and Protocol 3, respectively (p < 0.016). Protocol 3 was the best option to obtain the lowest stress values over the screws under all types of loading conditions (p < 0.016). In conclusion, Protocol 2 was biomechanically more ideal than Protocol 1 and Protocol 3 to manage the posterior edentulism.

Was the Devonian placoderm Titanichthys a suspension feeder?

Large nektonic suspension feeders have evolved multiple times. The apparent trend among apex predators for some evolving into feeding on small zooplankton is of interest for understanding the associated shifts in anatomy and behaviour, while the spatial and temporal distribution gives clues to an inherent relationship with ocean primary productivity and how past and future perturbations to these may impact on the different tiers of the food web. The evolution of large nektonic suspension feeders-'gentle giants'-occurred four times among chondrichthyan fishes (e.g. whale sharks, basking sharks and manta rays), as well as in baleen whales (mysticetes), the Mesozoic pachycormid fishes and at least twice in radiodontan stem group arthropods (Anomalocaridids) during the Cambrian explosion. The Late Devonian placoderm Titanichthys has tentatively been considered to have been a megaplanktivore, primarily due to its gigantic size and narrow, edentulous jaws while no suspension-feeding apparatus have ever been reported. Here, the potential for microphagy and other feeding behaviours in Titanichthys is assessed via a comparative study of jaw mechanics in Titanichthys and other placoderms with presumably differing feeding habits (macrophagy and durophagy). Finite-element models of the lower jaws of Titanichthys termieri in comparison to Dunkleosteus terrelli and Tafilalichthys lavocati reveal considerably less resistance to von Mises stress in this taxon. Comparisons with a selection of large-bodied extant taxa of similar ecological diversity reveal similar disparities in jaw stress resistance. Our results, therefore, conform to the hypothesis that Titanichthys was a suspension feeder with jaws ill-suited for biting and crushing but well suited for gaping ram feeding.

The use of extruded finite-element models as a novel alternative to tomography-based models: a case study using early mammal jaws

Finite-element (FE) analysis has been used in palaeobiology to assess the mechanical performance of the jaw. It uses two types of models: tomography-based three-dimensional (3D) models (very accurate, not always accessible) and two-dimensional (2D) models (quick and easy to build, good for broad-scale studies, cannot obtain absolute stress and strain values). Here, we introduce extruded FE models, which provide fairly accurate mechanical performance results, while remaining low-cost, quick and easy to build. These are simplified 3D models built from lateral outlines of a relatively flat jaw and extruded to its average width. There are two types: extruded (flat mediolaterally) and enhanced extruded (accounts for width differences in the ascending ramus). Here, we compare mechanical performance values resulting from four types of FE models (i.e. tomography-based 3D, extruded, enhanced extruded and 2D) in Morganucodon and Kuehneotherium. In terms of absolute values, both types of extruded model perform well in comparison to the tomography-based 3D models, but enhanced extruded models perform better. In terms of overall patterns, all models produce similar results. Extruded FE models constitute a viable alternative to the use of tomography-based 3D models, particularly in relatively flat bones.

Warped finite element models predict whole shell failure in turtle shells

Finite element (FE) models have become increasingly popular in comparative biomechanical studies, with researchers continually developing methods such as 'warping' preexisting models to facilitate analyses. However, few studies have investigated how well FE models can predict biologically crucial whole-structure performance or whether 'warped' models can provide useful information about the mechanical behavior of actual specimens. This study addresses both of these issues through a validation of warped FE models of turtle shells. FE models for 40 turtle specimens were built using 3D landmark coordinates and thin-plate spline interpolations to warp preexisting turtle shell models. Each actual turtle specimen was loaded to failure, and the load at failure and mode of fracture were then compared with the behavior predicted by the models. Overall, the models performed very well, despite the fact that many simplifying assumptions were made for analysis. Regressions of observed on predicted loads were significant for the dataset as a whole, as well as in separate analyses within two turtle species, and the direction of fracture was generally consistent with the patterns of stresses observed in the models. This was true even when size (an important factor in determining strength) was removed from analyses - the models were also able to predict which shells would be relatively stronger or weaker. Although some residual variation remains unexplained, this study supports the idea that warped FE models run with simplifying assumptions at least can provide useful information for comparative biomechanical studies.

Cancellous bone and theropod dinosaur locomotion. Part II-a new approach to inferring posture and locomotor biomechanics in extinct tetrapod vertebrates

This paper is the second of a three-part series that investigates the architecture of cancellous bone in the main hindlimb bones of theropod dinosaurs, and uses cancellous bone architectural patterns to infer locomotor biomechanics in extinct non-avian species. Cancellous bone is widely known to be highly sensitive to its mechanical environment, and therefore has the potential to provide insight into locomotor biomechanics in extinct tetrapod vertebrates such as dinosaurs. Here in Part II, a new biomechanical modelling approach is outlined, one which mechanistically links cancellous bone architectural patterns with three-dimensional musculoskeletal and finite element modelling of the hindlimb. In particular, the architecture of cancellous bone is used to derive a single 'characteristic posture' for a given species-one in which bone continuum-level principal stresses best align with cancellous bone fabric-and thereby clarify hindlimb locomotor biomechanics. The quasi-static approach was validated for an extant theropod, the chicken, and is shown to provide a good estimate of limb posture at around mid-stance. It also provides reasonable predictions of bone loading mechanics, especially for the proximal hindlimb, and also provides a broadly accurate assessment of muscle recruitment insofar as limb stabilization is concerned. In addition to being useful for better understanding locomotor biomechanics in extant species, the approach hence provides a new avenue by which to analyse, test and refine palaeobiomechanical hypotheses, not just for extinct theropods, but potentially many other extinct tetrapod groups as well.

An assessment of the role of the falx cerebri and tentorium cerebelli in the cranium of the cat (Felis silvestris catus)

The falx cerebri and the tentorium cerebelli are two projections of the dura mater in the cranial cavity which ossify to varying degrees in some mammalian species. The idea that the ossification of these structures may be necessary to support the loads arising during feeding has been proposed and dismissed in the past, but never tested quantitatively. To address this, a biomechanical model of a domestic cat (Felis silvestris catus) skull was created and the material properties of the falx and tentorium were varied for a series of loading regimes incorporating the main masticatory and neck muscles during biting. Under these loading conditions, ossification of the falx cerebri does not have a significant impact on the stress in the cranial bones. In the case of the tentorium, however, a localized increase in stress was observed in the parietal and temporal bones, including the tympanic bulla, when a non-ossified tentorium was modelled. These effects were consistent across the different analyses, irrespective of loading regime. The results suggest that ossification of the tentorium cerebelli may play a minor role during feeding activities by decreasing the stress in the back of the skull.

Analyzing the sclerocarpy adaptations of the Pitheciidae mandible

Primates are interpreted to be ancestrally adapted to frugivory, although some modern groups show clear adaptations to other diets. Among them, pitheciids stand out for specifically predating seeds. This dietary specialization is known as sclerocarpy and refers to the extraction of seeds from surrounding hard tissues using the anterior dentition followed by the mastication of seeds by the molars. It has been proposed that Callicebus-Pithecia-Chiropotes-Cacajao represent a morphocline of increasingly specialized anatomical traits for sclerocarpic foraging. This study addresses whether there is a sclerocarpic specialization gradient in the mandibular morphology of pitheciids. Finite element analysis (FEA) was used to simulate two biting scenarios and the obtained stress values were compared between different pitheciids. Geometric morphometrics (GM) were used to display the morphological variation of this group. No support was found for the morphocline hypothesis from a biomechanical viewpoint since all pitheciins showed similar stress values and on average Chiropotes rather than Cacajao exhibited the strongest mandible. From a morphological perspective, it was found that there is indeed relative "robusticity" continuum in the pitheciid mandible for some aspects of shape as expected for the morphocline hypothesis, but this gradient could be related to other factors rather than sclerocarpic specialization. The present results are expected to contribute to a better insight regarding the ecomorphological relationship between mandibular morphology and mechanical performance among pitheciids.

The intervals method: a new approach to analyse finite element outputs using multivariate statistics

Background

In this paper, we propose a new method, named the intervals’ method, to analyse data from finite element models in a comparative multivariate framework. As a case study, several armadillo mandibles are analysed, showing that the proposed method is useful to distinguish and characterise biomechanical differences related to diet/ecomorphology.

Methods

The intervals’ method consists of generating a set of variables, each one defined by an interval of stress values. Each variable is expressed as a percentage of the area of the mandible occupied by those stress values. Afterwards these newly generated variables can be analysed using multivariate methods.

Results

Applying this novel method to the biological case study of whether armadillo mandibles differ according to dietary groups, we show that the intervals’ method is a powerful tool to characterize biomechanical performance and how this relates to different diets. This allows us to positively discriminate between specialist and generalist species.

Discussion

We show that the proposed approach is a useful methodology not affected by the characteristics of the finite element mesh. Additionally, the positive discriminating results obtained when analysing a difficult case study suggest that the proposed method could be a very useful tool for comparative studies in finite element analysis using multivariate statistical approaches.

The Tarsometatarsus of the Ostrich Struthio camelus: Anatomy, Bone Densities, and Structural Mechanics

Background

The ostrich Struthio camelus reaches the highest speeds of any extant biped, and has been an extraordinary subject for studies of soft-tissue anatomy and dynamics of locomotion. An elongate tarsometatarsus in adult ostriches contributes to their speed. The internal osteology of the tarsometatarsus, and its mechanical response to forces of running, are potentially revealing about ostrich foot function.

Methods/Principal Findings

Computed tomography (CT) reveals anatomy and bone densities in tarsometatarsi of an adult and a young juvenile ostrich. A finite element (FE) model for the adult was constructed with properties of compact and cancellous bone where these respective tissues predominate in the original specimen. The model was subjected to a quasi-static analysis under the midstance ground reaction and muscular forces of a fast run. Anatomy–Metatarsals are divided proximally and distally and unify around a single internal cavity in most adult tarsometatarsus shafts, but the juvenile retains an internal three-part division of metatarsals throughout the element. The juvenile has a sparsely ossified hypotarsus for insertion of the m. fibularis longus, as part of a proximally separate third metatarsal. Bone is denser in all regions of the adult tarsometatarsus, with cancellous bone concentrated at proximal and distal articulations, and highly dense compact bone throughout the shaft. Biomechanics–FE simulations show stress and strain are much greater at midshaft than at force applications, suggesting that shaft bending is the most important stressor of the tarsometatarsus. Contraction of digital flexors, inducing a posterior force at the TMT distal condyles, likely reduces buildup of tensile stresses in the bone by inducing compression at these locations, and counteracts bending loads. Safety factors are high for von Mises stress, consistent with faster running speeds known for ostriches.

Conclusions/Significance

High safety factors suggest that bone densities and anatomy of the ostrich tarsometatarsus confer strength for selectively critical activities, such as fleeing and kicking predators. Anatomical results and FE modeling of the ostrich tarsometatarsus are a useful baseline for testing the structure’s capabilities and constraints for locomotion, through ontogeny and the full step cycle. With this foundation, future analyses can incorporate behaviorally realistic strain rates and distal joint forces, experimental validation, and proximal elements of the ostrich hind limb.

An integrative method for testing form-function linkages and reconstructed evolutionary pathways of masticatory specialization

Morphology serves as a ubiquitous proxy in macroevolutionary studies to identify potential adaptive processes and patterns. Inferences of functional significance of phenotypes or their evolution are overwhelmingly based on data from living taxa. Yet, correspondence between form and function has been tested in only a few model species, and those linkages are highly complex. The lack of explicit methodologies to integrate form and function analyses within a deep-time and phylogenetic context weakens inferences of adaptive morphological evolution, by invoking but not testing form-function linkages. Here, we provide a novel approach to test mechanical properties at reconstructed ancestral nodes/taxa and the strength and direction of evolutionary pathways in feeding biomechanics, in a case study of carnivorous mammals. Using biomechanical profile comparisons that provide functional signals for the separation of feeding morphologies, we demonstrate, using experimental optimization criteria on estimation of strength and direction of functional changes on a phylogeny, that convergence in mechanical properties and degree of evolutionary optimization can be decoupled. This integrative approach is broadly applicable to other clades, by using quantitative data and model-based tests to evaluate interpretations of function from morphology and functional explanations for observed macroevolutionary pathways.

Cranial biomechanics, bite force and function of the endocranial sinuses in Diprotodon optatum, the largest known marsupial

The giant extinct marsupial Diprotodon optatum has unusual skull morphology for an animal of its size, consisting of very thin bone and large cranial sinuses that occupy most of the internal cranial space. The function of these sinuses is unknown as there are no living marsupial analogues. The finite element method was applied to identify areas of high and low stress, and estimate the bite force of Diprotodon to test hypotheses on the function of the extensive cranial sinuses. Detailed three-dimensional models of the cranium, mandible and jaw adductor muscles were produced. In addition, manipulations to the Diprotodon cranial model were performed to investigate changes in skull and sinus structure, including a model with no sinuses (sinuses 'filled' with bone) and a model with a midsagittal crest. Results indicate that the cranial sinuses in Diprotodon significantly lighten the skull while still providing structural support, a high bite force and low stress, indicating the cranium may have been able to withstand higher loads than those generated during feeding. Data from this study support the hypothesis that pneumatisation is driven by biomechanical loads and occurs in areas of low stress. The presence of sinuses is likely to be a byproduct of the separation of the outer surface of the skull from the braincase due to the demands of soft tissue including the brain and the large jaw adductor musculature, especially the temporalis. In very large species, such as Diprotodon, this separation is more pronounced, resulting in extensive cranial sinuses due to a relatively small brain compared with the size of the skull.

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.

Comparative finite element analysis of the cranial performance of four herbivorous marsupials

Marsupial herbivores exhibit a wide variety of skull shapes and sizes to exploit different ecological niches. Several studies on teeth, dentaries, and jaw adductor muscles indicate that marsupial herbivores exhibit different specializations for grazing and browsing. No studies, however, have examined the skulls of marsupial herbivores to determine the relationship between stress and strain, and the evolution of skull shape. The relationship between skull morphology, biomechanical performance, and diet was tested by applying the finite element method to the skulls of four marsupial herbivores: the common wombat (Vombatus ursinus), koala (Phascolarctos cinereus), swamp wallaby (Wallabia bicolor), and red kangaroo (Macropus rufus). It was hypothesized that grazers, requiring stronger skulls to process tougher food, would have higher biomechanical performance than browsers. This was true when comparing the koala and wallaby (browsers) to the wombat (a grazer). The cranial model of the wombat resulted in low stress and high mechanical efficiency in relation to a robust skull capable of generating high bite forces. However, the kangaroo, also a grazer, has evolved a very different strategy to process tough food. The cranium is much more gracile and has higher stress and lower mechanical efficiency, but they adopt a different method of processing food by having a curved tooth row to concentrate force in a smaller area and molar progression to remove worn teeth from the tooth row. Therefore, the position of the bite is crucial for the structural performance of the kangaroo skull, while it is not for the wombat which process food along the entire tooth row. In accordance with previous studies, the results from this study show the mammalian skull is optimized to resist forces generated during feeding. However, other factors, including the lifestyle of the animal and its environment, also affect selection for skull morphology to meet multiple functional demands.

The sensitivity of biological finite element models to the resolution of surface geometry: a case study of crocodilian crania

The reliability of finite element analysis (FEA) in biomechanical investigations depends upon understanding the influence of model assumptions. In producing finite element models, surface mesh resolution is influenced by the resolution of input geometry, and influences the resolution of the ensuing solid mesh used for numerical analysis. Despite a large number of studies incorporating sensitivity studies of the effects of solid mesh resolution there has not yet been any investigation into the effect of surface mesh resolution upon results in a comparative context. Here we use a dataset of crocodile crania to examine the effects of surface resolution on FEA results in a comparative context. Seven high-resolution surface meshes were each down-sampled to varying degrees while keeping the resulting number of solid elements constant. These models were then subjected to bite and shake load cases using finite element analysis. The results show that incremental decreases in surface resolution can result in fluctuations in strain magnitudes, but that it is possible to obtain stable results using lower resolution surface in a comparative FEA study. As surface mesh resolution links input geometry with the resulting solid mesh, the implication of these results is that low resolution input geometry and solid meshes may provide valid results in a comparative context.

Are cranial biomechanical simulation data linked to known diets in extant taxa? A method for applying diet-biomechanics linkage models to infer feeding capability of extinct species

Performance of the masticatory system directly influences feeding and survival, so adaptive hypotheses often are proposed to explain craniodental evolution via functional morphology changes. However, the prevalence of "many-to-one" association of cranial forms and functions in vertebrates suggests a complex interplay of ecological and evolutionary histories, resulting in redundant morphology-diet linkages. Here we examine the link between cranial biomechanical properties for taxa with different dietary preferences in crown clade Carnivora, the most diverse clade of carnivorous mammals. We test whether hypercarnivores and generalists can be distinguished based on cranial mechanical simulation models, and how such diet-biomechanics linkages relate to morphology. Comparative finite element and geometric morphometrics analyses document that predicted bite force is positively allometric relative to skull strain energy; this is achieved in part by increased stiffness in larger skull models and shape changes that resist deformation and displacement. Size-standardized strain energy levels do not reflect feeding preferences; instead, caniform models have higher strain energy than feliform models. This caniform-feliform split is reinforced by a sensitivity analysis using published models for six additional taxa. Nevertheless, combined bite force-strain energy curves distinguish hypercarnivorous versus generalist feeders. These findings indicate that the link between cranial biomechanical properties and carnivoran feeding preference can be clearly defined and characterized, despite phylogenetic and allometric effects. Application of this diet-biomechanics linkage model to an analysis of an extinct stem carnivoramorphan and an outgroup creodont species provides biomechanical evidence for the evolution of taxa into distinct hypercarnivorous and generalist feeding styles prior to the appearance of crown carnivoran clades with similar feeding preferences.

Finite Element Analysis of the Cingulata Jaw: An Ecomorphological Approach to Armadillo's Diets

Finite element analyses (FEA) were applied to assess the lower jaw biomechanics of cingulate xenarthrans: 14 species of armadillos as well as one Pleistocene pampathere (11 extant taxa and the extinct forms Vassallia, Eutatus and Macroeuphractus). The principal goal of this work is to comparatively assess the biomechanical capabilities of the mandible based on FEA and to relate the obtained stress patterns with diet preferences and variability, in extant and extinct species through an ecomorphology approach. The results of FEA showed that omnivorous species have stronger mandibles than insectivorous species. Moreover, this latter group of species showed high variability, including some similar biomechanical features of the insectivorous Tolypeutes matacus and Chlamyphorus truncatus to those of omnivorous species, in agreement with reported diets that include items other than insects. It remains unclear the reasons behind the stronger than expected lower jaw of Dasypus kappleri. On the other hand, the very strong mandible of the fossil taxon Vassallia maxima agrees well with the proposed herbivorous diet. Moreover, Eutatus seguini yielded a stress pattern similar to Vassalia in the posterior part of the lower jaw, but resembling that of the stoutly built Macroeuphractus outesi in the anterior part. The results highlight the need for more detailed studies on the natural history of extant armadillos. FEA proved a powerful tool for biomechanical studies in a comparative framework.

Bone-breaking bite force of Basilosaurus isis (Mammalia, Cetacea) from the late Eocene of Egypt estimated by finite element analysis

Bite marks suggest that the late Eocence archaeocete whale Basilosaurus isis (Birket Qarun Formation, Egypt) fed upon juveniles of the contemporary basilosaurid Dorudon atrox. Finite element analysis (FEA) of a nearly complete adult cranium of B. isis enables estimates of its bite force and tests the animal's capabilities for crushing bone. Two loadcases reflect different biting scenarios: 1) an intitial closing phase, with all adductors active and a full condylar reaction force; and 2) a shearing phase, with the posterior temporalis active and minimized condylar force. The latter is considered probable when the jaws were nearly closed because the preserved jaws do not articulate as the molariform teeth come into occulusion. Reaction forces with all muscles active indicate that B. isis maintained relatively greater bite force anteriorly than seen in large crocodilians, and exerted a maximum bite force of at least 16,400 N at its upper P3. Under the shearing scenario with minimized condylar forces, tooth reaction forces could exceed 20,000 N despite lower magnitudes of muscle force. These bite forces at the teeth are consistent with bone indentations on Dorudon crania, reatract-and-shear hypotheses of Basilosaurus bite function, and seizure of prey by anterior teeth as proposed for other archaeocetes. The whale's bite forces match those estimated for pliosaurus when skull lengths are equalized, suggesting similar tradeoffs of bite function and hydrodynamics. Reaction forces in B. isis were lower than maxima estimated for large crocodylians and carnivorous dinosaurs. However, comparison of force estimates from FEA and regression data indicate that B. isis exerted the largest bite forces yet estimated for any mammal, and greater force than expected from its skull width. Cephalic feeding biomechanics of Basilosaurus isis are thus consistent with habitual predation.

3D patient-specific model of the tibia from CT for orthopedic use

OBJECTIVES

3D patient-specific model of the tibia is used to determine the torque needed to initialize the tibial torsion correction.

METHODS

The finite elements method is used in the biomechanical modeling of tibia. The geometric model of the tibia is obtained from CT images. The tibia is modeled as an anisotropic material with non-homogeneous mechanical properties.

CONCLUSIONS

The maximum stress is located in the shaft of tibia diaphysis. With both meshes are obtained similar results of stresses and displacements. For this patient-specific model, the torque must be greater than 30 Nm to initialize the correction of tibial torsion deformity.

Functional anatomy and feeding biomechanics of a giant Upper Jurassic pliosaur (Reptilia: Sauropterygia) from Weymouth Bay, Dorset, UK

Pliosaurs were among the largest predators in Mesozoic seas, and yet their functional anatomy and feeding biomechanics are poorly understood. A new, well-preserved pliosaur from the Kimmeridgian of Weymouth Bay (UK) revealed cranial adaptations related to feeding. Digital modelling of computed tomography scans allowed reconstruction of missing, distorted regions of the skull and of the adductor musculature, which indicated high bite forces. Size-corrected beam theory modelling showed that the snout was poorly optimised against bending and torsional stresses compared with other aquatic and terrestrial predators, suggesting that pliosaurs did not twist or shake their prey during feeding and that seizing was better performed with post-symphyseal bites. Finite element analysis identified biting-induced stress patterns in both the rostrum and lower jaws, highlighting weak areas in the rostral maxillary-premaxillary contact and the caudal mandibular symphysis. A comparatively weak skull coupled with musculature that was able to produce high forces, is explained as a trade-off between agility, hydrodynamics and strength. In the Kimmeridgian ecosystem, we conclude that Late Jurassic pliosaurs were generalist predators at the top of the food chain, able to prey on reptiles and fishes up to half their own length.

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.

A sensitivity analysis to the role of the fronto-parietal suture in Lacerta bilineata: a preliminary finite element study

Cranial sutures are sites of bone growth and development but micromovements at these sites may distribute the load across the skull more evenly. Computational studies have incorporated sutures into finite element (FE) models to assess various hypotheses related to their function. However, less attention has been paid to the sensitivity of the FE results to the shape, size, and stiffness of the modeled sutures. Here, we assessed the sensitivity of the strain predictions to the aforementioned parameters in several models of fronto-parietal (FP) suture in Lacerta bilineata. For the purpose of this study, simplifications were made in relation to modeling the bone properties and the skull loading. Results highlighted that modeling the FP as either an interdigitated suture or a simplified butt suture, did not reduce the strain distribution in the FP region. Sensitivity tests showed that similar patterns of strain distribution can be obtained regardless of the size of the suture, or assigned stiffness, yet the exact magnitudes of strains are highly sensitive to these parameters. This study raises the question whether the morphogenesis of epidermic scales in the FP region in the Lacertidae is related to high strain fields in this region, because of micromovement in the FP suture.

Functional evolution of the feeding system in rodents

The masticatory musculature of rodents has evolved to enable both gnawing at the incisors and chewing at the molars. In particular, the masseter muscle is highly specialised, having extended anteriorly to originate from the rostrum. All living rodents have achieved this masseteric expansion in one of three ways, known as the sciuromorph, hystricomorph and myomorph conditions. Here, we used finite element analysis (FEA) to investigate the biomechanical implications of these three morphologies, in a squirrel, guinea pig and rat. In particular, we wished to determine whether each of the three morphologies is better adapted for either gnawing or chewing. Results show that squirrels are more efficient at muscle-bite force transmission during incisor gnawing than guinea pigs, and that guinea pigs are more efficient at molar chewing than squirrels. This matches the known diet of nuts and seeds that squirrels gnaw, and of grasses that guinea pigs grind down with their molars. Surprisingly, results also indicate that rats are more efficient as well as more versatile feeders than both the squirrel and guinea pig. There seems to be no compromise in biting efficiency to accommodate the wider range of foodstuffs and the more general feeding behaviour adopted by rats. Our results show that the morphology of the skull and masticatory muscles have allowed squirrels to specialise as gnawers and guinea pigs as chewers, but that rats are high-performance generalists, which helps explain their overwhelming success as a group.

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.

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.

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.

Model sensitivity and use of the comparative finite element method in mammalian jaw mechanics: mandible performance in the gray wolf

Finite Element Analysis (FEA) is a powerful tool gaining use in studies of biological form and function. This method is particularly conducive to studies of extinct and fossilized organisms, as models can be assigned properties that approximate living tissues. In disciplines where model validation is difficult or impossible, the choice of model parameters and their effects on the results become increasingly important, especially in comparing outputs to infer function. To evaluate the extent to which performance measures are affected by initial model input, we tested the sensitivity of bite force, strain energy, and stress to changes in seven parameters that are required in testing craniodental function with FEA. Simulations were performed on FE models of a Gray Wolf (Canis lupus) mandible. Results showed that unilateral bite force outputs are least affected by the relative ratios of the balancing and working muscles, but only ratios above 0.5 provided balancing-working side joint reaction force relationships that are consistent with experimental data. The constraints modeled at the bite point had the greatest effect on bite force output, but the most appropriate constraint may depend on the study question. Strain energy is least affected by variation in bite point constraint, but larger variations in strain energy values are observed in models with different number of tetrahedral elements, masticatory muscle ratios and muscle subgroups present, and number of material properties. These findings indicate that performance measures are differentially affected by variation in initial model parameters. In the absence of validated input values, FE models can nevertheless provide robust comparisons if these parameters are standardized within a given study to minimize variation that arise during the model-building process. Sensitivity tests incorporated into the study design not only aid in the interpretation of simulation results, but can also provide additional insights on form and function.