The effects of the periodontal ligament on mandibular stiffness: a study combining finite element analysis and geometric morphometrics

A new biomechanical model of the mammal jaw based on load path analysis

The primary function of the tetrapod jaw is to transmit jaw muscle forces to bite points. The routes of force transfer in the jaw have never been studied but can be quantified using load paths - the shortest, stiffest routes from regions of force application to support constraints. Here, we use load path analysis to map force transfer from muscle attachments to bite point and jaw joint, and to evaluate how different configurations of trabecular and cortical bone affect load paths. We created three models of the mandible of the Virginia opossum, Didelphis virginiana, each with a cortical bone shell, but with different material properties for the internal spaces: (1) a cortical-trabecular model, in which the interior space is modeled with bulk properties of trabecular bone; (2) a cortical-hollow model, in which trabeculae and mandibular canal are modeled as hollow; and (3) a solid-cortical model, in which the interior is modeled as cortical bone. The models were compared with published in vivo bite force and bone strain data, and the load paths calculated for each model. The trabecular model, which is preferred because it most closely approximates the actual morphology, was best validated by in vivo data. In all three models, the load path was confined to cortical bone, although its route within the cortex varied depending on the material properties of the inner model. Our analysis shows that most of the force is transferred through the cortical, rather than trabecular bone, and highlights the potential of load path analysis for understanding form-function relationships in the skeleton.

Is the distribution of cortical bone in the mandibular corpus and symphysis linked to loading environment in modern humans? A systematic review

OBJECTIVE

The human mandible is a unique bone with specific external and internal morphological characteristics, influenced by a complex and challenging loading environment. Mandibular cortical thickness distribution in cross-sections is reported to be related to facial divergence patterns, cultural and dietary habits and more generally, specific loading environment. This review hypothesises that a process of environmental mechanical sensitivity is involved in the distribution of cortical bone in the mandibular corpus and symphysis in modern humans, and that loading regimes can influence this distribution pattern. Based on a review of the recent literature, this study aims to answer the following question: "Is the distribution of cortical bone in the mandibular corpus and symphysis linked to the loading environment in modern humans?"

DESIGN

A systematic review was undertaken using the PubMed/Medline, Scopus and Cochrane Library databases for publications from 1984 to 2022 investigating the relationship between cortical bone distribution in the mandibular corpus and the loading environment. A subgroup meta-analysis was performed to determine the overall effect of facial divergence on cortical thickness.

RESULTS

From a total of 2791 studies, 20 fulfilled the inclusion criteria. The meta-analyses were performed in eight studies using a randomised model, finding a significant overall effect of facial divergence on cortical thickness in posterior areas of the mandible (p < 0.01).

CONCLUSIONS

Within the limitations of this review, specific loading regimes and their consequent variables (diet, culture, facial divergence) were linked to cortical thickness distribution. Sex was found to be unrelated to cortical thickness pattern.

The effects of material and structural properties of the periodontal ligament in mechanical function of tooth-PDL-bone complex in dental trauma: A sensitivity study using finiteelement analysis

Periodontal ligament (PDL) plays a crucial role in transferring load from tooth to its adjacent bone, and its role is more pronounced in case of trauma, due to its shock-absorbing character, which has not been fully understood yet. Different constitutive models have correlated mechanical function of PDL with its anisotropic, inhomogeneous, non-linear elastic nature, and it was variably modeled using Finite Element (FE) simulations of dental trauma. Furthermore, since capturing accurate dimension of PDL is difficult, various thicknesses were considered for PDL in FE reconstruction process. In this study, the sensitivity of FE analyses to variation in mechanical properties, including a large range of elastic properties for a linear elastic model, also a hyper-elastic material model, and various thicknesses of PDL was investigated by developing a CT-based FE model of tooth-PDL-bone complex. Results of this study highlighted the crucial role of PDL in absorption and dissipation of energy, as well as in stress distribution within alveolar bone during dental trauma. It was observed that as Young's modulus of PDL decreases and its thickness increases, its shock-absorbing capacity would be escalated. Moreover, it was found that inclusion of PDL reduces the maximum von Mises stress exerted on the alveolar bone by about 60% in some areas, compared to the case in which the PDL is absent. Results of this work underscore the need of presenting comprehensive constitutive models to describe mechanical behavior of PDL, with the goal of understanding the behavior of a tooth-PDL-bone complex in pathological conditions, such as trauma.

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.

Finite Element Analysis of the Mechanical Performance of Non-Restorable Crownless Primary Molars Restored with Intracoronal Core-Supported Crowns: A Proposed Treatment Alternative to Extraction for Severe Early Childhood Caries

Early childhood caries (ECC) involve extensive coronal tooth structure loss, and tooth reconstruction remains highly challenging. To fulfill preclinical assessment, the present study investigated the biomechanics of non-restorable crownless primary molars that were restored by stainless steel crowns (SSC) using different composite core build-up materials. Computer-aided design-integrated 3D finite element and modified Goodman fatigue analyses were performed to determine stress distribution, risk of failure, fatigue life and dentine-material interfacial strength for the restored crownless primary molars. A dual-cured resin composite (MultiCore Flow), a light-cured bulk-fill resin composite (Filtek Bulk Fill posterior), a resin-modified glass-ionomer cement (Fuji II LC) and a nano-filled resin-modified glass-ionomer cement (NRMGIC; Ketac N100) were used as core build-up composite materials in the simulated models. The finite element analysis showed that types of core build-up materials affected the maximum von Mises stress only in the core materials (p-value = 0.0339). NRMGIC demonstrated the lowest von Mises stresses and revealed the highest minimum safety factor. The weakest sites were along the central grooves regardless of type of material, and the ratio of shear bond strength to maximum shear stress at the core-dentine interface of the NRMGIC group was lowest among the tested composite cores. However, all groups provided lifetime longevity from the fatigue analysis. In conclusion, core build-up materials differentially influenced the von Mises stress (magnitude and distribution) and the safety factor in crownless primary molars restored with core-supported SSC. However, all materials and the remaining dentine of crownless primary molars provided lifetime longevity. The reconstruction by core-supported SSC, as an alternative to tooth extraction, may successfully restore non-restorable crownless primary molars without unfavorable failures throughout their lifespan. Further clinical studies are required to evaluate the clinical performance and suitability of this proposed method.

Comparative evaluation of a patient-specific customised plate designs and screws for partial mandibular reconstruction

Mandibles with odontogenic tumors are often partially reconstructed with a metallic bone graft analogue with dental roots, crowns, along with a customized plate fixed with monocortical or bicortical screws, following resection of the tumor. In this study, two different designs of patient specific customized Ti reconstruction plates, solid and plate with holes, were considered. Fixation through both bicortical and monocortical screw types were investigated. FE models of the reconstructed mandibles were developed to analyse the influence of the plate-screw type combination on the load transfer across the mandibles under a mastication cycle. The effective homogenized orthotropic material properties of the lattice structures with 0.6 mm fibre diameter with 0.5 mm inter-fibre space were assigned to material properties for the bone graft analogue. The study shows that the combination of plate and screw types influences the state of stresses in the reconstructed mandible. Based on the results of this patient specific study, following resection of the tumor, either solid Ti plate with bicortical screws or Ti plate with holes along with monocortical screws may be used for partial mandibulectomy. It should also be noted that stresses in none of the plates or screws exceeded the yield limit for Ti under the mastication cycle indicating that the components are safe for mandibular reconstruction. However, the choice of this combination of reconstruction plates and screws is dependant on the condition and severity of the tumor in the diseased mandible.

The biomechanical significance of the elongated rodent incisor root in the mandible during incision

Rodents are characterised by a distinctive masticatory apparatus which includes a single pair of enlarged and continually growing incisors. This morphology, termed diprotodonty, has also independently evolved in a number of other mammals, including the aye-aye. This study examined the functional significance of the internal "root" of the elongated rodent-like incisor. The mandibles of four rodents and an aye-aye were modelled to exhibit incrementally shorter incisor roots. Finite element analysis was used to predict stress and strain patterns across the jaw to determine whether the length of the incisor root contributes to the resistance of mechanical forces encountered in the mandible during incision. It was found that von Mises stresses increase in the region of the mandible local to where the incisor is removed, but that the stress distribution across the wider mandible is only minimally affected. Thus, the long internal incisor appears to play a small role in resisting bending forces close to the incisor alveolus, and may act with the arch-like mandibular shape to strengthen the mandible in this region. However, the impact across the whole mandible is relatively limited, suggesting the highly elongate incisor in diprotodont mammals may be principally driven by other factors such as rapid incisor wear.

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.

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.

Stress influence on orthodontic system components under simulated treatment loadings

BACKGROUND AND OBJECTIVE

Mini-implants have been developed and effectively used by clinicians as anchorage for orthodontic tooth movement. The objective of this study was to elucidate the stress response of orthodontic forces on the periodontal system, bone tissues, mini-implant and the bracket-enamel interface.

METHODS

Computer tomography images of a commercially available mini-implant, an orthodontic bracket bonded to a central incisor, and jawbone section models were used to reconstruct three dimensional computer models. These models were exported and meshed in an ABAQUS^Ⓡ finite-element package. Material properties, multi-segment interactions, boundary and loading conditions were then applied to each component. Finite-element analyses were conducted to elucidate the effect of orthodontic force on the equivalent von Mises stress response within the simulated orthodontic system.

RESULTS

The highest stress values in the orthodontic system were predicted at the mini-implant neck, at the interface of the cortical bone, and gradually decreased in the internal apical direction of the miniscrew. On the alveolar bone, the maximum stress values were located in the alveolar cortical bone near the cervical areas of the mini-implant, which is in line with clinical findings of area where bone loss was found post orthodontic tooth treatment. Another peak of von Mises stress response was found in the enamel bracket junction with a maximum up to 186.05 MPa. To ensure good bonding between the enamel and bracket, it is vital to select carefully the type and amount of bonding materials used in the bracket-enamel interface to assure an appropriate load distribution between the teeth and alveolar bone. The results also revealed the significance of the periodontal ligaments, acting as an intermediate cushion element, in the load transfer mechanism.

CONCLUSIONS

This study is sought to identify the stress response in a simulated orthodontic system to minimize the failure rate of mini-implants and bracket loss during orthodontic treatment.

Investigation of a Modified Novel Technique in Bilateral Sagittal Splitting Osteotomy Fixation: Finite Element Analysis and In Vitro Biomechanical Test

Purpose

To evaluate the biomechanical properties of the modified novel 2-hole monocortical plate fixation (2HMCPf) and traditional 4-hole monocortical plate fixation (4HMCPf) techniques in bilateral sagittal splitting osteotomy (BSSO) synthesis using a finite element analysis (FEA) and an in vitro biomechanical test with the application of a shearing loading force on a sawbone mandible model.

Materials and Methods

A three-dimensional mandible models were generated using the geometry obtained from the computerized tomography image of a sawbone mandible. Plates and screws were generated and combined with the mandible in a CAD environment. The 2HMCPf and traditional 4HMCPf techniques for BSSO osteosynthesis were then analyzed under the occlusal load using the FEA. An in vitro biomechanical test was executed to verify the result of FEA. The force on fixation failure and pattern of failure were recorded.

Results

The results revealed that the von Mises Stress on the mandible cortical bone (75.98 MPa) and the screw/plate (457.19 MPa) of the 2HMCPf group was lower than that of the 4HMCPf group (987.68 MPa, 1781.59 MPa). The stress concentrated on the central region of the 4HMCPf group and the distal set of the 2HMCPf group. In vitro study using the sawbone mandible model showed mechanical failure at the region of the proximal segment near the osteotomy site with the 4HMCPf group (average 32.198 N) but no failure on the fixation sites with the 2HMCPf group. Instead, the mandible sawbone fractured on the condyle neck region (average 44.953 N).

Conclusion

From the biomechanical perspective, we proved that the 2HMCPf method was able to withstand a higher shearing loading force than the 4HMCPf fixation method in BSSO osteosynthesis.

Linear Momenta Transferred to the Dental Implant-Bone and Natural Tooth-PDL-Bone Constructs Under Impact Loading: A Comparative in-vitro and in-silico Study

During dental trauma, periodontal ligament (PDL) contributes to the stability of the tooth-PDL-bone structure. When a dental implant is inserted into the bone, the dental implant-bone construct will be more prone to mechanical damage, caused by impact loading, than the tooth-PDL-bone construct. In spite of the prevalence of such traumas, the behavioral differences between these two constructs have not been well-understood yet. The main goal of this study was to compare the momentum transferred to the tooth-PDL-bone and dental implant-bone constructs under impact loading. First, mechanical impact tests were performed on six canine mandibles of intact (N = 3) and implanted (N = 3) specimens using a custom-made drop tower apparatus, from release heights of 1, 2, and 3 cm. Next, computed tomography-based finite element models were developed for both constructs, and the transferred momenta were calculated. The experimental results indicated that, for the release heights of 1, 2, and 3 cm, the linear momenta transferred to the dental implant-bone construct were 33.1, 31.0, and 27.5% greater than those of the tooth-PDL-bone construct, respectively. Moreover, results of finite element simulations were in agreement with those of the experimental tests (error <7.5%). This work tried to elucidate the effects of impact loading on the dental implant-bone and tooth-PDL-bone constructs using both in-vitro tests and validated in-silico simulations. The findings can be employed to modify design of the current generation of dental implants, based on the lessons one can take from the biomechanical behavior of a natural tooth structure.

Broad-scale morpho-functional traits of the mandible suggest no hard food adaptation in the hominin lineage

An on-going debate concerning the dietary adaptations of archaic hominins and early Homo has been fuelled by contradictory inferences obtained using different methodologies. This work presents an extensive comparative sample of 30 extant primate species that was assembled to perform a morpho-functional comparison of these taxa with 12 models corresponding to eight fossil hominin species. Finite Element Analysis and Geometric Morphometrics were employed to analyse chewing biomechanics and mandible morphology to, firstly, establish the variation of this clade, secondly, relate stress and shape variables, and finally, to classify fossil individuals into broad ingesta related hardness categories using a support vector machine algorithm. Our results suggest that some hominins previously assigned as hard food consumers (e.g. the members of the Paranthropus clade) in fact seem to rely more strongly on soft foods, which is consistent with most recent studies using either microwear or stable isotope analyses. By analysing morphometric and stress results in the context of the comparative framework, we conclude that in the hominin clade there were probably no hard-food specialists. Nonetheless, the biomechanical ability to comminute harder items, if required as fallback option, adds to their strategy of increased flexibility.

Load transfer across a mandible during a mastication cycle: The effects of odontogenic tumour

The extent to which load transfer in a diseased mandible with odontogenic tumour might influence the potential risk of pathological fracture has scarcely been investigated. The study sought to investigate the quantitative deviations in load transfer across healthy and cancer-affected (diseased) mandibles having odontogenic tumours. The effect of size of the tumours (small: 9 mm diameter, large: 19 mm diameter), and variation in bone mechanical (elastic) properties of the mandible on load transfer in cancer-affected mandibles during a mastication cycle have been investigated. Based on patient-specific computed tomography-scan datasets, detailed three-dimensional finite element models of healthy and diseased mandibles were developed. High stresses of 25-30 MPa and strains ∼700 µε were observed in the healthy mandible during the right molar bite. However, marginal deviations were observed in principal stress distributions in the diseased mandibles with small- and large-sized tumours, as compared to the healthy mandible. Maximum principal strains of ∼1474 µε were found in the body region adjacent to the symphysis region for small-sized tumour. Whereas for large-sized tumour, maximum strains of ∼2700 µε were observed in the right buccal regions. Reduction in Young's modulus due to different stages of odontogenic tumours had a localised effect on the principal stress distributions, but triggered an abrupt increase in the principal tensile strains. It appears that there is a potential risk of pathological fracture for large-sized odontogenic tumour, owing to high tensile stresses and strains.

Influence of Different Implants on the Biomechanical Behavior of a Tooth-Implant Fixed Partial Dentures: A Three-Dimensional Finite Element Analysis

This study analyzed the biomechanical behavior of rigid and nonrigid tooth-implant supported fixed partial dentures. Different implants were used to observe the load distribution over teeth, implants, and adjacent bone using three-dimensional finite element analysis. A simulation of tooth loss of the first and second right molars was created with an implant placed in the second right molar and a prepared tooth with simulated periodontal ligament (PDL) in the second right premolar. Configurations of two types of implants and their respective abutments-external hexagon (EX) and Morse taper (MT)-were transformed into a 3D format. Metal-ceramic fixed partial dentures were constructed with rigid and nonrigid connections. Mesh generation and data processing were performed on the 3D finite element analysis (FEA) results. Static loading of 50 N (premolar) and 100 N (implant) were applied. When an EX implant was used, with a rigid or nonrigid connection, there was intrusion of the tooth in the distal direction with flexion of the periodontal ligament. Tooth intrusion did not occur when the MT implant was used independent of a rigid or nonrigid connection. The rigid or nonrigid connection resulted in a higher incidence of compressive forces at the cortical bone as well as stress in the abutment/pontic area, regardless of whether EX or MT implants were used. MT implants have a superior biomechanical performance in tooth-implant supported fixed partial dentures. This prevents intrusion of the tooth independent of the connection. Both types of implants studied caused a greater tendency of compressive forces at the crestal area.

The Mechanical Effect of the Periodontal Ligament on Bone Strain Regimes in a Validated Finite Element Model of a Macaque Mandible

The primary anatomical function of the periodontal ligament (PDL) is to attach teeth to their sockets. However, theoretical and constitutive mechanical models have proposed that during mastication the PDL redistributes local occlusal loads and reduces the jaw's resistance to torsional deformations. These hypotheses imply that accurately modeling the PDL's material properties and geometry in finite element analysis (FEA) is a prerequisite to obtaining precise strain and deformation data. Yet, many finite element studies of the human and non-human primate masticatory apparatus exclude the PDL or model it with simplicity, in part due to limitations in μCT/CT scan resolution and material property assignment. Previous studies testing the sensitivity of finite element models (FEMs) to the PDL have yielded contradictory results, however a major limitation of these studies is that FEMs were not validated against in vivo bone strain data. Hence, this study uses a validated and subject specific FEM to assess the effect of the PDL on strain and deformation regimes in the lower jaw of a rhesus macaque (Macaca mulatta) during simulated unilateral post-canine chewing. Our findings demonstrate that the presence of the PDL does influence local and global surface strain magnitudes (principal and shear) in the jaw. However, the PDL's effect is limited (diff. ~200-300 με) in areas away from the alveoli. Our results also show that varying the PDL's Young's Modulus within the range of published values (0.07-1750 MPa) has very little effect on global surface strains. These findings suggest that the mechanical importance of the PDL in FEMs of the mandible during chewing is dependent on the scope of the hypotheses being tested. If researchers are comparing strain gradients across species/taxa, the PDL may be excluded with minimal effect on results, but, if researchers are concerned with absolute strain values, sensitivity analysis is required.

Why ruminating ungulates chew sloppily: Biomechanics discern a phylogenetic pattern

There is considerable debate regarding whether mandibular morphology in ungulates primarily reflects phylogenetic affinities or adaptation to specific diet. In an effort to help resolve this debate, we use three-dimensional finite element analysis (FEA) to assess the biomechanical performance of mandibles in eleven ungulate taxa with well-established but distinct dietary preferences. We found notable differences in the magnitude and the distribution of von Mises stress between Artiodactyla and Perissodactyla, with the latter displaying lower overall stress values. Additionally, within the order Artiodactyla the suborders Ruminantia and Tylopoda showed further distinctive stress patterns. Our data suggest that a strong phylogenetic signal can be detected in biomechanical performance of the ungulate mandible. In general, Perissodactyla have stiffer mandibles than Artiodactyla. This difference is more evident between Perissodactyla and ruminant species. Perissodactyla likely rely more heavily on thoroughly chewing their food upon initial ingestion, which demands higher bite forces and greater stress resistance, while ruminants shift comminution to a later state (rumination) where less mechanical effort is required by the jaw to obtain sufficient disintegration. We therefore suggest that ruminants can afford to chew sloppily regardless of ingesta, while hindgut fermenters cannot. Additionally, our data support a secondary degree of adaptation towards specific diet. We find that mandibular morphologies reflect the masticatory demands of specific ingesta within the orders Artiodactyla and Perissodactyla. Of particular note, stress patterns in the white rhinoceros (C. simum) look more like those of a general grazer than like other rhinoceros’ taxa. Similarly, the camelids (Tylopoda) appear to occupy an intermediate position in the stress patterns, which reflects the more ancestral ruminating system of the Tylopoda.

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.

Biomechanical studies on the effect of iatrogenic dentin removal on vertical root fractures

Introduction

The aim of this study was to understand the mechanism by which iatrogenic root dentin removal influences radicular stress distribution and subsequently affects the resistance to vertical root fractures (VRF) in endodontically treated teeth.

Materials and Methods

The experiments were conducted in two phases. Phase 1: freshly extracted premolar teeth maintained in phosphate-buffered saline were instrumented to simulate three different degrees of dentin removal, designated as low, medium, and extreme groups. Micro-Ct analyzes were performed to quantitatively determine: (a) the amount of dentin removed, (b) the remaining dentin volume, and (c) the moment of inertia of root dentin. The specimens were then subjected to thermomechanical cycling and continuous loading to determine (a) the mechanical load to fracture and (b) dentin microcracking (fractography) using scanning electron microscopy. Phase 2: Finite element analysis was used to evaluate the influence of dentin removal on the stress distribution pattern in root dentin. The data obtained were analyzed using one-way ANOVA and Tukey's post hoc test (P < 0.05).

Results

Phase 1: A significantly greater volume of dentin was removed from teeth in extreme group when compared to low group (P < 0.01). The mechanical analysis showed that the load to fracture was significantly lower in teeth from extreme group (P < 0.05). A linear relationship was observed between the moment of inertia and load to fracture in all experimental groups (R² = 0.52). Fractography showed that most microcracks were initiated from the root canal walls in extreme group. Phase 2: The numerical analysis showed that the radicular stress distribution increased apically and buccolingually with greater degree of root canal dentin removal.

Conclusions

The combined experimental/numerical analyses highlighted the influence of remaining root dentin volume on the radicular bending resistance, stress distribution pattern, and subsequent propensity to VRF.

Approach towards the porous fibrous structure of the periodontal ligament using micro-computerized tomography and finite element analysis

The periodontal ligament (PDL) is a porous and fibrous soft tissue situated around the tooth, which plays a key role in the transmission of loads from the tooth to the alveolar bone of the mandible. Although several studies have tried to characterize its mechanical properties, the behaviour of this tissue is not clear yet. In this study, a new simulation methodology based on a material model which considers the contribution of porous and fibrous structure with different material model formulations depending on the effort direction is proposed. The defined material model was characterized by a non-linear approximation of the porous fibrous matrix to experimental results obtained from samples of similar species and was validated by rigorous test simulations under tensile and compressive loads. The global PDL response was also validated using the parameters of the characterization in a finite element model of full human canine tooth obtained by micro-tomography. The results suggest that the porous contribution has high influence during compression because the bulk modulus of the material depends on the ability of interstitial fluid to drain. On the other hand, the collagen fibres running along the load direction are the main responsible of the ligament stiffness during tensile efforts. Thus, a material model with distinct responses depending of the load direction is proposed. Furthermore, the results suggest the importance of considering 3D finite element models based of the real morphology of human PDL for representing the irregular stress distribution caused by the coupling of complex material models and irregular morphologies.

The biomechanical role of the chondrocranium and sutures in a lizard cranium

The role of soft tissues in skull biomechanics remains poorly understood. Not least, the chondrocranium, the portion of the braincase which persists as cartilage with varying degrees of mineralization. It also remains commonplace to overlook the biomechanical role of sutures despite evidence that they alter strain distribution. Here, we examine the role of both the sutures and the chondrocranium in the South American tegu lizard Salvator merianae We use multi-body dynamics analysis (MDA) to provide realistic loading conditions for anterior and posterior unilateral biting and a detailed finite element model to examine strain magnitude and distribution. We find that strains within the chondrocranium are greatest during anterior biting and are primarily tensile; also that strain within the cranium is not greatly reduced by the presence of the chondrocranium unless it is given the same material properties as bone. This result contradicts previous suggestions that the anterior portion (the nasal septum) acts as a supporting structure. Inclusion of sutures to the cranium model not only increases overall strain magnitudes but also leads to a more complex distribution of tension and compression rather than that of a beam under sagittal bending.

Inclusion of periodontal ligament fibres in mandibular finite element models leads to an increase in alveolar bone strains

Alveolar bone remodelling is vital for the success of dental implants and orthodontic treatments. However, the underlying biomechanical mechanisms, in particular the function of the periodontal ligament (PDL) in bone loading and remodelling, are not well understood. The PDL is a soft fibrous connective tissue that joins the tooth root to the alveolar bone and plays a critical role in the transmission of loads from the tooth to the surrounding bone. However, due to its complex structure, small size and location within the tooth socket it is difficult to study in vivo. Finite element analysis (FEA) is an ideal tool with which to investigate the role of the PDL, however inclusion of the PDL in FE models is complex and time consuming, therefore consideration must be given to how it is included. The aim of this study was to investigate the effects of including the PDL and its fibrous structure in mandibular finite element models. A high-resolution model of a human molar region was created from micro-computed tomography scans. This is the first time that the fibrous structure of the PDL has been included in a model with realistic tooth and bone geometry. The results show that omission of the PDL creates a more rigid model, reducing the strains observed in the mandibular corpus which are of interest when considering mandibular functional morphology. How the PDL is modelled also affects the strains. The inclusion of PDL fibres alters the strains in the mandibular bone, increasing the strains in the tooth socket compared to PDL modelled without fibres. As strains in the alveolar bone are thought to play a key role in bone remodelling during orthodontic tooth movement, future FE analyses aimed at improving our understanding and management of orthodontic treatment should include the fibrous structure of the PDL.

A biomechanical approach to understand the ecomorphological relationship between primate mandibles and diet

The relationship between primate mandibular form and diet has been previously analysed by applying a wide array of techniques and approaches. Nonetheless, most of these studies compared few species and/or infrequently aimed to elucidate function based on an explicit biomechanical framework. In this study, we generated and analysed 31 Finite Element planar models of different primate jaws under different loading scenarios (incisive, canine, premolar and molar bites) to test the hypothesis that there are significant differences in mandibular biomechanical performance due to food categories and/or food hardness. The obtained stress values show that in primates, hard food eaters have stiffer mandibles when compared to those that rely on softer diets. In addition, we find that folivores species have the weakest jaws, whilst omnivores have the strongest mandibles within the order Primates. These results are highly relevant because they show that there is a strong association between mandibular biomechanical performance, mandibular form, food hardness and diet categories and that these associations can be studied using biomechanical techniques rather than focusing solely on morphology.

Finite element analysis of implant-assisted removable partial dentures: Framework design considerations

STATEMENT OF PROBLEM

Connecting an acrylic resin base to both a metal framework and a rigidly fixed implant may affect the rotational displacement of the prosthesis during loading.

PURPOSE

The purpose of this finite element analysis study was to analyze the effect of connecting a denture base metal framework to an implant with the aim of decreasing the rotational movement of an implant-assisted removable partial denture.

MATERIAL AND METHODS

A mesial occlusal rest direct retainer and a distal occlusal rest direct retainer were modeled and adapted to incorporate a modified denture base metal framework in the connection area for each model. The stress and deformation patterns of the prosthesis structure were determined using finite element analysis and compared for both situations.

RESULTS

A maximum von Mises stress of 923 MPa was observed on the metal framework of the prosthesis with a mesial occlusal rest, and the maximum value was 1478 MPa for the distal occlusal rest. A maximum von Mises stress of 17 MPa occurred on the acrylic resin denture base for the mesial occlusal rest, and a maximum von Mises stress of 29 MPa occurred for the distal occlusal rest.

CONCLUSIONS

The distal occlusal rest direct retainer is stiffer than the mesial design and undergoes approximately 66% less deformation. The modified denture base framework with an I-bar and distal occlusal rest design provides more effective support to the acrylic resin structure.

The Effect of Varying Jaw-elevator Muscle Forces on a Finite Element Model of a Human Cranium

Finite element analyses simulating masticatory system loading are increasingly undertaken in primates, hominin fossils and modern humans. Simplifications of models and loadcases are often required given the limits of data and technology. One such area of uncertainty concerns the forces applied to cranial models and their sensitivity to variations in these forces. We assessed the effect of varying force magnitudes among jaw-elevator muscles applied to a finite element model of a human cranium. The model was loaded to simulate incisor and molar bites using different combinations of muscle forces. Symmetric, asymmetric, homogeneous, and heterogeneous muscle activations were simulated by scaling maximal forces. The effects were compared with respect to strain distribution (i.e., modes of deformation) and magnitudes; bite forces and temporomandibular joint (TMJ) reaction forces. Predicted modes of deformation, strain magnitudes and bite forces were directly proportional to total applied muscle force and relatively insensitive to the degree of heterogeneity of muscle activation. However, TMJ reaction forces and mandibular fossa strains decrease and increase on the balancing and working sides according to the degree of asymmetry of loading. These results indicate that when modes, rather than magnitudes, of facial deformation are of interest, errors in applied muscle forces have limited effects. However the degree of asymmetric loading does impact on TMJ reaction forces and mandibular fossa strains. These findings are of particular interest in relation to studies of skeletal and fossil material, where muscle data are not available and estimation of muscle forces from skeletal proxies is prone to error. Anat Rec, 299:828-839, 2016. © 2016 Wiley Periodicals, Inc.

Validity and sensitivity of a human cranial finite element model: implications for comparative studies of biting performance

Finite element analysis (FEA) is a modelling technique increasingly used in anatomical studies investigating skeletal form and function. In the case of the cranium this approach has been applied to both living and fossil taxa to (for example) investigate how form relates to function or infer diet or behaviour. However, FE models of complex musculoskeletal structures always rely on simplified representations because it is impossible completely to image and represent every detail of skeletal morphology, variations in material properties and the complexities of loading at all spatial and temporal scales. The effects of necessary simplifications merit investigation. To this end, this study focuses on one aspect, model geometry, which is particularly pertinent to fossil material where taphonomic processes often destroy the finer details of anatomy or in models built from clinical CTs where the resolution is limited and anatomical details are lost. We manipulated the details of a finite element (FE) model of an adult human male cranium and examined the impact on model performance. First, using digital speckle interferometry, we directly measured strains from the infraorbital region and frontal process of the maxilla of the physical cranium under simplified loading conditions, simulating incisor biting. These measured strains were then compared with predicted values from FE models with simplified geometries that included modifications to model resolution, and how cancellous bone and the thin bones of the circum-nasal and maxillary regions were represented. Distributions of regions of relatively high and low principal strains and principal strain vector magnitudes and directions, predicted by the most detailed FE model, are generally similar to those achieved in vitro. Representing cancellous bone as solid cortical bone lowers strain magnitudes substantially but the mode of deformation of the FE model is relatively constant. In contrast, omitting thin plates of bone in the circum-nasal region affects both mode and magnitude of deformation. Our findings provide a useful frame of reference with regard to the effects of simplifications on the performance of FE models of the cranium and call for caution in the interpretation and comparison of FEA results.

The impact of simplifications on the performance of a finite element model of a Macaca fascicularis cranium

In recent years finite element analysis (FEA) has emerged as a useful tool for the analysis of skeletal form-function relationships. While this approach has obvious appeal for the study of fossil specimens, such material is often fragmentary with disrupted internal architecture and can contain matrix that leads to errors in accurate segmentation. Here we examine the effects of varying the detail of segmentation and material properties of teeth on the performance of a finite element model of a Macaca fascicularis cranium within a comparative functional framework. Cranial deformations were compared using strain maps to assess differences in strain contours and Procrustes size and shape analyses, from geometric morphometrics, were employed to compare large scale deformations. We show that a macaque model subjected to biting can be made solid, and teeth altered in material properties, with minimal impact on large scale modes of deformation. The models clustered tightly by bite point rather than by modeling simplification approach, and fell out as being distinct from another species. However localized fluctuations in predicted strain magnitudes were recorded with different modeling approaches, particularly over the alveolar region. This study indicates that, while any model simplification should be undertaken with care and attention to its effects, future applications of FEA to fossils with unknown internal architecture may produce reliable results with regard to general modes of deformation, even when detail of internal bone architecture cannot be reliably modeled.

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.

Distalization pattern of whole maxillary dentition according to force application points

Objective

The purpose of this study was to observe stress distribution and displacement patterns of the entire maxillary arch with regard to distalizing force vectors applied from interdental miniscrews.

Methods

A standard three-dimensional finite element model was constructed to simulate the maxillary teeth, periodontal ligament, and alveolar process. The displacement of each tooth was calculated on x, y, and z axes, and the von Mises stress distribution was visualized using color-coded scales.

Results

A single distalizing force at the archwire level induced lingual inclination of the anterior segment, and slight intrusive distal tipping of the posterior segment. In contrast, force at the high level of the retraction hook resulted in lingual root movement of the anterior segment, and extrusive distal translation of the posterior segment. As the force application point was located posteriorly along the archwire, the likelihood of extrusive lingual inclination of the anterior segment increased, and the vertical component of the force led to intrusion and buccal tipping of the posterior segment. Rotation of the occlusal plane was dependent on the relationship between the line of force and the possible center of resistance of the entire arch.

Conclusions

Displacement of the entire arch may be dictated by a direct relationship between the center of resistance of the whole arch and the line of action generated between the miniscrews and force application points at the archwire, which makes the total arch movement highly predictable.

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

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

The biomechanical function of periodontal ligament fibres in orthodontic tooth movement

Orthodontic tooth movement occurs as a result of resorption and formation of the alveolar bone due to an applied load, but the stimulus responsible for triggering orthodontic tooth movement remains the subject of debate. It has been suggested that the periodontal ligament (PDL) plays a key role. However, the mechanical function of the PDL in orthodontic tooth movement is not well understood as most mechanical models of the PDL to date have ignored the fibrous structure of the PDL. In this study we use finite element (FE) analysis to investigate the strains in the alveolar bone due to occlusal and orthodontic loads when PDL is modelled as a fibrous structure as compared to modelling PDL as a layer of solid material. The results show that the tension-only nature of the fibres essentially suspends the tooth in the tooth socket and their inclusion in FE models makes a significant difference to both the magnitude and distribution of strains produced in the surrounding bone. The results indicate that the PDL fibres have a very important role in load transfer between the teeth and alveolar bone and should be considered in FE studies investigating the biomechanics of orthodontic tooth movement.

Dental application of novel finite element analysis software for three-dimensional finite element modeling of a dentulous mandible from its computed tomography images

This study focused on the application of novel finite-element analysis software for constructing a finite-element model from the computed tomography data of a human dentulous mandible. The finite-element model is necessary for evaluating the mechanical response of the alveolar part of the mandible, resulting from occlusal force applied to the teeth during biting. Commercially available patient-specific general computed tomography–based finite-element analysis software was solely applied to the finite-element analysis for the extraction of computed tomography data. The mandibular bone with teeth was extracted from the original images. Both the enamel and the dentin were extracted after image processing, and the periodontal ligament was created from the segmented dentin. The constructed finite-element model was reasonably accurate using a total of 234,644 nodes and 1,268,784 tetrahedral and 40,665 shell elements. The elastic moduli of the heterogeneous mandibular bone were determined from the bone density data of the computed tomography images. The results suggested that the software applied in this study is both useful and powerful for creating a more accurate three-dimensional finite-element model of a dentulous mandible from the computed tomography data without the need for any other software.

Ontogeny of material stiffness heterogeneity in the macaque mandibular corpus

Evidence is accumulating that bone material stiffness increases during ontogeny, and the role of elastic modulus in conditioning attributes of strength and toughness is therefore a focus of ongoing investigation. Developmental changes in structural properties of the primate mandible have been documented, but comparatively little is known about changes in material heterogeneity and their impact on biomechanical behavior. We examine a cross-sectional sample of Macaca fascicularis (N = 14) to investigate a series of hypotheses that collectively evaluate whether the patterning of material stiffness (elastic modulus) heterogeneity in the mandible differs among juvenile, subadult and adult individuals. Because differences in age-related activity patterns are known to influence bone stiffness and strength, these data are potentially useful for understanding the relationship between feeding behavior on the one hand and material and structural properties of the mandible on the other. Elastic modulus is shown to be spatially dependent regardless of age, with this dependence being explicable primarily by differences in alveolar versus basal cortical bone. Elastic modulus does not differ consistently between buccal and lingual cortical plates, despite likely differences in the biomechanical milieu of these regions. Since we found only weak support for the hypothesis that the spatial patterning of heterogeneity becomes more predictable with age, accumulated load history may not account for regional differences in bone material properties in mature individuals with respect to the mandibular corpus.

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.

Comparative Study of Two Different Types of Human Mandible Boundary Conditions Used in Finite Element Calculations

The aim of the presented work is compare a two different way of prescribing muscles and chewing force boundary condition. First variant of boundary condition consider muscle forces and their direction taken from literatures. Second variant of boundary condition consider muscles modeled as finite elements connecting lower jaw and skull together. At second variant a muscles material characteristic of Young ́s modulus was changed in range from 1e4 MPa to 2,1e5 MPa. Models of living tissues were created on base of CT images and modeled in 3D CAD software SolidWorks. Calculations were computed in the finite element software ANSYS. Material models were considered as homogenous, isotropic and linearly elastic for all parts. First, both variants of boundary condition were analyzed separately and after that, selected variables (as muscle forces and muscle direction scale factors) from both variant were compared together.

The morphology of the mouse masticatory musculature

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

The importance of accurate muscle modelling for biomechanical analyses: a case study with a lizard skull

Computer-based simulation techniques such as multi-body dynamics analysis are becoming increasingly popular in the field of skull mechanics. Multi-body models can be used for studying the relationships between skull architecture, muscle morphology and feeding performance. However, to be confident in the modelling results, models need to be validated against experimental data, and the effects of uncertainties or inaccuracies in the chosen model attributes need to be assessed with sensitivity analyses. Here, we compare the bite forces predicted by a multi-body model of a lizard (Tupinambis merianae) with in vivo measurements, using anatomical data collected from the same specimen. This subject-specific model predicts bite forces that are very close to the in vivo measurements and also shows a consistent increase in bite force as the bite position is moved posteriorly on the jaw. However, the model is very sensitive to changes in muscle attributes such as fibre length, intrinsic muscle strength and force orientation, with bite force predictions varying considerably when these three variables are altered. We conclude that accurate muscle measurements are crucial to building realistic multi-body models and that subject-specific data should be used whenever possible.

Cranial biomechanics of Diplodocus (Dinosauria, Sauropoda): testing hypotheses of feeding behaviour in an extinct megaherbivore

Sauropod dinosaurs were the largest terrestrial herbivores and pushed at the limits of vertebrate biomechanics and physiology. Sauropods exhibit high craniodental diversity in ecosystems where numerous species co-existed, leading to the hypothesis that this biodiversity is linked to niche subdivision driven by ecological specialisation. Here, we quantitatively investigate feeding behaviour hypotheses for the iconic sauropod Diplodocus. Biomechanical modelling, using finite element analysis, was used to examine the performance of the Diplodocus skull. Three feeding behaviours were modelled: muscle-driven static biting, branch stripping and bark stripping. The skull was found to be 'over engineered' for static biting, overall experiencing low stress with only the dentition enduring high stress. When branch stripping, the skull, similarly, is under low stress, with little appreciable difference between those models. When simulated for bark stripping, the skull experiences far greater stresses, especially in the teeth and at the jaw joint. Therefore, we refute the bark-stripping hypothesis, while the hypotheses of branch stripping and/or precision biting are both consistent with our findings, showing that branch stripping is a biomechanically plausible feeding behaviour for diplodocids. Interestingly, in all simulations, peak stress is observed in the premaxillary-maxillary 'lateral plates', supporting the hypothesis that these structures evolved to dissipate stress induced while feeding. These results lead us to conclude that the aberrant craniodental form of Diplodocus was adapted for food procurement rather than resisting high bite forces.