Validating a voxel-based finite element model of a human mandible using digital speckle pattern interferometry

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

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

Validation of Experimental and Finite Element Biomechanical Evaluation of Human Cadaveric Mandibles

Background: Biomechanical analysis of human mandible is important not only to understand mechanical behavior and structural properties, but also to diagnose and develop treatment options for mandibular disorders. Therefore, the objective of this research was to generate analytical and experimental data on mandibles, construct custom 3D models, and compare the analytically derived maximum strains with strain gage data in five areas of interest for each mandible. Methods: We investigated the surface strains in the cadaveric human mandibles under different configurations of cyclic compressive loads in an experimental setting and compared these experimental strain data with results derived from computational finite element analysis (FEA), accurately replicating the experiments. Strains on the surface of each mandible were measured with strain gauges, and subsequently a subject-specific finite element (FE) volume mesh was generated from computed tomography (CT) scans of each mandible. Strain patterns of each mandible were derived from the FEA simulating the experimental setup and matched with the experimental data. Findings: Analysis of experimental data showed that strain as measured at the condylar locations was significantly different from those at other locations on the mandible, and that the sex and age of the subject did not have a significant correlation with the strain. Comparing the FE numerical predictions with the experimental data, we found a good statistical correlation and statistical agreement between in-vitro measurements and FE results. Interpretation: The study demonstrates that our methodology of generating subject-specific FE models is a valid and accurate, non-invasive method to evaluate the complex biomechanical behavior of human mandibles.

Design and Finite Element Analysis of Patient-Specific Total Temporomandibular Joint Implants

In this manuscript, we discuss our approach to developing novel patient-specific total TMJ prostheses. Our unique patient-fitted designs based on medical images of the patient’s TMJ offer accurate anatomical fit, and better fixation to host bone. Special features of the prostheses have potential to offer improved osseo-integration and durability of the devices. The design process is based on surgeon’s requirements, feedback, and pre-surgical planning to ensure anatomically accurate and clinically viable device design. We use the validated methodology of FE modeling and analysis to evaluate the device design by investigating stress and strain profiles under functional/normal and para-functional/worst-case TMJ loading scenarios.

Experimental validation of a voxel-based finite element model simulating femoroplasty of lytic lesions in the proximal femur

Femoroplasty is a procedure where bone cement is injected percutaneously into a weakened proximal femur. Uncertainty exists whether femoroplasty provides sufficient mechanical strengthening to prevent fractures in patients with femoral bone metastases. Finite element models are promising tools to evaluate the mechanical effectiveness of femoroplasty, but a thorough validation is required. This study validated a voxel-based finite element model against experimental data from eight pairs of human cadaver femurs with artificial metastatic lesions. One femur from each pair was left untreated, while the contralateral femur was augmented with bone cement. Finite element models accurately predicted the femoral strength in the defect (R² = 0.96) and augmented (R² = 0.93) femurs. The modelled surface strain distributions showed a good qualitative match with results from digital image correlation; yet, quantitatively, only moderate correlation coefficients were found for the defect (mean R² = 0.78) and augmented (mean R² = 0.76) femurs. This was attributed to the presence of vessel holes in the femurs and the jagged surface representation of our voxel-based models. Despite some inaccuracies in the surface measurements, the FE models accurately predicted the global bone strength and qualitative deformation behavior, both before and after femoroplasty. Hence, they can offer a useful biomechanical tool to assist clinicians in assessing the need for prophylactic augmentation in patients with metastatic bone disease, as well as in identifying suitable patients for femoroplasty.

Effect of crown-to-implant ratio and crown height space on marginal bone stress: a finite element analysis

BACKGROUND

Crown-to-implant ratio and crown height space, associated with the use of short implants, have been related with marginal bone loss. However, it is unclear which of the two entities would play the most important role on the bone remodelling process. Using a finite element analysis, the present work aims to help clarifying how those two factors contribute for the stress generation at the marginal bone level. A numerical model (reference model), with a crown-to-implant ratio of 4, was double validated and submitted to a numerical calculation. Then, it was modified in two different ways: (a) by decreasing the prosthetic height obtaining crown-to-implant ratios of 3, 2.5 and 2 and (b) by increasing the implants length obtaining a crown-to-implant ratio of 2.08. The new models were also submitted to numerical calculations.

RESULTS

The reference model showed a marginal bone stress of 96.9 MPa. The increase in the implants' length did not show statistically significant differences in the marginal bone stress (p-value = 0.2364). The decrease in the prosthetic height was accompanied with a statistically significant decrease in the marginal bone stresses (p-value = 2.2e- 16).

CONCLUSIONS

The results represent a paradigm change as the crown height space appears to be more responsible for marginal bone stress than the high crown-to-implant ratios or the implants' length. New prosthetic designs should be attempted to decrease the stress generated at the marginal bone level.

3D Printing Experimental Validation of the Finite Element Analysis of the Maxillofacial Model

Contacts used in finite element (FE) models were considered as the best simulation for interactions in the temporomandibular joint (TMJ). However, the precision of simulations should be validated through experiments. Three-dimensional (3D) printing models with the high geometric and loading similarities of the individuals were used in the validation. This study aimed to validate the FE models of the TMJ using 3D printing models. Five asymptomatic subjects were recruited in this study. 3D models of mandible, disc, and maxilla were reconstructed according to cone-beam CT (CBCT) image data. PLA was chosen for 3D printing models from bottom to top. Five pressure forces corresponding to the central occlusion were applied to the 3D printing models. Ten strain rosettes were distributed on the mandible to record the horizontal and vertical strains. Contact was used in the FE models with the same geometries, material properties, loadings, and boundary conditions as 3D printing models to simulate the interaction of the disc-condyle, disc-temporal bone, and upper-lower dentition. The differences of the simulated and experimental results for each sample were less than 5% (maximum 4.92%) under all five loadings. In conclusion, it was accurate to use contact to simulate the interactions in TMJs and upper-lower dentition.

Patient-specific finite element models of the human mandible: Lack of consensus on current set-ups

The use of finite element analysis (FEA) has increased rapidly over the last decennia and has become a popular tool to design implants, osteosynthesis plates and prostheses. With increasing computer capacity and the availability of software applications, it has become easier to employ the FEA. However, there seems to be no consensus on the input variables that should be applied to representative FEA models of the human mandible. This review aims to find a consensus on how to define the representative input factors for a FEA model of the human mandible. A literature search carried out in the PubMed and Embase database resulted in 137 matches. Seven papers were included in this current study. Within the search results, only a few FEA models had been validated. The material properties and FEA approaches varied considerably, and the available validations are not strong enough for a general consensus. Further validations are required, preferably using the same measuring workflow to obtain insight into the broad array of mandibular variations. A lot of work is still required to establish validated FEA settings and to prevent assumptions when it comes to FEA applications.

Comparison of conventional methods of simultaneous intrusion and retraction of maxillary anterior: a finite element analysis

OBJECTIVE

To study the biomechanical effects of the three-piece intrusion arch and Kalra simultaneous intrusion and retraction arch (K-SIR) on simultaneous intrusion and retraction of maxillary anterior teeth.

DESIGN

Three-dimensional analysis of stresses and displacement of the anterior and posterior teeth with the three-piece intrusion arch and K-SIR arch was done using the finite element method (FEM).

SETTING

Department of Orthodontics, Surendera Dental College and Research Institute, India.

MATERIAL AND METHODS

For this investigation, the geometric model of the maxilla was constructed using a computed tomography scan. 0.022 × 0.028-inch MBT brackets and molar tubes were modelled, with the specified tip and torque values for all maxillary teeth. The wire components for the three-piece intrusion arch and K-SIR arch were modelled initially as a line diagram and then converted to three dimensional models. The material characteristics which include the Young's modulus and Poisson's ratio were assigned. After defining the boundary conditions, force systems were applied as per design. The analysis was carried out using ANSYS Version 12.1 software. The von Mises stress, principal stress on PDL and alveolar bone, change in the inclination of incisors and initial displacement of the teeth in bucco-palatal, mesio- distal and vertical direction were analysed.

RESULTS

Stresses in cortical bone were greater than cancellous. Both modalities showed intrusion of the anterior teeth, although this was slightly more in the three- piece intrusion arch. On studying the principal stresses in the PDL, the three-piece intrusion arch displayed uniform stress distribution compared to K-SIR arch.

CONCLUSION

The FEM cannot reflect actual biological responses within the human body to orthodontic forces but based on these findings, the three-piece intrusion arch showed better stress distribution and controlled tooth movement than the K-SIR arch.

An Investigation of Two Finite Element Modeling Solutions for Biomechanical Simulation Using a Case Study of a Mandibular Bone

The method used in biomechanical modeling for finite element method (FEM) analysis needs to deliver accurate results. There are currently two solutions used in FEM modeling for biomedical model of human bone from computerized tomography (CT) images: one is based on a triangular mesh and the other is based on the parametric surface model and is more popular in practice. The outline and modeling procedures for the two solutions are compared and analyzed. Using a mandibular bone as an example, several key modeling steps are then discussed in detail, and the FEM calculation was conducted. Numerical calculation results based on the models derived from the two methods, including stress, strain, and displacement, are compared and evaluated in relation to accuracy and validity. Moreover, a comprehensive comparison of the two solutions is listed. The parametric surface based method is more helpful when using powerful design tools in computer-aided design (CAD) software, but the triangular mesh based method is more robust and efficient.

Digital reconstruction of the Ceprano calvarium (Italy), and implications for its interpretation

The Ceprano calvarium was discovered in fragments on March 1994 near the town of Ceprano in southern Latium (Italy), embedded in Middle Pleistocene layers. After reconstruction, its morphological features suggests that the specimen belongs to an archaic variant of H. heidelbergensis, representing a proxy for the last common ancestor of the diverging clades that respectively led to H. neanderthalensis and H. sapiens. Unfortunately, the calvarium was taphonomically damaged. The postero-lateral vault, in particular, appears deformed and this postmortem damage may have influenced previous interpretations. Specifically, there is a depression on the fragmented left parietal, while the right cranial wall is warped and angulated. This deformation affected the shape of the occipital squama, producing an inclination of the transverse occipital torus. In this paper, after X-ray microtomography (μCT) of both the calvarium and several additional fragments, we analyze consistency and pattern of the taphonomic deformation that affected the specimen, before the computer-assisted retrodeformation has been performed; this has also provided the opportunity to reappraise early attempts at restoration. As a result, we offer a revised interpretation for the Ceprano calvarium’s original shape, now free from the previous uncertainties, along with insight for its complex depositional and taphonomic history.

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

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

Structural organization and tooth development in a Homo aff. erectus juvenile mandible from the Early Pleistocene site of Garba IV at Melka Kunture, Ethiopian highlands

OBJECTIVES

The immature partial mandible GAR IVE from the c. 1.7 Ma old Garba IV site at Melka Kunture (Upper Awash Basin, Ethiopia), the earliest human representative from a mountain-like environment, represents one of the oldest early Homo specimens bearing a mixed dentition. Following its first description (Condemi, ), we extended the analytical and comparative record of this specimen by providing unreported details about its inner morphology, tooth maturational pattern and age at death, crown size, and tooth tissue proportions.

MATERIALS AND METHODS

The new body of quantitative structural information and virtual imaging derives from a medical CT record performed in 2013.

RESULTS

Compared to the extant human condition and to some fossil representatives of comparable individual age, the GAR IVE mandible reveals absolutely and relatively thick cortical bone. Crown size of the permanent lateral incisor and the canine fit the estimates of H. erectus s.l., while the dm2 and the M1 more closely approach those of H. habilis-rudolfensis. Molar crown pulp volumes are lower than reported in other fossil specimens and in extant humans. The mineralization sequence of the permanent tooth elements is represented four times in our reference sample of extant immature individuals (N = 795).

CONCLUSIONS

The tooth developmental pattern displayed by the immature individual from Garba IV falls within the range of variation of extant human populations and is also comparable with that of other very young early fossil hominins. Taken together, the evidence presented here for mandibular morphology and dental development suggest GAR IVE is a robust 2.5- to 3.5-year old early Homo specimen.

A new condyle implant design concept for an alloplastic temporomandibular joint in bone resorption cases

The purpose of this article is to present and evaluate an innovative intramedullary implant concept developed for total alloplastic reconstruction in bone resorption cases. The main goal of this innovative concept is to avoid the main problems experienced with temporomandibular (TMJ) devices on the market, associated with bone fixation and changes in kinematics. A three-dimensional finite element model was developed based on computed tomography (CT) scan images, before and after implantation of the innovative implant concept. To validate the numerical model, a clean cadaveric condyle was instrumented with four rosettes and loaded before and after implantation with the innovative concept TMJ implant. The experimental results validate the numerical models comparing the intact and implanted condyles, as they present good correlation. They show that the most critical region is around rosette #1, with an increase in strains in the proximal region of the condyle of 140%. The maximum principal strain and stress generated with the implant is less than 2200 με and 75 MPa in the posterior region of the cortical bone. Shortly after insertion of this press-fit implant, stress and strain results appear to be within the normal limits and show some similarities with the intact condyle. If these responses do not change over time, the screw fixation used at present could be avoided or replaced. This solution reduces bone resection and lessens surgical damage to the muscles.

Experimental and numerical predictions of Biomet(®) alloplastic implant in a cadaveric mandibular ramus

The purpose of this study was to evaluate experimentally the behaviors of an intact and an implanted cadaveric ramus, to compare and analyze load mechanism transfers between two validated finite element models. The intact, clean cadaveric ramus was instrumented with four rosettes and loaded with the temporal reaction load. Next, the Biomet microfixation implant was fixed to the same cadaveric mandibular ramus after resection. The mandibular ramus was reconstructed from computed tomographic images, and two finite element models were developed. The experimental results for the mandibular ramus present a linear behavior of up to 300 N load in the condyle, with the Biomet implant influencing strain distribution; the maximum influence was near the implant (rosette #4) and approximately 59%. The experimental and numerical results present a good correlation, with the best correlation in the intact ramus condition, where R(2) reaches 0.935 and the slope of the regression line is 1.045. The numerical results show that screw #1 is the most critical, with maximum principal strains in the bone around 21,000 με, indicating possible bone fatigue and fracture. The experimental results show that the Biomet temporomandibular joint mandibular ramus implant changes the load transfer in the ramus, compared to the intact ramus, with its strain-shielding effect. The numerical results demonstrate that only three screws are important for the Biomet TMJ fixation. These results indicate that including two proximal screws should reduce stresses in the first screws and strains in the bone.

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 stock alloplastic temporomandibular joint implant can influence the behavior of the opposite native joint: A numerical study

PURPOSE

The objective of the study was to investigate the effect of total stock temporomandibular implants on load mechanisms in both condyles in a specific patient. The patient presented with a disc with wear, and the introduction of a total temporomandibular prosthesis was simulated to compare the articular behavior.

MATERIAL AND METHODS

Based on specific patient computed tomographic images, two finite element models were created: one model with two intact temporomandibular joints (one joint with pathology), and other model with one implanted joint. The simulations considered the five most important muscles acting in the mandible, and it was possible to evaluate the biomechanical changes in the structures (skull, mandible, and articular disc).

RESULTS

The results revealed more load transfer in the opposite condyle than in the damaged one; the insertion of a total temporomandibular implant changed the load transfer to the opposite condyle. There was decreased stress in the disc by about 50% and increased strain distribution. In the mandibular condyle with implant, the screw fixation is critical, with minimum strain around -9430 με for first screw position. In the cranium, the implant changed the bone strains with a minimum principal strain observed around -2500 με in six screw positions.

CONCLUSION

This study indicates that replacing the damaged joint by an implant in an ideal position will improve joint position and consequently redistribute the loads. The study findings provide strong evidence that placing an implant on one side of the mandible will affect the load distribution on that structure and particularly on the opposite side. The temporomandibular joint changes condyle movement; with an implanted condyle, the movement is almost blocked.

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.

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.

Bite of the cats: relationships between functional integration and mechanical performance as revealed by mandible geometry

Cat-like carnivorous mammals represent a relatively homogeneous group of species whose morphology appears constrained by exclusive adaptations for meat eating. We present the most comprehensive data set of extant and extinct cat-like species to test for evolutionary transformations in size, shape and mechanical performance, that is, von Mises stress and surface traction, of the mandible. Size and shape were both quantified by means of geometric morphometrics, whereas mechanical performance was assessed applying finite element models to 2D geometry of the mandible. Additionally, we present the first almost complete composite phylogeny of cat-like carnivorans for which well-preserved mandibles are known, including representatives of 35 extant and 59 extinct species of Felidae, Nimravidae, and Barbourofelidae. This phylogeny was used to test morphological differentiation, allometry, and covariation of mandible parts within and among clades. After taking phylogeny into account, we found that both allometry and mechanical variables exhibit a significant impact on mandible shape. We also tested whether mechanical performance was linked to morphological integration. Mechanical stress at the coronoid process is higher in sabertoothed cats than in any other clade. This is strongly related to the high degree of covariation within modules of sabertooths mandibles. We found significant correlation between integration at the clade level and per-clade averaged stress values, on both original data and by partialling out interclade allometry from shapes when calculating integration. This suggests a strong interaction between natural selection and the evolution of developmental and functional modules at the clade level.

Influences of implant condyle geometry on bone and screw strains in a temporomandibular implant

A 3D finite element model of an in vitro implanted mandible was analysed. The load point was placed on the condyle in three positions (inside the mouth, centred and outside) to simulate different contact points between the mandible condyle and the temporal bone. The strain fields in the condyle were assessed and detailed around the surgical screws. The temporomandibular implant studied here was modelled on a commercial device that uses four screws to fix it in vivo in a very similar position. The boundary conditions of the numerical model simulated a load on the incisors with a 15 mm mouth aperture. The same contact loads were applied to the two condyles. Numerical results were successfully obtained for the three different contact points: the inside contact produced lower strains on the condyle. The first screw created a critical strain distribution in the bone, just under the screw. The study shows that centred and inside contact induces lower strain distributions. This suggests that spherical condyle geometry should be applied in order to reduce the strains in fixation. As the top screw was observed to play the most critical role, the third screw is in fact unnecessary, since the lower strain distribution suggests that it will be loosened.

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.

Do erupted third molars weaken the mandibular angle after trauma to the chin region? A 3D finite element study

It has been suggested that third molars increase mandibular fragility because they do not contribute to its strength. For ethical reasons, a human study design that would permit the elucidation of this interference is not possible. This study evaluated the impact of the presence of erupted third molars on the mandibular angle of resistance when submitted to trauma. A three-dimensional (3D) mandibular model was obtained through finite element methodology using computed tomography (CT) with the geometry and mechanical properties to reproduce a normal mandibular structure. Human mandibles with no, one or two erupted third molars were evaluated. Whenever the third molar was present there was a greater concentration of tensions around the cervical part of its alveolus. Approximated Von Mises equivalent stress of the third molar region was 107.035 MPa in the mandible with teeth and 64.6948 MPa in the mandible without teeth. In the condylar region it was 151.65 MPa when the third molar was present and 184.496 MPa when it was absent. The digital models created proved that the mandibular angle becomes more fragile in the presence of third molars. When they are absent the energy concentrates on the lateral e posterior aspect of the condylar neck.

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

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

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

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

Full-field optical deformation measurement in biomechanics: digital speckle pattern interferometry and 3D digital image correlation applied to bird beaks

In this paper two easy-to-use optical setups for the validation of biomechanical finite element (FE) models are presented. First, we show an easy-to-build Michelson digital speckle pattern interferometer (DSPI) setup, yielding the out-of-plane displacement. We also introduce three-dimensional digital image correlation (3D-DIC), a stereo photogrammetric technique. Both techniques are non-contact and full field, but they differ in nature and have different magnitudes of sensitivity. In this paper we successfully apply both techniques to validate a multi-layered FE model of a small bird beak, a strong but very light biological composite. DSPI can measure very small deformations, with potentially high signal-to-noise ratios. Its high sensitivity, however, results in high stability requirements and makes it hard to use it outside an optical laboratory and on living samples. In addition, large loads have to be divided into small incremental load steps to avoid phase unwrapping errors and speckle de-correlation. 3D-DIC needs much larger displacements, but automatically yields the strains. It is more flexible, does not have stability requirements, and can easily be used as an optical strain gage.

Modeling the human mandible under masticatory loads: which input variables are important?

Finite element analyses (FEA) that have simulated masticatory loadings of the human mandible differ significantly with regard to their basic input variables such as material properties, constraints, and applied forces. With sensitivity analyses it is possible to assess how the choice of different input values and the degree of model simplification affect FEA results. However, published FEA studies are rarely accompanied by sensitivity analyses so that the robusticity of their results is impossible to assess. Here, we conduct a sensitivity analysis with an FE model of a human mandible to quantify the relative importance of several modeling decisions: (1) the material properties assigned to the cancellous bone tissue; (2) the inclusion or not of the periodontal ligament; (3) the constraints at the joints and bite point; and (4) the orientation of applied muscle forces. We study the effects of varying these properties by analysing the strain magnitudes and directions across the model surface. In addition, we perform a geometric morphometric analysis of the deformation resulting from the loading of each model. The results show that the effects of altering the different model properties can be significant and that most effects are potentially large enough to cause problems for the biological interpretation of FEA results. We therefore recommend that researchers conduct more sensitivity analyses than at present to assess the robusticity of their FEA results and their biological conclusions.

Human skull shape and masticatory induced stress: Objective comparison through the use of non-rigid registration

Variation in masticatory induced stress, caused by shape changes in the human skull, is quantified in this article. A comparison on masticatory induced stress is presented subject to a variation in human skull shape. Non-rigid registration is employed to obtain appropriate computational domain representations. This procedure allows the isolation of shape from other variations that could affect the results. An added benefit, revealed through the use of non-rigid registration to acquire appropriate domain representation, is the possibility of direct and objective comparison and manipulation. The effect of mapping uncertainty on the direct comparison is also quantified. As shown in this study, exact difference values are not necessarily obtained, but a non-rigid map between subject shapes and numerical results gives an objective indication on the location of differences.

A comparison of methods to evaluate the behavior of finite element models with rough surfaces

Finite element (FE) modeling of rough surfaces is becoming increasingly common. However, the quality of the assumptions being made in these models, and thus the quality of the models themselves, is often unclear. Decisions about the geometry of the surface to be modeled, including the size of the surface to be modeled, the lateral resolution of the measured surface data to be used, and the formulation of the probabilistic surface to be used, can have a significant effect on a model's behavior. Similarly, varying model parameters, including the FE mesh density, can change the results by a factor of three or more. This work examines some of the metrics that can be used to evaluate the influence of these assumptions and parameters on FE models with rough surfaces and discusses the relative merits of each option. In particular, qualitative comparison of result plots, quantitative comparison and convergence of results parameters, qualitative and quantitative comparison of distributions of result values over various model dimensions, and more sophisticated comparison techniques inspired by image and signal processing are discussed.

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.

Why do humans have chins? Testing the mechanical significance of modern human symphyseal morphology with finite element analysis

The modern human mandibular symphysis differs from those of all other primates in being vertically orientated and possessing a chin, but the functional significance of this unique morphology is not well understood. Some hypotheses propose that it is an adaptation to specific loads occurring during masticatory function. This study uses finite element analysis to examine these symphyseal loads in a model of a modern human mandible. By modifying the symphyseal cross-sectional form, the mechanical significance of the presence of the chin and symphyseal orientation is tested, and modern human and Neanderthal symphyseal cross-sections are compared with regard to their ability to withstand different loads. The results show that changes in symphyseal form have profound effects on the strains. The presence of a chin leads to lower symphyseal strains overall, whereas a vertical orientation of the symphysis results in higher strains under wishboning, but not under vertical bending in the coronal plane and dorsoventral shear. Compared to Neanderthals, the modern human symphysis shows higher strains during dorsoventral shear and wishboning, but is as effective as the Neanderthal symphysis in resisting vertical bending in the coronal plane and the loads resulting from simulated incision and unilateral molar biting. In general, the results of this study corroborate prior hypotheses about the mechanical effects of the human chin and vertical symphyseal orientation and support the idea that the relative importance of wishboning and vertical bending in the coronal plane might have played a role in the evolution of modern human symphyseal morphology.

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

It is generally accepted that the periodontal ligament (PDL) plays a crucial role in transferring occlusal forces from the teeth to the alveolar bone. Studies using finite element analysis (FEA) have helped to better understand this role and show that the stresses and strains in the alveolar bone are influenced by whether and how PDL is included in FE models. However, when the overall distribution of stresses and strains in crania and mandibles are of interest, PDL is often not included in FE models, although little is known about how this affects the results. Here we study the effect of representing PDL as a layer of solid material with isotropic homogeneous properties in an FE model of a human mandible using a novel application of geometric morphometrics. The results show that the modelling of the PDL affects the deformation and thus strain magnitudes not only of the alveolar bone around the biting tooth, but that the whole mandible deforms differently under load. As a result, the strain in the mandibular corpus is significantly increased when PDL is included, while the strain in the bone beneath the biting tooth is reduced. These results indicate the importance of the PDL in FE studies. Thus we recommend that the PDL should be included in FE models of the masticatory apparatus, with tests to assess the sensitivity of the results to changes in the Young's modulus of the PDL material.

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

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

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

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

Considerations for the incorporation of measured surfaces in finite element models

This work discusses some of the benefits, techniques, challenges, and considerations associated with the incorporation of measured surfaces in finite element (FE) models including how much surface data to measure and import into the model, the shape of the surface geometry to create, the presence and effect of surface layers and impurities, the required mesh density for rough surfaces, the nature of the element formulations and material properties at small length scales, the differences between measurement and FE coordinate systems, the limitations and idealizations of the FE method, issues associated with boundary conditions and their ability to impose or prevent conformal contact, and issues associated with the size of the pinball region and the contact stiffness relative to the nature of the surface. It also describes some current and future research directions that can be used to validate and expand existing techniques and to improve our understanding of surface phenomena.