In-vitro results of rapid maxillary expansion on adults compared with finite element simulations

This study was mainly performed to investigate the effects of high maxillary expansion forces on the skull with fresh and thiel-fixed human skulls. The maxillary suture was not weakened except in one experiment. This study compares the strain measured on the zygomatic process of the skull with the results of a finite element model generated for this purpose. An increasing transversal force was applied on the alveolar process (teeth) until rupture. Strain on the zygomatic process, maxilla displacement and the expanding forces were registered.The results of this study show linear material behaviour of the skull before rupture. The highest stress during the experiments and FE simulation was observed on the alveolar process.Conclusions of this study are the necessity of the existence of appropriate models and that female specimens seem to rupture at a lower force than male ones. Both male and female specimens show a similar linear behaviour in the force/strain curve within each gender group. The probability of maxillary suture opening in adults during ultra-rapid maxillary expansion with tooth anchorage is very low. Complications and unwanted rupture could occur.     

Maxillary expansion treatment using bone anchors: development and validation of a 3D finite element model

OBJECTIVE: Develop a finite element (FE) model of a skull to perform biomechanical studies of maxillary expansion using bone anchors (BA). MATERIALS AND METHODS: A skull model was developed and assigned material properties based on Hounsfield unit (HU) values of cone-beam computerized tomography (CBCT) images. A 3 mm diameter cylindrical BA was modelled and inserted in the palatal bone. A 4 mm transverse displacement was applied on the anchor. An evaluation on the effect on local stresses of BA implantation inclination angle was performed. RESULTS: Proper displacement results and strain-stress trends for the expansion process were present. Stress distribution patterns were similar as reported in the literature. No significant difference between BA inclination angles was found. CONCLUSION: This work leads to a better understanding and prediction of craniofacial and maxillary bone remodelling during ME with BA treatments and is a first step towards the development of patient specific treatments.     

Maxillary expansion treatment using bone anchors: development and validation of a 3D finite element model

Objective: Develop a finite element (FE) model of a skull to perform biomechanical studies of maxillary expansion using bone anchors (BA).

Materials and methods: A skull model was developed and assigned material properties based on Hounsfield unit (HU) values of cone-beam computerized tomography (CBCT) images. A 3 mm diameter cylindrical BA was modelled and inserted in the palatal bone. A 4 mm transverse displacement was applied on the anchor. An evaluation on the effect on local stresses of BA implantation inclination angle was performed.

Results: Proper displacement results and strain–stress trends for the expansion process were present. Stress distribution patterns were similar as reported in the literature. No significant difference between BA inclination angles was found.

Conclusion: This work leads to a better understanding and prediction of craniofacial and maxillary bone remodelling during ME with BA treatments and is a first step towards the development of patient specific treatments.     

Finite element analysis of a hemi-pelvis: the effect of inclusion of cartilage layer on acetabular stresses and strain

An appropriate method of application of the hip-joint force and stress analysis of the pelvic bone, in particular the acetabulum, is necessary to investigate the changes in load transfer due to implantation and to calculate the reference stimulus for bone remodelling simulations. The purpose of the study is to develop a realistic 3D finite element (FE) model of the hemi-pelvis and to assess stress and strain distribution during a gait cycle. The FE modelling approach of the pelvic bone was based on CT scan data and image segmentation of cortical and cancellous bone boundaries. Application of hip-joint force through an anatomical femoral head having a cartilage layer was found to be more appropriate than a perfectly spherical head, thereby leading to more accurate stress–strain distribution in the acetabulum. Within the acetabulum, equivalent strains varied between 0.1% and 0.7% strain in the cancellous bone. High compressive (15–30 MPa) and low tensile (0–5 MPa) stresses were generated within the acetabulum. The hip-joint force is predominantly transferred from the acetabulum through the lateral cortex to the sacroiliac joint and the pubic symphysis. The study is useful to understand the load transfer within the acetabulum and for further investigations on acetabular prosthesis.     

3-D stress analysis in first maxillary premolar

The aim of this study was to investigate the stress distribution in a 3-D model of two-rooted tooth (first maxillary premolar) under two different occlusal force vectors by using finite element analysis. In the first model overall force of 200 N was divided into three vectors (cusp to fossa occlusion), and in the second model overall force was divided into 4 vectors (cusp to fossa and cusp to marginal ridge occlusion). The greatest compressive stress was found at the dentino- enamel junction in the cervical area of the both models (about -200 MPa). The greatest tensile stress was found at the vestibular aspect of buccal cusp in second model (about +3 MPa) and in the central fossa of the both models (about +28 MPa). Results indicate that in the both types of occlusal loadings the stress distribution was mainly compression and compressive forces were predominant over tensile stresses. In the second model with 4 vectors, stresses generated in the tooth structure were higher compared to the stresses generated in the first model with 3 vectors.     

Functional relationship between skull form and feeding mechanics in Sphenodon, and implications for diapsid skull development

The vertebrate skull evolved to protect the brain and sense organs, but with the appearance of jaws and associated forces there was a remarkable structural diversification. This suggests that the evolution of skull form may be linked to these forces, but an important area of debate is whether bone in the skull is minimised with respect to these forces, or whether skulls are mechanically "over-designed" and constrained by phylogeny and development. Mechanical analysis of diapsid reptile skulls could shed light on this longstanding debate. Compared to those of mammals, the skulls of many extant and extinct diapsids comprise an open framework of fenestrae (window-like openings) separated by bony struts (e.g., lizards, tuatara, dinosaurs and crocodiles), a cranial form thought to be strongly linked to feeding forces. We investigated this link by utilising the powerful engineering approach of multibody dynamics analysis to predict the physiological forces acting on the skull of the diapsid reptile Sphenodon. We then ran a series of structural finite element analyses to assess the correlation between bone strain and skull form. With comprehensive loading we found that the distribution of peak von Mises strains was particularly uniform throughout the skull, although specific regions were dominated by tensile strains while others were dominated by compressive strains. Our analyses suggest that the frame-like skulls of diapsid reptiles are probably optimally formed (mechanically ideal: sufficient strength with the minimal amount of bone) with respect to functional forces; they are efficient in terms of having minimal bone volume, minimal weight, and also minimal energy demands in maintenance.     

Stress amplifications in dental non-carious cervical lesions

This study aims to investigate the influence of the presence, shape and depth of NCCLs on the mechanical response of a maxillary second premolar subjected to functional and non-functional occlusal loadings using 3-D finite element (FE) analysis. A three-dimensional model of a maxillary second premolar and its supporting bone was constructed based on the contours of their cross-sections. From the sound model, cervical defects having either V- or U-shapes, as found clinically, were subtracted in three different depths. The models were loaded with 105 N to simulate normal chewing forces according to a functional occlusal loading (F1) vertically applied and two non-functional loadings (F2 and F3) obliquely oriented. Two alveolar bone crest heights were tested. Ansys™ FE software was used to compute stress distributions and maximum principal stress for each of the models. The presence of a lesion had no effect on the overall stress distribution of the system, but affected local stress concentrations. Non-functional loadings exhibited tensile stresses concentrating at the cervical areas and root surfaces, while the functional loading resulted in homogeneous stress distributions within the tooth. V-shaped lesions showed higher stress levels concentrated at the zenith of the lesion, whereas in U-shaped defect stresses concentrated over a wider area. As the lesions advanced in depth, the stress was amplified at their deepest part. A trend of stress amplification was observed with decreasing bone height. These results suggest a non-linear lesion progression with time, with the progression rate increasing with patient's age (deeper lesions and lower bone support).     

Finite element sub-modeling analyses of damage to enamel at the incisor enamel/adhesive interface upon de-bonding for different orthodontic bracket bases

This study investigates the micro-mechanical behavior associated with enamel damage at an enamel/adhesive interface for different bracket bases subjected to various detachment forces using 3-D finite element (FE) sub-modeling analysis. Two FE macro-models using triangular and square bracket bases subjected to shear, tensile and torsional de-bonding forces were established using μCT images. Six enamel/adhesive interface sub-models with micro- resin tag morphology and enamel rod arrangement were constructed at the corresponding stress concentrations in macro-model results. The boundary conditions for the sub-models were determined from the macro-model results and applied in sub-modeling analysis. The enamel and resin cement stress concentrations for triangular and square bases were observed at the adhesive bottom towards the occlusal surface under shear force and at the mesial and distal side planes under tensile force. The corresponding areas under torsional force were at the three corners of the adhesive for the triangular base and at the adhesive bottom toward/off the occlusal surface for the square base. In the sub-model analysis, the concentration regions were at the resin tag base and in the region around the etched holes in the enamel. These were perfectly consistent with morphological observations in a parallel in vitro bracket detachment experiment. The critical de-bonding forces damaging the enamel for the square base were lower than those of the triangular base for all detached forces. This study establishes that FE sub-modeling can be used to simulate the stress pattern at the micro-scale enamel/adhesive interface, suggesting that a square base bracket might be better than a triangular bracket. A de-bonding shear force can detach a bracket more easily than any other force with a lower risk of enamel loss.     

Three-dimensional model of the human craniofacial skeleton: method and preliminary results using finite element analysis

The purpose of this study was to develop a three-dimensional finite element model of the craniofacial skeleton using a dry human skull. The model consisted of 2918 nodes and 1776 solid elements, and was used to investigate the biomechanical effect of a distally directed orthopaedic force on the craniofacial complex. The force was applied at the level of the maxillary first molar. The results indicated that in response to the force system applied: the nasomaxillary complex displaces in a backward and downward direction and rotates in clockwise sense; the nasomaxillary complex, including the zygomatic bone, experiences high stress levels in comparison with those at the remaining bones; the stress distribution in the maxillary basal bone area is relatively uniform; and the stress distribution across the opposing surface of the bony margins of the sutures is non-uniform.     

Load transfer across the scapula during humeral abduction

Stress analysis in the individual parts of the scapula under normal physiological conditions is necessary to understand the load transfer mechanism, its relation with morphology of bone and to analyse the deviations in stress patterns due to implantation of the glenoid. The purpose of this study was to obtain stress distribution in the scapula during abduction of the arm and to obtain a qualitative estimate of the function of coracoacromial ligament. An accurate three-dimensional (3D) finite element (FE) model of the natural scapula has been developed for this purpose, using computed tomography data and shell-solid modelling approach. The model was experimentally validated. A musculoskeletal shoulder model of forces that calculates all muscle, ligament and joint reaction forces, in six load cases (30-180 degrees) during unloaded humeral abduction was used as applied loading conditions for the 3D FE model. High tensile and compressive stresses (15-60 MPa) were generated in the thick bony ridges of the scapula, like the scapular spine, lateral border, glenoid and acromion. High compressive stresses (45-58 MPa) were evoked in the glenoid and at the connection of glenoid-scapular spine-infraspinous fossa. The stresses in the infraspinous fossa and supraspinous fossa were low (0.05-15 MPa). These results indicated that the transfer of major muscle and joint reaction take place predominantly through the thick bony ridges, whereas the fossa area act more as attachment sites of large muscles. During humeral abduction, coracoacromial ligament was stretched, and presumably will be under tension.     

Implications of predatory specialization for cranial form and function in canids

The shape of the cranium varies widely among members of the order Carnivora, but the factors that drive the evolution of differences in shape remain unclear. Selection for increased bite force, bite speed or skull strength may all affect cranial morphology. We investigated the relationship between cranial form and function in the trophically diverse dog family, Canidae, using linear morphometrics and finite element (FE) analyses that simulated the internal and external forces that act on the skull during the act of prey capture and killing. In contrast to previous FE-based studies, we compared models using a newly developed method that removes the effects of size and highlights the relationship between shape and performance. Cranial shape varies among canids based on diet, and different selective forces presumably drove evolution of these phenotypes. The long, narrow jaws of small prey specialists appear to reflect selection for fast jaw closure at the expense of bite force. Generalists have intermediate jaw dimensions and produce moderate bite forces, but their crania are comparable in strength to those of small prey specialists. Canids that take large prey have short, broad jaws, produce the largest bite forces and possess very strong crania. Our FE simulations suggest that the remarkable strength of skulls of large prey specialists reflect the additional ability to resist extrinsic loads that may be encountered while struggling with large prey items.     

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

Background

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

Methods/Principal Findings

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

Conclusions/Significance

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

The effect of direct and indirect force transmission on peri-implant bone stress – a contact finite element analysis

In almost all finite element (FE) studies in dentistry, virtual forces are applied directly to dentures. The purpose of this study was to develop a FE model with non-linear contact simulation using an antagonist as force transmitter and to compare this with a similar model that uses direct force transmission. Furthermore, five contact situations were created in order to examine their influence on the peri-implant bone stresses, which are relevant to the survival rate of implants. It was found that the peri-implant bone stresses were strongly influenced by the kind of force transmission and contact number.     

On the importance of considering porosity when simulating the fatigue of bone cement

Fatigue cracking in the cement mantle of total hip replacement has been identified as a possible cause of implant loosening. Retrieval studies and in vitro tests have found porosity in the cement may facilitate fatigue cracking of the mantle. The fatigue process has been simulated computationally using a finite element/continuum damage mechanics (FE/CDM) method and used as a preclinical testing tool, but has not considered the effects of porosity. In this study, experimental tensile and four-point bend fatigue tests were performed. The tensile fatigue S-N data were used to drive the computational simulation (FE/CDM) of fatigue in finite element models of the tensile and four-point bend specimens. Porosity was simulated in the finite element models according to the theory of elasticity and using Monte Carlo methods. The computational fatigue simulations generated variability in the fatigue life at any given stress level, due to each model having a unique porosity distribution. The fracture site also varied between specimens. Experimental validation was achieved for four-point bend loading, but only when porosity was included. This demonstrates that the computational simulation of fatigue, driven by uniaxial S-N data can be used to simulate nonuniaxial loadcases. Further simulations of bone cement fatigue should include porosity to better represent the realities of experimental models.     

The application of muscle wrapping to voxel-based finite element models of skeletal structures

Finite elements analysis (FEA) is now used routinely to interpret skeletal form in terms of function in both medical and biological applications. To produce accurate predictions from FEA models, it is essential that the loading due to muscle action is applied in a physiologically reasonable manner. However, it is common for muscle forces to be represented as simple force vectors applied at a few nodes on the model’s surface. It is certainly rare for any wrapping of the muscles to be considered, and yet wrapping not only alters the directions of muscle forces but also applies an additional compressive load from the muscle belly directly to the underlying bone surface. This paper presents a method of applying muscle wrapping to high-resolution voxel-based finite element (FE) models. Such voxel-based models have a number of advantages over standard (geometry-based) FE models, but the increased resolution with which the load can be distributed over a model’s surface is particularly advantageous, reflecting more closely how muscle fibre attachments are distributed. In this paper, the development, application and validation of a muscle wrapping method is illustrated using a simple cylinder. The algorithm: (1) calculates the shortest path over the surface of a bone given the points of origin and ultimate attachment of the muscle fibres; (2) fits a Non-Uniform Rational B-Spline (NURBS) curve from the shortest path and calculates its tangent, normal vectors and curvatures so that normal and tangential components of the muscle force can be calculated and applied along the fibre; and (3) automatically distributes the loads between adjacent fibres to cover the bone surface with a fully distributed muscle force, as is observed in vivo. Finally, we present a practical application of this approach to the wrapping of the temporalis muscle around the cranium of a macaque skull.     

Of arcs and vaults: the biomechanics of bone‐cracking in spotted hyenas (Crocuta crocuta)

The ability to break open large bones has evolved independently in only three groups of carnivorous mammals, all of which have robust teeth, vaulted foreheads, and pronounced sagittal crests. One unusual skull feature, present in bone‐cracking members of the family Hyaenidae, is a caudally elongated frontal sinus, hypothesized to function in resistance to bending and stress dissipation during bone‐cracking. In the present study, we used finite element (FE) analysis to examine patterns of stress distribution in the spotted hyena (Crocuta crocuta) skull during unilateral biting, and inquire about the functional role of the fronto‐parietal sinus in stress dissipation. We constructed and compared three FE models: (1) a ‘normal’ model of an adult Crocuta skull; (2) a model in which the caudal portion of the fronto‐parietal sinus was filled with bone; and (3) a model in which we flattened the sagittal crest to resemble the plate‐like crests of other mammals. During biting, an arc of stress extends from the bite point up through the vaulted forehead and along the sagittal crest. Our results suggest that pneumatization of the hyena's skull both enhances its ability to resist bending and, together with the vaulted forehead, plays a critical role in evenly dissipating stress away from the facial region. © 2008 The Linnean Society of London, Biological Journal of the Linnean Society, 2008, 95 , 246–255.     

Numerical study of tension and strain distribution around rat molars]

A knowledge of the mechanical processes triggered in the bone and periodontal ligament (PDL) by orthodontic forces applied to a tooth is of decisive importance for an understanding of the subsequent remodelling around the tooth. To investigate these mechanical relationships, three-dimensional finite element (FE) models of the first lower molar in the rat were established. On the basis of digitized serial histological sections, these FE models were generated semi-automatically. Using various simplified geometrical variations, an appropriate FE model for the analysis of the stress and strain distributions was established. The numerical analyses were carried out under a mesially directed force of 0.1 N. Stress distributions in the bone and PDL showed a similar pattern, while strains in the bone were lower than in the PDL by a factor of 10-5. The data confirm the assumption that strain patterns in the PDL may be the key stimulus of bone remodelling.     

Development and validation of a subject-specific finite element model of a human clavicle

This study aimed to develop and validate a finite element (FE) model of a human clavicle which can predict the structural response and bone fractures under both axial compression and anterior–posterior three-point bending loads. Quasi-static non-injurious axial compression and three-point bending tests were first conducted on a male clavicle followed by a dynamic three-point bending test to fracture. Then, two types of FE models of the clavicle were developed using bone material properties which were set to vary with the computed tomography image density of the bone. A volumetric solid FE model comprised solely of hexahedral elements was first developed. A solid-shell FE model was then created which modelled the trabecular bone as hexahedral elements and the cortical bone as quadrilateral shell elements. Finally, simulations were carried out using these models to evaluate the influence of variations in cortical thickness, mesh density, bone material properties and modelling approach on the biomechanical responses of the clavicle, compared with experimental data. The FE results indicate that the inclusion of density-based bone material properties can provide a more accurate reproduction of the force–displacement response and bone fracture timing than a model with uniform bone material properties. Inclusion of a variable cortical thickness distribution also slightly improves the ability of the model to predict the experimental response. The methods developed in this study will be useful for creating subject-specific FE models to better understand the biomechanics and injury mechanism of the clavicle.     

Implementation of asymmetric yielding in case-specific finite element models improves the prediction of femoral fractures

Although asymmetric yielding in bone is widely shown in experimental studies, previous case-specific non-linear finite element (FE) studies have mainly adopted material behaviour using the Von Mises yield criterion (VMYC), assuming equal bone strength in tension and compression. In this study, it was verified that asymmetric yielding in FE models can be captured using the Drucker-Prager yield criterion (DPYC), and can provide better results than simulations using the VMYC. A sensitivity analysis on parameters defining the DPYC (i.e. the degree of yield asymmetry and the yield stress settings) was performed, focusing on the effect on bone failure. In this study, the implementation of a larger degree of yield asymmetry improved the prediction of the fracture location; variations in the yield stress mainly affected the predicted failure force. We conclude that the implementation of asymmetric yielding in case-specific FE models improves the prediction of femoral bone strength.     

Evaluation of threshold stress for bone resorption around screws based on in vivo strain measurement of miniplate

The purpose of this study is to investigate the critical threshold stress causing bone resorption evaluated from strain measurement in vivo, comparing the various finite element models. In this study strains of miniplates used for mandibular fractures were measured once a week until the strains reduced. The maximum bite force for each patient was applied in the incisal, right molar and left molar region. The strains increased and reached a peak level at 2-4 weeks, whereas the bite forces increased during the period of measurements. A 3-D osteosynthesis model using finite element method showed that the compressive stresses of the bone surrounding screws ranged within approximately -40 MPa under the condition generating the same amounts of strains measured in the miniplates. Furthermore, various finite element models simulating mandibular reconstruction using the fibular graft were constructed. The models for reconstruction using single strut fibula showed distinct stress concentration in the cortical bone surrounding screws, and the peak stress levels were 2 to 3 times as strong as that of the fracture model. We conclude that critical threshold for bone resorption should be approximately -50 MPa (3600 micro strain).