The effects of modeling simplifications on craniofacial finite element models: the alveoli (tooth sockets) and periodontal ligaments

Several finite element models of a primate cranium were used to investigate the biomechanical effects of the tooth sockets and the material behavior of the periodontal ligament (PDL) on stress and strain patterns associated with feeding. For examining the effect of tooth sockets, the unloaded sockets were modeled as devoid of teeth and PDL, filled with teeth and PDLs, or simply filled with cortical bone. The third premolar on the left side of the cranium was loaded and the PDL was treated as an isotropic, linear elastic material using published values for Young's modulus and Poisson's ratio. The remaining models, along with one of the socket models, were used to determine the effect of the PDL's material behavior on stress and strain distributions under static premolar biting and dynamic tooth loading conditions. Two models (one static and the other dynamic) treated the PDL as cortical bone. The other two models treated it as a ligament with isotropic, linear elastic material properties. Two models treated the PDL as a ligament with hyperelastic properties, and the other two as a ligament with viscoelastic properties. Both behaviors were defined using published stress-strain data obtained from in vitro experiments on porcine ligament specimens. Von Mises stress and strain contour plots indicate that the effects of the sockets and PDL material behavior are local. Results from this study suggest that modeling the sockets and the PDL in finite element analyses of skulls is project dependent and can be ignored if values of stress and strain within the alveolar region are not required.     

Comparative cranial myology and biomechanics of Plateosaurus and Camarasaurus and evolution of the sauropod feeding apparatus

Sauropodomorpha represents an important group of Mesozoic megaherbivores, and includes the largest terrestrial animals ever known. It was the first dinosaur group to become abundant and widespread, and its members formed a significant component of terrestrial ecosystems from the Late Triassic until the end of the Cretaceous. Both of these factors have been explained by their adoption of herbivory, but understanding the evolution of sauropodomorph feeding has been hampered by the scarcity of biomechanical studies. To address this, the jaw adductor musculature of the basal sauropodomorph Plateosaurus and the sauropod Camarasaurus have been reconstructed. These reconstructions provide boundary conditions for finite element models to assess differences in structural performance between the two taxa. Results demonstrate that Camarasaurus was capable of much greater bite forces than Plateosaurus, due to greater relative adductor muscle mass and shape changes to the mandible. The skull and mandible of Camarasaurus are also ‘stronger’ under static biting. The Plateosaurus mandible appears to compromise structural efficiency and force transmission in order to maintain relatively high jaw closure speed. This supports suggestions of facultative omnivory in basal sauropodomorph taxa. The expanded mandibular symphysis and ‘lateral plates’ of sauropods each lead to greater overall craniomandibular robustness, and may have been especially important in accommodating forces related to asymmetric loading. The functional roles of these characters, and observed general shape changes in increasing skull robustness, are consistent with hypotheses linking bulk‐herbivory with the origin of Sauropoda and the evolution of gigantism.     

Finite element simulation of the behavior of the periodontal ligament: A validated nonlinear contact model

Due to its significance in tooth movement, the stress/deformation field of periodontium and the alveolar bone remodeling process, periodontal ligament (PDL) cannot be excluded from the studies investigating dental biomechanics regarding its excessive deformability. Therefore, many analytical and numerical researches are carried out to simulate its response and to create a constitutive model via experiments intending to discover the material properties of PDL. The aim of this study is to formulate a user specified contact model that can be used in conjunction with finite element (FE) software and reflects PDL’s influence on neighboring structures based on the currently available information, without requiring an actual volumetric finite element mesh of ligament. The results show good agreement with available experimental tooth mobility data. Smooth stress fields are obtained on the tooth root and alveolar bone, which is a significant aspect in bone-remodeling studies. The advantage of simulating PDL as a contact model at the interface of tooth root and the alveolar process instead of a solid-meshed FE model with poor geometric morphology and/or very dense mesh is expected to save pre/post-processing workforce, to increase the accuracy and to contribute to the smoothness of interface stress distributions.     

Experiments to determine the time dependent material properties of the periodontal ligament]

The periodontal ligament is a tissue that attaches the tooth (root) to its alveolar socket, and thus plays an important role in the regulation of tooth movements. Detailed knowledge of the material properties of the periodontal ligament is therefore essential to an understanding of tooth reaction to forces applied during orthodontic treatment. A knowledge of material parameters can also be used in simulations of long-term tooth movements with the aim of improving orthodontic treatment. To this end, this study investigated time-dependent material properties, namely the hysteresis behaviour of the periodontal ligament under constant-velocity loading, the influence of loading velocity on the hysteresis, and its failure under constant loading. Specimens obtained from pigs were used for testing purposes, and the experiments were conducted in a special test setup using a material testing device. The material behaviour of the periodontal ligament was shown to be viscoelastic, and the elastic parameters of material behaviour were also determined. Under constant-velocity loading, material behaviour showed a nonlinear course of the stress-strain curve, also known as hysteresis. When loading was repeated several times, the maximum stress of the hysteresis decreased with each cycle. Determination of the deflection of the specimen at different velocities showed maximum stress to be dependent on the loading rate. The measured stress-strain curves were approximated by bilinear behaviour, permitting the use of finite element calculations. Also investigated was the failure behaviour of the periodontal ligament, which revealed tissue rupture to be inconstant.     

Three-dimensional analysis of orthodontic tooth movement

A three-dimensional finite element model was used to investigate the biomechanical response of an upper canine tooth. The physical model was developed from ceramic replicas and X-rays, and consisted of cancellous and cortical bone, the periodontal ligament, dentine and pulp chamber. Horizontal forces were applied at the tip of the crown and at the cervical margin and a rotational force was applied at the cervical margin of the tooth crown. The resulting displacements and stress field for each load case are presented with particular emphasis being placed on the response of the periodontal ligament. The investigation shows that quantitative information on initial tooth movement can be accurately predicted and used to evaluate the response of orthodontic treatment.     

A knee-specific finite element analysis of the human anterior cruciate ligament impingement against the femoral intercondylar notch

This work presents a finite element analysis of anterior cruciate ligament (ACL) impingement against the intercondylar notch during tibial external rotation and abduction, as a mechanism of noncontact ACL injuries. Experimentally, ACL impingement was measured in a cadaveric knee in terms of impingement contact pressure and six degrees-of-freedom tibiofemoral kinematics. Three-dimensional geometries of the ACL, femur and tibia were incorporated into the finite element model of the individual knee specimen. A fiber-reinforced model was adopted, which accounts for the anisotropy, large deformation, nonlinearity and incompressibility of the ACL. With boundary conditions specified based on the experimental tibiofemoral kinematics, the finite element analysis showed that impingement between the ligament and the lateral wall of intercondylar notch could occur when qthe knee at 45° was externally rotated at 29.1° and abducted at 10.0°. Strong contact pressure and tensile stress occurred at the impinging and nonimpinging sides of the ligament, respectively. The impingement force and contact area estimated from the model matched their counterparts from the corresponding cadaver experiment. The modeling and experimental approach provides a useful tool to characterize potential ACL impingement on a knee-specific basis, which may help elucidate the ACL injury mechanism and develop more effective treatments.     

Free body analysis,beam mechanics,and finite element modeling of the mandible of Alligator mississippiensis

The mechanical behavior of mammalian mandibles is well‐studied, but a comprehensive biomechanical analysis (incorporating detailed muscle architecture, accurate material properties, and three‐dimensional mechanical behavior) of an extant archosaur mandible has never been carried out. This makes it unclear how closely models of extant and extinct archosaur mandibles reflect reality and prevents comparisons of structure–function relationships in mammalian and archosaur mandibles. We tested hypotheses regarding the mechanical behavior of the mandible of Alligator mississippiensis by analyzing reaction forces and bending, shear, and torsional stress regimes in six models of varying complexity. Models included free body analysis using basic lever arm mechanics, 2D and 3D beam models, and three high‐resolution finite element models of the Alligator mandible, incorporating, respectively, isotropic bone without sutures, anisotropic bone with sutures, and anisotropic bone with sutures and contact between the mandible and the pterygoid flange. Compared with the beam models, the Alligator finite element models exhibited less spatial variability in dorsoventral bending and sagittal shear stress, as well as lower peak values for these stresses, suggesting that Alligator mandibular morphology is in part designed to reduce these stresses during biting. However, the Alligator models exhibited greater variability in the distribution of mediolateral and torsional stresses than the beam models. Incorporating anisotropic bone material properties and sutures into the model reduced dorsoventral and torsional stresses within the mandible, but led to elevated mediolateral stresses. These mediolateral stresses were mitigated by the addition of a pterygoid‐mandibular contact, suggesting important contributions from, and trade‐offs between, material properties and external constraints in Alligator mandible design. Our results suggest that beam modeling does not accurately represent the mechanical behavior of the Alligator mandible, including important performance metrics such as magnitude and orientation of reaction forces, and mediolateral bending and torsional stress distributions. J.Morphol. 2011. © 2011 Wiley‐Liss, Inc.     

A two-step procedure for coupling development and usage of a pair of human neck models

Both finite element models and multi-body models of human head-neck complex had been widely used in neck injuries analysis, as the former could be used to generate detailed stress strain information and the later could generate dynamic responses with high efficiency. Sometimes, detailed stress and strain information were hoped to be obtained more efficiently, but current methods were not effective enough when they were used to analyze responses of human head neck complex to long duration undulate accelerations. In this paper, a two-step procedure for ‘parallel’ development and ‘sequential’ usage of a pair of human head neck models was discussed. The pair of models contained a finite element model and a multi-body model, which were developed based on the coupling ‘parallel’ procedure using the same bio-realistic geometry. After being validated using available data, the pair of human neck models were applied to analyze biomechanical responses of pilot’s neck during arrested landing operation according to the ‘sequential’ procedure, because typical sustained undulate accelerations usually appeared during such processes. The results, including both kinematic and detailed biomechanical responses of human head-neck complex, were obtained with preferable efficiency. This research provided an effective way for biomechanical analysis of human head neck responses to sustained undulate accelerations.     

Three-dimensional finite element modelling of the human ACL: simulation of passive knee flexion with a stressed and stress-free ACL

In this study, a three-dimensional finite element model of the human anterior cruciate ligament (ACL) was developed and simulations of passive knee flexion were performed. The geometrical model of the ACL was built from experimental measurements performed on a cadaveric knee specimen which was also subjected to kinematics tests. These experiments were used to enforce the particular boundary conditions used in the numerical model. A previously developed transversely isotropic hyperelastic material model was implemented and the ability to pre-stress the ligament was also included. The model exhibited the key characteristics of connective soft tissues: anisotropy, nonlinear behaviour, large strains, very high compliance for compressive or bending loading along the collagen fibres and incompressibility. Simulations of passive knee flexion were performed, with and without pre-stressing the ACL. The resultant force generated by the ACL was monitored and the results compared to existing experimental data. The stress distribution within the ligament was also assessed. When the ACL was pre-stressed, there was a good correlation between the predicted and experimental resultant forces reported in the literature over the entire flexion-extension range. The stress distribution in the pre-stressed and stress-free ACL were similar, although the magnitudes in the pre-stressed ACL were higher, particularly at low flexion angles.     

The Biomechanical Effects of Sagittal Split Ramus Osteotomy on Temporomandibular Joint

Abstract

The aim of this study was to evaluate the stress distributions and deformations of the temporomandibular joint (TMJ) during different periods before and after sagittal split ramus osteotomy (SSRO). A three-dimensional finite element model of the mandible and TMJ was established, based on the preoperative CT of a patient with mandibular prognathism. Numerical SSRO was performed and the models of three postoperative periods were established. Contact elements were used to simulate the interaction between the articular discs and the articular cartilages. Nonlinear cable elements were used to simulate the disc attachments and the ligaments. Muscle forces and boundary conditions corresponding to the central occlusion were applied on all the models. The results showed that the stress distributions of the patient’s TMJs were not the same as those of asymptomatic subjects. The stress distributions and deformations of the disc, condylar and temporal cartilage were changed at different periods after SSRO. The biomechanical parameters of TMJ were improved after SSRO. And the postoperative results showed that appropriate functional training could help to avoid TMJ diseases. Therefore SSRO could improve the stress distributions of the TMJ and relieve the symptoms of temporomandibular disorder (TMD).     

Development and validation of a weight-bearing finite element model for total knee replacement

Total knee arthroplasty (TKA) is a successful procedure for osteoarthritis. However, some patients (19%) do have pain after surgery. A finite element model was developed based on boundary conditions of a knee rig. A 3D-model of an anatomical full leg was generated from magnetic resonance image data and a total knee prosthesis was implanted without patella resurfacing. In the finite element model, a restarting procedure was programmed in order to hold the ground reaction force constant with an adapted quadriceps muscle force during a squat from 20° to 105° of flexion. Knee rig experimental data were used to validate the numerical model in the patellofemoral and femorotibial joint. Furthermore, sensitivity analyses of Young’s modulus of the patella cartilage, posterior cruciate ligament (PCL) stiffness, and patella tendon origin were performed. Pearson’s correlations for retropatellar contact area, pressure, patella flexion, and femorotibial ap-movement were near to 1. Lowest root mean square error for retropatellar pressure, patella flexion, and femorotibial ap-movement were found for the baseline model setup with Young’s modulus of 5 MPa for patella cartilage, a downscaled PCL stiffness of 25% compared to the literature given value and an anatomical origin of the patella tendon. The results of the conducted finite element model are comparable with the experimental results. Therefore, the finite element model developed in this study can be used for further clinical investigations and will help to better understand the clinical aspects after TKA with an unresurfaced patella.     

Investigation of effective intrusion and extrusion force for maxillary canine using finite element analysis

Abstract

Orthodontic tooth movement is mainly regulated by the biomechanical responses of loaded periodontal ligament (PDL). We investigated the effective intervals of orthodontic force in pure maxillary canine intrusion and extrusion referring to PDL hydrostatic stress and logarithmic strain. Finite element analysis (FEA) models, including a maxillary canine, PDL and alveolar bone, were constructed based on computed tomography (CT) images of a patient. The material properties of alveolar bone were non-uniformly defined using HU values of CT images; PDL was assumed to be a hyperelastic–viscoelastic material. The compressive stress and tensile stress ranging from 0.47 to 12.8?kPa and 18.8 to 51.2?kPa, respectively, were identified as effective for tooth movement; a strain 0.24% was identified as the lower limit of effective strain. The stress/strain distributions within PDL were acquired in canine intrusion and extrusion using FEA; root apex was the main force-bearing area in intrusion–extrusion movements and was more prone to resorption. Owing to the distinction of PDL biomechanical responses to compression and tension, the effective interval of orthodontic force was substantially lower in canine intrusion (80–90?g) than in canine extrusion (230–260?g). A larger magnitude of force remained applicable in canine extrusion. This study revised and complemented orthodontic biomechanical behaviours of tooth movement with intrusive–extrusive force and could further help optimize orthodontic treatment.     

Finite element modeling of the breakage behavior of agricultural biomass pellets under different heights during handling and storage

It is very important to determine the amount of mechanical damage to biomass pellets during handling, transportation, and storage. However, it is difficult to determine the amount of damage to biomass pellets caused by existing external forces. However, a useful method is the finite element methods, which can be used in different engineering fields to simulate the posture of the material under defined boundary conditions. In this research, a drop test simulation of biomass pellet samples was performed by using the finite element method. An experimental study (compressive test) was carried out to measure some mechanical properties of the sample and use the obtained data in the finite element method simulation. The stress–strain curve of different biomass pellets was determined. Yield strength, Poisson’s ratio, ultimate strength and modulus of elasticity, and stress were identified. In the end, the maximum equivalent stress, highest contact force (generated normal force from target surface at impact), and shape of deformation of samples at impact were obtained from simulation results. The drop scenario was created with 25 steps after the impact site, and the FEM simulation was solved. The maximum stress value was 9.486 MPa, and the maximum generated force was 485.31 N. at step 8 of the FEM simulation. When the stress magnitudes were assessed, simulation outputs indicated that simulation stress values are inconsistent with experimental data.     

A Transversely Isotropic Hyperelastic Constitutive Model of the PDL. Analytical and Computational Aspects

This study describes the development of a constitutive law for the modelling of the periodontal ligament (PDL) and its practical implementation into a commercial finite element code. The constitutive equations encompass the essential mechanical features of this biological soft tissue: non-linear behaviour, large deformations, anisotropy, distinct behaviour in tension and compression and the fibrous characteristics. The approach is based on the theory of continuum fibre-reinforced composites at finite strain where a compressible transversely isotropic hyperelastic strain energy function is defined. This strain energy density function is further split into volumetric and deviatoric contributions separating the bulk and shear responses of the material. Explicit expressions of the stress tensors in the material and spatial configurations are first established followed by original expressions of the elasticity tensors in the material and spatial configurations. As a simple application of the constitutive model, two finite element analyses simulating the mechanical behaviour of the PDL are performed. The results highlight the significance of integrating the fibrous architecture of the PDL as this feature is shown to be responsible for the complex strain distribution observed.     

Tooth Eruption Results from Bone Remodelling Driven by Bite Forces Sensed by Soft Tissue Dental Follicles: A Finite Element Analysis

Intermittent tongue, lip and cheek forces influence precise tooth position, so we here examine the possibility that tissue remodelling driven by functional bite-force-induced jaw-strain accounts for tooth eruption. Notably, although a separate true ‘eruptive force’ is widely assumed, there is little direct evidence for such a force. We constructed a three dimensional finite element model from axial computerized tomography of an 8 year old child mandible containing 12 erupted and 8 unerupted teeth. Tissues modelled included: cortical bone, cancellous bone, soft tissue dental follicle, periodontal ligament, enamel, dentine, pulp and articular cartilage. Strain and hydrostatic stress during incisive and unilateral molar bite force were modelled, with force applied via medial and lateral pterygoid, temporalis, masseter and digastric muscles. Strain was maximal in the soft tissue follicle as opposed to surrounding bone, consistent with follicle as an effective mechanosensor. Initial numerical analysis of dental follicle soft tissue overlying crowns and beneath the roots of unerupted teeth was of volume and hydrostatic stress. To numerically evaluate biological significance of differing hydrostatic stress levels normalized for variable finite element volume, ‘biological response units’ in Nmm were defined and calculated by multiplication of hydrostatic stress and volume for each finite element. Graphical representations revealed similar overall responses for individual teeth regardless if incisive or right molar bite force was studied. There was general compression in the soft tissues over crowns of most unerupted teeth, and general tension in the soft tissues beneath roots. Not conforming to this pattern were the unerupted second molars, which do not erupt at this developmental stage. Data support a new hypothesis for tooth eruption, in which the follicular soft tissues detect bite-force-induced bone-strain, and direct bone remodelling at the inner surface of the surrounding bony crypt, with the effect of enabling tooth eruption into the mouth.     

A transversely isotropic hyperelastic constitutive model of the PDL. Analytical and computational aspects

This study describes the development of a constitutive law for the modelling of the periodontal ligament (PDL) and its practical implementation into a commercial finite element code. The constitutive equations encompass the essential mechanical features of this biological soft tissue: non-linear behaviour, large deformations, anisotropy, distinct behaviour in tension and compression and the fibrous characteristics. The approach is based on the theory of continuum fibre-reinforced composites at finite strain where a compressible transversely isotropic hyperelastic strain energy function is defined. This strain energy density function is further split into volumetric and deviatoric contributions separating the bulk and shear responses of the material. Explicit expressions of the stress tensors in the material and spatial configurations are first established followed by original expressions of the elasticity tensors in the material and spatial configurations. As a simple application of the constitutive model, two finite element analyses simulating the mechanical behaviour of the PDL are performed. The results highlight the significance of integrating the fibrous architecture of the PDL as this feature is shown to be responsible for the complex strain distribution observed.     

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.     

Cell survival and gene expression under compressive stress in a three-dimensional in vitro human periodontal ligament-like tissue model

This study investigated cell survival and gene expression under various compressive stress conditions mimicking orthodontic force by using a newly developed in vitro model of human periodontal ligament-like tissue (HPdLLT). The HPdLLT was developed by three-dimensional culturing of human periodontal ligament fibroblasts in a porous poly-l-lactide matrix with threefold increased culture media permeability due to hydrophilic modification. In vitro HPdLLTs in experimental groups were subjected to 5, 15, 25 and 35 g/cm² compressive stress for 1, 3, 7 or 14 days; controls were cultured over the same periods without compressive stress. Cell morphology and cell apoptosis in the experimental and control groups were investigated using scanning electron microscopy and caspase-3/7 detection. Real-time polymerase chain reaction was performed for seven osteogenic and osteoclastic genes. Similar extracellular matrix and spindle-shaped cells were observed inside or on the surface of in vitro HPdLLTs, with no relation to compressive stress duration or intensity. Similar caspase-3/7 activity indicating comparable apoptosis levels was observed in all samples. Receptor activator of nuclear factor kappa-B ligand and bone morphogenetic protein 2 genes showed characteristic “double-peak” expression at 15 and 35 g/cm² on day 14, and alkaline phosphatase and periodontal ligament-associated protein 1 expression peaked at 5 g/cm² on day 14; other genes also showed time-dependent and load-dependent expression patterns. The in vitro HPdLLT model system effectively mimicked the reaction and gene expression of the human periodontal ligament in response to orthodontic force. This work provides new information on the effects of compressive stress on human periodontal ligament tissue.     

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.     

Finite element analysis of stress distribution in intact and porcelain veneer restored teeth

The aim of this study was to investigate the stress distribution generated in a veneer restoration of an upper central incisor compared to intact teeth using the finite element analysis after applying a lingual buccal loading at the incisal edge. Methods: Two models were developed: one model contained enamel, dentine, cementum, periodontal ligament, cortical and trabecullar bones, and the other model was a veneer restoration; both models were developed using MSC/Nastran software (MacNeal-Schwendler Corporation, Los Angeles, CA, USA) as the pre- and post-processor. A 10-N load was applied at the incisal edge from the lingual to the buccal side to simulate oral conditions in this area (protrusion). Results: Von Mises stresses were then analysed for three different regions: A-B (enamel elements under the veneer or second enamel layer), A'-B' (buccal enamel and/or veneer element layer) and C-D (lingual enamel elements layer). A higher stress mode was observed for both models at the lingual cervical region. Conclusions: The presence of a veneer restoration on the incisors is a good alternative to mimic the behaviour of enamel under protrusion loading conditions. The use of veneers to replace enamel during rehabilitations is recommended.