A literature review on the linear elastic material properties assigned in finite element analyses in dental research

Introduction: Finite element analysis (FEA) is a numerical procedure utilised in the engineering analysis of structures and is one of the most common numerical methods utilised in many research activities in dentistry such as implantology, prosthodontics and restoration. FEA can be considered a useful tool in order to describe the deformation aspects of dental components that cannot be measured easily by in vivo models. The geometry, material properties, finite element model (mesh structure) and boundary conditions defined for a particular FEA setup are the factors affecting the accuracy of the results of a FEA. Most especially, material models employed in FEA play a critical role, however, the literature cannot provide standard material models and data in agreement to be defined in the FEA studies handled specifically for human teeth. The aim of this study is reviewing the most utilised data related to material properties (limited to linear homogeneous isotropic material model) of the tooth components, evaluate the sources and reasons for the different values defined in dental research and provide filtered material data which can be utilised in related FEA studies. Material and methods: Electronic databases (PubMed and Web of Science) were reviewed for publications on FEA utilised in dentistry research. 155 research publications in total were considered in this paper. The search keywords of “finite element analysis”, “finite element study”, “mechanical properties” and “teeth” were combined through Boolean operators. The primary question under review was: “How were the material properties of the tooth components and numerical ranges, which are assigned in a FEA utilised in dental research, obtained and verified?”. Results: It was possible to determine sixteen different elastic modulus (EM) and seven Poisson’ ratio (PR) values for enamel, eighteen EM and five PR values for dentin, sixteen EM and four PR values for periodontal ligament, eight EM and one PR values for pulp, ten EM and five PR values for cementum, twelve EM and four PR values for cortical bone, and eleven EM and four PR values for cancellous bone. As a result, it was seen that various EM, PR, density and strength values were considered and these were obtained from a limited number of FEA studies. Conclusion: Average ranges for the core material properties such as EM, PR, density and strength values to be utilised in a FEA set up were presented. Further studies, specifically on determination of the mechanical properties of tooth components are still needed in order to successfully utilise them and confirm the accuracy of the FEA studies related to dental research

Explore the Dynamic Characteristics of Dental Structures: Modelling, Remodelling, Implantology and Optimisation

The properties of a structure can be both narrowly and broadly described. The mechanical properties, as a narrow sense of property, are those that are quantitative and can be directly measured through experiments. They can be used as a metric to compare the benefits of one material versus another. Examples include Young’s modulus, tensile strength, natural frequency, viscosity, etc. Those with a broader definition, can be hardly measured directly. This thesis aims to study the dynamic properties of dental complex through experiments, clinical trials and computational simulations, thereby bridging some gaps between the numerical study and clinical application. The natural frequency and mode shapes, of human maxilla model with different levels of integrities and properties of the periodontal ligament (PDL), are obtained through the complex modal analysis. It is shown that the comprehensiveness of a computational model significantly affects the characterisation of dynamic behaviours, with decreasing natural frequencies and changed mode shapes as a result of the models with higher extents of integrity and preciseness. It is also found that the PDL plays a very important role in quantifying natural frequencies. Meanwhile, damping properties and the heterogeneity of materials also have an influence on the dynamic properties of dental structures. The understanding of dynamic properties enables to further investigate how it can influence the response when applying an external stimulus. In a parallel preliminary clinical trial, 13 patients requiring bilateral maxillary premolar extractions were recruited and applied with mechanical vibrations of approximately 20 g and 50 Hz, using a split mouth design. It is found that both the space closure and canine distalisation of the vibration group are significantly faster and higher than those of the control group (p<0.05). The pressure within the PDL is computationally calculated to be higher with the vibration group for maxillary teeth for both linguo-buccal and mesial-distal directions. A further increased PDL response can be observed if increasing the frequency until reaching a local natural frequency. The vibration of 50 Hz or higher is thus approved to be a potential stimulus accelerating orthodontic treatment. The pivotal role of soft tissue the PDL is further studied by quantitatively establishing pressure thresholds regulating orthodontic tooth movement (OTM). The centre of resistance and moment to force ratio are also examined via simulation. Distally-directed tipping and translational forces, ranging from 7.5 g to 300 g, are exerted onto maxillary teeth. The hydrostatic stress is quantified from nonlinear finite element analysis (FEA) and compared with normal capillary and systolic blood pressure for driving the tissue remodelling. Localised and volume-averaged hydrostatic stress are introduced to describe OTM. By comparing with clinical results in past literature, the volume average of hydrostatic stress in PDL was proved to describe the process of OTM more indicatively. Global measurement of hydrostatic pressure in the PDL better characterised OTM, implying that OTM occurs only when the majority of PDL volume is critically stressed. The FEA results provide new insights into relevant orthodontic biomechanics and help establish optimal orthodontic force for a specific patient. Implant-supported fixed partial denture (FPD) with cantilever extension can transfer excessive load to the bone surrounding implants and stress/strain concentration which potentially leads to bone resorption. The immediate biomechanical response and long-term bone remodelling outcomes are examined. It is indicated that during the chewing cycles, the regions near implant necks and apexes experience high von Mises stress (VMS) and equivalent strain (EQS) than the middle regions in all configurations, with or without the cantilever. The patient-specific dynamic loading data and CT based mandibular model allow us to model the biomechanical responses more realistically. The results provide the data for clinical assessment of implant configuration to improve longevity and reliability of the implant-supported FPD restoration. On the other hand, the results show that the three-implant supported and distally cantilevered FPDs see noticeable and continuous bone apposition, mainly adjacent to the cervical and apical regions. The bridged and mesially cantilevered FPDs show bone resorption or no visible bone formation in some areas. Caution should be taken when selecting the FPD with cantilever due to the risk of overloading bone resorption. The position of FPD pontics plays a critical role in mechanobiological functionality and bone remodelling. As an important loading condition of dental biomechanics, the accurate assignment of masticatory loads has long been demanded. Methods involving different principles have been applied to acquire or assess the muscular co-activation during normal or unhealthy stomatognathic functioning. Their accuracy and capability of direct quantification, especially when using alone, are however questioned. We establish a clinically validated Sequential Kriging Optimisation (SKO) model, coupled with the FEM and in vivo occlusal records, to further the understanding of muscular functionality following a fibula free flap (FFF) surgery. The results, within the limitations of the current study, indicates the statistical advantage of agreeing occlusal measurements and hence the reliability of using the SKO model over the traditionally adopted optimality criteria. It is therefore speculated that mastication is not optimally controlled to a definite degree. It is also found that the maximum muscular capacity slightly decreases whereas the actual muscle forces fluctuate over the 28-month period

Computational Modeling of Fracture Failure in Mineralized and Prosthetic Biomaterials

Natural mineralized tissues, e.g., teeth and bone, have the capacity to tolerate the daily physiological loading. However, due to their high mineralized composition, they have been recognized as a class of relatively brittle biomaterials. The inherent brittle nature and fairly high susceptibility to mechanical failure present a more critical problem in biomedical research field. To replace such diseased or damaged mineralized tissues, prosthetic materials are largely applied in the areas of dental and osteo clinical treatments. Ceramic materials provide numerous favourable characteristics, including biocompatibility and chemical resistance. In addition to the dental industry, applications of osteofixation/osteosynthiesis devices are considered fundamental to stabilize various treatments of bone defects for promoting osteointegration and reconstruction. However, clinical observations and specialized literature have revealed that dental restorative materials and prosthetic fixation devices are often subject to high stress, leading to fracture either by catastrophic overloading or cyclic fatigue failure. The aim of this thesis is to develop a computational modelling framework on the basis of the extended finite element method (XFEM) to investigate the fracture behaviors of mineralised and synthetic biomaterials in various medical applications. The XFEM modelling results are validated by being compared with the in-vitro experiments and/or clinical observations. Through the research in this thesis studies, XFEM has been demonstrated to be a powerful tool to analyse fracture behaviors in the bio-structures subjected to not only static loadings but also cyclic loadings. The outcomes generated in this thesis help gain some insightful understanding failure of the native or prosthetic structures, which is anticipated to provide some clinical guidelines for the design optimisation of patient-specific prosthetic devices to ensure their reliability and longevity

Tooth crown dimensions and cusp number in hypodontia: assessed by a new three-dimensional technique

Background: Development of the dentition is a valuable model for studying craniofacial and general development. It is a Complex Adaptive System (CAS) in which the outcome of interactions between genetic, epigenetic and environmental factors, at the molecular, cellular and tissue levels leads to a phenotype with variation in tooth number, size, shape and mineralization. These variations are important as they underpin evolutionary change. This study is part of a major international collaborative project investigating hypodontia: a variation of tooth number. The project aims to investigate the development of hypodontia from genotype to phenotype in the same group of patients. The phenotype of hypodontia is more extensive than agenesis. The present study investigates part of the phenotype of hypodontia, the relationship of congenitally absent teeth and the crown size and shape of the formed teeth. Aim: Compare the crown dimensions and cusp numbers in patients with mild or moderate hypodontia to matched controls with normal numbers of teeth. Materials and Methods: The sample consisted of 69 patients, 36 females and 33 males, with between 1 and 5 congenitally missing teeth and a set of matched controls. From imaging the dental study casts 3D digital models were produced. Linear measurements were made of the mesio-distal (MD), bucco-lingual (BL) and crown height (CH) dimensions. In addition, the cusp numbers of premolar and molar teeth were counted. Statistical methods used included linear mixed effect models and generalized estimating equations. The new method was validated against traditional 2D calipers, the measuring tool software was tested for repeatability, and for the intra and inter-operator reliability. Results: Intra-class correlation coefficient (ICC) and technical error of measurements (TEM) were used to determine reliability. ICC values were above 0.75 in almost all analyses, and the TEM was negligible, which is indicative of high agreement. The crown dimensions of the hypodontia group were statistically significantly (p<0.05) smaller than the control group in the majority of all three dimensions (MD, BL and CH). There were fewer cusps present on the occlusal surfaces of the first premolar and first molar teeth in the hypodontia patients than in the control group. Interestingly, patients with hypodontia of one upper lateral incisor who retained the antimeric incisor, had significantly reduced crown dimensions when compared to the remaining hypodontia group. Conclusion: The findings of this study confirm that the phenotype of hypodontia includes reduction in all three tooth crown dimensions and in cusp numbers of existing teeth as well as agenesis. The results support the concept that dental development is a Complex Adaptive System whose outcomes are a range of variations of number, size and shape of teeth. These variations are compatible with evolutionary changes and the suggestion of recent reductions in the human dentition.Thesis (MPhil) -- University of Adelaide, Adelaide Dental School, 201

Three-dimensional modeling of the human jaw/teeth using optics and statistics.

Object modeling is a fundamental problem in engineering, involving talents from computer-aided design, computational geometry, computer vision and advanced manufacturing. The process of object modeling takes three stages: sensing, representation, and analysis. Various sensors may be used to capture information about objects; optical cameras and laser scanners are common with rigid objects, while X-ray, CT and MRI are common with biological organs. These sensors may provide a direct or an indirect inference about the object, requiring a geometric representation in the computer that is suitable for subsequent usage. Geometric representations that are compact, i.e., capture the main features of the objects with a minimal number of data points or vertices, fall into the domain of computational geometry. Once a compact object representation is in the computer, various analysis steps can be conducted, including recognition, coding, transmission, etc. The subject matter of this dissertation is object reconstruction from a sequence of optical images using shape from shading (SFS) and SFS with shape priors. The application domain is dentistry. Most of the SFS approaches focus on the computational part of the SFS problem, i.e. the numerical solution. As a result, the imaging model in most conventional SFS algorithms has been simplified under three simple, but restrictive assumptions: (1) the camera performs an orthographic projection of the scene, (2) the surface has a Lambertian reflectance and (3) the light source is a single point source at infinity. Unfortunately, such assumptions are no longer held in the case of reconstruction of real objects as intra-oral imaging environment for human teeth. In this work, we introduce a more realistic formulation of the SFS problem by considering the image formation components: the camera, the light source, and the surface reflectance. This dissertation proposes a non-Lambertian SFS algorithm under perspective projection which benefits from camera calibration parameters. The attenuation of illumination is taken account due to near-field imaging. The surface reflectance is modeled using the Oren-Nayar-Wolff model which accounts for the retro-reflection case. In this context, a new variational formulation is proposed that relates an evolving surface model with image information, taking into consideration that the image is taken by a perspective camera with known parameters. A new energy functional is formulated to incorporate brightness, smoothness and integrability constraints. In addition, to further improve the accuracy and practicality of the results, 3D shape priors are incorporated in the proposed SFS formulation. This strategy is motivated by the fact that humans rely on strong prior information about the 3D world around us in order to perceive 3D shape information. Such information is statistically extracted from training 3D models of the human teeth. The proposed SFS algorithms have been used in two different frameworks in this dissertation: a) holistic, which stitches a sequence of images in order to cover the entire jaw, and then apply the SFS, and b) piece-wise, which focuses on a specific tooth or a segment of the human jaw, and applies SFS using physical teeth illumination characteristics. To augment the visible portion, and in order to have the entire jaw reconstructed without the use of CT or MRI or even X-rays, prior information were added which gathered from a database of human jaws. This database has been constructed from an adult population with variations in teeth size, degradation and alignments. The database contains both shape and albedo information for the population. Using this database, a novel statistical shape from shading (SSFS) approach has been created. Extending the work on human teeth analysis, Finite Element Analysis (FEA) is adapted for analyzing and calculating stresses and strains of dental structures. Previous Finite Element (FE) studies used approximate 2D models. In this dissertation, an accurate three-dimensional CAD model is proposed. 3D stress and displacements of different teeth type are successfully carried out. A newly developed open-source finite element solver, Finite Elements for Biomechanics (FEBio), has been used. The limitations of the experimental and analytical approaches used for stress and displacement analysis are overcome by using FEA tool benefits such as dealing with complex geometry and complex loading conditions

Biomechanics and Remodelling for Design and Optimisation in Oral Prosthesis and Therapeutical Procedure

The purpose of dental prostheses is to restore the oral function for edentulous patients. Introducing any dental prosthesis into mouth will alter biomechanical status of the oral environment, consequently inducing bone remodelling. Despite the advantageous benefits brought by dental prostheses, the attendant clinical complications and challenges, such as pain, discomfort, tooth root resorption, and residual ridge reduction, remain to be addressed. This thesis aims to explore several different dental prostheses by understanding the biomechanics associated with the potential tissue responses and adaptation, and thereby applying the new knowledge gained from these studies to dental prosthetic design and optimisation. Within its biomechanics focus, this thesis is presented in three major clinical areas, namely prosthodontics, orthodontics and dental implantology. In prosthodontics, the oral mucosa plays a critical role in distributing occlusal forces a denture to the underlying bony structure, and its response is found in a complex, dynamic and nonlinear manner. It is discovered that interstitial fluid pressure in mocosa is the most important indicator to the potential resorption induced by prosthetic denture insertion, and based on this finding, patient-specific analysis is performed to investigate the effects caused by various types of dentures and prediction of the bone remodelling activities. In orthodontic treatments, a dynamic algorithm is developed to analyse and predict potential bone remodelling around the target tooth during orthodontic treatment, thereby providing a numerical approach for treatment planning. In dental implantology, a graded surface morphology of an implant is designed to improve osseointegration over that of a smooth uniform surface in both the short and long term. The graded surface can be optimised to achieve the best possible balance between the bone-implant contact and the peak Tresca stress for the specific clinical application need

An Assessment of the Neurovascular Structures of the Trigeminal Nerve and Their Relationship to Diet in Primates

The inferior alveolar nerve (IAN) enters the mandible via the mental foramen, supplies nervous sensation to the mandibular teeth as it travels through the mandibular canal, and exits the mandibular foramen to send information to the brain to maintain chewing cycles and protect the teeth from damage. Although bony canals and foramina have been shown to form around soft-tissue structures, there are some examples (e.g., the hypoglossal nerve/canal) where the nervous structures do not comprise most of the canal/foramina space. It is important to know the size of nerves because it has been established that larger nerves convey more information at faster rates. However, no previous work has established the size of the IAN in primates or if the mandibular canal and associated foramina can be used as proxies for the nervous tissues. The purpose of this dissertation is to assess the variation seen in the IAN in using both a hard-tissue dataset comprised of tooth and mandibular canal measurements and a soft-tissue dataset comprised of the cross-sectional area (CSA) and volumetric measurements of the IAN. These two datasets explore the relationship between the IAN and the roots and enamel surfaces of I1, C1, P4, and M1, the CSA and volume of the mandibular canal, and the dietary categories of primates. Overall, the IAN is related to the bony structures of the mandible by size across primates. There were significant relationships between the tooth surface areas and the IAN throughout the mandible, with most showing either isometric or negatively allometric relationships. Additionally, the nerve CSA measurements at the mental foramen, mandibular foramen, beneath P4, beneath M1, and overall canal volumes showed significant relationships with the corresponding IAN measurements. However, while these relationships may be significant there is no evidence to support the hypothesis that the IAN fills most of the mandibular canal. Teeth are under strong selective pressure to change shape in response to a change in environment or diet in primate species. Therefore, it was hypothesized that the nervous tissues – because of their direct relationship to the teeth by supplying somatic sensation – would be under these same selective pressures. However, there was only one significant relationship found between the shape of the premolar tooth and the nervous tissue variables, with no other teeth showing significant relationships with the shape of the tooth’s surface. These relationships were further supported when there were no significant relationships between the IAN and dietary categories – reinforcing the conclusion that there are little to no differences in IAN size across primates based on diet. All cranial nerves in mammals are highly conserved in their shape, pathways, and functions, indicating strong selective pressures to maintain these nerves for their vital functions. These data showed that the IAN – a termination of cranial nerve V – is highly constrained across primates (and some mammal species) and is more likely related to the overall size of the mandible rather than selective pressures such as diet

Sexual Dimorphism

Sexual Dimorphism- Various biological studies on the subject of sex differences have been published. The subjects of these studies are not only humans, but also other mammals, birds, amphibians, insects, extending to ostracoda in the Paleozoic era. Moreover, original methods in individual studies have been used. This book provides convincing reasons which explain sex differences. The book also shows that, even if considered that some living things do not have sex differences, in reality they do. The somewhat different data on sex differences in this book will offer new ideas not only to life scientists and biologists, but social and cultural scientists as well

Mechanical performance of endodontic restorations with prefabricated posts: sensitivity analysis of parameters with a 3D finite element model

Many studies have investigated the effect of different parameters of the endodontically restored tooth on its final strength, using in vitro tests and model simulations. However, the differences in the experimental set-up or modelling conditions and the limited number of parameters studied in each case prevent us from obtaining clear conclusions about the relative importance of each parameter. In this study, a validated 3D biomechanical model of the restored tooth was used for an exhaustive sensitivity analysis. The individual influence of 20 different parameters on the mechanical performance of an endodontic restoration with prefabricated posts was studied. The results bring up the remarkable importance of the loading angle on the final restoration strength. Flexural loads are more critical than compressive or tensile loads. Young’s modulus of the post and its length and diameter are the most influential parameters for strength, whereas other parameters such as ferrule geometry or core and crown characteristics are less significant