Quasi-automatic 3D finite element model generation for individual single-rooted teeth and periodontal ligament

Tissue Engineering for Periodontal Ligament Regeneration: Biomechanical Specifications

The periodontal biomechanical environment is very difficult to investigate. By the complex geometry and composition of the periodontal ligament (PDL), its mechanical behavior is very dependent on the type of loading (compressive versus tensile loading; static versus cyclic loading; uniaxial versus multiaxial) and the location around the root (cervical, middle, or apical). These different aspects of the PDL make it difficult to develop a functional biomaterial to treat periodontal attachment due to periodontal diseases. This review aims to describe the structural and biomechanical properties of the PDL. Particular importance is placed in the close interrelationship that exists between structure and biomechanics: the PDL structural organization is specific to its biomechanical environment, and its biomechanical properties are specific to its structural arrangement. This balance between structure and biomechanics can be explained by a mechanosensitive periodontal cellular activity. These specifications have to be considered in the further tissue engineering strategies for the development of an efficient biomaterial for periodontal tissues regeneration.

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

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

Design and Development of a Novel Oral Care Simulator for the Training of Nurses

OBJECTIVE

A Novel Oral Care Simulator was designed and developed to measure and visualise the facial and lingual forces exerted on teeth by the action of tooth brushing, considering the irregular geometry and structural composition of human dentition and the emulation of the realistic biomechanical deflection of the teeth.

METHOD

FEA simulations were carried out on a central incisor under facial loading and an appropriate force sensing mechanism was designed. An anatomically accurate mandibular jaw and 16 teeth were 3D printed, on which 16 force sensing structures were embedded. The signals from the sensors were amplified using a multichannel signal amplifier built using instrumentation amplifiers which were then visualised through a GUI.

RESULTS

The developed simulator is capable of indicating the magnitude of a force upto 15 N exerted on to the facial and lingual surfaces of teeth at a frequency of 60 Hz and above and it is capable of alerting the user if the force exceeds a pre-specified threshold.

CONCLUSION

The designed force sensing mechanism considers the irregular geometry and structural composition of human dentition in measuring the facial and lingual forces. It provides a reliable feedback by indicating the force and emulating the realistic biomechanical deflection of teeth.

SIGNIFICANCE

Nurses who care for the disabled, elderly and sick have explicitly stated the requirement for a simulator to train themselves on brushing the teeth of their subjects as their incorrect technique can cause longterm dental damage, for which a device has not been developed to date.

Data-Driven Approach to Inversion Analysis of Three-Dimensional Inner Soil Structure via Wave Propagation Analysis

Various approaches based on both computational science and data science/machine learning have been proposed with the development of observation systems and network technologies. Computation cost associated with computational science can be reduced by introducing the methods based on data science/machine learning. In the present paper, we focus on a method to estimate inner soil structure via wave propagation analysis. It is regarded as one of the parameter optimization approaches using observation data on the surface. This application is in great demand to ensure better reliability in numerical simulations. Typical optimization requires many forward analyses; thus, massive computation cost is required. We propose an approach to substitute evaluation using neural networks for most cases of forward analyses and to reduce the number of forward analyses. Forward analyses in the proposed method are used for producing the training data for a neural network; thereby they can be computed independently, and the actual elapsed time can be reduced by using a large-scale supercomputer. We demonstrated that the inner soil structure was estimated with the sufficient accuracy for practical damage evaluation. We also confirmed that the proposed method achieved estimating parameters within a shorter timeframe compared to a typical approach based on simulated annealing.

Parallelized Monte Carlo software to efficiently simulate the light propagation in arbitrarily shaped objects and aligned scattering media

A GPU-based Monte Carlo software (MCtet) was developed to calculate the light propagation in arbitrarily shaped objects, like a human tooth, represented by a tetrahedral mesh. A unique feature of MCtet is a concept to realize different kinds of light-sources illuminating the complex-shaped surface of an object, for which no preprocessing step is needed. With this concept, it is also possible to consider photons leaving a turbid media and reentering again in case of a concave object. The correct implementation was shown by comparison with five other Monte Carlo software packages. A hundredfold acceleration compared with central processing units-based programs was found. MCtet can simulate anisotropic light propagation, e.g., by accounting for scattering at cylindrical structures. The important influence of the anisotropic light propagation, caused, e.g., by the tubules in human dentin, is shown for the transmission spectrum through a tooth. It was found that the sensitivity to a change in the oxygen saturation inside the pulp for transmission spectra is much larger if the tubules are considered. Another "light guiding" effect based on a combination of a low scattering and a high refractive index in enamel is described.

New finite element study protocol: Clinical simulation of orthodontic tooth movement

The aim of this work was to model tooth movement in a more clinically-exact fashion, thanks to the use of new IT tools and imaging systems (cone-beam). Image segmentation and 3D reconstruction now enable us to model the anatomy realistically, while finite element (FE) analysis makes it possible to evaluate stresses and their distribution on the level of the tooth, the periodontal ligament (PDL) and the alveolar bone when a force is applied. The principle is to monitor tooth movement by obtaining optical impressions at each stage of treatment. The model corresponds to a genuine clinical situation. FE analysis is correlated with the clinically-observed displacement. The protocol remains long and complex. It nevertheless makes it possible to obtain, throughout the duration of treatment, patient-specific models that can be exploited using finite element methods. It requires further validation in more thorough studies but offers interesting prospects: precise study of induced tooth movement, distribution of stresses in the PDL, and development of a customized previsualization tool.

Viscoelasticity of periodontal ligament: an analytical model

BACKGROUND

Understanding of viscoelastic behaviour of a periodontal membrane under physiological conditions is important for many orthodontic problems. A new analytic model of a nearly incompressible viscoelastic periodontal ligament is suggested, employing symmetrical paraboloids to describe its internal and external surfaces.

METHODS

In the model, a tooth root is assumed to be a rigid body, with perfect bonding between its external surface and an internal surface of the ligament. An assumption of almost incompressible material is used to formulate kinematic relationships for a periodontal ligament; a viscoelastic constitutive equation with a fractional exponential kernel is suggested for its description.

RESULTS

Translational and rotational equations of motion are derived for ligament's points and special cases of translational displacements of the tooth root are analysed. Material parameters of the fractional viscoelastic function are assessed on the basis of experimental data for response of the periodontal ligament to tooth translation. A character of distribution of hydrostatic stresses in the ligament caused by vertical and horizontal translations of the tooth root is defined.

CONCLUSIONS

The proposed model allows generalization of the known analytical models of the viscoelastic periodontal ligament by introduction of instantaneous and relaxed elastic moduli, as well as the fractional parameter. The latter makes it possible to take into account different behaviours of the periodontal tissue under short- and long-term loads. The obtained results can be used to determine loads required for orthodontic tooth movements corresponding to optimal stresses, as well as to simulate bone remodelling on the basis of changes in stresses and strains in the periodontal ligament caused by such movements.

In vivo measurements and numerical analysis of the biomechanical characteristics of the human periodontal ligament

The periodontal ligament is a complex tissue with respect to its biomechanical behaviour. It is important to understand the mechanical behaviour of the periodontal ligament during physiological loading in healthy patients as well as during the movement of the tooth in orthodontic treatment or in patients with periodontal disease, as these might affect the mechanical properties of the periodontal ligament (PDL). Up to now, only a limited amount of in vivo data is available concerning this issue. The aim of this study has been to determine the time dependent material properties of the PDL in an experimental in vivo study, using a novel device that is able to measure tooth displacement intraorally. Using the intraoral loading device, tooth deflections at various velocities were realised in vivo on human teeth. The in vivo investigations were performed on the upper left central incisors of five volunteers aged 21-33 years with healthy periodontal tissue. A deflection, applied at the centre of the crown, was linearly increased from 0 to 0.15mm in a loading period of between 0.1 and 5.0s. Individual numerical models were developed based on the experimental results to simulate the relationship between the applied force and tooth displacement. The numerical force/displacement curves were fitted to the experimental ones to obtain the material properties of the human PDL. For the shortest loading time of 0.1s, the experimentally determined forces were between 7.0 and 16.2N. The numerically calculated Young's modulus varied between 0.9MPa (5.0s) and 1.2MPa (0.1s). By considering the experimentally and numerically obtained force curves, forces decreased with increasing loading time. The experimental data gained in this study can be used for the further development and verification of a multiphasic constitutive law of the PDL.

Bone stress and strain modification in diastema closure: 3D analysis using finite element method

The aim of this study was to analyse the stress and strain distribution in the alveolar bone between two central incisors in the process of diastema closure with a constant force. A 3-dimensional computer modeling based on finite element techniques was used for this purpose. A model of an anterior segment of the mandible containing cortical bone, spongy bone, gingivae, PDL and two central incisors with a bracket in the labial surface of each tooth were designed. The von Mises stress and strain was evaluated in alveolar bone along a path of nodes defined in a cresto-apical direction in the midline between two teeth. It was observed that stress and strain of alveolar bone increased in midline with a constant force to close the diastema regardless of the type of movement in gradual steps of diastema closure, however the stress was higher in the tipping movement than the bodily so it can be suggested that a protocol of force system modification should be introduced to compensate for the stress and strain changes caused by the reduced distance to avoid the unwanted stress alteration during the diastema closure.

2D and 3D finite element analysis of central incisor generated by computerized tomography

The purpose of this study was to compare the results of different hierarchical models in engineering analysis applied to dentistry with 2D and 3D models of a tooth and its supporting structures under 100 N occlusal loading at 45° and examine the reliability of simplified 2D models in dental research. Five models were built from computed-tomography scans: four 2D models with Plane Strain and Plane Stress State with linear triangular and quadratic quadrilateral elements and one 3D model. The finite element results indicated that the stress distribution was similar qualitatively in all models but the stress magnitude was quite different. It was concluded that 2D models are acceptable when investigating the biomechanical behavior of upper central incisor qualitatively. However, quantitative stress analysis is less reliable in 2D-finite element analysis, because 2D models overestimate the results and do not represent the complex anatomical configuration of dental structures. Therefore 3D finite element analyses of dental biomechanics cannot be simplified.

Effects of rigid and nonrigid extracoronal attachments on supporting tissues in extension base partial removable dental prostheses: a nonlinear finite element study

STATEMENT OF PROBLEM

Resilient (nonrigid) and non-resilient (rigid) attachments are used in extension base partial removable dental prostheses for retention. However, the biomechanical effects of these 2 types of retainers on the terminal abutment and supporting tissues, which may influence clinical treatment planning, have not been compared.

PURPOSE

The purpose of this study was to compare the mechanical effects of 2 types of extracoronal attachments (rigid and nonrigid) in distal extension removable partial prostheses on the alveolar ridge and abutment tooth periodontal ligament.

MATERIAL AND METHODS

A finite element model of a human left mandible edentulous arch distal to the second premolar was fabricated. The second premolar was the terminal abutment for an attachment-retained denture. Two types of attachments (rigid and nonrigid) were modeled in the study. For the nonrigid attachment, there was movement between the patrix and matrix component of the attachment, but there was no movement between the 2 component parts for the rigid attachment. Six levels of loading (100, 150, 200, 250, 300, and 350 N) were applied from 3 directions (axial, buccolingual, and mesiodistal) on the central fossa of the first and second molars. Denture motion and stress distributions of denture supporting tissues were observed. Maximum equivalent stress values (SEQV) were recorded for 6 regions (cervical bone, cervical and apical periodontal ligaments, mesial and distal ridges, and mucosa). The data were divided into 2 groups according to the attachment type. Paired t tests were used to compare the values of the 2 groups. Factorial ANOVA was used to test the difference between the loading directions (α=.05). Multiple linear regression was used to analyze the interactions among the factors of region, direction, and level (α=.05).

RESULTS

Stress distributions in the rigid and nonrigid attachment models were similar but the magnitudes were different. For all 3 loading directions, significantly different stresses in the alveolar ridge and periodontal tissue of the terminal abutment were found between the rigid and nonrigid groups (P<.05). There were significant differences among the 3 loading directions (P<.05). In the nonrigid group, the stress ratio of the mesial to the distal area was higher than that of the rigid group from axial and mesiodistal loading (P<.05). Linear interactions were found between the direction and level and region and level combinations (P<.05). Movement between the patrix and matrix components increased as loading increased. The most obvious movement of attachment occurred when loading was in the buccolingual direction.

CONCLUSIONS

Stress on the terminal abutment can be reduced by the use of an extracoronal resilient attachment that allocates more loads onto the distal edentulous ridge. The level of loading influenced the extent of reduction. A resilient attachment with a universal hinge had the most movement when loading was in the buccolingual direction. Interactions were found between direction and level, as well as region and level combinations (P<.05).

Correspondences of hydrostatic pressure in periodontal ligament with regions of root resorption: a clinical and a finite element study of the same human teeth

INTRODUCTION

The main objectives of this study were to generate individual finite element models of extracted human upper first premolars, and to simulate the distribution of the hydrostatic pressure in the periodontal ligament (PDL) of these models for evaluation of the risk of root resorption.

METHODS

The individual extracted teeth were from a previous in vivo study that investigated root resorption after application of continuous intrusive forces. The results of experimental examination and simulations were compared on these identical tooth roots. The applied force system was 0.5N and 1.0N of intrusive force.

RESULTS

The simulated results during intrusion of 0.5N showed regions near the apical thirds of the roots with hydrostatic pressure over the human capillary blood pressure. These regions correlated with the electron microscopies of previous studies performed in Brazil with the identical teeth. An increased force of 1.0N resulted in increased areas and magnitudes of the hydrostatic pressure.

CONCLUSIONS

The key parameter indicating beginning root resorption used in this study was an increased value for hydrostatic pressure in the PDL.

The adaptive response of periodontal ligament to orthodontic force loading - a combined biomechanical and biological study

BACKGROUND

The studies on biomechanics of orthodontic tooth movement (OTM) are mainly performed at analytical, tissue and cellular levels. The prime aim of this study was to elucidate the periodontal response to orthodontic force loading by integrating biomechanical and biological approaches.

METHODS

We designed and conducted a multilevel study consisting of three parts. (1) At the analytical/theoretical level, 3D finite element (FE) method was used to analyze stress distribution and changing during OTM. (2) At the tissue level, we explored the effects of tensile and compressive forces on the expressions of Type I collagen, matrix metalloproteinases Type I (MMP-1) and tissue inhibitor of metalloproteinase Type I (TIMP-1) in rat's periodontal ligament (PDL) in vivo. (3) At the cellular level, we studied the effects of variant strain patterns and magnitudes on functional expression of rat's osteoblasts in vitro.

FINDINGS

(1) In the 3D FE model, the canine tipping and bodily movements showed different ways in stress distribution and degeneration. However, in both tooth movement modalities, tensile zones and compressive zones had similar stress distribution pattern. (2) Tensile and compressive forces imposed different effects on the expressions of Type I collagen, MMP-1 and TIMP-1 in PDL, with Type I collagen and TIMP-1being increased significantly in the tensile zones and MMP-1 being increased significantly in both zones. (3) Differences in strain pattern (dynamic vs. static) and magnitude (light vs. heavy) resulted in different levels of osteoblast's functional expression indicated by alkaline phosphatase (ALP) and osteocalcin (OC). It was found that dynamic loading was more effective for ALP expression whilst static loading was more effective for OC secretion and 3kPa strain force in vitro was optimal for the both.

INTERPRETATION

It is suggested that there may exist an optimal force system in both magnitude and pattern of loading that could induce efficient OTM.

Anisotropic finite element modeling for patient-specific mandible

This paper presents an ad hoc modular software tool to quasi-automatically generate patient-specific three-dimensional (3D) finite element (FE) model of the human mandible. The main task is taking into account the complex geometry of the individual mandible, as well as the inherent highly anisotropic material law. At first, by computed tomography data (CT), the individual geometry of the complete range of mandible was well reproduced, also the separation between cortical and cancellous bone. Then, taking advantage of the inherent shape nature as 'curve' long bone, the algorithm employed a pair of B-spline curves running along the entire upper and lower mandible borders as auxiliary baselines, whose directions are also compatible with that of the trajectory of maximum material stiffness throughout the cortical bone of the mandible. And under the guidance of this pair of auxiliary baselines, a sequence of B-spline surfaces were interpolated adaptively as curve cross-sections to cut the original geometry. Following, based on the produced curve contours and the corresponding curve cross-section surfaces, quite well structured FE volume meshes were constructed, as well as the inherent trajectory vector fields of the anisotropic material (orthotropic for cortical bone and transversely isotropic for cancellous bone). Finally, a sensitivity analysis comprising various 3D FE simulations was carried out to reveal the relevance of elastic anisotropy for the load carrying behavior of the mandible.

Periodontal Ligament Hydrostatic Pressure with Areas of Root Resorption after Application of a Continuous Torque Moment

Objective: To evaluate the risk of root resorption, individual finite element models (FEMs) of extracted human maxillary first premolars were created, and the distribution of the hydrostatic pressure in the periodontal ligament (PDL) of these models was simulated.

Materials and Methods: A continuous lingual torque of 3 Nmm and 6 Nmm respectively was applied in vivo to the aforementioned teeth. After extraction, FEMs of these double-rooted teeth were created based on high-resolution microcomputed tomographics (micro CT, voxel size: 35 microns). This high volumetric resolution made the recognition of very small resorption lacunae possible. Scanning electron micrographs of the root surfaces were created as well. This enabled the investigation of advantages and disadvantages of the different imaging techniques from the viewpoint of the examination of root resorption. Using the FEMs, the same loading conditions as applied in vivo were simulated.

Results: The results of clinical examination and simulations were compared using the identical roots of the teeth. The regions that showed increased hydrostatic pressure (&gt;0.0047 MPa) correlated well with the locations of root resorption for each tooth. Increased torque resulted in increased high-pressure areas and increased magnitudes of hydrostatic pressure, correlating with the experiments.

Conclusion: If hydrostatic pressure exceeds typical human capillary blood pressure in the PDL, the risk of root resorption increases.

3D finite element mesh generation of complicated tooth model based on CT slices

An interactive three-dimensional finite element generation method is presented for modelling a multi-connected teeth and mandible structure. The tetrahedron is chosen as the basic element type due to its rigorous adaptability to structures with geometric complexities. The mesh generation is implemented by allocating two quadrangles in adjacent CT image slices to form a set of tetrahedrons. By examining all the possible allocations and their degradations, an algorithm is developed for interactive mesh generation, resulting in a series of tetrahedrons consistent with all the others without overlapping and spacing. The developed system was applied to a tooth-mandibular structure, generating a complicated 3D FEM model consisting of 4762 nodes and 18,534 tetrahedral elements with nine different materials. This 3D model was successfully used to evaluate different tooth restoration strategies, which proved the viability and effectiveness of the proposed method.

Towards automated 3D finite element modeling of direct fiber reinforced composite dental bridge

An automated 3D finite element (FE) modeling procedure for direct fiber reinforced dental bridge is established on the basis of computer tomography (CT) scan data. The model presented herein represents a two-unit anterior cantilever bridge that includes a maxillary right incisor as an abutment and a maxillary left incisor as a cantilever pontic bonded by adhesive and reinforced fibers. The study aims at gathering fundamental knowledge for design optimization of this type of innovative composite dental bridges. To promote the automatic level of numerical analysis and computational design of new dental biomaterials, this report pays particular attention to the mathematical modeling, mesh generation, and validation of numerical models. To assess the numerical accuracy and to validate the model established, a convergence test and experimental verification are also presented.