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Effect of Geometric Dimensions and Material Models of the Periodontal Ligament in Orthodontic Tooth Movement
Abstract
Objectives
The aim of the present work was set to explore the role of root diameter, root length, and thickness of periodontal ligament (PDL) and its material properties (linear and nonlinear elastic material models) on the stress and strain distribution, tooth displacement and centre of resistance (CR) location.
Setting and Sample Population
Both the bone and tooth were considered as rigid bodies and the PDL was modelled as a paraboloid with different geometric dimensions and material properties.
Materials and Methods
To achieve this goal, a horizontal force of 1 N was applied in the CR location and the stress and strain distribution and tooth displacement were quantified. Locations of CR were estimated through iterative finite element procedure.
Results
It was predicted that the position of CR is in the range of 34% to 39% of the root length, slightly higher than one‐third of the root length reported in the literature. The geometrical dimensions of the PDL had no significant effect on the position of CR, especially in the nonlinear material model of the PDL, while the initial displacement of the tooth was found to be highly dependent on the geometrical and mechanical properties of the PDL.
Conclusion
The simplified PDL modelling approach with nonlinear material behaviour can be suggested for the estimation of initial tooth movement for individual clinical applications without the use of advanced 3D scans.
... The finite element method is a very powerful tool for the analysis of orthopedics and dental biomechanics [38][39][40]. Approximately two decades ago, scholars developed an FE model of the entire mandible to simulate the effects of different occlusal modes. ...
... Additionally, Caballero et al. [12] and Bouton et al. [8] used similar methods to analyze the biomechanical effect of orthodontic forces on tooth movement. Although most studies have hypothesized the PDL to be a linear elastic material, the physiological structure of the PDL is a connective tissue composed of a considerable amount of collagen fiber [38,[43][44][45]. Therefore, researchers have inferred that the PDL has nonlinear elasticity. ...
Objective
The study objective was to investigate four common occlusal modes by using the finite element (FE) method and to conduct a biomechanical analysis of the periodontal ligament (PDL) and surrounding bone when orthodontic force is applied.
Materials and methods
A complete mandibular FE model including teeth and the PDL was established on the basis of cone-beam computed tomography images of an artificial mandible. In the FE model, the left and right mandibular first premolars were not modeled because both canines required distal movement. In addition, four occlusal modes were simulated: incisal clench (INC), intercuspal position (ICP), right unilateral molar clench (RMOL), and right group function (RGF). The effects of these four occlusal modes on the von Mises stress and strain of the canine PDLs and bone were analyzed.
Results
Occlusal mode strongly influenced the distribution and value of von Mises strain in the canine PDLs. The maximum von Mises strain values on the canine PDLs were 0.396, 1.811, 0.398, and 1.121 for INC, ICP, RMOL, and RGF, respectively. The four occlusal modes had smaller effects on strain distribution in the cortical bone, cancellous bone, and miniscrews.
Conclusion
Occlusal mode strongly influenced von Mises strain on the canine PDLs when orthodontic force was applied.
Clinical relevance
When an FE model is used to analyze the biomechanical behavior of orthodontic treatments, the effect of muscle forces caused by occlusion must be considered.
... 1,4 In orthodontic treatment, the PDL transmits orthodontic forces and influences bone remodeling. 5,6 Changes in periodontal blood flow trigger osteoclast differentiation on the compressive side for bone resorption and osteoblast differentiation on the tensile side for bone deposition. Therefore, PDL plays an important role in physiological processes such as mastication and orthodontic treatment. ...
The periodontal ligament (PDL) plays a crucial role in transmitting and dispersing occlusal force, acting as mechanoreceptor for muscle activity during chewing, as well as mediating orthodontic tooth movement. It transforms mechanical stimuli into biological signals, influencing alveolar bone remodeling. Recent research has delved deeper into the biological and mechanical aspects of PDL, emphasizing the importance of understanding its structure and mechanical properties comprehensively. This review focuses on the latest findings concerning both macro- and micro- structural aspects of the PDL, highlighting its mechanical characteristics and factors that influence them. Moreover, it explores the mechanotransduction mechanisms of PDL cells under mechanical forces. Structure-mechanics-mechanotransduction interplay in PDL has been integrated ultimately. By providing an up-to-date overview of our understanding on PDL at various scales, this study lays the foundation for further exploration into PDL-related biomechanics and mechanobiology.
... Because it plays a positioning role mainly in the daily use of teeth instead of resisting tensile loads. Healthy teeth have certain physiological mobility during daily chewing behaviors, and the distance between the rotation center of a single root tooth and the alveolar crest is 1/3 [30,31]. The amount of movement in the neck region is greater compared to other regions when the tooth rotates. ...
Collagen fibers of the Periodontal ligament (PDL) play a crucial role in determining its mechanical properties. Based on this premise, we investigated the effect of the volume fraction of human PDL collagen fibers on the hyperelastic mechanical behavior under transient loading. Samples were obtained from different root regions (neck, middle, and apex) of the PDL, prepared from fresh human anterior teeth. The collagen fibers volume fraction in various regions of the PDL was quantified by staining techniques combined with image processing software. The collagen fiber volume fractions were found to be 60.3% in the neck region, 63.1% in the middle region, and 52.0% in the apex region. A new hyperelastic constitutive model was constructed based on the volume fraction. A uniaxial tensile test was conducted on these samples, and the accuracy of the constitutive model was validated by fitting the test data. Also, relevant model parameters were derived. The results demonstrated that human PDL exhibited hyperelastic mechanical properties on the condition of transient loading. With an increase in the volume fraction of collagen fibers, the tensile resistance of the PDL was enhanced, demonstrating more significant hyperelastic mechanical properties. The hyperelastic constitutive model showed a good fit with the experimental results (R² > 0.997), describing the hyperelastic mechanical properties of the human PDL effectively.
... Orthodontic appliances consisting of an activated nickeltitanium coil spring (MX-1109-01, Mingxing Spring Co., LTD, Chengdu) were ligated from the maxillary first molar (M1) to the central incisor to deliver a force (20N) for tooth movement (Fig. 1a). One end of the orthodontic nickel-titanium coil spring was fixed on the first molar through an orthodontic ligature wire, while the other end of the ligature wire was directly fixed on the incisor and bonded with a flowable composite resin (3 M ESPE) under anesthesia (Fig. 1b) [18][19][20]. The orthodontic force was applied to the mice immediately after the appliance placement. ...
Background
The purpose of this study is to explore the effects of CB2 on bone regulation during orthodontic tooth movement.
Methods
Thirty male mice were allocated into 2 groups (n = 15 in each group): wild type (WT) group and CB2 knockout (CB2−/−) group. Orthodontic tooth movement (OTM) was induced by applying a nickel-titanium coil spring between the maxillary first molar and the central incisors. There are three subgroups within the WT groups (0, 7 and 14 days) and the CB2−/− groups (0, 7 and 14 days). 0-day groups without force application. Tooth displacement, alveolar bone mass and alveolar bone volume were assessed by micro-CT on 0, 7 and 14 days, and the number of osteoclasts was quantified by tartrate-resistant acid phosphatase (TRAP) staining. Moreover, the expression levels of RANKL and OPG in the compression area were measured histomorphometrically.
Results
The WT group exhibited the typical pattern of OTM, characterized by narrowed periodontal space and bone resorption on the compression area. In contrast, the accelerated tooth displacement, increased osteoclast number (P < 0.0001) and bone resorption on the compression area in CB2−/− group. Additionally, the expression of RANKL was significantly upregulated, while OPG showed low levels in the compression area of the CB2 − / − group (P < 0.0001).
Conclusions
CB2 modulated OTM and bone remodeling through regulating osteoclast activity and RANKL/OPG balance.
... Based on the theory of "pressure and tension," proposed by Oppenheim et al. and Schwarz et al., it is generally accepted that bone remodeling is dependent on the hydrostatic pressure conditions equivalent to capillary pulse pressure. Osteogenesis, the formation of new bone, predominantly occurs on the tension side of the PDL, whereas resorption, the removal of bone tissue, is primarily observed on the compression sides of the PDL [20]. ...
Orthodontic procedures can be inconvenient in nature. To overcome this problem, accelerated orthodontics play a
very important role to reduce existing trouble and discomfort. The most common inconvenience caused during
orthodontic treatment procedures is that they are very time consuming which can result in several drawbacks,
including an increased risk of tooth decay, gingival recession, and root resorption. Various methods can be
employed to expedite orthodontic treatment by accelerating tooth movement, including surgical-assisted procedures,
biological interventions, and the utilization of devices. These approaches effectively reduce the overall
period of treatment. The purpose of this review is to study the effective techniques for orthodontic tooth
movement as well as highlight various orthodontic accelerating methods in the respective approaches. Some nonsurgical
studies indicated that drug-induced methods can have a therapeutic effect on tooth movement. One of the
approaches involves the local administration of Vitamin 1.25D, which has been found to expedite tooth movement.
Vibrational orthodontic devices are a painless and cost-effective option that is considered the least invasive
approach for accelerating tooth movement. Meanwhile, surgical approach is also a successful method, wherein
great results and strong PDL tissue response were observed, but they cause a lot of pain and discomfort to the
patient. Therefore, due to the strengths and limitations of each procedure covered in the study, more research
should be done to identify the fastest way to speed up tooth mobility.
... Studies indicated that initial tooth movement is highly dependent on the mechanical properties of the PDL (Middleton et al., 1996;Bourauel et al., 1999;Qian et al., 2008). Based on linear elastic models, tooth displacements have generally been overstated when compared to non-linear elastic models (Shokrani et al., 2020). Non-linear mechanical properties of PDL substantially alters predicted biomechanical outcomes, not only the predicted displacements but also the stress or strain distribution (Hohmann et al., 2011). ...
Introduction: Open gingival embrasure (OGE) is a common complication in adults following clear aligner therapy and the influence of gingival or alveolar bone biotype on OGE is of great concern. Unfortunately, due to the limited number of patients with clearaligner therapy and the clinical methods to distinguish the gingival biotype of patients being invasive, it is difficult to carry out clinical studies on the gingival or alveolar bone biotype of the OGE. In the meanwhile, the detailed biomechanics of the occurrence of OGE remains unknown. The goal of this study was to establish a new model to simulate the virtual space region, namely, the OGE region, to investigate the relationship between alveolar bone biotype and the occurrence of OGE, and explore potential biomechanical factors related to OGE.
Methods: The OGE region in the interproximal space was established using a filler with a very low modulus of elasticity (1 × 10⁻⁶ MPa). To illustrate the biomechanics of OGE more exhaustively, a line was created at the top of the alveolar crest along the proximal tooth root. FEA was then used to analyze the biomechanics of the surrounding tissues, the OGE region and the line at the top of the alveolar crest along the proximal tooth root of the central incisor under two different labial bone thicknesses (thick and thin) with an axial inclination of 80°, 90° and 100°.
Results: During intrusion of the incisors in clear aligner therapy, as inclination increased or bone tissue became thinner, the stress in the surrounding tissues [tooth root, alveolar crest, and periodontal ligament (PDL)] was greater. In the OGE region and interproximal alveolar crest, the strain increased with increasing inclination and labial bone thinning. The results from the line at the top of the alveolar crest along the proximal tooth root showed more detailed biomechanics: In all groups, stress and strain were focused on the mesial-labial alveolar crest. Interestingly, our results also demonstrated that when OGE occurs, other complications may arise, including root resorption and bone dehiscence.
... Concerning the modeling procedure, we utilized simplified average model. Creating the simplified average model does not need much labor and time that are required in modeling based on CT images [31]. In addition, the simplified average model can generalize and evaluate the loading condition without considering numerous varieties of the teeth owing to tooth wear [28] or occlusal trauma [32] that were caused by anterior open bite. ...
An anterior open bite is one of the most difficult malocclusions in orthodontic treatment. For such malocclusion, orthodontic miniscrew insertion into both buccal and palatal alveolar regions has been indicated for molar intrusion, but it involves a risk of tooth root injury. To solve the problem, a midpalatal miniscrew-attached extension arm (MMEA) is adopted. However, this method causes palatal tipping of the molar because intrusive loads were applied only from the palatal side. Currently, a transpalatal arch is added to avoi0d tipping movement, but it induces the patient’s discomfort. Hence, the objective of this study was to evaluate the loading conditions for maxillary molar intrusion without tipping movement, only by MMEA through finite element (FE) analysis. FE models of maxillary right first molar and surrounding tissues were created. Three hook positions of MMEA were set at 6.0 mm perpendicular intervals in the occluso-apical direction along the mucosal contour. An intrusive unit load was applied from the palatal side of the molar, and various counter loads were applied from the buccal side. An optimal counter load for molar intrusion without palatal tipping was observed in each hook position. In conclusion, an ideal maxillary molar intrusion can be achieved only by MMEA with an optimal counter load.
Background
The correct torque of the incisors helps assess the effect of orthodontic treatment; however, evaluating it effectively remains a challenge. Improper anterior teeth torque angle can cause cortical bone fracture and root exposure.
Methods
A three-dimensional finite element model of the maxillary central incisor torque controlled by a self-made four-curvature auxiliary arch was established, And the experiments were divided to simulate four different group: (1) molar ligation group ; (2) micro-implant ligation group; (3) molar retraction group ༛(4) micro-implant retraction group༛and the retracted traction force was set at 1.15 N. The displacement of the maxillary dentition and periodontal ligament stress values were analyzed with different torque forces (0.5 N, 1 N, 1.5 N, 2 N) placed on the incisors.
Results
Provided the absence of a tooth extraction gap, when the four-curvature auxiliary arch was used in conjunction with absolute anchorage, the recommended force value was of < 1.5 N. when maxillary central incisor retraction, a force value of < 1 N was recommended. In the case of no-implant anchorage, whether there is tooth extraction gap or not, the recommended force value was of < 1 N. The stress on the other teeth did not exceed the value of that on the periodontal ligament. The effect of using the four-curvature on the incisors was significant.
Conclusions
The proposed approach may help improve treatment maxillary central incisor for poor torque and avoid cortical bone fracture and root exposure
This scoping review is intended to synthesize the techniques proposed to model the tooth‐ periodontal‐ligament‐bone‐complex (TPBC), while also evaluating the suggested PDL material properties. It is concentrated on the recent advancements on the PDL and TPBC models, while identifying the advantages and limitations of the proposed approaches. Systematic searches were conducted up to December 2020 for articles that proposed PDL models to assess OTM in Compendex, Web of Science, EMBASE, MEDLINE, PubMed, ScienceDirect, Google Scholar, and Scopus databases. Although there have been many studies focused on the evaluation of PDL material properties through numerous modelling approaches, only a handful of approaches have been identified to investigate the interface properties of the PDL as a complete dynamical system (TPBC models). Past reviews on the analytical and experimental determination of the PDL properties already show a concerning range in reported output values – some nearly six orders of magnitude in difference – that strongly suggested the need for further investigation. Surprisingly, it has not yet been possible to determine a narrower range of values for the PDL material properties. Moreover, very few scientific approaches address the TPBC as an integrated complex system model. In consequence, current methods for capturing the PDL material behaviour in a clinical setting are limited and inconclusive. This synthesis encourages more systematic, pragmatic, and phenomenological research in this area.
Background
Introducing tooth mobility simulation in laboratory studies can provide results with high accuracy and predictability.
Objectives
This study aims to review in vitro methodologies replicating tooth mobility and provide a recommended approach for future laboratory models.
Methods
Databases, such as PubMed, Cochrane Database of Systematic Review, BioMed Central and Chinese databases are searched, and twelve articles are included in the final review.
Results
Simulation methods of tooth mobility involving socket enlargement, screw loosening, alveolar bone loss simulation and a combination approach are identified from the extracted data. The materials used in preparing artificial teeth, artificial sockets and periodontal ligament simulator are discussed with a focus on their limitations. The achieved degrees of mobility and the presence of the centre of rotation are also evaluated. A timeline of the review articles is constructed to understand the trend of the preferred methods in tooth mobility simulation.
Conclusion
Future in vitro investigations can achieve clinical reliability, particularly for materials tested in the field of dental traumatology and periodontology, by recognising the importance of incorporating tooth mobility in laboratory studies. Improvised methods are proposed to ensure that potential laboratory models can resemble the actual oral environment.
Objective
The aim of this study was to investigate the three-dimensional (3D) position of the center of resistance of 4 mandibular anterior teeth, 6 mandibular anterior teeth, and the complete mandibular dentition by using 3D finite-element analysis.
Methods
Finite-element models included the complete mandibular dentition, periodontal ligament, and alveolar bone. The crowns of teeth in each group were fixed with buccal and lingual arch wires and lingual splint wires to minimize individual tooth movement and to evenly disperse the forces onto the teeth. Each group of teeth was subdivided into 0.5-mm intervals horizontally and vertically, and a force of 200 g was applied on each group. The center of resistance was defined as the point where the applied force induced parallel movement.
Results
The center of resistance of the 4 mandibular anterior teeth group was 13.0 mm apical and 6.0 mm posterior, that of the 6 mandibular anterior teeth group was 13.5 mm apical and 8.5 mm posterior, and that of the complete mandibular dentition group was 13.5 mm apical and 25.0 mm posterior to the incisal edge of the mandibular central incisors.
Conclusions
Finite-element analysis was useful in determining the 3D position of the center of resistance of the 4 mandibular anterior teeth group, 6 mandibular anterior teeth group, and complete mandibular dentition group.
Orthodontic tooth movement occurs as a result of resorption and formation of the alveolar bone due to an applied load, but the stimulus responsible for triggering orthodontic tooth movement remains the subject of debate. It has been suggested that the periodontal ligament (PDL) plays a key role. However, the mechanical function of the PDL in orthodontic tooth movement is not well understood as most mechanical models of the PDL to date have ignored the fibrous structure of the PDL. In this study we use finite element (FE) analysis to investigate the strains in the alveolar bone due to occlusal and orthodontic loads when PDL is modelled as a fibrous structure as compared to modelling PDL as a layer of solid material. The results show that the tension-only nature of the fibres essentially suspends the tooth in the tooth socket and their inclusion in FE models makes a significant difference to both the magnitude and distribution of strains produced in the surrounding bone. The results indicate that the PDL fibres have a very important role in load transfer between the teeth and alveolar bone and should be considered in FE studies investigating the biomechanics of orthodontic tooth movement.
It is important that all members of the dental team understand the reasons for undertaking orthodontic treatment and the principal treatment options that are available to the patient, says Jayne Harrison, Consultant Orthodontist at Liverpool University Dental Hospital.
The purpose of this investigation was to analyse the influence of geometric and material parameters of a human canine on initial tooth mobility, and the stress and strain profiles in the periodontal ligament. While the material parameters of tooth and bony structures are known within an uncertain limit of approximately a factor of 10, values reported for the elasticity parameters of the periodontal ligament differ significantly. In the course of this study, bilinear behaviour was assumed for the mechanical property of the periodontium. The finite element model of an elliptical paraboloid was created as an approximation to the geometry of a human canine to reduce calculation time and to determine influences of the geometry on numerical results. The results were compared with those obtained for a realistic human canine model. The root length of both models was 19.5 mm. By calculating pure rotational and pure tipping movements, the centre of resistance (CR) was determined for both models. They were located on the long axis of the tooth approximately 7.2 mm below the alveolar crest for the idealized model and 8.2 mm for the canine model. Thus, the centre of resistance of a human canine seems to be located around two-fifths of the root length from the alveolar margin. Using these results, uncontrolled tipping (1 N of mesializing force and 5 Nmm of derotating momentum), as well as pure translation (additionally about 10 Nmm of uprighting momentum) were calculated. Comparing the idealized and the realistic models, the uncontrolled tipping was described by the parabolic-shaped model within an accuracy limit of 10 per cent as compared with the canine model, whereas the results for bodily movement differed significantly showing that it is very difficult to achieve a pure translation with the realistic canine model.
Direct or indirect resorption are both perceived as a reaction to an applied force. This is in contrast to orthopaedic surgeons who describe apposition as 'the reaction to loading of bone'. The article reviews the literature on intrusion of teeth with periodontal breakdown, and on the basis of clinical and experimental studies. The conclusion is reached that intrusion can lead to an improved attachment level, and that forces have to be to low and continuous. The tissue reaction to a force system generating translation of premolars and molars in the five Macaca fascicularis monkeys is described. Three force levels, 100, 200, and 300 cN were applied for a period of 11 weeks. Undecalcified serial sections were cut parallel to the occlusal plane and a grid consisting of three concentric outlines of the root intersected by six radii was placed on each section so that areas anticipated to be subject to differing stress/strain distributions were isolated. A posteriori tests were utilized in order to separate areas that differed with regard to parameters reflecting bone turnover. Based on these results and a finite element model simulating the loading, a new hypothesis regarding tissue reaction to change in the stress strain distribution generated by orthodontic forces is suggested. The direct resorption could be perceived as a result of lowering of the normal strain from the functioning periodontal ligament (PDL) and as such as a start of remodelling, in the bone biological sense of the word. Indirect remodelling could be perceived as sterile inflammation attempting to remove ischaemic bone under the hyalinized tissue. At a distance from the alveolus, dense woven bone was observed as a sign of a regional acceleratory phenomena (RAP). The results of the intrusion could, according to the new hypothesis, be perceived as bending of the alveolar wall produced by the pull from Sharpey's fibres.
In orthodontics, the 3D translational and rotational movement of a tooth is determined by the force-moment system applied and the location of the tooth's centre of resistance (CR). Because of the practical constraints of in-vivo experiments, the finite element (FE) method is commonly used to determine the CR. The objective of this study was to investigate the geometric model details required for accurate CR determination, and the effect of material non-linearity of the periodontal ligament (PDL). A FE model of a human lower canine derived from a high-resolution µCT scan (voxel size: 50 µm) was investigated by applying four different modelling approaches to the PDL. These comprised linear and non-linear material models, each with uniform and realistic PDL thickness. The CR locations determined for the four model configurations were in the range 37.2-45.3% (alveolar margin: 0%; root apex: 100%). We observed that a non-linear material model introduces load-dependent results that are dominated by the PDL regions under tension. Load variation within the range used in clinical orthodontic practice resulted in CR variations below 0.3%. Furthermore, the individualized realistic PDL geometry shifted the CR towards the alveolar margin by 2.3% and 2.8% on average for the linear and non-linear material models, respectively. We concluded that for conventional clinical therapy and the generation of representative reference data, the least sophisticated modelling approach with linear material behaviour and uniform PDL thickness appears sufficiently accurate. Research applications that require more precise treatment monitoring and planning may, however, benefit from the more accurate results obtained from the non-linear constitutive law and individualized realistic PDL geometry.
Material structure-property relationship is strongly related to the employed process technology. Over the past years, laser processing of engineering materials has been proposed in many fields and different uses for diode lasers have been found in dentistry. In this contest, the potential of GaN- and InGaN-based laser diodes to cure dental materials was analysed. Two wavelengths of 405 nm and 445 nm were used as heat or light sources for warm condensation of gutta-percha, light transmission in dental posts and brackets or light curing of dental composites. Additive manufacturing approach was considered to fabricate 3D root analogues, suitable supports, positioning systems and moulds for optical measurements. A three-axis CAD/CAM system was implemented for positioning and aligning the laser beam.
The ability of diode-pumped solid-state lasers to cure dental materials or to transmit light was compared to that of a traditional instrument. Temperature profile at the apex of an additive manufactured root canal sealed with gutta-percha, light transmission through translucent quartz fiber post or through aesthetic ceramic bracket, bending properties and morphological features of light cured dental composites (Gradia Direct - GC Corporation and Venus Diamond - Heraeus Kulzer) were measured. Results showed a very high potential of diode-pumped solid-state lasers to be used in endodontics, orthodontics and restorative dentistry.
Objectives:
To evaluate the accuracy of three-dimensional stereophotogrammetry by comparing values obtained from direct anthropometry and the 3dMDface system. To achieve a more comprehensive evaluation of the reliability of 3dMD, both linear and surface measurements were examined.
Setting and sample population:
UCLA Section of Orthodontics. Mannequin head as model for anthropometric measurements.
Material and methods:
Image acquisition and analysis were carried out on a mannequin head using 16 anthropometric landmarks and 21 measured parameters for linear and surface distances. 3D images using 3dMDface system were made at 0, 1 and 24 hours; 1, 2, 3 and 4 weeks. Error magnitude statistics used include mean absolute difference, standard deviation of error, relative error magnitude and root mean square error. Intra-observer agreement for all measurements was attained.
Results:
Overall mean errors were lower than 1.00 mm for both linear and surface parameter measurements, except in 5 of the 21 measurements. The three longest parameter distances showed increased variation compared to shorter distances. No systematic errors were observed for all performed paired t tests (P<.05). Agreement values between two observers ranged from 0.91 to 0.99.
Conclusions:
Measurements on a mannequin confirmed the accuracy of all landmarks and parameters analysed in this study using the 3dMDface system. Results indicated that 3dMDface system is an accurate tool for linear and surface measurements, with potentially broad-reaching applications in orthodontics, surgical treatment planning and treatment evaluation.
Objectives
The objective of this study was to graphically display the pattern and magnitude of stress distribution along the periodontal ligament and the alveolar bone of upper first molars on application of intrusive forces using microscrew implants.
Materials and methods
A computer simulation of threedimensional model of maxillary first molars and second molars bilaterally with their periodontal ligament and alveolar bone, with microscrew implants, force element and a transpalatal arch were constructed on the basis of average anatomic morphology. Finite element analysis was done to evaluate the amount of stress and its distribution during orthodontic intrusive force.
Results
Overall maximum stress in this study was seen in the alveolar bone in the implant insertion area of 7.155 N/mm 2. Maximum stress in the periodontal ligament was seen in middle third distocervical palatal root surface of the first molar (0.008993 N/mm ² ). Maximum stress in the enamel was seen in the distal aspect of the cementoenamel junction (0.423 N/mm ² ). Maximum stress in the dentin was observed in apical one-third of the mesiobuccal root surface of first molar (0.1785 N/mm ² ).
Conclusion
In this study with the use of palatal implant and transpalatal arch, we found that there was no tipping observed during intrusion. This study demonstrates that significant true intrusion of maxillary molars could be obtained in a wellcontrolled manner by using fixed appliances with microscrew implant as bony anchorage.
How to cite this article
Pavithra AS, Prashanth GS, Mathew S, Shekar SE. Analysis of Stress in the Periodontal Ligament and Alveolar Bone of the Maxillary First Molars during Intrusion with Microscrew Implants: A 3D Finite Element Study. World J Dent 2014;5(1):11-16.
While orthodontic tooth movement (OTM) gains considerable popularity and clinical success, the roles played by relevant tissues involved, particularly periodontal ligament (PDL), remain an open question in biomechanics. This paper develops a soft-tissue induced external (surface) remodeling procedure in a form of power law formulation by correlating time-dependent simulation in-silico with clinical data in-vivo (p<0.05), thereby providing a systematic approach for further understanding and prediction of OTM. The biomechanical stimuli, namely hydrostatic stress and displacement vectors experienced in PDL, are proposed to drive tooth movement through an iterative hyperelastic finite element analysis (FEA) procedure. This algorithm was found rather indicative and effective to simulate OTM under different loading conditions, which is of considerable potential to predict therapeutical outcomes and develop a surgical plan for sophisticated orthodontic treatment.
Closed-form analytical formulas for a tooth of paraboloidal shape in pure translation are presented. These formulas are based on both the approximation of normal and tangential strains in terms of the translational displacement of the tooth and the tooth equilibrium of the thin surrounding periodontal membrane (or on the strain energy conservation equivalently). The tooth is considered to be a rigid body while the surrounding membrane is assumed to be an elastic foundation of uniform thickness. The proposed formulas are capable of determining the most important quantities involved in the case of tooth translation; these are the stiffness of the tooth-support in translation, the distribution of strain and stress tensors in the membrane, the maximum value of hydrostatic stress, as well as the location of the center of resistance. It was found that the proposed formulas involve not only the root length h, as the previous literature reports, but also the root diameter D. The theory is successfully compared to three-dimensional finite element results for an upper central incisor.
A dedicated software package that allows simulation of tooth movement can lead to shortening of the treatment program in orthodontics. A first step in the development of this software is the modelling of the movement of a single tooth. Forces applied to the crown of the tooth are transmitted to the alveolar bone through the periodontal ligament, stretching, and compressing the ligament, eventually resulting in tooth movement. This paper presents an analytical model that predicts stresses and strains inside this ligament by approximating the shape of the root as an elliptic paraboloid. The model input consists of 2 material parameters and 4 geometrical parameters. To assess the accuracy of the model a finite element model (FEM) was constructed to compare the results and the influence of the eccentricity of the root was studied. The results show that the model is able to successfully describe the global behavior of the PDL and, except at a region near the alveolar crest, the differences between analytical and FEM results are small. In contrast to FEM, the analytical model does not require setting up a 3D-model and creating a mesh, allowing for significantly lower computational times and reducing cost when implementing in clinical practice.
Many attempts have been made to reproduce theoretically the
stress-strain curves obtained from experiments on the isothermal
deformation of highly elastic 'rubberlike' materials. The existence of a
strain-energy function has usually been postulated, and the
simplifications appropriate to the assumptions of isotropy and
incompressibility have been exploited. However, the usual practice of
writing the strain energy as a function of two independent strain
invariants has, in general, the effect of complicating the associated
mathematical analysis (this is particularly evident in relation to the
calculation of instantaneous moduli of elasticity) and, consequently,
the basic elegance and simplicity of isotropic elasticity is sacrificed.
Furthermore, recently proposed special forms of the strain-energy
function are rather complicated functions of two invariants. The purpose
of this paper is, while making full use of the inherent simplicity of
isotropic elasticity, to construct a strain-energy function which: (i)
provides an adequate representation of the mechanical response of
rubberlike solids, and (ii) is simple enough to be amenable to
mathematical analysis. A strain-energy function which is a linear
combination of strain invariants defined by φ
(α)=(a1α+a2α+a3α-3)/α
is proposed; and the principal stretches a1,a2 and
a3 are used as independent variables subject to the
incompressibility constraint a1a2a3=1.
Principal axes techniques are used where appropriate. An excellent
agreement between this theory and the experimental data from simple
tension, pure shear and equibiaxial tension tests is demonstrated. It is
also shown that the present theory has certain repercussions in respect
of the constitutive inequality proposed by Hill (1968a, 1970b).
Orthodontic tooth movements are based on the ability of bone to react to mechanical stresses with the apposition and resorption of alveolar bone. Currently, the underlying biophysical, biochemical, and cellular processes are the subject of numerous studies. At present, however, an analytical description of orthodontic tooth movements including all components of the processes involved seems to be impossible. It was the aim of the present study to develop a mechanics-based phenomenological model capable of describing the alveolar bone remodeling. Thus, 2 different models were developed. The first is based on the assumption that deformations of the periodontal ligament (PDL) are the key stimulus to starting orthodontic tooth movement. The second supposes that deformations of the alveolar bone are the basis of orthodontic bone remodeling. Both models were integrated into a finite element package calculating stresses, strains and deformations of tooth and tooth supporting structures and from this simulating the movement of the tooth and its alveolus through the bone. Clinically induced canine retractions in 5 patients as well as force systems were exactly measured and the tooth movements were simulated using both models. The results show that the first model allows reliable simulation of orthodontic tooth movements, whereas the second is to be rejected.
A numerical model that calculates bone apposition and resorption around a tooth root on the basis of bone remodeling theories was developed to simulate orthodontic tooth movements. The model was used to calculate different kinds of orthodontic tooth movements, that were then compared with the expected movements based on clinical experience. For simulation of the movements the root of a canine was modeled in an idealized way in the form of an elliptical paraboloid and was processed with a finite element program. The finite element model was loaded with defined force systems. Two model assumptions were used to calculate the bone remodeling process. The mechanical loads firstly in the periodontal ligament and secondly in the alveolar bone were taken to simulate the following tooth movements: 1. mesial tipping around the center of resistance (force system at the bracket: isolated torque MY = Nmm), 2. Rotation around the long axis of the tooth (MZ = 5 Nmm), 3. uncontrolled tipping around the root tip (FX = 1 N, MZ = 5 Nmm), 4. canine retraction (FX = 1 N, MY = −9.5 Nmm, MZ = 5 Nmm), 5. and 6. extrusion/intrusion (FZ = ±0.5 N, MX = ±2.5 Nmm). Comparison with clinical experience was performed by calculating the orthodontic tooth movements based on the assumption of a fixed position of the center of resistance.
It could be demonstrated that the numerical model of orthodontic bone remodeling can be used to calculate orthodontic tooth movements. However, the results are strongly dependent on the model assumptions. The model simulating the bone remodeling on the basis of the loading of the periodontal ligament delivers results that are in very good accordance with the biomechanical assumptions of the position of the center of resistance. However, marked side effects occurned with the second model, especially in the simulations of uncontrolled tipping, translation and intrusion/extrusion. Clinically, these side effects cannot be observed.
This review is intended to highlight and discuss discrepancies in the literature of the periodontal ligament's (PDL) mechanical properties and the various analytical models, approaches and assumptions used in simulating its behaviour. The present study then offers to propose a model development that allows for a better phenomenological description of PDL behaviour under static, near clinical, orthodontic loading conditions.
Searches were performed on biomechanical and orthodontic publications (in databases: Compendex, EMBASE, MEDLINE, PubMed, ScienceDirect and Scopus).
The review revealed that significant variations exist, some on the order of six orders of magnitude, in the PDL's elastic constants and mechanical properties. Possible explanations may be attributable to different modelling approaches and behavioural assumptions.
The discrepancies highlight the need for further research into determining what the key factors that contribute to tooth movement are, their correlations and their degree of impact. Despite the PDL's definitive role in orthodontic tooth movement, proposed models of the PDL's mechanical behaviour thus far have been unsatisfactorily inadequate. Hence, there is a need to develop a robust PDL model that more accurately simulates the PDL's biomechanical response to orthodontic loads. Better understanding of the PDL's biomechanical behaviour under physiologic and traumatic loading conditions might enhance the understanding of the PDL's biologic reaction in health and disease. Providing a greater insight into the response of the PDL would be instrumental to orthodontists and engineers for designing more predictable, and therefore more efficacious, orthodontic appliances.
Finite element analysis (FEA) is a widespread technique to evaluate the stress/strain distributions in teeth or dental supporting tissues. However, in most studies occlusal forces are usually simplified using a single vector (i.e., point load) either parallel to the long tooth axis or oblique to this axis. In this pilot study we show how lower first molar occlusal information can be used to investigate the stress distribution with 3D FEA in the supporting bone structure. The LM(1) and the LP(2) -LM(1) of a dried modern human skull were scanned by μCT in maximum intercuspation contact. A kinematic analysis of the surface contacts between LM(1) and LP(2) -LM(1) during the power stroke was carried out in the occlusal fingerprint analyzer (OFA) software to visualize contact areas during maximum intercuspation contact. This information was used for setting the occlusal molar loading to evaluate the stress distribution in the supporting bone structure using FEA. The output was compared to that obtained when a point force parallel to the long axis of the tooth was loaded in the occlusal basin. For the point load case, our results indicate that the buccal and lingual cortical plates do not experience notable stresses. However, when the occlusal contact areas are considered, the disto-lingual superior third of the mandible experiences high tensile stresses, while the medio-lingual cortical bone is subjected to high compressive stresses. Developing a more realistic loading scenario leads to better models to understand the relationship between masticatory function and mandibular shape and structures. Am J Phys Anthropol, 2012. © 2011 Wiley Periodicals, Inc.
The finite element method is a promising tool to investigate the material properties and the structural response of the periodontal ligament (PDL). To obtain realistic and reproducible results during finite element simulations of the PDL, suitable bio-fidelic finite element meshes of the geometry are essential.
In this study, 4 independent coworkers generated altogether 17 volume meshes (3-dimensional) based on the same high-resolution computed-tomography image data set of a tooth obtained in vivo to compare the influence of the different model generation techniques on the predicted response to loading for low orthodontic forces.
It was shown that the thickness of the PDL has a significant effect on initial tooth mobility but only a remarkably moderate effect on the observed stress distribution in the PDL. Both the tooth and the bone can be considered effectively rigid when exploring the response of the PDL under low loads. The effect of geometric nonlinearities could be neglected for the applied force system.
Most importantly, this study highlights the sensitivity of the finite element simulation results for accurate geometric reconstruction of the PDL.
Printout. Thesis (Ph. D.)--University of Alabama at Birmingham, 2002. Includes bibliographical references (leaf 57).
Orthodontic tooth movement (OTM) is achieved by applying an orthodontic force system to the brackets. The (re)modeling processes of the alveolar support structures are triggered by alterations in the stress/strain distribution in the periodontium. According to the classical OTM theories, symmetric zones of compression and tension are present in the periodontium, but these do not consider the complex mechanical properties of the PDL, the alveolar structures' morphology, and the magnitude of the force applied.
Human jaws segments obtained from autopsy were microCT-scanned and sample-specific finite element (FE) models were generated. The material behavior of the PDL was considered to be nonlinear and non-symmetric and the alveolar bone was modeled according to its actual morphology. A series of FE-analyzes investigated the influence of the moment-to-force ratio, force magnitude, and chewing forces on the stress/strain in the alveolar support structures and OTM.
Stress/strain findings were dependent on alveolar bone's morphology. Because of the nonlinear behavior of the PDL, distinct areas of tension, and compression could not be detected. Secondary load transfer mechanisms were activated and the stress/strain distribution in the periodontium was concealed by occlusal forces.
We could not confirm the classical ideas of distinct and symmetrical compressive and tensile areas in the periodontium in relation to different OTM scenarios. Light continuous orthodontics forces will be perceived as intermittent by the periodontium. Because roots and alveolar bone morphology are patient-specific, FE-analysis of orthodontic loading regime should not be based on general models.
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.
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.
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.
The key parameter indicating beginning root resorption used in this study was an increased value for hydrostatic pressure in the PDL.
A strain gauge measurement device with low force clip gauges, for measurement of initial tooth displacement in two dimensions has been developed. An experimental model simulating a maxillary central incisor is loaded with different known and controlled force systems. The resulting tooth displacements are described by the position of the centre of rotation and the generated angle of rotation for the total tooth movement. The effect of a single force, a moment, and force-moment combinations producing different moment to force ratios were studied. From these results the required force system needed to produce tooth movements with different centres of rotation for a central incisor of average root length are calculated. Furthermore, the model allows us to measure the accuracy of the measuring device by comparing results to analytical and laser holographic data, obtained on similar models. Some preliminary measurements and results, using human autopsy material are presented.
This study was designed to investigate the stress levels induced in the periodontal tissue by orthodontic forces using the three-dimensional finite element method. The three-dimensional finite element model of the lower first premolar was constructed on the basis of average anatomic morphology and consisted of 240 isoparametric elements. Principal stresses were determined at the root, alveolar bone, and periodontal ligament (PDL). In all loading cases for the buccolingually directed forces, three principal stresses in the PDL were very similar. At the surface of the root and the alveolar bone, large bending stresses acting almost in parallel to the root were generally observed. During tipping movement, stresses nonuniformly varied with a large difference from the cervix to the apex of the root. On the other hand, in case of movement approaching translation, the stresses induced were either tensile or compressive at all occlusogingival levels with some difference of the stress from the cervix to the apex. The pattern and magnitude of stresses in the periodontium from a given magnitude of force were markedly different, depending on the center of rotation of the tooth.
A new tool for measuring tooth movement--laser holography--offers an accurate, noninvasive approach for determining movement in three dimensions. This in vitro study is designed to establish the required force system applied on the crown of a maxillary incisor that would produce different centers of rotation, as in lingual tipping, translation, and root movement. The relationship between moment-to-force ratios and centers of rotation is shown. The experimental data are compared to theoretic approaches. With respect to the location of the center of resistance and centers of rotation, force systems needed to produce different centers of rotation are given for a central incisor of average root length.
In the past, vertical intrusive movement of teeth has been considered difficult and most routine clinical vertical movement of teeth has been confined to extrusion. It has been suggested that attempts at intrusion may result in an increased incidence of root resorption and also in occasional devitalization.
The displacement and resulting stress fields associated with such treatment can be successfully studied using the finite element method. In the case being considered initial movements are known to be small; therefore, the assumption in the study that the material behaves linear-elastically is considered to be reasonable.
This study of vertical tooth movement demonstrated that the maximum cervical margin stress in the periodontal ligament was 0·0046 N/mm ² , whilst the highest apical stress was 0·00205 N/mm ² when intrusive and extrusive forces of 1 Newton were applied to the buccal surface of the crown of a tooth model. These stresses were evaluated in the light of previous studies and found to be within the suggested clinical optimum level. However, the periodontal stress distribution following orthodontic loading within this three-dimensional finite element model was found to be highly complex.
Current remodeling theories, as applied to long bones, suggest that such processes are controlled by mechanical strains either within or on the bone surface. In this study, the stresses and strains within the periodontal ligament and surrounding bone, consequent to orthodontic loading of a tooth, were investigated by application of the finite element method. Previously, various authors have applied two and three dimensional instantaneous (essentially static) models to analyze the problems. The study reported in this article describes an initial time-dependent (continuous/dynamic) finite element model for tooth movement that uses newly developed software, the results being cross-referenced against historical data. These early results, from a two-dimensional mathematical model of a loaded canine tooth, suggest that the remodeling process may be controlled by the periodontal ligament rather than the bone. In the finite element model, bone was found to experience a low strain of 1 x 10(-5), whereas the periodontal ligament experienced a strain of 0.1 when the "tooth model" is loaded. Only this latter figure is above the threshold usually reported to be necessary to initiate the remodeling process. Further developments in this rapidly advancing area of biomechanical research should facilitate a greater increase in our knowledge of tissue stress and strain after loading.
The position of the centre of resistance (Cre) as well as the centre of rotation (Cro) of a tooth under a force-system is still an open question. This paper presents a reliable and efficient three-dimensional rigid-body finite element technique to accurately estimate these centres. The influence of not only the root length but also the root diameter, the thickness of the periodontal ligament, as well as its material properties on the position of the Cre and Cro is investigated. Additionally, an explanation is given for the meaning of the coefficient (0.068 h(2) ) involved in Burstone's theoretical formula which is generalised and is expressed as the ratio of the flexibilities of tooth support in translation and pure moment rotation, respectively. The former ratio determines the position of the centres of rotation as a function of the applied moment-to-force ratio (M/F) and the relevant curve remains an isosceles hyperbola for any arbitrary-shaped tooth. The present study focuses on single-rooted teeth, such as maxillary canines and maxillary incisors, but the proposed methodology is generally applicable to any tooth.
This study was undertaken to determine the types of orthodontic forces that cause high stress at the root apex. A 3-dimensional finite element model of a maxillary central incisor, its periodontal ligament (PDL), and alveolar bone was constructed on the basis of average anatomic morphology. The maxillary central incisor was chosen for study because it is one of the teeth at greatest risk for apical root resorption. The material properties of enamel, dentin, PDL, and bone and 5 different load systems (tipping, intrusion, extrusion, bodily movement, and rotational force) were tested. The finite element analysis showed that purely intrusive, extrusive, and rotational forces had stresses concentrated at the apex of the root. The principal stress from a tipping force was located at the alveolar crest. For bodily movement, stress was distributed throughout the PDL; however, it was concentrated more at the alveolar crest. We conclude that intrusive, extrusive, and rotational forces produce more stress at the apex. Bodily movement and tipping forces concentrate forces at the alveolar crest, not at the apex.
The purpose of the study was to use the finite element method to simulate the effect of alveolar bone loss on orthodontically induced stress in the periodontal ligament of the maxillary first molar. A 3-dimensional finite element model of a tooth with different levels of bone height was constructed to estimate the reduction in force and the increase in moment to force (M/F) ratio necessary to obtain evenly distributed stress in the periodontal ligament of a tooth with horizontal bone loss. The 3-dimensional finite model comprised a maxillary first molar, the periodontal ligament, and alveolar bone and consisted of 3097 nodes and 2521 elements. An anterior force of 300 g was applied at the center of the buccal crown surfaces of teeth with normal bone height and with bone loss that ranged from 2.0 to 6.0 mm. The results showed that force magnitude required lowering from 80% (2-mm bone loss) and gradually to 37% (6-mm bone loss) of the initial load applied to the tooth without bone loss. The countertipping moment (gram-millimeters) to force (gram) ratio should increase from 9 (no bone loss) to nearly 13 (6-mm bone loss) to maintain the same range of stress in the periodontal ligament as was obtained without bone loss. A linear relationship was observed between the amount of bone loss, the desired reduction in force magnitude, and the increase in M/F ratio. The results of this study indicate that a combination of force reduction and increased M/F ratio is required to achieve uniform stress in the periodontal ligament of a tooth with bone loss.
Orthodontic tooth movement is achieved by (re)modeling processes of the alveolar bone, which are triggered by changes in the stress/strain distribution in the periodontium. In the past, the finite element (FE) method has been used to describe the stressed situation within the periodontal ligament (PDL) and surrounding alveolar bone. The present study sought to determine the impact of the modeling process on the outcome from FE analyses and to relate these findings to the current theories on orthodontic tooth movement. In a series of FE analyses simulating teeth subjected to orthodontic loading, the influence of geometry/morphology, material properties, and boundary conditions was evaluated. The accurate description of alveolar bone morphology and the assignment of non-linear mechanical properties for the PDF elements demonstrate that loading of the periodontium cannot be explained in simple terms of compression and tension along the loading direction. Tension in the alveolar bone was far more predominant than compression.
The paper demonstrates how to generate an individual 3D volume model of a human single-rooted tooth using an automatic workflow. It can be implemented into finite element simulation. In several computational steps, computed tomography data of patients are used to obtain the global coordinates of the tooth's surface. First, the large number of geometric data is processed with several self-developed algorithms for a significant reduction. The most important task is to keep geometrical information of the real tooth. The second main part includes the creation of the volume model for tooth and periodontal ligament (PDL). This is realized with a continuous free form surface of the tooth based on the remaining points. Generating such irregular objects for numerical use in biomechanical research normally requires enormous manual effort and time. The finite element mesh of the tooth, consisting of hexahedral elements, is composed of different materials: dentin, PDL and surrounding alveolar bone. It is capable of simulating tooth movement in a finite element analysis and may give valuable information for a clinical approach without the restrictions of tetrahedral elements. The mesh generator of FE software ANSYS executed the mesh process for hexahedral elements successfully.
The stressed state of the periodontal ligament (PDL) is understood to play a critical role in the tooth movement initiated by orthodontic treatment. Finite element simulations have been used to describe PDL stresses for orthodontic loading; however, these models have predominantly assumed linear mechanical properties for the PDL. The present study sought to determine the importance of using nonlinear mechanical properties and nonuniform geometric data in computer predictions of periodontal ligament stresses and tooth movements. A 2-dimensional plane-strain finite element model of a mandibular premolar was constructed based on anatomic data of transverse sections of tooth, PDL, and bone from a 24-year-old cadaveric man. A second model was constructed of the same tooth but with a PDL of uniform thickness. Each of these was prescribed linear or nonlinear elastic mechanical properties, as obtained in our own experiments. Predictions of the maximum and minimum principal stresses and von Mises stresses in the PDL were determined for extrusive and tipping forces. The results indicated that biofidelic finite element models predicted substantially different stresses in the PDL for extrusive loading than did the uniform thickness model, suggesting that incorporation of the hourglass shape of the PDL is warranted. In addition, incorporation of nonlinear mechanical properties for the PDL resulted in dramatic increases in the stresses at the apex and cervical margin as compared with the linear models.
Orthodontic tooth movements are based on the ability of bone reaction to mechanical stimulus with the deposition and resorption of alveolar bone. The numerical simulation of tooth movement could be helpful for the treatment strategy. However, at present, few calculations have been carried out on the tooth movement simulation.
Finite element (FE) models were developed to simulate an orthodontic treatment of mandibular canine tipping movement during a therapy period with decayed loads. The tooth movement was based on the surface bone remodeling method, and the normal strain of periodontal ligament was assumed as the key mechanical stimulus for alveolar bone remodeling. Changes in the tooth position and the geometry of the tooth supporting structures were taken into account.
The highest normal strain in the periodontal ligament was observed at the cervix or apex and the lowest normal strain was observed near the middle of the root. The tipping degrees of the simulation were similar to the observed in clinical studies.
It was acceptable to simulate clinical tooth tipping movements by finite element method based on these mechanical assumptions. Such a numerical simulation would be used to predict clinical tooth movements and help the planning of the therapy.
Digital tools in the interdisciplinary orthodontic treatment of adult patients
- Ogodescu AS
On the development of an integrated bone remodelling law for orthodontic tooth movements models using the finite element method(dissertation)
- Mengonim
Mengoni M. On the development of an integrated bone remodelling law for orthodontic tooth movements models using the finite element method (dissertation). Université de Liège, Belgium;
2012.
Biomechanics of periodontal ligament specific to clinical orthodontics(dissertation)
- Tomssr
Digital tools in the interdisciplinary orthodontic treatment of adult patients
- A S Ogodescu
- C Sinescu
- E A Ogodescu
- M Negrutiu
- E Bratu
Ogodescu AS, Sinescu C, Ogodescu EA, Negrutiu M, Bratu E.
Digital tools in the interdisciplinary orthodontic treatment of adult
patients. Int J Biol Biomed Eng. 2010;4:97-105.