Time-related PDL: viscoelastic response during initial orthodontic tooth movement of a tooth with functioning interproximal contact-a mathematical model

Most anteroposterior orthodontic movements of posterior teeth have to overcome the "resistance" of adjacent teeth with functioning interproximal contacts. The aim of this study was to develop a mathematical model describing initial posterior tooth movement associated with functioning interproximal contacts in relation to the viscoelastic mechanical behavior of the human periodontal ligament (PDL). A linear viscoelastic 2D mathematical model was modified to depict tipping movement around the center of rotation (C(rot)) of a premolar where tipping is restrained by adjacent teeth. Equilibrium equations were applied taking into account the sagittal moment developed around the C(rot). The constants of the model were analyzed and applied to a numerical model that can simulate short-term tooth creep movement caused by a tipping force. Changes in force magnitude (0.5-3N) and crown length (6-10mm) were analyzed until no movement was observed (steady state). Premolar displacement in contact with adjacent teeth showed a non-linear progression over time with an initial sharp tipping movement followed by a transient period of 2.6-7.1min. As tipping force increased the transient period increased. A similar but smaller effect was observed with an increase in crown length. The premolar initial displacement within the arch (3.2-19.5microm) is about seven-fold smaller than retraction/protraction movement of an incisor. These suggest reduction in tooth displacement when functioning interproximal contact is present and clinically recommend establishing a space in the direction of tooth displacement before tooth movement.     

Three-dimensional analysis of orthodontic tooth movement

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

Finite element-based force/moment-driven simulation of orthodontic tooth movement

The objectives of this study were to develop a numerically controlled experimental set-up to predict the movement caused by the force systems of orthodontic devices and to experimentally verify this system. The presented experimental set-up incorporated an artificial tooth fixed via a 3D force/moment sensor to a parallel kinematics robot. An algorithm determining the initial movement of the tooth in its elastic embedding controlled the set-up. The initial tooth movement was described by constant compliances. The constants were obtained prior to the experiment in a parameterised finite element (FE) study on the basis of a validated FE model of a human molar. The long-term tooth movement was assembled by adding up a multiple of incremental steps of initial tooth movements. A pure translational movement of the tooth of about 8 mm resulted for a moment to force ratio of ? 8.85 mm, corresponding to the distance between the bracket and the centre of resistance. The correct behaviour of this linear elastic model in its symmetry plane allows for simulating single tooth movement induced by orthodontic devices.     

Computer simulation of orthodontic tooth movement using CT image-based voxel finite element models with the level set method

Orthodontic tooth movement (OTM) is an adaptive biomechanical response of dentoalveolar components to orthodontic forces, in which remodeling of the alveolar bone occurs in response to changes in the surrounding mechanical environment. In this study, we developed a framework for OTM simulation by combining an image-based voxel finite element method, with a surface-tracking level set method using three-dimensional computer models. For a case study to demonstrate its capability of expressing clinical tooth movement, we observed displacement and rotation of the tooth under three types of force conditions. The simulation results demonstrate that the proposed simulation method has the potential to predict clinical OTM.     

A new method for finite element simulation of orthodontic appliance-teeth-periodontium-alveolus system

This paper describes a new simulation method to analyze the initial behavior of the total system comprising orthodontic appliance, teeth, and their supporting structures. It is based on a finite element method which additionally takes account of a rotational degree of freedom. Beam and rod elements are used for finite element idealization of orthodontic appliance. Through spring elements it is connected with the teeth supported by the alveolar structures. The technique of 'initial strain' is introduced so as to analyze the effects of a gable bend and activation on the force system which is delivered by the orthodontic appliance. As compared with the photoelastic technique hitherto used, this method serves to investigate systematically and quantitatively the initial aspect of orthodontic tooth movement.     

Comparison of the finite helical axis and the rectangular coordinate system in representing orthodontic tooth movement

In orthodontics, tooth movement is typically described using the rectangular coordinate system (XYZ); however, this system has several disadvantages when performing biomechanical analyses. An alternative method is the finite helical axis (FHA) system, which describes movement as a rotation about and a translation along a single axis located in space. The purpose of this study was to examine differences between the FHA and the XYZ systems in analyzing orthodontic tooth movement. Maxillary canine retraction was done using sliding mechanics or a retraction spring with midpalatal orthodontic implants used as measuring references. Tooth movement calculated with the FHA was compared with the corresponding movement in the rectangular coordinate system weekly over a 2-month interval in eight patients. The FHA showed that sliding mechanics controlled rotation of the canine better than the retraction spring (Ricketts retractor), and that the Ricketts retractor controlled tipping better. Changes in the FHA direction and position vectors with time showed that the biomechanical forces are not uniform during the treatment period. In both mechanics, the FHA provided a simple biomechanical model for canine retraction.     

Simulation of bone remodelling in orthodontic treatment

Orthodontic treatments not only displace irregular teeth but also induce responses in surrounding bone tissues. Bone remodelling is regarded as the regulatory mechanism triggered by mechanical loading. This study was aimed at investigating the effect of orthodontic loading on both tooth movement and neighbouring bone density distribution. A set of computational algorithms incorporating both external and internal remodelling mechanisms was implemented into a patient-specific 3D finite element (FE) model to investigate and analyse orthodontic treatment under four typical modes of orthodontic loading. The consequence of orthodontic treatment was reproduced numerically by using this FE-based technique. The results indicated that the diverse modes of orthodontic loading would result in different magnitudes of tooth movement and particular morphology of bone density distribution. It is illuminated that the newly developed algorithms may replicate the clinical situation more closely compared with the previous proposed method.     

Concept for development of new individual treatment devices in orthodontics using 3-dimensional numerical simulation of bone remodeling]

The present study is part of a research project that includes different components for the simulation of orthodontic tooth movement and comparing experimental results. This concept includes the development of a bone remodelling algorithm, as well as experimental studies on tooth movement. After the acquisition and evaluation of specific experimental data of the patient's situation, the individual components have to be integrated to verify and forecast tooth movement. The aim is to design individual treatment devices as well as to shorten treatment while making it more effective. The geometry of the teeth and that of the surrounding alveolar bone both influence the orthodontic tooth movement. For this reason, an exact morphological tooth model for the valid simulation of the tooth movement is needed, and can be constructed from computed tomography data. Simulation of tooth movement can then be compared with "in vivo" measurements of the orthodontic tooth movement. In this study, a specially developed hybrid retraction spring is employed. This spring enables the application of a defined, almost constant force system. The "in vivo" determined tooth movement is simulated with the aid of special positioning and measuring devices. Meanwhile, the active force system can be determined by 6-component force/moment sensors. The experimentally measured force system, "in vivo" measurements of tooth movement and the CT model are now available for numerical simulation for the first time.     

A novel method for the three-dimensional (3-D) analysis of orthodontic tooth movement-calculation of rotation about and translation along the finite helical axis.

The purpose of this study was to establish a novel method for evaluating orthodontic tooth movement in three-dimensional (3-D) space. The present system consisted of the following procedures at a given treatment period: (1) 3-D tooth positions were measured with a 3-D surface-scanning system using a slit laser beam; (2) the 3-D shape data were registered automatically at the maxillary first molars, and the coordinate systems were normalized; (3) the rotation matrix and translation vector were calculated from the automatic registration of the two position data for a given tooth; (4) the finite helical axes of teeth were calculated as the locus of zero rotational displacement; and (5) tooth movement was presented as rotation about and translation along the finite helical axis. To test this system, a male patient (age 22 yr 2 months) with Angle Class III malocclusion and moderate crowding of the anterior teeth, who had been treated using a standard multi-bracket appliance, was used as a model case in this study. Impressions for a dental cast model were taken at five phases; immediately before and after application of the appliance, and 10 days, 1 month and 2 months after beginning treatment. The results demonstrated that the present analytical method can more simply describe the movement of a given tooth by rotation about and translation along the finite helical axis, and provides quantitative visual 3-D information on complicated tooth movement during orthodontic treatment.     

Numerical study of tension and strain distribution around rat molars]

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

Finite element modeling of superelastic nickel–titanium orthodontic wires

Thanks to its good corrosion resistance and biocompatibility, superelastic Ni–Ti wire alloys have been successfully used in orthodontic treatment. Therefore, it is important to quantify and evaluate the level of orthodontic force applied to the bracket and teeth in order to achieve tooth movement. In this study, three dimensional finite element models with a Gibbs-potential-based-formulation and thermodynamic principles were used. The aim was to evaluate the influence of possible intraoral temperature differences on the forces exerted by NiTi orthodontic arch wires with different cross sectional shapes and sizes. The prediction made by this phenomenological model, for superelastic tensile and bending tests, shows good agreement with the experimental data. A bending test is simulated to study the force variation of an orthodontic NiTi arch wire when it loaded up to the deflection of 3 mm, for this task one half of the arch wire and the 3 adjacent brackets were modeled. The results showed that the stress required for the martensite transformation increases with the increase of cross-sectional dimensions and temperature. Associated with this increase in stress, the plateau of this transformation becomes steeper. In addition, the area of the mechanical hysteresis, measured as the difference between the forces of the upper and lower plateau, increases.     

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

Abstract

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

微种植体支抗内收及压低上前牙的有限元研究

目的:探讨在利用微种植体支抗整体内收前牙过程中增加前牙区不同位置压低力对上颌前后牙的生物力学效应的影响。方法:采用螺旋CT扫描获取图像并结合MIMICS等软件进行三维重建,建立拔除上颌第一前磨牙整体内收前牙的三维有限元模型,分析利用第二前磨牙与第一磨牙间微种植体整体内收前牙过程中,增加前牙区不同位置压低力后前后牙的生物力学效应。结果:增加前牙区压低力后,前牙舌向倾斜移动明显减小,不同位置的垂直向力对前牙的影响不同,第一磨牙在整体内收过程中表现为远中倾斜移动。结论:1增加前牙区压低力能够实现对前牙转矩的有效控制;2增加前牙区的压低力使前牙更趋向于整体移动;3在微种植体支抗内收前牙过程实现了较好的垂直向控制。     

Comparison of methods to determine the centre of resistance of teeth

In orthodontic treatment, the locations of the centre of resistance (CR) of individual teeth and the applied load system are the major determinants for the type of tooth movement achieved. Currently, CR locations have only been specified for a relatively small number of tooth specimen for research purposes. Analysing cone beam computed tomography data samples from three upper central incisors, this study explores whether the effort to establish accurate CR estimates can be reduced by (i) morphing a pre-existing simplified finite element (FE) mesh to fit to the segmented 3D tooth-bone model, and (ii) individualizing a mean CR location according to a small parameter set characterising the morphology of the tooth and its embedding. The FE morphing approach and the semi-analytical approach led to CR estimates that differ in average only 0.04 and 0.12 mm respectively from those determined by very time-consuming individual FE modelling (standard method). Both approaches may help to estimate the movement of individual teeth during orthodontic treatment and, thus, increase the therapeutic efficacy.     

正畸牙移动相关信号通路研究进展

<正>畸牙移动是在机械力的作用下,通过对牙周膜产生牵张或压缩的力来引起牙周组织在生理限度内的组织改建,从而达到牙齿移动、矫治畸形的目的。由于没有明显的年龄限制,正畸矫治在全球范围已变得越来越普遍。因此,相关的研究也日益增多。牙齿移动的生物学基础是正畸力作用于牙周组织激活一系列信号转导通路,进而引起牙周膜的修复改建。为指导临床、加速正畸矫治疗程提供新的思路,本文综述了近年来有关正畸牙移动相关信号通路的研究进展。发现最新的研究集中在MAPK信号通路,Wnt/β-catenin信号通路,PI3K/AKt/m TOR信号通路,BMP-2信号通路,Caspase-3介导的凋亡通路较多。但是正畸牙移动引起的牙周组织改建是一个多种生物力学信号转导通路相互调节相互作用的过程,对于上述信号通路之间的相互关系还有待于我们更进一步的探索。     

Effect of variable periodontal ligament thickness and its non-linear material properties on the location of a tooth’s centre of resistance

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.     

The Biomechanical Function of Periodontal Ligament Fibres in Orthodontic Tooth Movement

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.     

Experimental model of tooth mobility in the human "in vivo"]

The aim of the present study was to investigate experimentally the mechanical properties of tooth deflection under external loading. These properties have a significant impact on tooth movement during orthodontic treatment. The stresses and strains caused by tooth movement influence bone remodelling, which is the basis of orthodontic treatment. The movement of a tooth as a direct reaction to the forces acting on it is termed "initial" movement. It is nonlinear and has a clearly time-dependent component. While the initial tooth movement represents the totality of the reaction mechanisms of all the tissues of the tooth unit, it is determined primarily by the mechanical properties of the periodontal ligament (PDL). The PDL is the softest tissue of the tooth unit and is therefore subject to the largest deformations when forces act on the crown of the tooth. The objective of orthodontic treatment is to achieve as precise and rapid tooth movement as possible, without provoking such undesired effects as bone and root resorption. To enable the implementation of an optimal orthodontic force system that meets these requirements, a thorough knowledge of the biomechanics of tooth movement is a must.     

Numerical analysis of orthodontic treatment elements of pseudo-elastic NiTi alloys]

In orthodontic treatment malpositions of teeth are often corrected by fixed appliances, consisting, in part, of loops made by the orthodontist. The most important alloys in use are steel, cobalt-chromium, or titanium-molybdenium alloys. The static force systems of fixed appliances made of these materials are well known from experimental and numerical studies, but as they may change during tooth movement, we are often confronted with problems in therapy. The introduction of pseudoelastic nickel titanium alloys (NiTi) into orthodontic treatment, offers the chance of improving the effectiveness and reliability of orthodontic devices. In the present paper a plane finite element (FE) for the analysis of orthodontic loops is presented. It enables the determination of the nonlinear behaviour of pseudoelastic NiTi-alloys and is capable of simulating large structural displacements and rotations accompanied by moderate strains. A comparative numerical and experimental study shows the efficiency of this element. The associated results reflect pseudoelastic effects on certain loop designs, and reveal the benefits for the orthodontist and his patients.     

Determination of stress levels and profiles in the periodontal ligament by means of an improved three-dimensional finite element model for various types of orthodontic and natural force systems

This study was undertaken to investigate the stress-strain levels and distribution within the periodontal ligament for various types of physiological and orthodontic force systems, assuming that the bone resorption process, leading to tooth movements, is partly controlled by those conditions. Two finite element models were developed, simulating a full and partial mandibular morphology, respectively. Both models were based on morphology and physical parameters of human autopsy material. The effect of changing material parameters and structure, type of boundary conditions, calculation method and fineness of the model on the stress levels and profiles in the periodontal ligament was evaluated by a series of tests. A structure optimization technique was used to investigate the load bearing characteristics of the mandible and the influence of the anisotropic material properties of both the mandible and the segment. A ‘multiple modelling’ technique based on both the mandible and the segment was developed to test various types of boundary conditions in the analysis of the segment. Results presented as ‘stress profiles’ showing the correlation between the applied force system and the stress distribution in the periodontal ligament, based on the improved finite element models, were established.