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.     

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.     

Quantitative Approach for the Prediction of Tooth Movement During Orthodontic Treatment

The orthodontic treatment is aimed to displace and/or rotate the teeth to obtain the functionally correct occlusion and the best aesthetics and consists in applying forces and/or couples to tooth crowns. The applied loads are generated by the elastic recovery of metallic wires linked to the tooth crowns by brackets. These loads generate a stress state into the periodontal ligament and hence, in the alveolar bone, causing the bone remodeling responsible for the tooth movement. The orthodontic appliance is usually designed on the basis of the clinical experience of the orthodontist. In this work, a quantitative approach for the prediction of the tooth movement is presented that has been developed as a first step to build up a computer tool to aid the orthodontist in designing the orthodontic appliance. The model calculates the tooth movement through time with respect to a fixed Cartesian frame located in the middle of the dental arch. The user interface panel has been designed to allow the orthodontist to manage the standard geometrical references and parameters usually adopted to design the treatment. Simulations of specific cases are reported for which the parameters of the model are selected in order to reproduce forecasts of tooth movement matching data published in experimental works.     

Distribution of 3H-proline within transseptal fibers of the rat following release of orthodontic forces

Maxillary right first molar teeth of rats were tipped mesially with an orthodontic appliance for 2 weeks (experimental group), 3H-proline was injected, and orthodontic forces were removed 6 hr later (time 0). The contralateral molar teeth of treated (internal control group) and age- and weight-matched untreated animals (external control group) were also studied. Diastemata were created between the molar teeth by the orthodontic appliance, and transseptal fibers between first and second (P less than 0.001) and second and third molars (P less than 0.005) were significantly lengthened as compared to external and internal controls at time 0. Diastemata between molar teeth were closed 5 days after removal of orthodontic force. Transseptal fibers adjacent to the source of the orthodontic force (mesial region) had the highest mean number of 3H-proline-labeled proteins at time 0 and at all times following removal of the force (P less than 0.001), and had the highest rate of labeled protein removal (P less than 0.001). Half-lives for removal of 3H-proline-labeled transseptal fiber proteins were significantly greater in mesial and distal regions and significantly less in middle regions of experimentals than in corresponding regions of external controls (P less than 0.001). These data suggest the following: 1) transseptal fibers adjust their length by rapid remodeling in regions experiencing a tensile force; 2) collagenous protein turnover within the middle third of the transseptal fibers is more rapid subsequent to release of orthodontic force than during normal physiologic drift, suggesting that this region adapts rapidly to changes in adjacent tooth position and that these fibers do not play a significant role in relapse of orthodontically relocated teeth; and 3) significant differences in turnover rates of 3H-proline-labeled transseptal ligament proteins of external and internal control quadrants suggest that tooth movement produces both local and systemic effects on collagenous protein metabolism.     

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.     

Quantitative approach for the prediction of tooth movement during orthodontic treatment

The orthodontic treatment is aimed to displace and/or rotate the teeth to obtain the functionally correct occlusion and the best aesthetics and consists in applying forces and/or couples to tooth crowns. The applied loads are generated by the elastic recovery of metallic wires linked to the tooth crowns by brackets. These loads generate a stress state into the periodontal ligament and hence, in the alveolar bone, causing the bone remodeling responsible for the tooth movement. The orthodontic appliance is usually designed on the basis of the clinical experience of the orthodontist. In this work, a quantitative approach for the prediction of the tooth movement is presented that has been developed as a first step to build up a computer tool to aid the orthodontist in designing the orthodontic appliance. The model calculates the tooth movement through time with respect to a fixed Cartesian frame located in the middle of the dental arch. The user interface panel has been designed to allow the orthodontist to manage the standard geometrical references and parameters usually adopted to design the treatment. Simulations of specific cases are reported for which the parameters of the model are selected in order to reproduce forecasts of tooth movement matching data published in experimental works.     

Cervical helical axis characteristics and its center of rotation during active head and upper arm movements-comparisons of whiplash-associated disorders, non-specific neck pain and asymptomatic individuals

The helical axis model can be used to describe translation and rotation of spine segments. The aim of this study was to investigate the cervical helical axis and its center of rotation during fast head movements (side rotation and flexion/extension) and ball catching in patients with non-specific neck pain or pain due to whiplash injury as compared with matched controls. The aim was also to investigate correlations with neck pain intensity. A finite helical axis model with a time-varying window was used. The intersection point of the axis during different movement conditions was calculated. A repeated-measures ANOVA model was used to investigate the cervical helical axis and its rotation center for consecutive levels of 15 degrees during head movement. Irregularities in axis movement were derived using a zero-crossing approach. In addition, head, arm and upper body range of motion and velocity were observed. A general increase of axis irregularity that correlated to pain intensity was observed in the whiplash group. The rotation center was superiorly displaced in the non-specific neck pain group during side rotation, with the same tendency for the whiplash group. During ball catching, an anterior displacement (and a tendency to an inferior displacement) of the center of rotation and slower and more restricted upper body movements implied a changed movement strategy in neck pain patients, possibly as an attempt to stabilize the cervical spine during head movement.     

Finite centroid and helical axis estimation from noisy landmark measurements in the study of human joint kinematics

Recent work on joint kinematics indicates that the finite centroid (centre of rotation) and the finite helical axis (axis of rotation, screw axis, twist axis) are highly susceptible to measurement errors when they are experimentally determined from landmark position data. This paper presents an analytical model to describe these effects, under isotropic conditions for the measurement errors and for the spatial landmark distribution. It appears that the position and direction errors are inversely proportional to the rotation magnitude, and that they are much more error-prone than the relatively well-determined rotation and translation magnitudes. Furthermore, the direction and rotation magnitude errors are inversely proportional to the landmark distribution radius, and the position and translation magnitude errors are minimal if the mean position of the landmarks coincides with the centroid or helical axis. For the planar centroid, the use of rigid-body constraints results in considerable precision improvement relative to the classical, finite Reuleaux method for centroid reconstruction. These analytical results can be used to define suitable measurement configurations, and they are used in this paper to explain experimental results on R?ntgenphotogrammetrically acquired in vitro wrist joint movement.     

Mandibular kinematics represented by a non-orthogonal floating axis joint coordinate system

There are many methods used to represent joint kinematics (e.g., roll, pitch, and yaw angles; instantaneous center of rotation; kinematic center; helical axis). Often in biomechanics internal landmarks are inferred from external landmarks. This study represents mandibular kinematics using a non-orthogonal floating axis joint coordinate system based on 3-D geometric models with parameters that are "clinician friendly" and mathematically rigorous. Kinematics data for two controls were acquired from passive fiducial markers attached to a custom dental clutch. The geometric models were constructed from MRI data. The superior point along the arc of the long axis of the condyle was used to define the coordinate axes. The kinematic data and geometric models were registered through fiducial markers visible during both protocols. The mean absolute maxima across the subjects for sagittal rotation, coronal rotation, axial rotation, medial-lateral translation, anterior-posterior translation, and inferior-superior translation were 34.10 degrees, 1.82 degrees, 1.14 degrees, 2.31, 21.07, and 6.95 mm, respectively. All the parameters, except for one subject's axial rotation, were reproducible across two motion recording sessions. There was a linear correlation between sagittal rotation and translation, the dominant motion plane, with approximately 1.5 degrees of rotation per millimeter of translation. The novel approach of combining the floating axis system with geometric models succinctly described mandibular kinematics with reproducible and clinician friendly parameters.     

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.     

Histological evidence that metformin reverses the adverse effects of diabetes on orthodontic tooth movement in rats

This study evaluated the effects of metformin on orthodontic tooth movement in a rat model of type 2 diabetes mellitus. Rats were fed a high-fat diet for 4 weeks to induce fat accumulation and insulin resistance, and then injected with a low dose of streptozotocin (35 mg/kg) intraperitoneally to induce type 2 diabetes. An orthodontic appliance was placed in normoglycemic, type 2 diabetes, and type 2 diabetes with metformin-administrated rats. After 14 days, type 2 diabetes rats exhibited greater orthodontic tooth movement and had a higher number of tartrate-resistant acid phosphatase-positive osteoclasts, stronger cathepsin K expression, and weaker alkaline phosphatase immunostaining than normoglycemic rats. Metformin administration resulted in normalization of osteoclast numbers, cathepsin K immunostaining, and of tooth movement as well as partly recovery of alkaline phosphatase expression in diabetic rats. Metformin also reduced sclerostin expression and improved the immunolocalization of dentin matrix protein 1 in osteocytes of type 2 diabetes rats. These results suggest that metformin administration reversed the adverse effects of diabetes on orthodontic tooth movement.     

A visco-elastic model for the prediction of orthodontic tooth movement

This study presents a biomechanical model of orthodontic tooth movement. Although such models have already been presented in the literature, most of them incorporate computationally expensive finite elements (FE) methods to determine the strain distribution in the periodontal ligament (PDL). In contrast, the biomechanical model presented in this work avoids the use of FE methods. The elastic deformation of the PDL is modelled using an analytical approach, which does not require setting up a 3D model of the tooth. The duration of the lag phase is estimated using the calculated hydrostatic stresses, and bone remodelling is predicted by modelling the alveolar bone as a viscous material. To evaluate the model, some typically used motion patterns were simulated and a sensitivity analysis was carried out on the parameters. Results show that despite some shortcomings, the model is able to describe commonly used motion patterns in orthodontic tooth movement, in both single- and multi-rooted teeth.     

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.     

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.     

Numerical Estimation of the Centres of Rotation and Resistance in Orthodontic Tooth Movement

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.     

General method for calculating helical parameters of polymer chains from bond lengths,bond angles,and internal-rotation angles

Helical conformations of infinite polymer chains may be described by the helical parameters, d and θ (the translation along the helix axis and the angle of rotation about the axis per repeat unit), _pi (the distance of the ith atom from the axis), d_ij, and d_ij (the translation along the axis and the angle of rotation, respectively, on passing from the ith atom to the jth). A general method has been worked out for calculating all those helical parameters from the bond lengths, bond angles, and internal-rotation angles. The positions of the main chain and side chain atoms with respect to the axis may also be calculated. All the equations are applicable to any helical polymer chain and are readily programmed for electronic computers. A method is also presented for calculating the partial derivatives of helical parameters with respect to molecular parameters.     

成年人个别牙早失伴错(牙合)畸形修复前正畸治疗的临床观察

目的:探讨成年人个别牙缺失伴错牙合患者,通过正畸治疗校正错牙合后,修复治疗的疗效情况。方法:对16例成年人个别牙缺失致前牙散在间隙或伴有反牙合患者,采用直丝弓矫治技术进行修复前正畸治疗。结果:16例成年人个别牙缺失伴错牙合畸形的患者经过修复前正畸治疗后,再进行牙列缺损修复治疗,获得了令患者较为满意的疗效,外貌也得到了改善。结论:通过正畸、修复相结合的口腔综合治疗,可以有效地使便利体获得更加完善的口腔功能及美观效果。     

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.     

Expression of genes for gelatinases and tissue inhibitors of metalloproteinases in periodontal tissues during orthodontic tooth movement

Orthodontic tooth movement progresses by a combination of periodontal ligament (PDL) tissue and alveolar bone remodeling processes. Besides the remodeling of alveolar bone around the moving teeth, the major extracellular matrix (ECM) components of PDLs, collagens, are degenerated, degraded, and restructured. Matrix metalloproteinases (MMPs) and their specific inhibitors, tissue inhibitors of metalloproteinases (TIMPs), act in a co-ordinated fashion to regulate the remodeling of periodontal tissues. We hypothesized that the expression levels of the genes for MMP-2, MMP-9, and TIMPs 1–3 are increased transiently in the periodontal tissue during orthodontic tooth movement. To test this hypothesis, we employed an animal model of tooth movement using rats, as well as in situ hybridization to analyze the expression levels of Mmp-2, Mmp-9, and Timps 1-3. The expression levels of these genes increased transiently in cells of periodontal tissues, which include cementoblasts, fibroblasts, osteoblasts, and osteoclasts, at the compression side of the moving teeth. The transient increases in gene expression at the tension side were mainly limited to osteoblasts and cementoblasts. In conclusion, the expression levels of Mmp-2, Mmp-9, and Timps 1-3 increase transiently during orthodontic tooth movement at both the tension and compression sides. The expression of these genes is regulated differentially in the periodontal tissue of the tension side and compression side. This altered pattern of gene expression may determine the rate and extent of remodeling of the collagenous ECM in periodontal tissues during orthodontic tooth movement.