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.     

Histochemical examination of cathepsin K,MMP1 and MMP2 in compressed periodontal ligament during orthodontic tooth movement in periostin deficient mice

The purpose of this study was to investigate immunolocalization of collagenolytic enzymes including cathepsin K, matrix metalloproteinase (MMP) 1 and 2 in the compressed periodontal ligament (PDL) during orthodontic tooth movement using a periostin deficient (Pn-/-) mouse model. Twelve-week-old male mice homozygous for the disrupted periostin gene and their wild type (WT) littermates were used in these experiments. The tooth movement was performed according to Waldo’s method, in which elastic bands of 0.5 mm thickness were inserted between the first and second upper molars of mice under anesthesia. At 1 and 3 days after orthodontic force application, mice were fixed with transcardial perfusion of 4 % paraformaldehyde in 0.1 M phosphate buffer (pH 7.4), and the first molars and peripheral alveolar bones were extracted for histochemical analyses. Compared with WT mice, immunolocalization of cathepsin K, MMP1 and MMP2 was significantly decreased at 1 and 3 days after orthodontic tooth movement in the compressed PDL of Pn-/- mice, although MMP1-reactivity and MMP2-reactivity decreased at different amounts. Very little cathepsin K-immunoreactivity was observed in the assessed regions of Pn-/- mice, both before and after orthodontic force application. Furthermore, Pn-/- mice showed a much wider residual PDL than WT mice. Taken together, we concluded that periostin plays an essential role in the function of collagenolytic enzymes like cathepsin K, MMP1 and MMP2 in the compressed PDL after orthodontic force application.     

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.     

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.     

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.     

Stress analysis of irradiated human tooth enamel using finite element methods

The objectives of this project were to use finite element methods to determine how changes in the elastic modulus due to oral cancer therapeutic radiation alter the distribution of mechanical stresses in teeth and to determine if observed failures in irradiated teeth correlate with changes in mechanical stresses. A thin slice section finite element (FE) model was constructed from micro CT sections of a molar tooth using MIMICS and 3-Matic software. This model divides the tooth into three enamel regions, the dentin-enamel junction (DEJ) and dentin. The enamel elastic modulus was determined in each region using nano indentation for three experimental groups namely – control (non-radiated), in vitro irradiated (simulated radiotherapy following tooth extraction) and in vivo irradiated (extracted subsequent to oral cancer patient radiotherapy) teeth. Physiological loads were applied to the tooth models at the buccal and lingual cusp regions for all three groups (control, in vitro and in vivo). The principal tensile stress and the maximum shear stress were used to compare the results from different groups since it has been observed in previous studies that delamination of enamel from the underlying dentin was one of the major reasons for the failure of teeth following therapeutic radiation. From the FE data, we observed an increase in the principal tensile stress within the inner enamel region of in vivo irradiated teeth (9.97 ± 1.32 MPa) as compared to control/non-irradiated teeth (8.44 ± 1.57 MPa). Our model predicts that failure occurs at the inner enamel/DEJ interface due to extremely high tensile and maximum shear stresses in in vivo irradiated teeth which could be a cause of enamel delamination due to radiotherapy.     

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.     

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.     

3-D finite element modelling of facial soft tissue and preliminary application in orthodontics

Prediction of soft tissue aesthetics is important for achieving an optimal outcome in orthodontic treatment planning. Previously, applicable procedures were mainly restricted to 2-D profile prediction. In this study, a generic 3-D finite element (FE) model of the craniofacial soft and hard tissue was constructed, and individualisation of the generic model based on cone beam CT data and mathematical transformation was investigated. The result indicated that patient-specific 3-D facial FE model including different layers of soft tissue could be obtained through mathematical model transformation. Average deviation between the transformed model and the real reconstructed one was 0.47 ± 0.77 mm and 0.75 ± 0.84 mm in soft and hard tissue, respectively. With boundary condition defined according to treatment plan, such FE model could be used to predict the result of orthodontic treatment on facial soft tissue.     

On the importance of modelling organ geometry and boundary conditions for predicting three-dimensional prostate deformation

The use of an ultrasound probe or a needle guide during biopsy deforms both the rectal wall and the prostate, resulting in lesion motion. An accurate patient-specific finite element (FE)-based biomechanical model can be used to predict prostate deformations. In this study, an FE model of a prostate phantom is developed using magnetic resonance images, while soft-tissue elasticity is estimated in vivo using an ultrasound-based acoustic radiation force impulse imaging technique. This study confirms that three-dimensional FE-predicted prostate deformation is predominantly dependent on accurate modelling of prostate geometry and boundary conditions. Upon application of various compressive displacements, our results show that a linear elastic FE model can accurately predict prostate deformations. The maximum global error between FE-predicted simulations and experimental results is 0.76 mm. Moreover, the effect of including the urethra, puboprostatic ligament and urinary bladder on prostate deformations is investigated by a sensitivity study.     

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.     

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.     

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.     

Interactive graph-cut segmentation for fast creation of finite element models from clinical ct data for hip fracture prediction

In this study, we propose interactive graph cut image segmentation for fast creation of femur finite element (FE) models from clinical computed tomography scans for hip fracture prediction. Using a sample of N = 48 bone scans representing normal, osteopenic and osteoporotic subjects, the proximal femur was segmented using manual (gold standard) and graph cut segmentation. Segmentations were subsequently used to generate FE models to calculate overall stiffness and peak force in a sideways fall simulations. Results show that, comparable FE results can be obtained with the graph cut method, with a reduction from 20 to 2–5 min interaction time. Average differences between segmentation methods of 0.22 mm were not significantly correlated with differences in FE derived stiffness (R² = 0.08, p = 0.05) and weakly correlated to differences in FE derived peak force (R² = 0.16, p = 0.01). We further found that changes in automatically assigned boundary conditions as a consequence of small segmentation differences were significantly correlated with FE derived results. The proposed interactive graph cut segmentation software MITK-GEM is freely available online at https://simtk.org/home/mitk-gem.     

Semi-automatic generation of finite element meshes fo dental preparations]

The mechanical properties and elastic behaviour of periodontal tissue are a decisive factor in understanding initial tooth mobility and bone remodelling processes in orthodontics. An experimental set-up was designed to precisely determine a tooth's elastic response to different loading conditions. Segments of pig's maxilla bearing separated molars were used, and their mechanical response to loading was recorded. Subsequently, finite element analysis (FEA) was performed on the basis of the experimental data. The combination of experimental and numerical methods was used to determine the material properties of the periodontal ligament (PDL). The geometries of the preparations were reconstructed and FE meshes generated semi-automatically with the aid of the special computer program, CAGOG (Computer Aided Generator for Orthodontic Geometries) to optimally match the experimental geometry. Nonlinear material parameters were determined for the PDL and verified by comparing experimental and numerical results obtained in other specimens with an error of about 10%. This good correlation indicates that the selected method of mesh generation is appropriate for creating realistic FE models that can be compared with experimental results.     

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.     

Mechanical responses of the periodontal ligament based on an exponential hyperelastic model: a combined experimental and finite element method

The V–W exponential hyperelastic model is adopted to describe the instantaneous elastic response of the periodontal ligament (PDL). The general theoretical framework of constitutive modeling is described based on nonlinear continuum mechanics, and the elasticity tensor used to develop UMAT subroutine is formulated. Nanoindentation experiment is performed to characterize mechanical properties of an adult pig PDL specimen. Then the experiment is simulated by using the finite element (FE) analysis. Meanwhile, the optimized material parameters are identified by the inverse FE method. The good agreement between the simulated results and experimental data demonstrates that the V–W model is capable of describing the mechanical behavior of the PDL. Therefore, the model and its implementation into FE code are validated. By using the model, we simulate the tooth movement under orthodontic loading to predict the mechanical responses of the PDL. The results show that local concentrations of stress and strain in the PDL are found.     

Matrix metalloproteinase 2 activity decreases in human periodontal ligament fibroblast cultures submitted to simulated orthodontic force

Orthodontic force compresses the periodontal ligament promoting the expression of pro-inflammatory mediators and matrix metalloproteinases responsible for tooth movement. The extent in time while periodontal cells are being treated and the increment in the amount of mechanical stress caused by the orthodontic force is thought to regulate the levels of metalloproteinases in the periodontal tissue. To study the possible regulation in the activity of metalloproteinases 2, 3, 7, 9, and 10 by simulated orthodontic force, human periodontal ligament fibroblast cultures were centrifuged (141×g) for 30, 60, 90, and 120 min, simulating the orthodontic force. Cell viability, protein quantification, and activity of metalloproteinases by zymography were evaluated at 24, 48, and 72 h after centrifugation in both cell lysates and growth medium. The activity of the 72-kDa matrix metalloproteinase 2 was decreased at 24 h regardless of the duration of centrifugation and at 48 h in cells centrifuged for 30 min only. Decrease in the amount of total protein in lysates was seen at 48 and 72 h with no change in cell viability. The data seem to indicate that the amount of mechanical stress regulates the levels of secreted matrix metalloproteinase 2. In addition, the centrifugation as a model for simulated orthodontic force may be used as a simple and reliable method to study the role played by matrix metalloproteinases in periodontal ligament when submitted to mechanical force as occurring during 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.     

Finite element method analysis of the tooth movement induced by orthodontic forces

The finite element method is a useful technique for measuring structural stress and for movement analyses. The objective of this investigation was to get a more accurate estimation of tooth movement depending on application point when a tipping orthodontic force is applied. The three-dimensional model of un upper canine, consisting of 4,000 hexahedron elements with 2,367 nodes was obtained. Horizontal, orally directed 1N tipping orthodontic force was applied to the model on five different levels of the tooth crown. The three-dimensional mathematical finite element model is useful in analyzing the tooth movement in response to orthodontic forces. The tipping tooth movement is greater if the force is applied closer to its neck, or more gingivally.