Centre of resistance and centre of rotation of a tooth: experimental determination, computer simulation and the effect of tissue nonlinearity

Effect of occlusal hypofunction on centre of resistance in maxillary central incisor using the finite element method

OBJECTIVES

To determine differences in the location of centre of resistance (Cres) between functional and hypofunctional teeth and to evaluate the relationship between the pulp cavity volume and locations of the Cres, using the finite element (FE) method.

DESIGN

Retrospective cohort study.

PARTICIPANTS

FE models of right maxillary central incisor, derived from cone-beam computed tomography (CBCT) images of 46 participants, were divided into normal function (n = 23) and hypofunction (n = 23) groups using anterior overbite and cephalometric measurements.

METHODS

Measurements of the tooth and pulp cavity volume were made from the CBCT. Cres levels were presented as percentages of the root length from the root's apex. All data were analysed and compared using the independent t-test (P < 0.05). The relationship between the location of Cres and volume ratios were evaluated statistically.

RESULTS

The means of the pulp cavity/tooth volume and root canal/ root volume ratio of the maxillary central incisor in the anterior open bite group were significantly greater than those in the normal group. The average location of Cres in the anterior open bite group was 0.6 mm (3.7%) apically from the normal group, measured from root apex. The difference was statistically significant (P < 0.01). There was a significant correlation between root canal/root volume ratio and locations of Cres (r = -0.780, P < 0.001).

CONCLUSIONS

The Cres in the hypofunctional group was located more apical than the functional group. As the pulp cavity volume increased, the level of Cres shifted apically.

Three-dimensional positions of the center of resistance of the maxillary canine distal movement under orthodontic force loading

Using finite-element analysis, we aimed to determine the center of resistance (CRes) of the maxillary canine for setting orthodontic forces. The inclination of the canine was measured by first loading from the mesial to the distal side of the mesial root surface, then the position and direction of the load that minimized the inclination were investigated. The CRes was defined as the set of midpoints of the minimum distances between two inclination lines. Twenty-one CRes values were calculated from a set of seven lines. These CRes data were then aggregated as a 95% confidence ellipsoid of width 0.170×0.016×0.009 mm with center points 4.269, 0.224, and 4.315 mm in the apical, mesial, and lingual directions from the origin, respectively. Further studies are required to effectively apply the CRes identified in this study to clinical applications.

Comparative study of stress characteristics around the adjacent teeth tissues during insertion of mini-screws with different insertion angles: A three-dimensional finite element study

With a limited alveolar bone position, there is a high risk that mini-screws (MS) implants could cause damage to the adjacent teeth. To reduce this damage, the position and tilt angle of the MS must be optimized. The aim of this study was to assess the effect of MS implantation angle on the stress exerted on adjacent periodontal membrane and roots. A three-dimensional finite element model containing dentition, periodontal ligament, jaw and MS were established based on the CBCT images and MS scanning data. The MS was first inserted perpendicular to the surface of the bone at specific locations and then tilted at an angle of 10° and 20° to the mesial and distal teeth, respectively. The stress distribution in the periodontal tissue of the adjacent teeth was analyzed after MS implantation at different angles.The stress on the adjacent tooth root and periodontal ligament was most uniformly distributed when the MS was inserted vertically. It changed 9.4-97.7% when the axis of MS was tilted at 10-degree and 20-degree angles from the point of vertical insertion. The stresses experienced by the periodontal ligament and the root are similar. When the horizontal angle of the MS insertion was changed, the MS was closer to the adjacent tooth, resulting in greater stress near the PDL and root. It was recommended to insert the MS vertically into the alveolar bone surface to avoid root damage due to excessive stress.

Investigating the role of aligner material and tooth position on orthodontic aligner biomechanics

The primary objective of this work was to investigate the effect of material selection and tooth position on orthodontic aligner biomechanics. Additionally, material property changes with thermoforming were studied to elucidate its role in material performance in-vitro. An orthodontic simulator (OSIM) was used to evaluate forces and moments at 0.20 mm of lingual displacement for central incisor, canine and second premolar using Polyethylene terephthalate (PET), Polyurethane (PU) and Glycol-modified polyethylene terephthalate (PET-G) materials. The OSIM was scanned to generate a model used to fabricate aligners using manufacturer-specified thermoforming procedures. Repeated measures of MANOVA was used to analyze the effect of teeth and material on forces/moments. The role of thermoforming was evaluated by flexural modulus estimated by 3-point bend tests. Pre-thermoformed and post-thermoformed samples were prepared using as-received sheets and those thermoformed over a simplified arch using rectangular geometry, respectively. Groups were compared using Two-way ANOVA. The PET, PU, and PET-G materials exerted maximum buccal force and corresponding moments on the canine. PU exerted more buccal force than PET-G on the canine and second premolar, and more than PET on the second premolar. The impact of thermoforming varied according to the specific polymer: PET-G remained stable, there was a slight change for PET, and a significant increase was noted for PU from pre-thermoformed to post-thermoforming. The results of this study elucidate the influence of material and arch position on the exerted forces and moments. Further, the mechanical properties of thermoplastic materials should be evaluated after thermoforming to characterize their properties for clinical application.

Does pulp cavity affect the center of resistance in three-dimensional tooth model? A finite element method study

OBJECTIVES

To compare the center of resistance (Cres) of the maxillary central incisor in models with and without the pulp cavity and to evaluate the association of pulp cavity/tooth volume ratio and difference in Cres position between the two models.

MATERIALS AND METHODS

CBCT images of the right maxillary central incisor were collected from 18 subjects. Pulp cavity/tooth volume ratio was measured, and finite element models of teeth and periodontal structures were generated. Cres location was presented as a percentage of root length measured from the root apex. Differences in Cres positions between models were compared using the paired t-test, while the correlation between pulp cavity/tooth volume ratio and a difference in Cres was evaluated by Pearson's correlation coefficient.

RESULTS

For the pulp cavity model, the average location of the Cres measured from the apex of the root was 58.8% ± 3.0%, which resulted in a difference of 4.1% ± 1.1% (0.5 mm) apically, when compared with the model without pulp cavity. Differences in Cres between the models were statistically significant (P < 0.01), while the correlation between pulp cavity/tooth volume ratio and a difference in Cres between models was significantly positive (r = 0.709, P = 0.001).

CONCLUSIONS

In the pulp cavity model, the Cres was located in a more apical position. The difference in Cres between models increased as the pulp cavity/tooth volume ratio increased.

CLINICAL RELEVANCE

The line of force must be applied more apically in the pulp cavity model to achieve the desired orthodontic tooth movement.

Three-dimensional finite element analysis of the effect of alveolar cleft bone graft on the maxillofacial biomechanical stabilities of unilateral complete cleft lip and palate

BACKGROUND

The objective is to clarify the effect of alveolar cleft bone graft on maxillofacial biomechanical stabilities, the key areas when bone grafting and in which should be supplemented with bone graft once bone resorption occurred in UCCLP (unilateral complete cleft lip and palate).

METHODS

Maxillofacial CAD (computer aided design) models of non-bone graft and full maxilla cleft, full alveolar cleft bone graft, bone graft in other sites of the alveolar cleft were acquired by processing the UCCLP maxillofacial CT data in three-dimensional modeling software. The maxillofacial bone EQV (equivalent) stresses and bone suture EQV strains under occlusal states were obtained in the finite element analysis software.

RESULTS

Under corresponding occlusal states, the EQV stresses of maxilla, pterygoid process of sphenoid bone on the corresponding side and anterior alveolar arch on the non-cleft side were higher than other maxillofacial bones, the EQV strains of nasomaxillary, zygomaticomaxillary and pterygomaxillary suture on the corresponding side were higher than other maxillofacial bone sutures. The mean EQV strains of nasal raphe, the maximum EQV stresses of posterior alveolar arch on the non-cleft side, the mean and maximum EQV strains of nasomaxillary suture on the non-cleft side in full alveolar cleft bone graft model were all significantly lower than those in non-bone graft model. The mean EQV stresses of bilateral anterior alveolar arches, the maximum EQV stresses of maxilla and its alveolar arch on the cleft side in the model with bone graft in lower 1/3 of the alveolar cleft were significantly higher than those in full alveolar cleft bone graft model.

CONCLUSIONS

For UCCLP, bilateral maxillae, pterygoid processes of sphenoid bones and bilateral nasomaxillary, zygomaticomaxillary, pterygomaxillary sutures, anterior alveolar arch on the non-cleft side are the main occlusal load-bearing structures before and after alveolar cleft bone graft. Alveolar cleft bone graft mainly affects biomechanical stabilities of nasal raphe and posterior alveolar arch, nasomaxillary suture on the non-cleft side. The areas near nasal floor and in the middle of the alveolar cleft are the key sites when bone grafting, and should be supplemented with bone graft when the bone resorbed in these areas.

WITHDRAWN: A method to isolate forces and moments applied to teeth: An in vitro experiment

The publisher regrets that this article has been temporarily removed. A replacement will appear as soon as possible in which the reason for the removal of the article will be specified, or the article will be reinstated. The full Elsevier Policy on Article Withdrawal can be found at https://www.elsevier.com/about/our-business/policies/article-withdrawal.

A multi-patient analysis of the center of rotation trajectories using finite element models of the human mandible

Studying different types of tooth movements can help us to better understand the force systems used for tooth position correction in orthodontic treatments. This study considers a more realistic force system in tooth movement modeling across different patients and investigates the effect of the couple force direction on the position of the center of rotation (CRot). The finite-element (FE) models of human mandibles from three patients are used to investigate the position of the CRots for different patients’ teeth in 3D space. The CRot is considered a single point in a 3D coordinate system and is obtained by choosing the closest point on the axis of rotation to the center of resistance (CRes). A force system, consisting of a constant load and a couple (pair of forces), is applied to each tooth, and the corresponding CRot trajectories are examined across different patients. To perform a consistent inter-patient analysis, different patients’ teeth are registered to the corresponding reference teeth using an affine transformation. The selected directions and applied points of force on the reference teeth are then transformed into the registered teeth domains. The effect of the direction of the couple on the location of the CRot is also studied by rotating the couples about the three principal axes of a patient’s premolar. Our results indicate that similar patterns can be obtained for the CRot positions of different patients and teeth if the same load conditions are used. Moreover, equally rotating the direction of the couple about the three principal axes results in different patterns for the CRot positions, especially in labiolingual direction. The CRot trajectories follow similar patterns in the corresponding teeth, but any changes in the direction of the force and couple cause misalignment of the CRot trajectories, seen as rotations about the long axis of the tooth.

An in vitro evaluation of orthodontic aligner biomechanics around the maxillary arch

INTRODUCTION

The objective of this study was to evaluate the forces and moments exerted by orthodontic aligners on 3 different displaced maxillary teeth and their adjacent supporting teeth.

METHODS

An in vitro orthodontic simulator was used to measure the forces and moments of a 0.75-mm thick glycol-modified polyethylene terephthalate material for 3 maxillary teeth: central incisor, canine, and second premolar. Forces and moments were recorded for tested teeth displaced lingually one by one for 0.20 mm. Repeated measures of multivariate analysis of variance was used to assess the outcome.

RESULTS

The mean buccolingual force applied on a displaced canine (2.25 ± 0.38 N) was significantly (P <0.001) more than the central incisor (1.49 ± 0.18 N) and second premolar (1.50 ± 0.16 N). The mean moment (that tends to tip the teeth buccally) exerted on a canine (-20.11 ± 5.27 Nmm) was significantly more (P <0.001) than the central incisor (-8.42 ± 1.67 Nmm) and second premolar (-11.45 ± 1.29 Nmm). The forces and moments acting on teeth adjacent to the displaced tooth were clinically significant and acted in opposing directions to those on the displaced tooth.

CONCLUSIONS

The results of this study highlighted that for the same amount of displacement on a given tooth, the forces and moments imposed by the orthodontic aligner depend on location around the arch. These findings highlight the need to further study aligner mechanics around the dental arch and optimize aligner design to impose desired mechanical loads to avoid detrimental effects during orthodontic tooth movement.

Modelling and evaluating periodontal ligament mechanical behaviour and properties: A scoping review of current approaches and limitations

This scoping review is intended to synthesize the techniques proposed to model the tooth-periodontal ligament-bone complex (TPBC), while also evaluating the suggested periodontal ligament (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 orthodontic tooth movement 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.

Where is the center of resistance of a maxillary first molar? A 3-dimensional finite element analysis

INTRODUCTION

The center of resistance (C_Res) is regarded as the fundamental reference point for predictable tooth movement. Accurate estimation can greatly enhance the efficiency of orthodontic tooth movement. Only a handful of studies have evaluated the C_Res of a maxillary first molar; however, most had a low sample size (in single digits), used idealized models, or involved 2-dimensional analysis. The objectives of this study were to: (1) determine the 3-dimensional (3D) location of the C_Res of maxillary first molars, (2) evaluate its variability in a large sample, and (3) investigate the effects of applying orthodontic load from 2 directions on the location of the C_Res.

METHODS

Cone-beam computed tomography scans of 50 maxillary molars from 25 patients (mean age, 20.8 ± 8.7 years) were used. The cone-beam computed tomography volume images were manipulated to extract 3D biological structures via segmentation. The segmented structures were cleaned and converted into virtual mesh models made of tetrahedral triangles having a maximum edge length of 1 mm. The block, which included the molars and periodontal ligament, consisted of a mean of 7753 ± 2748 nodes and 38,355 ± 14,910 tetrahedral elements. Specialized software was used to preprocess the models to create an assembly and assign material properties, interaction conditions, boundary conditions, and load applications. Specific loads were applied, and custom-designed algorithms were used to analyze the stress and strain to locate the C_Res. The C_Res was measured in relation to the geometric center of the buccal surface of the molar and the trifurcation of the molar roots.

RESULTS

The average location of the C_Res for the maxillary first molar was 4.94 ± 1.39 mm lingual, 2.54 ± 2.7 mm distal, and 7.86 ± 1.66 mm gingival relative to the geometric center of the buccal surface of the molar and 0.136 ± 1.51 mm lingual (P <0.01), 1.48 ± 2.26 mm distal (P <0.01), and 0.188 ± 1.75 mm gingival (P >0.01) relative to the trifurcation of the molar roots. In the anteroposterior (y-axis) and the vertical (z-axis) planes, the C_Res showed significant association with root divergence (P <0.01).

CONCLUSIONS

The C_Res of the maxillary first molar was located apical and distal to the trifurcation area. It showed significant variation in its location. The 3D location of and also varied with the force direction. In some samples, this deviation was large. For accurate and predictable movement, tooth-specific C_Res need to be calculated.

Orthodontic Tooth Movement Studied by Finite Element Analysis: an Update. What Can We Learn from These Simulations?

PURPOSE OF REVIEW

To produce an updated overview of the use of finite element (FE) analysis for analyzing orthodontic tooth movement (OTM). Different levels of simulation complexity, including material properties and level of morphological representation of the alveolar complex, will be presented and evaluated, and the limitations will be discussed.

RECENT FINDINGS

Complex formulations of the PDL have been proposed, which might be able to correctly predict the behavior of the PDL both when chewing forces and orthodontic forces are simulated in FE models. The recent findings do not corroborate the simplified view of the classical OTM theories. The use of complex and biologically coherent FE models can help understanding the mechanisms leading to OTM as well as predicting the risk of root resorption related to specific force systems and magnitudes.

Three-dimensional nonlinear prediction of tooth movement from the force system and root morphology

OBJECTIVES

To determine the different impact of moment-to-force ratio (M:F) variation for each tooth and spatial plane and to develop a mathematical model to predict the orthodontic movement for every tooth.

MATERIALS AND METHODS

Two full sets of teeth were obtained combining cone-beam computed tomography (CBCT) and optical scans for two patients. Subsequently, a finite element analysis was performed for 510 different force systems for each tooth to evaluate the centers of rotation.

RESULTS

The center of CROT locations were analyzed, showing that the M:F effect was related to the spatial plane on which the moment was applied, to the force direction, and to the tooth morphology. The tooth dimensions on each plane were mathematically used to derive their influence on the tooth movement.

CONCLUSION

This study established the basis for an orthodontist to determine how the teeth move and their axes of resistance, depending on their morphology alone. The movement is controlled by a parameter (k), which depends on tooth dimensions and force system features. The k for a tooth can be calculated using a CBCT and a specific set of covariates.

Tooth Mobility Reproduction in Dental Material Research: A Scoping Review

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.

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.