Locating the center of resistance in individual teeth via two- and three-dimensional radiographic data

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.

Are aligners capable of inducing palatal bodily translation or palatal root torque of upper central incisors? A biomechanical in vitro study

OBJECTIVES

Previous studies have shown that aligners have limited ability to control root movements. The purpose of this study was to investigate which modification geometry and foil thickness are optimal for generating the force-moment (F/M) systems required for palatal root torque of maxillary central incisors.

MATERIALS AND METHODS

Tooth 11 was separated from a maxillary acrylic model and connected to a movement unit via a 3D F/M sensor. Different modification geometries (crescent, capsular, double-spherical) with different depths were digitally implemented in the labio-cervical region of tooth 11 to induce an increased contact force. We evaluated the F/M systems exerted by aligners with thicknesses of 0.4-1.0 mm. F/M measurements were taken with tooth 11 in the neutral position and during palatal displacement of tooth 11 (simulating its initial clinical movement).

RESULTS

The mechanical requirements of palatal root torque are a palatally directed force (- Fy) and a palatal root torquing moment (- Mx). These requirements were reliably achieved with modification depths > 0.5 mm. The modification depth and foil thickness had a significant influence on - Fy magnitudes (linear mixed-effect models, p < 0.01). With the 0.75-mm aligners combined with 1.5-mm deep modifications, the palatal root torque range (palTR) started after an initial palatal crown displacement of 0.09, 0.12, and 0.12 mm for the capsular, crescent, and double-spherical modification geometries, respectively.

CONCLUSIONS

A relatively early start of the palatal torque range (after a 0.1-mm palatal crown displacement) and appropriate - Fy magnitudes were achieved with 0.75-mm-thick aligners containing 1.5-mm deep capsular or crescent pressure regions. Subsequent clinical trials are required to confirm the clinical effects of these modifications.

CLINICAL RELEVANCE

In vitro testing indicated that modified aligners are capable of generating the F/M components required for palatal root torque of upper central incisors.

The center of resistance of a tooth: a review of the literature

The center of resistance is considered the fundamental reference point for controlled tooth movement. Accurate determination of its location can greatly enhance the efficiency of orthodontic treatment. The purpose of this review was to analyse the scientific literature related to the location of center of resistance of tooth determined by various approaches. The literature describes three essential approaches to identify the center of resistance point, one being experimental in nature, one based on an analytical physical approach, and one using a numerical physical approach that uses a finite element simulation. A review on data referring to the location of the center of resistance, limited to single rooted tooth has been performed from electronic databases. It showed variation in its location related to the assumptions used in the model. The center of resistance of tooth therefore cannot be considered a static point, but rather as the composite point of all factors offering resistance to the applied force such as the tooth morphology and mass distribution within the tooth, the structure of the periodontium, the alveolar bone level, the adjacent teeth and direction of force applied.

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.

Types of tooth movement, bodily or tipping, do not affect the displacement of the tooth's center of resistance but do affect the alveolar bone resorption

OBJECTIVE

To investigate how types of tooth movement, bodily or tipping, influence the displacement of the center of resistance in teeth and alveolar bone resorption.

MATERIALS AND METHODS

Ten-week-old female Wistar rats were divided into eight groups of different factors, as follows: type of movement (bodily and tipping) and force magnitude (10, 25, 50, and 100 cN). The maxillary left first molars were moved mesially with nickel-titanium coil springs for 28 days. Micro-computed tomography (micro-CT) images were taken before and after tooth movement. The position of the center of resistance was determined by using finite element models constructed from the micro-CT image. The displacement of the center of resistance and the volume of alveolar bone resorption were measured.

RESULTS

The displacement of the center of resistance showed no significant difference between the bodily and tipping groups. The displacements of the center of resistance were increased with force magnitude at 10 and 25 cN, whereas they were not further increased at 50 and 100 cN. On the other hand, cervical alveolar bone resorption was significantly greater in the tipping group than in the bodily group.

CONCLUSIONS

Displacement of the center of resistance was not influenced by the types of tooth movement. However, volume of cervical alveolar bone resorption was greater in the tipping movement group than in the bodily movement group.

Influence of tooth dimension on the initial mobility based on plaster casts and X-ray images : A numerical study

AIMS

The goal was to determine the influence of different geometric parameters of the tooth on the initial tooth mobility and the position of the center of resistance employing numerical models based on scaled X-ray images and plaster casts.

METHODS

The dimensions of tooth 21 were measured in 21 patients, using radiographs and dental casts. Length and mesiodistal width of the tooth were obtained from the X-ray image and the orovestibular diameter from the plaster cast. Finite element models were generated. Cortical and cancellous bone and the periodontal ligament were simulated to create realistic models. Root length (11-17 mm), mesiodistal width (6-10 mm) and orovestibular thickness (7-9 mm) were varied in 1-mm steps to generate 105 models. In the simulation, each model was loaded with a force of 10 N in vestibulopalatinal direction and with a torque of 10 Nmm to determine tooth displacements and center of resistance.

RESULTS

Initial tooth displacement and thus mobility increased with decreasing total root surface. The shortest, slimmest and thinnest tooth showed a total deflection of 0.14 mm at the incisal edge, while the longest, widest and thickest tooth showed a total deflection of 0.10 mm. Changes in mesiodistal width had the greatest influence on initial tooth mobility and changes in orovestibular thickness the least. The teeth's center of resistance was positioned between 37 and 43% of the root length measured from the cervical margin of the alveolar bone. The center of resistance of the longest dental root investigated was located around 6% more cervically compared to the one of the shortest dental root. The influence of root width and thickness on the position of the center of resistance was significantly lower than root length.

CONCLUSION

Geometric parameters significantly impact initial tooth mobility and position of the center of resistance. Thus, tooth dimensions should be considered in orthodontic treatment planning. Dental radiographs represent a sufficient validation tool to estimate the quality of a pure dental tipping during orthodontic treatment, as the orovestibular thickness has little influence. However, for three-dimensional tooth displacements all geometric parameters should be determined accurately using plaster casts or DVT.

Forces and moments delivered by PET-G aligners to an upper central incisor for labial and palatal translation

OBJECTIVES

Aligners made of polyethylene terephthalate glycol (PET-G) were tested in an experimental study for labial and palatal translation of an upper central incisor to quantify the forces and moments thus delivered and to biomechanically evaluate the capability of bodily movement.

MATERIALS AND METHODS

Using a resin model of the upper dentition, tooth 21 was separated and connected to a 3D force/moment (F/M) sensor to record the forces and moments delivered by aligners for labial and palatal displacement. An impression was taken with tooth 21 in its neutral position to obtain casts for standardized thermoplastic fabrication of aligners varying in make and foil thickness (Duran® 0.5/0.625/0.75 mm; Erkodur® 0.5/0.6/0.8 mm; Track-A® 0.5/0.63/0.8 mm). Upon placing each aligner over the teeth of the resin model, the separated tooth was subjected to 0.01 mm increments of labial and palatal translation by 0.25 mm in either direction.

RESULTS

The mean forces delivered by the thinnest (0.5 mm) aligners for 0.25 mm of palatal displacement of tooth 21 were 3.01 ± 0.07 N (Duran®), 5.31 ± 0.89 N (Erkodur®), and 3.69 ± 0.81 N (Track-A®). The thickest (0.75 or 0.8 mm) aligners delivered 4.49 ± 0.16 N (Duran®), 7.22 ± 0.45 N (Erkodur®), and 5.20 ± 0.68 N (Track-A®). The mean forces for palatal as compared to labial displacement were higher by a mean of 48% with the Erkodur® and by 23% with the Track-A® aligners but were smaller by 37% with the Duran® aligners. The moment-to-force (M/F) ratios, calculated in relation to the center of resistance of the separated measurement tooth, ranged from -9.91 to -12.22 mm, thus, approaching the value of -8.80 mm for uncontrolled tipping of this tooth.

CONCLUSION

Manufacturers of PET-G aligners have recommended setup increments of 0.5-1 mm, which appears excessive based on our results. PET-G aligners not featuring modifications (e.g., reinforcing ribs or composite attachments bonded to the teeth) are unsuitable for bodily movement of upper central incisors in labial or palatal directions.

Estimating the location of the center of resistance of canines

OBJECTIVE

To develop a method to quickly estimate the location of center of resistance (CR) in mesial-distal (MD) and buccal-lingual (BL) directions from the tooth's image.

MATERIALS AND METHODS

The maxillary cone-beam computed tomography (CBCT) scans of 18 patients were used. Finite element (FE) models of the canines and their surrounding tissues were built based on their CBCT scans to calculate the locations of CR. Root length, centroid of the contact surface (CCS), and centroid of projection of the contact surface (CPCS) were also obtained from the images. The CCS and CPCS locations were projected on the tooth's long axis, which were represented as percentages of the root length measured from the root's apex.

RESULTS

Using the FE results as the standards, the errors of using CCS or CPCS to estimate CR were calculated. The average location of CR calculated using the FE method was 60.2% measured from the root's apex in the MD direction and 58.4% in the BL direction. The location of the CCS was 60.9%. The difference in CR was 0.7% in the MD direction and 2.5% in the BL direction. The location of CPCS was 60.2% in the MD direction and 59.1% in the BL direction, which resulted in a 0.1% and 0.8% difference with the reference CR, respectively. The average difference of CR in the MD and BL directions was small but statistically significant (P < .05).

CONCLUSION

The locations of the CR of a human canine in the MD and BL directions can be estimated by finding the CPCSs in those directions.