Search

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., (© 2020 by The EH Angle Education and Research Foundation, Inc.)

Objectives: To test the hypothesis that periodontal ligament (PDL) stress relationships that yield resistance numbers representing load proportions between different teeth depend on alignment load type., Materials and Methods: Finite element models of all teeth, except the third molars, were produced. Four different types of loads were applied, and the third principal stresses of different teeth in standardized areas of most compression were calculated. Based on these results, resistance numbers, representing the load proportions for each tooth derived from PDL stress, were determined., Results: The third principal stress values for typical alignment loads in the areas of most stress were very different for different load types for each tooth. Differences in resistance numbers between teeth also varied with different loads., Conclusion: Resistance numbers, that is, load proportion numbers between teeth to achieve similar stress at the compressive PDL zone, depend on the type of applied load., (© 2015 John Wiley & Sons A/S. Published by John Wiley & Sons Ltd.)

Introduction: The orthodontic load system, especially ideal moment-to-force ratios, is the commonly used design parameter of segmental T-loops for canine retraction. However, the load system, including moment-to-force ratios, can be affected by the changes in canine angulations and interbracket distances. We hypothesized that clinical changes in canine position and angulation during canine retraction will significantly affect the load system delivered to the tooth., Methods: The load systems of 2 T-loop groups, one for translation and the other for controlled tipping, from 9 bilateral canine retraction patients were made to the targeted values obtained from finite element analyses and validated. Each loop was tested on the corresponding maxillary dental cast obtained in the clinic. The casts were made before and after each treatment interval so that both initial and residual load systems could be obtained. The pretreatment and posttreatment interbracket distances were recorded for calculating interbracket distance changes., Results: As the interbracket distances decreased, the average retraction-force drop per interbracket distance reduction was 36 cN/mm, a 30% drop per 1 mm of interbracket distance decrease. The average antitipping-moment drops per interbracket distance reductions were 0.02 N-mm per millimeter for controlled tipping and 1.4 N-mm per millimeter for translation, about 0.6% and 17% drops per 1 mm of interbracket decrease, respectively. Consequently, the average moment-to-force ratio increases per 1 mm of interbracket distance reduction were 1.24 mm per millimeter for controlled tipping and 6.34 mm per millimeter for translation. There was a significant residual load, which could continue to move the tooth if the patient missed the next-scheduled appointment., Conclusions: Clinical changes in canine position and angulation during canine retraction significantly affect the load system. The initial planned moment-to-force ratio needs to be lower to reach the expected average ideal value. Patients should be required to follow the office visit schedule closely to prevent negative effects because of significant moment-to-force ratios increases with time., (Copyright © 2013 American Association of Orthodontists. Published by Mosby, Inc. All rights reserved.)

Optimum stresses for a favorable response to orthodontics are still unknown. Here, we compared the effects of initial periodontal ligament (PDL) stresses over time in orthodontic external root resorption (OERR), necrosis, and the TRAP+ cell population. Forty-two rats (Fischer CDF) were treated with 10 cN of force for 5 different time periods. Finite element (FE) models of the first maxillary molars were constructed from μCT scans to calculate initial PDL stresses. The scans were also used for OERR measurements before histology. Time, stress, and their interaction were significant to result in an OERR increase only in the regions of medium and high stress. OERR was not significantly different between control and treated animals over time in the region of low stress. After 30 days, OERR was increased by 5- and 3-fold in the zone of high- and medium-stress regions, respectively. The TRAP+ cell population initially followed the stress gradient, but changed after bone and necrotic tissue resorption. In the 30-day modeling cycle, the correspondent 3rd principal stress range to promote direct bone resorption and insignificant OERR was between -9.92 and -7.75 KPa. These translate to approximate forces of 30 to 40 cN applied at the bracket level (tipping) of a human maxillary canine.

Introduction: The center of resistance is considered the most important reference point for tooth movement. It is often stated that forces through this point will result in tooth translation. The purpose of this article is to report the results of numeric experiments testing the hypothesis that centers of resistance do not exist in space as 3-dimensional points, primarily because of the geometric asymmetry of the periodontal ligament. As an alternative theory, we propose that, for an arbitrary tooth, translation references can be determined by 2-dimensional projection intersections of 3-dimensional axes of resistance., Methods: Finite element analyses were conducted on a maxillary first molar model to determine the position of the axes of rotation generated by 3-dimensional couples. Translation tests were performed to compare tooth movement by using different combinations of axes of resistance as references., Results: The couple-generated axes of rotation did not intersect in 3 dimensions; therefore, they do not determine a 3-dimensional center of resistance. Translation was obtained by using projection intersections of the 2 axes of resistance perpendicular to the force direction., Conclusions: Three-dimensional axes of resistance, or their 2-dimensional projection intersections, should be used to plan movement of an arbitrary tooth. Clinical approximations to a small 3-dimensional "center of resistance volume" might be adequate in nearly symmetric periodontal ligament cases., (Copyright © 2013 American Association of Orthodontists. Published by Mosby, Inc. All rights reserved.)

Introduction: The P2X7 receptor plays a crucial role in bone biology and inflammation. Its main function is to promote necrotic tissue metabolism by ensuring a normal acute-phase inflammatory response. We used a mouse model to describe and compare orthodontic mechanotransduction in wild-type and P2X7 knock-out mice., Methods: By using finite element analysis, mouse orthodontic mechanics were scaled to produce typical human stress levels. External root resorption, bone modeling, and bone remodeling were analyzed with fluorescent bone labels, Masson trichrome stain, and microcomputed tomography. Relationships between the biologic responses and the calculated stresses were statistically tested and compared between mouse types., Results: There were direct relationships between certain stress magnitudes and root resorption and bone formation. Hyalinization and root and bone resorption were different in the 2 types of mice., Conclusions: Orthodontic responses are related to the principal stress patterns in the periodontal ligament, and the P2X7 receptor plays a significant role in their mechanotransduction.

Introduction: Tooth movement simulation is important for planning the optimal force system and appliance design to correct a specific malocclusion. Experimental verification of a 3-dimensional force system is described for a unique molar root movement strategy that can be adapted to many clinical scenarios., Methods: The force system was measured for molar root movement springs that had adjustable alpha (anterior) and beta (posterior) moments. A 3-dimensional transducer assessed moments and forces in 3 planes during deactivation and simulated molar rotation. Two experimental situations were compared by using 10 springs in each group: spring reactivation was performed to compensate for changes in the force system caused by molar movement, or there was no reactivation., Results: Without reactivation, the force system becomes unfavorable after approximately 5 degrees of molar movement (rotation). With reactivations, a favorable force system through 20 degrees of molar movement is maintained., Conclusions: Present root-movement appliances require periodic adjustment to achieve optimal tooth movement. Additional studies are needed to design orthodontic appliances for delivering optimal force systems for the entire range of tooth movement.

Introduction: The tension-compression theory of bone mechanotransduction is ubiquitous in orthodontics. However, partly due to deficiencies in the characterization of the mechanical environment, there is no consensus on the mechanisms that link stimuli to root resorption and bone response. In this study, we analyzed the predominant directions of tension and compression in the alveolar structures., Methods: An idealized tooth model was constructed with computer-aided design for finite element stress analysis. The principal stress magnitudes and directions were calculated in tipping and translation., Results: The highest principal stress magnitudes in the root, periodontal ligament (PDL), and alveolar surface occurred predominantly in the longitudinal, radial, and hoop directions, respectively. On the compression side, the only structure consistently in compression in all directions was the PDL; however, magnitudes were different in different directions., Conclusions: In the same region of root, PDL, and bone, there can be compression in 1 structure and tension in another. At a given point in a structure, compression and tension can coexist in different directions. Magnitudes of compression and tension are typically different in different directions. Because of direction swaps between principal stresses, previously published data of only stress magnitude plots can be confusing and perhaps impossible to understand or correlate with biological responses. To prevent ambiguities, a reference to a principal stress should include not only the structure, but also its predominant direction. Combined stress magnitude and direction results suggest that the PDL is the initiator of mechanotransduction.