Expansion with transpalatal arch or continuous arch mechanics


This study aimed to compare the 3-dimensional force system produced by transpalatal arch (TPA) mechanics with that produced by a continuous arch (CA) on the expansion of maxillary first molars.


A patient’s model with 2 molars in 4-mm crossbite had orthodontic appliances bonded to all teeth. The first and the second molars were connected to two 3-dimensional load cells to compare the forces in the transverse and anteroposterior planes (Fx and Fy) and the rotational moments (Mz) produced in both molars by the expanded TPA and by 0.016-in nickel-titanium CA. The data were evaluated using 6 independent t tests, and the net moment at the molar’s center of resistance was also calculated.


All forces and moments were different at both molars. At the first molar, CA produced Fx of 2.60 N, Fy of –0.08 N, Mz of –5.16 N·mm, and Net Mz of –5.68 N·mm, whereas the TPA produced Fx of 2.87 N, Fy of –0.60 N, Mz of –22.08 N·mm, and Net Mz of –25.09 N·mm. At the second molar, the TPA did not produce significant forces and moments, whereas the CA produced Fx of –1.00 N, Mz of 3.95 N·mm, Fy of –0.84 N, and Net Mz of –0.67 N·mm.


Based on our findings in a clinical set up with the specific horseshoe TPA and archwire tested, with the TPA used only on the first molars and the CA used from one second molar to the other, the mechanics produced different expansion forces at the first molar. The TPA produced a larger rotational side effect on the first molar, whereas the CA produced side effects on the second molar.


  • Transpalatal arch expansion forces were slightly larger than the continuous arch forces.

  • The transpalatal arch produced a larger rotational side effect on the first molar.

  • The continuous arch produced side effects on the second molar.

There are usually 2 treatment options for transverse problems in the general population, skeletal or dentoalveolar expansion. Although skeletal expansion is usually accomplished by rapid or surgically assisted maxillary expansion, dentoalveolar expansion can be done by archwire expansion with brackets or by other devices such as Quad-helix, , Hawley expanders, or transpalatal arch (TPA).

The Goshgarian TPA was first reported in literature in 1972 with the objective of correcting rotations and expanding, contracting, intruding, and torquing the maxillary molars. Its use and designs have been modified over the years, and it is currently used in a passive or active form to control rotations, to assist mechanics with miniscrews, or to modify transverse dimensions. Because both of its ends are inserted in the lingual sheaths, they will produce a 2-couple system, making it very difficult to calculate the force system produced analytically. Therefore, it is more appropriate to measure these systems with 3-dimensional (3D) load cells.

Simpler mechanics with continuous arch (CA) has been preferred by contemporary clinicians, and thus, it would be important to know if the use of flexible wires for the expansion of maxillary molars could produce a similar force system to a more elaborate mechanics, such as a TPA. In addition, the comparison between those 2 mechanics to ascertain if the side effects are similar would contribute immensely to clinical orthodontic practice.

According to the literature, dentoalveolar expansion can be achieved with a TPA , and CA ; however, a comparison between these 2 methods has not been made regarding their effects and side effects. Thus, this study aimed to compare the expansive force and side effects produced by CA mechanics using 0.016-in nickel-titanium (NiTi) wires with those produced using a 0.032-in × 0.032-in horseshoe TPA.

Material and methods

A model of a patient who had the maxillary left first molar in a crossbite was scanned (3D R700; 3Shape scanner, Copenhagen, Denmark) and had the contralateral molar placed in an identical crossbite using the Elemetrix software (Dentsply, Bohemia, NY), which was measured to be 4 mm lingual to its correct position. In addition, all other teeth were aligned and leveled digitally using the same software. The model was 3D printed (B9Creator; B9Creations, Rapid City, SD) and received a passive orthodontic appliance bonded to the teeth with epoxy glue (JB Weld, Sulfur Springs, Tex) 0.022-in slot Roth prescription brackets (Ovation; Dentsply), and tubes were bonded to all teeth (except for the first molars) using a 0.021-in × 0.025-in passive stainless steel (SS) archwire as guide ( Fig 1 , A ), whereas the first molars received double tubes and palatal tubes (hinge cap, slot 0.032-in; Ormco, Glendora, Calif). A passive beta-titanium (TMA) horseshoe TPA 0.032-in ×0.032-in (Ormco) assisted the parallel and passive positioning of the palatal tubes ( Fig 1 , A ), whereas a second 0.021-in × 0.025-in SS archwire aided the positioning of the first molar tubes ( Fig 1 , B ). This wire had a 4-mm lingual step bend made, and it was inserted into the brackets, allowing a passive positioning of the molar tube to the brackets regarding height, tipping, and mesiodistal position. Thus, with a continuous archwire placed into all brackets and tubes, it would be active only in the transverse direction on the first molar tube ( Fig 2 ).

Fig 1
A, Brackets and tubes positioned to the SS guide archwire to be completely passive once bonded to the teeth. Voids, which can be clearly seen at the second molar interface between its buccal surface and the tube’s base, were filled by the epoxy glue. B, A second archwire with a lingual bend was used to position the first molar, allowing it to activate the wire only in the buccal direction.

Fig 2
Activation produced in the first molar given by the position of the brackets and tubes.

The model was secured into an orthodontic force tester (OFT), and the first and second right maxillary molars were bonded to the 2 load cells (Multi-Axis Force/Torque Nano17; ATI Industrial Automation, Apex, NC) of the OFT, which have an amplitude of measurements 0-2,000 g (0.0-19,613.3 N) for force and 0-10,000 g·mm (0.0- 98,006.5 N·mm) for moments. Both teeth were then separated from the model and from the remaining teeth. Custom modification of the ATI transducer software (Department of Mechanical Engineering, Indiana University–Purdue University, Indianapolis, Ind) registered the moment-to-force ratios produced when a force was applied to the tubes and away from the load cells’ origin (center of the load cell). This modification allowed the insertion of those offset values into the software’s calibration and the transfer of the origin of the 3D measurements to the center of the respective tubes of each molar, with the x-axis perpendicular, the y-axis parallel, and the z-axis vertical to the center of the buccal tube ( Fig 3 ). The software also allowed rotational calibration of the origin of measurements in all 3 dimensions.

Fig 3
Load cells positioned and bonded to the first and second molars, which were separated from the model bonded to the OFT’s table. The reference grid of the data collected by the OFT at the first molar tube in 3 dimensions. The origin was transferred by the software form the center of the load cell to the center of the tube, and the grid orientated parallel and perpendicular to the tube.

Two types of molar correction mechanics were tested, TPA and CA. The TPA group was composed of 10 prefabricated 0.032-in × 0.032-in TMA horseshoe-shaped TPAs (Ormco), whereas the CA group was composed of ten 0.016-in NiTi archwires (Dentsply GAC, Islandia, NY). Two small sections of 0.016-in TMA wires were welded to the TPAs at the mesial and distal edges of the tubes to standardize their position and to assist the correct positioning of the TPAs. The welding was done at a low voltage, with a single short pulse on a precalibrated electronic spot welder; when this procedure is done correctly, there is no loss in the mechanical properties of TMA. ,

A scaled digital image of the model allowed the design of a template in the Loop Software (dHAL Software, Athens, Greece) to produce passive standardized TPAs to the molar tubes ( Fig 4 , A ). Their passivity was also verified using the measurements of forces and moments from the OFT software. The TPAs were expanded by 10 mm, and their activation was verified over a second template printed in life size, which was also made in the Loop Software ( Fig 4 , B ). The TPAs were stress relieved by trial activation as many times as needed until the preactivated shape matched the printed preactivation template.

Fig 4
Passive (A) and active (B) templates produced in the Loop Software.

Before each measurement, the OFT software and the load cells were zeroed. In the TPA group, the preactivated TPAs were inserted into palatal tube of the first maxillary molars, and the hinge caps were closed to register the load system produced ( Fig 5 , A ), whereas in the CA group, 0.016-in superelastic NiTi wires (Highland Metals, Franklin, Ind) were tied to all brackets and tubes of the model with elastic ligatures (GAC International; Fig 5 , B ). The entire system was inserted into an expanded rigid polystyrene plastic box with an external hot-air source (SMD Rework Station, Hakko 850B; Hakko, Osaka, Japan) controlled by a digital thermometer (Minipa MT-240; São Paulo, Brazil) maintaining the temperature at 37°C ± 1°C. The x-axis (Fx), y-axis (Fy), and z-axis (Mz) strength values were saved in an Excel 2010–compatible worksheet (Microsoft Office, Microsoft, Redmond, Wash).

Fig 5
Active TPA (A) and active continuous arch (B) tested in this study.

SPSS statistics software program (IBM SPSS version 20.0; Armonk, NY) was used for data analysis. An independent t test with a significance level of 5% was used to identify differences between the mechanics in each of 3 variables (Fx, Fy, Mz) for each molar, totaling 6 comparisons.

The estimated center of resistance (CR) of each tooth was used to calculate the Net Mz (resulting moment in the CR), which was estimated at the center of the crown. Measurement of distance from the center of the tube to the center of the crown was performed with a digital caliper and resulted in 6.5 mm in the first molar and 5.5 mm in the second molar.

The following formula was used for Net Mz calculation:

<SPAN role=presentation tabIndex=0 id=MathJax-Element-1-Frame class=MathJax style="POSITION: relative" data-mathml='Net Mz=Fy×(DistancefromvestibulartubetotheCR)+Mz’>Net Mz=Fy×(DistancefromvestibulartubetotheCR)+MzNet Mz=Fy×(DistancefromvestibulartubetotheCR)+Mz
Net Mz=Fy×(DistancefromvestibulartubetotheCR)+Mz

Then, to the first molar:

<SPAN role=presentation tabIndex=0 id=MathJax-Element-2-Frame class=MathJax style="POSITION: relative" data-mathml='TPA:Net Mz=(−0.60N)×(6.5mm)+(−22.08N⋅mm)’>TPA:Net Mz=(0.60N)×(6.5mm)+(22.08Nmm)TPA:Net Mz=(−0.60N)×(6.5mm)+(−22.08N⋅mm)
TPA:Net Mz=(−0.60N)×(6.5mm)+(−22.08N⋅mm)
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May 12, 2020 | Posted by in Orthodontics | Comments Off on Expansion with transpalatal arch or continuous arch mechanics
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