Force System with Vertical V-Bends: A 3D In Vitro Assessment of Elastic and Rigid Rectangular Archwires

Podsumowanie

The method presented here is designed to construct and validate an in vitro 3D model capable of measuring the force system generated by different archwires with V-bends placed between two brackets. Additional objectives are to compare this force system with different types of archwires and to previous models.

Streszczenie

A proper understanding of the force system created by various orthodontic appliances can make treatment of patients efficient and predictable. Reducing the complicated multi-bracket appliances to a simple two-bracket system for the purpose of force system evaluation will be the first step in this direction. However, much of the orthodontic biomechanics in this regard is confined to 2D experimental studies, computer modeling/analysis or theoretical extrapolation of existing models. The objective of this protocol is to design, construct and validate an in vitro 3D model capable of measuring the forces and moments generated by an archwire with a V-bend placed between two brackets. Additional objectives are to compare the force system generated by different types of archwires among themselves and to previous models. For this purpose, a 2 x 4 appliance representing a molar and an incisor has been simulated. An orthodontic wire tester (OWT) is constructed consisting of two multi-axis force transducers or load cells (nanosensors) to which the orthodontic brackets are attached. The load cells are capable of measuring the force system in all the three planes of space. Two types of archwires, stainless-steel and beta-titanium of three different sizes (0.016 x 0.022 inch, 0.017 x 0.025 inch and 0.019 x 0.025 inch), are tested. Each wire receives a single vertical V-bend systematically placed at a specific position with a predefined angle. Similar V-bends are replicated on different archwires at 11 different locations between the molar and incisor attachments. This is the first time an attempt has been made in vitro to simulate an orthodontic appliance utilizing V-bends on different archwires.

Wprowadzenie

An important aspect of clinical orthodontic treatment is the knowledge of the force system produced by multibracket appliances. A clear understanding of the underlying biomechanical principles can help deliver predictable results and minimize potential side effects¹. Recent years have seen a trend away from placing bends in archwires by building more activation with bracket position and design; however, comprehensive orthodontic treatment still requires placement of bends in archwires. Bends, when placed in different types and sizes of archwires, can create a wide variety of force systems suitable for different types of tooth movement. Although the force systems can become quite complex when multiple teeth are considered, a helpful starting point can involve a simple two-bracket system.

To date, V-bend mechanics have primarily been analyzed in the second order only, utilizing mathematical models^1,2,3,4,5 and/or computer-based analysis/simulations⁶. This has yielded a basic understanding of the force system involved in the second order interaction of the arch wires with adjacent brackets (Figure 1). However, these methods impose certain boundary conditions in order to run simulations that might not hold true in actual clinical situations and deviations might occur. Recently, a new in vitro model involving force transducers was proposed for measuring three dimensional (3D) forces and moments created by evaluating not only second order archwire-bracket interactions but also in the third order⁷. However, the effect of different types of archwires on the force system at various bend positions along the incisor molar archwire span was not evaluated. Also, the study only involved evaluation of elastic orthodontic archwires, which are not the primary archwires on which tooth movement occurs. Therefore, the aim of this study was to evaluate the force system created by the placement of a V-bend at different locations in rectangular stainless steel and beta-titanium archwires in a 3D set up involving the molar and incisor brackets. Clinicians need to know the force system applied on the dentition when a specific combination of archwire bracket combination is used to fix a malocclusion.

The described technique has been developed to study the orthodontic force system in all the three planes of space, mimicking clinical reality. It is to be understood that it is extremely difficult to measure the force system clinically; therefore, such measurements have to be carried out in vitro. It is assumed that the force system created by a V-bend in the laboratory would be similar if replicated in the patient's mouth. A workflow was created to evaluate how the experimental set up has to be configured (Figure 2).

The orthodontic wire tester (OWT) is an innovative product developed by Division of Orthodontics in collaboration with the Bioengineering & Biodynamics Laboratory, UConn Health, Farmington, CT, USA (Figure 3). It is designed to accurately mimic the arrangement of the maxillary teeth within the mouth and some intra-oral conditions while providing measurements of the force system created in all the three planes of space. The major mechanical components of the OWT are a Data acquisition device (DAQ), nano Force/Torque Sensors, humidity sensors, temperature sensors, and a personal computer. The testing apparatus is placed in a glass enclosure having temperature/humidity controls. This allows for partial simulation of the intraoral environment. The DAQ serves as the interface for the three sensors: humidity sensor, force/moment sensor, thermistor and the testing apparatus with the sensors situated on a platform (Figure 3). These are linked to a software program. The software is a platform and a development environment for visual programming and is used to control different types of hardware. It was chosen to automate the orthodontic wire tester.

A series of aluminum pegs are arranged on the testing apparatus to represent the teeth of the maxillary dental arch. Two of the pegs representing the right central incisor and right first molar are connected to sensors/load cells (S1 and S2). A load cell is a mechanical device that can measure the forces and moments applied to it in all the three planes (x-y-z): F_x, F_y, and F_z; and M_x, M_y, and M_z. The pegs are systematically positioned to create a dental arch form. Each peg is separated from the other by a precisely recorded measurement that is calculated using average tooth widths as observed in patients undergoing orthodontic treatment. The shape chosen for the experiment is an 'ovoid' arch form created from a standardized template.

Protokół

1. Experimental Setup

1. Mark the precise position for the placement of molar tubes and incisor brackets on the aluminum pegs of the OWT by using a customized 'jig'.
2. Bond standard self-ligating brackets with composite material. Light cure for 40 seconds.
3. Insert a 0.021 x 0.025-inch stainless steel (SS) 'ovoid' maxillary archwire into the bracket slots.
4. Place the testing apparatus in the glass chamber.
5. Check for any unintended archwire activation. Any activation of the archwire will automatically create a force system, which will be displayed on the computer screen.
6. Reposition the brackets if any archwire activation is observed. Repeat steps 1.2-1.5.

2. Fabrication of a Template Archwire (Figure 4)

1. Place an archwire (0.021 x 0.025 SS) in the testing apparatus.
2. Use a permanent marker to indicate the following: 1) the midline, 2) a point immediately distal to the incisor bracket (I), and 3) a point immediately mesial to the molar tube (M). Do the same for the contralateral side of the archwire. This is the template arch wire.
3. Transfer the archwire with the marked points to a graph paper.
4. Make a precise replica of the archwire on the graph paper.
   NOTE: This graph paper can be used to determine the position of the V-bend for all archwires of the sample.
5. Calculate the perimeter of the arch wire segment (L) from I to M.
6. Now, mark 11 points from I to M. Each point is a future V-bend position.
   1. Label each point from a₀ to a₁₀.
   2. Make sure that each bend position is separated from the other by an equal amount.
7. Obtain a unique number/ratio for each bend position by calculating a/L for each position.

3. Placement of V-bends

1. Take a new archwire from the sample.
2. Place it on the template archwire/graph paper and transfer one of the eleven bend positions bilaterally to the archwire.
3. Use a rectangular archwire plier or a light wire plier to make symmetrical V-bends at both the positions.
4. Place the archwire on a glass slab/flat platform and check the measurement of the angle made by the two ends of the archwire with a protractor.
5. Adjust the ends if necessary so that an angle of 150° is created.
6. Repeat steps 3.1 to 3.5 for all archwires of the sample.

4. Measuring the Force System (Figures 5 and 6)

1. Open the software program for data recording (see Table of Materials).
2. Create a new folder for the data to be saved in.
3. Click 'run' to start the software. The program will display each of the three forces and three-moment values at each sensor in real-time.
4. Wait for approximately 10-15 seconds for the fluctuations in data recording software to stop. Ensure that the graph lines on the software for all the components of the force system show a 'flat' line.
   NOTE: all six measurements at each sensor will show negligible values (forces < 1 g and moments < 10 g mm).
5. Gently remove the 'testing apparatus' from the platform. Use a Weingart plier to insert an archwire into the molar tubes.
6. Open the door of the incisor bracket with a periodontal scaler.
7. Lift the anterior portion of the archwire and insert it into the bracket slot. Make sure that the midline of the archwire coincides with the midline of the testing apparatus.
8. Return the testing apparatus to the platform and close the door of the glass chamber.
9. Set the temperature at 37 °C. Wait for one minute for the temperature of the glass chamber to adjust.
10. Click the 'start saving' button on the software and allow the software to save/transfer data for at least 10 seconds. Click the 'start saving' button again to end data transfer, then click 'stop'.
    NOTE: Each measurement cycle generates 100 readings over the 10 second period for each component (F_x, F_y, F_z, M_x, M_y, and M_z).
11. Go to the document containing the saved data, and copy/export the data set to a custom designed data analysis spreadsheet (see Supplementary Table). Choose the correct V-bend position number and the specific wire sample to insert the data.
12. Repeat steps 4.3 to 4.11 for the 10 archwires of that specific bend position.
13. Now, copy the calculated means and standard deviations for the archwires to a separate spreadsheet to create a graphical representation of the data.
14. Repeat steps 4.2 to 4.13 for all bend positions and types of archwires.
    NOTE: The archwires include, Stainless-Steel (SS) and Beta-Titanium (ß-Ti), with the following sizes: 0.016 x 0.022 inch, 0.017 x 0.025 inch, and 0.019 x 0.025 inch.

5. Error Evaluation

1. Run the computer/software as described in steps 4.1-4.4
2. Remove the 'testing apparatus' from the platform.
3. Obtain a straight length 0.021 x 0.025-inch SS wire. Using a light wire plier, bend one end of the wire into a small hook. Insert the free end of the archwire into the molar tube from the distal side.
4. Place the testing apparatus back on the platform.
5. Attach a known weight (50 g) to the hook. Let it hang freely in the vertical plane by removing any type of interference. Close the door of the glass chamber.
6. Follow steps 4.10-4.11.
7. Repeat steps 5.1-5.6 for the incisor bracket.
8. Enter the Fz values for both the brackets and Mx for the molar tube as 'measured value.'
9. Now apply the equations of equilibrium (see Supplementary Text) to calculate the 'expected value.'

Wyniki

The total force and total moment experienced by each sensor at the center of the sensor plate are represented by their three orthogonal components: F_x, F_y, and F_z representing the forces along the x-axis, y-axis, and z-axis, respectively; and M_x, M_y, and M_z representing the moments around the same axes. The initial measurements at the sensors are converted mathematically to the force and moment values experienced by the bra...

Dyskusje

Orthodontic archwires have been studied in various ways^8,9,10,11. They have also been evaluated for various mechanical properties, but they have seldom been analyzed for determining the force system they are going to create^12,13,14,15. Three-point bending tests are po...

Materiały

Name	Company	Catalog Number	Comments
Force/Torque  Sensors/Transducers	Nano17 F/T Sensors,  ATI Industrial Automation, Apex, NC, USA		Part of the OWT
CHS Series Humidity  Sensor Units	TDK Corporation		Part of the OWT
Temperature sensors	(Murata NTSDXH103FPB30 thermistor) Murata Manufacturing Co., Ltd		Part of the OWT
LabVIEW 7.1.	Laboratory Virtual Instrumentation Engineering Workbench, Version 7.1		Software Program
Self-Ligating brackets	Empower Series, American Orthodontics.		Orthodontic Brackets
Stainless steel archwires	Ultimate Wireforms, Inc. in Bristol, CT		Archwires
Beta-Titanium Archwires	Ultimate Wireforms, Inc. in Bristol, CT		Archwires
Data acquisition device (DAQ)	National Instruments (NI) USB 6210		Part of the OWT
Ortho Form III (Archform template)	3M Oral Care, St. Paul, MN, USA		Ovoid arch form
Weingart Plier	Hu-Friedy Mfg. Co., LLC Chicago, IL		Orthodontic Plier
Light wire Plier	Hu-Friedy Mfg. Co., LLC Chicago, IL		Orthodontic Plier