# An Efficient Distalization Technique Using Coil Springs and Mini Screws--A Finite Element Analysis
## 2 Materials and Methods  
We obtained a three-dimensional(3D) model of upper left dentition (Figure 2) for the FEM from a dry skull by taking computed tomography (CT) scans using a multi-image micro-CT scanner (3 DX, [PERSON], Kyoto, Japan) with a voxel size of 80 \(\upmu\)m. Image segmentation of the upper left dentition was performed on 3D image processing and editing software (Mimics 10.02, Materialize Software, Leuven, Belgium) to obtain 3D geometric data of the dentition, and then 3D surface data were exported in a Standard Triangulated Language (STL) format. The 3D surface data were imported to pre- and post-processing software for FEM ([PERSON] 2017, MSC Software Corp., Los Angeles, CA, USA) as shell elements. Each tooth was aligned in the pre-processing software so that it had normal inclination, and each interproximal distance became less than 0.01 mm to perform appropriate contact analysis between teeth. Subsequently, we constructed PDLs of 0.2 mm as solid elements on the root surface of each tooth. On top of that, 0.022-inch brackets and a 0.019 \(\times\) 0.025-inch archwire were added as orthodontic appliances. The material properties were configured according to previous articles. We assumed that the teeth were rigid bodies, which was the same assumption as in [10], and set the [PERSON]'s moduli and the Poisson's ratio to 204 GPa and 0.3, respectively, to make the teeth rigid enough. The PDL was configured as a bilinear elastic material whose elastic moduli ranged from 0.03 to 0.3 [13]. The Young's moduli and the Poisson's ratio of the brackets and the archwire were set to 204 GPa and 0.3, respectively, which are the material properties of stainless steel. The alveolar bone was also assumed to be a rigid body since it deforms little under small loads such as orthodontic force, as described in a previous study [10]. Thus, we constrained the displacement of outer surface of the PDL to simulate rigid bone and reduce the number of elements for efficient analysis. We compared two models, namely, a model without open-coil springs (NoSp model), which represents the conventional grouped distalization technique, and one with open-coil springs (Sp model), which represents our proposed technique. Elastic chains and open-coil springs were represented by external forces (Figure 3). A retraction force of 4 N to simulate an elastic chain was applied to the first premolar. The force was directed towards an anchor screw between the roots of the upper molar and the second molar, and the height of the anchor screw was 5.0 mm from the bracket level. In the Sp model, external forces of 3 N were applied reciprocally to the distal surface of the first premolar's bracket and the mesial surface of the second premolar's brackets, simulating an open-coil spring between them. External forces of 2 N were applied between the second premolar's bracket and the first molar's bracket, and forces of 1 N were applied between the first molar's bracket and the second molar's bracket in the same manner. Figure 2: FE model of the upper left dentition with 0.022-inch brackets and a 0.019 \(\times\) 0.025-inch archwire. Contact boundary conditions were applied between the teeth and between the archive and the brackets. The friction coefficient between the archive and the brackets was determined to be 0.08 according to previous studies [14; 15; 16], based on the assumption that friction coefficient becomes smaller under the vibration caused by mastication than that under static conditions. A symmetric boundary condition was applied to perform analysis unilaterally. A contact wall was placed at the midsagittal plane of the model, and the mesial end of the archive was constrained in the midsagittal plane while the mesial end was able to slide on the midsagittal plane. Using a symmetric boundary condition, the number of elements was reduced by half compared to the analysis using a full dentition, enabling us to reduce the analysis time.