矯正牙齒在臨床治療上已有很高的成功率，但是對於矯正齒的移動仍然無法提供一個良好的記錄方式。近年來牙齒移動的研究都侷限於石膏模型數位化量測或是錐狀射束電腦斷層掃描(CBCT)重建，然而這些方法在臨床追蹤上仍然有許多限制。因此本研究目的是依據先前實驗室的研究結果，利用立體影像系統來取得牙齒在空間中三維的資訊，追蹤其移動過程。藉由觀察一名受試者，進一步分析矯正齒平移及旋轉的方式;並利用六軸荷重元量測施加的矯正力，評估矯正力與矯正齒位移的關係。本研究使用兩台數位相機建立立體影像追蹤系統，並建立矯正器座標系於矯正器上，及牙齒坐標系於抵抗中心上(center of resistance)，用於分析牙齒位移的改變量;另外，使用數位口掃模型、Solidworks和3D-printing設計和製造荷重元的夾具，用於量測矯正力。實驗結果顯示立體影像系統精確度評估最大誤差小於2%，並且誤差來自於影像的清晰度。測量實驗結果顯示，由矯正器座標系來看前門齒，追蹤58天後總位移量為0.94mm，有一半的位移發生於第一天，並伴隨遠心往近心的Angulation及近心側，舌側往唇側順時鐘的Rotation。由牙齒座標系來看前門齒，追蹤58天後可以觀察總位移量為0.92 mm，但是在矯正初期有0.7mm大位移產生，並且伴隨者舌側往唇側的Torque。以定性的角度看，追蹤牙齒的角度變化量與臨床醫師判斷的結果是一致的，並且明顯的觀察到牙齒三個時期的移動趨勢(Initial phase、Lag phase、Postlag phase)。以定量的角度來看，矯正器座標系與牙齒坐標系角度變化量有相同的結果，顯示透過觀察矯正器角度改變量，同時可以用於描述牙根的角度改變量。但是在實驗初期牙齒座標系的位移量，與先前研究牙周韌帶最大變形量的結果相比，部分追蹤點的位移量有較大的誤差。本實驗成功的利用重疊矯正器座標系原點，量測角度變化量，並結合矯正器位移量，提供了一個用於描述矯正牙齒的移動過程的方法。

SUMMARY
The aim of this study is to track tooth movement under orthodontic treatment based on stereovision approach and combine with 3D scanning as well as 3D printing for orthodontic force measurement. The stereovision system tracks the movement of the orthodontic tooth by employing laser-markered brackets. This system consisted of two cameras with their relative positions calibrated. The measured movements were registered in the bracket coordinate system. Both translation and rotation were evaluated. Moreover, artificial model, from 3D printing, of the orthodontic system was established and integrated with six-axis load cell to measure the orthodontic force. The results showed that, qualitatively, the measured tooth movement was consistent with the clinical report (Kaare et al. 1969), that is a three-stage movements as the treatment progress. Quantitatively, the rotations, in addition to translation, could be identified directly from the follow up in clinical suitation. And the 3D model integrated with a six-axis load cell system provides a practical method to measure the orthodontic force in vitro, qualitatively validated by the measured tooth movement from stereovision. To conclude, the rotational and translational amounts of orthodontic tooth movement could be measured directly from the patient with the marked brackets using stereovision system. This provides a foundation to relate tooth movement with orthodontic force for the investigation of orthodontic mechanism.
Key words: stereovision, orthodontic tooth movement, orthodontic force

INTRODUCTION
Although, clinically, orthodontic tooth treatment possesses a high success rate, the mechanism of tooth movement induced by orthodontic force remains unclear. Dental cast or cone-beam computed tomography (CBCT) has been applied to measure the tooth movement under orthodontic force. However, the measured data provides insufficient information, lack of integrated force data, to understand the mechanism. Previous study[16] has employed stereovision to measure tooth movement under orthodontic treatment. Force data was correlated with the measured movement to identify the relationship between tooth movement and orthodontic force using finite element simulation. However, only tooth translation was measured, tooth rotation was neglected during simulation. The specific aims of this study were (1) to measure and describe tooth movement, including both translation and rotation, with the stereovision system in clinical follow-ups; (2) to build the artificial tooth models, based on the 3D scanning at different stages, to measure the orthodontic force with six-axis load cell and related to the movement data.
 
MATERIALS AND METHODS
Stereovision system setup and accuracy evaluation:
The stereovision system was established using two cameras (D3200, Nikon, Tokyo, Japan), with relative position calibrated, to capture the orthodontic tooth position at different treatment stages. Both cameras were connected to a cable releaser so that pictures could be captured simultaneously. To secure the relative position of the subject and camera, head of the subject was placed on a customized holder. Four markers were burned on the four corners of a bracket using laser. The location of the orthodontic tooth at any stages was then determined using the reconstructed 3D coordinates of these marker brackets with the stereovision system. The accuracy of this approach was evaluated by cementing three brackets on a caliper (resolution of 0.01 mm), as shown in Figure A. In the figure, bracket 1 was cemented onto the left side of the caliper while Brackets 2 and 3 were cemented onto the right side of the caliper. As the caliper moved by 0 mm, 0.5 mm, 1 mm, 1.5 mm, and 2 mm respectively, the distance between Bracket 1 and Bracket 2 should reflect the caliper movement while the distance between Bracket 2 and Bracket 3 should remain constant. The measured distances, by the stereovision system, between each pair of brackets could be used to justify the accuracy of the stereovision system.

Patient follow up:
In this study, one patient was recruited for orthodontic treatment observation during a two months follow-up period. The lower central incisor, 41, was the tooth to be treated. Three brackets were cemented respectively onto central incisor, lateral incisor, 42, and canine, 43. A .016 × .022 inch stainless steel wire as well as the ligature wires were used to tie the brackets on 42 and 43 so that these two tooth were served as an anchor unit. Orthodontic force was applied on 41 with a Nitinol wire as shown in Figure B. Stereo pictures were taken before and immediately after the application of the force, as well as after 1, 4, 5, and 10 hours fof force applied. Thereafter for every 100 hours, pictures were taken by the stereovision system till 1,400 hours after force applied. The relapse process was also observed before and immediately after force termination, as well as after 1, 2, 4, 24, and 100 hours of relapsing.

Bracket orientation and position:
After obtain the 3D coordinates in the camera coordination system of the four laser marked points, the bracket position was represented by the mean of these four markers. Subsequently, a plane was fitted with these four markers to represent the orientation of the bracket in order to describe the bracket rotation.

Measurement of tooth movement and rotation:
To describe the tooth movement, a base coordinate system obtained from the brackets on the anchor teeth was established and this base coordinate system was assumed to be immovable during the orthodontic treatment. To build this coordinate system, a reference plane was fitted with the eight markers on the bracket of 42 and 43 to represent the XY plane. The mean of these eight markers was selected as the original of the base coordinate system. The measured camera coordinate data at each stage were transferred to this base coordinate system, that is superimposed pictures from different stages by aligning the brackets on 42 and 43 so that the tooth movement of 41 can be calculated. To measuring the tooth rotation, the bracket positions of 41 at different stages were further superimposition and the orientation difference of 41 brackets at different stages were used to calculate the rotation.

Measurement of orthodontic force:
The orthodontic force was measured using a 6-axis load cell with an artificial model made from 3D printing. The artificial models were reconstructed based the 3D scanning data after 1, 200, 400, and 1,200 hours of force applied and printed using an MOD 3D printer. The six-load cell was fixed onto a holder designed within the model. Three brackets were cemented onto the artificial model, the same as the clinical practice as shown in Figure C. After the Nitinol wire was applied the force and torque were recorded.

RESULTS AND DISCUSSION
The accuracy evaluation revealed that the stereovision measurement system has a maximum error less than 2%. It noted that this accuracy was affected mostly by the camera resolution and the quality of the picture which influence the laser markers identification from pictures. For the patient observation, the lateral incisor 41 moved about 0.9 mm during 1,400 hours (60 days) of tracking. The movement could be identified as a three-phase movements, a maximum of 0.5 mm movement during the first day, PDL visco-elastic deformation. Then the movement almost stationary till roughly 30 days the movement increased linearly to 0.9mm in another 30 days, bone remodeling phase. After 100 hours of removing the the NiTinol wire, the tooth was relapsed by 0.5 mm (0.4 mm was observed within the first day). Observed from occlusal to gingival, tooth 41 rotated clockwise 7 degrees, this rotation direction is consistent with the treatment planning from a clinical point of view. The results indicated that qualitatively the observed tooth movement and rotational were consisted with the clinical situation. Orthodontic force evaluations from artificial models shown that the average orthodontic force was around 0.5N, the same order of clinical practice.

CONCLUSION
To conclude:
(1) The orthodontic tooth movement, both translation and rotation, could be described by a stereovision system with laser-markered brackets.
(2) Using artificial models from 3D scanner and 3D printer to integrate with six-axis load cell, orthodontic force could be quantitative measured in vitro.
This system provides a foundation to Integrating tooth movement tracking data with the applied orthodontic f orce to investigate the mechanism of orthodontic treatment.

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