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1 ORIGINAL ARTICLE 교정용미니스크류를이용한연속호선과분절호선의유한요소분석 이언화 a,b ㆍ유형석 c ㆍ이기준 d ㆍ박영철 c 설측의연속호선과분절호선의 3 차원유한요소모델에서레버암의길이와미니스크류의위치를달리하여전치부후방견인시의변위양상을비교하였다. 구개경사면견인시, 두호선공히레버암이짧을수록전치부의설측경사이동을, 20 mm 인경우중절치의치체이동및견치의치근이동양상을나타냈다. 정중구개봉합부견인시의변위양상은구개경사면의경우와유사하였으나, 레버암이 20 mm 인두호선에서절치의치체이동및연속호선에서전치부의함입소견을보였다. 호선종류에관계없이레버암이길어질수록절치의정출은감소하였고, 구개경사면에서의견인인경우와함께견치의협측변위가증가하였으며, 분절호선에서변위량이많았다. 연속호선상의제 2 소구치는근심경사이동및함입소견을, 대구치는레버암이길수록원심이동및협측변위를나타낸반면, 분절호선상의구치부도 3 차원적이동양상을나타냈으나변위량은미미하였다. 전치부후방견인시레버암작용에의해절치의경사이동과견치의측방이동경향이있었으며, 치체이동을위해서는약 20 mm 의레버암을추천할수있다. 또한호선의종류가치열변위양상및변위량에차이를나타냈다. ( 대치교정지 2011;41(4): ) 주요단어 : 유한요소분석, 레버암, 연속호선, 분절호선 서론 최근교정환자들은설측교정 1 이나투명교정등의심미적인장치사용을원할뿐만아니라, 좀더간단하고빠른치료방법을선호하는추세이다. Siding mechanics는과거의 loop mechanics와달리브라켓과호선사이의마찰로인해고정원이소실 2 될수있음에도불구하고, 이러한요구 (demand) 를충족시킬수있어임상에서보편적으로사용되고있으며, 이에대한효과적인역계 (force system) 등이보고되고있다. 3 교정력은벡터의수학이고저항중심에대한힘의작용선 (line of force) 에의해이동양상이달라지므로, 4 소구치발치 case에서술자가 a 진료교수, 인하대학교의과대학치과학교실. b 대학원생, c 교수, d 부교수, 연세대학교치과대학교정학교실. 교신저자 : 박영철. 서울시서대문구성산로 250, 연세대학교치과대학교정학교실 ; , ypark@yuhs.ac. 원고접수일 : 2011 년 3 월 7 일 / 원고최종수정일 : 2011 년 6 월 22 일 / 원고채택일 : 2011 년 6 월 24 일. * 본연구는연세대학교치과대학두개안면기형연구소의연구비로진행하였음. 원하는전치부이동양상을위해서는적절한힘벡터와모멘트의조절등이필요하다. 5 특히설측교정의경우, 순측과힘의작용점의차이로인해동일한교정력을제공시발생하는모멘트가달라지므로, 호선에보상만곡 (compensating curve) 1 을부여하거나레버암 6,7 등을사용하여전치부견인을시행할수있으며, 순측교정과의생역학적차이를이해하고적용한다면성공적인결과를가져올수있겠다. 8 한개의치아및치아군 (segment) 등의저항중심에대한연구가예전부터있어왔는데, Vanden Bulcke 등 9 은상악 6 전치의저항중심이중절치사이의인접치조골 (interproximal bone) 에서치근단쪽으로약 7 mm 에위치한다고보고하였고, 최근 Sia 등 10 은상악중절치의저항중심이치근첨으로부터치근길이의약 0.77 에해당한다고하였으며, Jeong 등 11 에의하면상악 6 전치저항중심은상악중절치절단연으로부터대략 14 mm 후방, 상방으로 13.5 mm 에존재한다고연구에서밝혔을뿐만아니라, Sung 등 12 에의하면치조골손실시상악전치부의저항중심이치근첨방향으로이동하며, 4 전치군과 237

2 이언화, 유형석, 이기준, 박영철 대치교정지 41 권 4 호, 2011 년 6 전치군의저항중심도후방으로이동한다고보고하였다. 전치부후방견인의효과적인역계 (force system) 를위해서는, 레버암의길이와 sagittal plane 상에서의위치및후방고정원의설계가중요한데, 미니스크류 13,14 는절대적고정원 (absolute anchoarge) 으로서의역할뿐만아니라식립부위에따라다양한수평, 수직적벡터를나타내어임상에서활용도가높다. Chung 등 18 은설측의 retractor 와 palatal plate 를이용하여전치부 en-masse 견인을시행하였고, Hong 등 19 은전치부 torque 조절을위한레버암과미니스크류시스템에관해보고하였다. 또한, sliding mechanics 를이용하여공간폐쇄시연속호선상의구치부에원하지않는치아이동소견이관찰되기도하는데, 구치부변위의방지와장치의단순화란측변에서분절호선 20,21 도고려될수있으나, 아직까지설측의연속호선상의치열변위양상 22 과분절호선의것을비교한연구는전무한실정이다. 치아군등에교정력을가하였을때나타나는치아의반응 1 및생물학적인영향 23 에관한분석방법중유한요소법 은컴퓨터프로그램을이용하여물체의 3 차원모델링후외력이가해졌을때발생하는 stress 와 strain 분포등을해석하는공학적방법이다. 이에본연구는레버암의길이와미니스크류의위치를달리하여상악전치부후방견인시, 두호선상에나타나는초기치열변위양상을 3 차원유한요소법으로비교분석하고, 치료목표에따른최적의역계및호선의선택을위해시행하였다. 연구방법 유한요소모델의제작 치아, 치근막과치조골 본실험의상악의 3차원유한요소모델은성인정상교합자의표본조사를통해제작된니신사의상악모형 (Nissin Dental Products, Kyoto, Japan) 을레이저로 3차원스캐닝한후제1소구치를발거하였고, 치아의 inclination과 angulation은 Andrews prescription 30 에준하였으며, 치열궁형태는 Ormco사 (Ormco, Orange, CA, USA) 의 broad arch form과동일하게제작하였다. 치근막의두께는 Kronfeld, 31 Coolidge 32 의연구를기초로하여 0.25 mm로균일하게설정하고치조골은손실없는것으로가정하여 cementoenamel junction (CEJ) 하방약 1 mm 에서형성하였다. 모델에서교합면에수직으로상악중절치의절단연에서브라켓슬롯까지의거리는 4.5 mm, CEJ 까지의거리는 11 mm 이며치조정까지의거리는 11.8 mm 로계측되었다. 브라켓, 주호선및미니스크류 브라켓의부착을위한기준평면설정및실험에사용된브라켓과주호선의크기는각치아의순측치관중점인 facial axis (FA) point 를연결한 Andrews plane 과평행하면서설측임상치관의 FA point 를지나는평면을설측중심평면 33 으로정하여, 본유한요소모델의설측에 inch 의 Ormco 사제 7 세대설측브라켓 (Ormco, Orange, CA, USA) 을부착하였다. 주호선은상악전치부와구치부를모두연결한연속호선과전치부만연결한분절호선으로나누어제작하였고, 두호선공히 inch 스테인레스스틸호선을사용하였다. 호선과브라켓사이의경계조건은 ANSYS 상의좌표변환기법 (coordinate transformation scheme) 을이용하여각브라켓에서호선의해당지점에서의좌표를계측하여 node coupling 에따라각 x, y, z 좌표계에서의브라켓변위량과호선의변위량을달리한구속조건식 (constraint equation) 을부여하고, 브라켓 slot 과호선사이에마찰및 clearance 없이상대적인 sliding 만허용하여불필요한 wire-bracket play 를방지하게하였다. 레버암은상악측절치와견치사이에 0.7 mm 직경의스테인레스스틸호선을사용하여교합평면에대하여 45 o 로위치시켰으며, 길이는각각 0, 10, 20 mm 로하였다. 미니스크류는상악제 1 대구치와제 2 대구치사이의설측치조골구개경사면 (palatal slope) 과정중구개봉합 (midpalatal suture) 부위에식립하였는데, 구개경사면에서의식립부위는전후방적으로상악제 1, 2 대구치치관의설측인접면위치이면서수직적으로두치아의치근이개부 (furcation area) 높이로정하였고, 정중구개봉합부의경우각각상악제 1, 2 대구치치관의설측인접면부위이면서두치아의치근단 (root apex) 높이로설정하였다. Mechanical property 본실험모델상에사용된치아, 치조골, 치근막과 238

3 Vol. 41, No. 4, Korean J Orthod 연속호선과분절호선의유한요소분석 Table 1. Material properties Young s modulus (g/mm 2 ) Poisson s ratio Periodontal ligament 5.0E Alveolar bone 2.0E Teeth 2.0E Stainless steel 2.0E 선재는모두등방 (isotrophy), 등질 (homogeneity) 의선형탄성체 (linear elasticity) 로가정하였고, 구성요소들의물성치로 Young s modulus 와 Poisson s ratio 를부여하였는데, Tanne 등 34 과 Sung 등 1 의연구자료를참고로하였다 (Table 1). 실험방법및유한요소의해석 견인조건의구분 연속호선과분절호선모델에서각각레버암의길이와미니스크류의식립위치를달리하여, 상악전치부에편측당 200 g 35 의후방견인력을부여하였을때나타나는치열변위양상을비교하였다. 구개경사면의미니스크류에서견인시레버암의길이에따른연속호선과분절호선상에서의치열변위양상의비교연속호선과분절호선모델상각각미니스크류를구개경사면에식립하고, 두호선상의레버암의길이를각각 0, 10, 20 mm 로하여전치부를후방견인하였다. A. 연속호선상의견인조건 (Fig 1A-a, Fig 1B-a) B. 분절호선상의견인조건 (Fig 1A-b, Fig 1B-b) 정중구개봉합부의미니스크류에서견인시레버암의길이에따른연속호선과분절호선상에서의치열변위양상의비교연속호선과분절호선모델상각각미니스크류를정중구개봉합부에식립하고, 레버암의길이를각각 0, 10, 20 mm 로하여전치부의후방견인을시행하였다. A. 연속호선상의견인조건 (Fig 1A-c, Fig 1B-c) B. 분절호선상의견인조건 (Fig 1A-d, Fig 1B-d) 유한요소해석 본연구에사용한유한요소분석방법은 ANYSYS version 11.0 (ANYSYS, Canonsburg, PA, USA) 이며, 실험모델의제작에사용된요소의형태는사면체이고, 총 element 수는 253,556 개이며, node 수는 50,216 개였으며, 모형의구개골기저부에대해서는 x, y, z 축방향으로의변위를제한하여구속하였다. 변위양상의계측역시, 상악양측중절치의절단연을이은선의중점을원점으로하고, 내외측 ( 협설측 ) 방향은 x 축으로하여치아의측방변위를나타내었고, 전후방 ( 순설측 ) 방향은 y 축으로하고치아의전후방적변위를관찰하였으며, 상하 ( 치관치근 ) 방향은 z 축으로정하여치아의수직적변위를표시하였다 (Fig 1C). 치아의초기이동반응을 contour plot 으로관찰하였고, 절치는절단연의중점과치근첨, 견치는치관첨과치근첨, 제 2 소구치는협측치관첨과치근첨, 대구치부는근심협측치관첨과설측치근첨에위치한절점의 x 축, y 축, z 축의좌표값을구하여각각의변위량을계산하였다. 연구성적 치아의전후방이동양상 (frontal displacement) (Figs 2 and 3) 미니스크류의식립위치가구개경사면인경우 (Fig 2, Tables 2 and 3) 레버암의길이가짧을수록연속호선과분절호선 (condition 1A, condition 2A, condition 1B, condition 2B) 에서전치부치관의설측경사이동이나타났고, 분절호선 (condition 2B) 상에서견치가치체이동양상을보였으며, 레버암이긴두호선 (condition 3A, condition 3B) 에서는공히중절치의치체이동및견치의치관순측변위및치근설측변위소견을나타냈다. 연속호선 (condition 1A, condition 2A, condition 3A) 상의제 2 소구치는치관근심경사이동을보인반면, 대구치는레버암이길어질수록 (condition 2A, condition 3A) 원심이동소견을나타냈다. 분절호선 (condition 1B, condition 2B, condition 3B) 상의구치부도대부분원심이동하였으나, 변위량은연속호선에서비해미미하였다. 239

4 이언화, 유형석, 이기준, 박영철 대치교정지 41권 4호, 2011년 Fig 1. A, Occlusal view of experimental groups. a, Continuous arch with lever arms and miniscrews in the palatal slope (condition 1A, lever arm length 0 mm; condition 2A, lever arm length 10 mm; condition 3A, lever arm length 20 mm); b, segmented arch with lever arms and miniscrews in the palatal slope (condition 1B, lever arm length 0 mm; condition 2B, lever arm length 10 mm; condition 3B, lever arm length 20 mm); c, continuous arch with lever arms and miniscrew in the midpalatal suture area (condition 1C, lever arm length 0 mm; condition 2C, lever arm length 10 mm; condition 3C, lever arm length 20 mm); d, segmented arch with lever arms and miniscrew in the midpalatal suture area (condition 1D, lever arm length 0 mm; condition 2D, lever arm length 10 mm; condition 3D, lever arm length 20 mm). B, Lateral view of experimental groups. a, Continuous arch with lever arms and miniscrews in the palatal slope; b, segmented arch with lever arms and miniscrews in the palatal slope; c, continuous arch with lever arms and miniscrew in the midpalatal suture area; d, segmented arch with lever arms and miniscrew in the midpalatal suture area. C, The coordinate system (X, medio-lateral direction ( ), medial ( ), lateral; Y, anterio-posterior direction ( ), anterior ( ), posterior; Z, superio-inferior direction ( ), superior ( ), inferior. 240

5 Vol. 41, No. 4, Korean J Orthod 연속호선과분절호선의유한요소분석 Fig 2. Contour plot of antero-posterior displacement of the continuous and segmented arches with miniscrews in the palatal slope. Condition 1A, Lever arm length of 0 mm with continuous arch; condition 2A, lever arm length of 10 mm with continuous arch; condition 3A, lever arm length of 20 mm with continuous arch; condition 1B, lever arm length of 0 mm with segmented arch; condition 2B, lever arm length of 10 mm with segmented arch; condition 3B, lever arm length of 20 mm with segmented arch. 미니스크류의식립위치가정중구개봉합부인경우 (Fig 3, Tables 4 and 5) 구개경사면견인의경우와유사하게레버암이짧을수록두호선 (condition 1C, condition 2C, condition 1D, condition 2D) 상의전치부는치관의설측경사이동을보였으나, 레버암이 20 mm 인연속호선과분절호선 (condition 3C, condition 3D) 에서는중절치와측절치의치체이동및견치는치관의순측변위와치근의설측변위소견을나타냈다. 연속호선상의제 2 소구치도치관의근심경사이동을, 대구치역시레버암이길어질수록 (condition 2C, condition 3C) 원심이동소견을보인반면, 분절호선 (condition 1D, condition 2D, condition 3D) 상의구치부후방변위는연속호선에서비해미약하였다. 치아의수직이동양상 (Vertical displacement) (Figs 4 and 5) 미니스크류의식립위치가구개경사면인경우 (Fig 4, Tables 2 and 3) 연속호선과분절호선 (condition 1A, condition 2A, condition 3A, condition 1B, condition 2B, condition 241

6 이언화, 유형석, 이기준, 박영철 대치교정지 41 권 4 호, 2011 년 Fig 3. Contour plot of antero-posterior displacement of continuous and segmented arches with miniscrew in the midpalatal suture area. Condition 1A, Lever arm length of 0 mm with continuous arch; condition 2A, lever arm length of 10 mm with continuous arch; condition 3A, lever arm length of 20 mm with continuous arch; condition 1B, lever arm length of 0 mm with segmented arch; condition 2B, lever arm length of 10 mm with segmented arch; condition 3B, lever arm length of 20 mm with segmented arch. 3B) 에서공히절치의정출소견이나타났고, 레버암이길어질수록두호선 (condition 3A, condition 2B, condition 3B) 상의견치는절단연의함입소견을보였고, 변위량은연속호선에비해분절호선에서많았다. 또한, 연속호선 (condition 1A, condition 2A, condition 3A) 상의제 2 소구치는레버암이길어질수록치관의함입소견을나타낸반면, 대구치는대부분이정출소견을보였으나, 분절호선상의구치부변위는미약하였다. 미니스크류의식립위치가정중구개봉합부인경우 (Fig 5, Tables 4 and 5) 구개경사면견인시와유사하게대부분의호선 (condition 1C, condition 2C, condition 1D, condition 2D, condition 3D) 에서전치부절단연의정출소견이나타났으나, 레버암이길어질수록분절호선 (condition 2D, condition 3D) 상의견치가함입양상을보였으며, 20 mm 인연속호선 (condition 3C) 의경우전치부의함입소견을나타냈다. 연속호선 (condition 1C, condition 2C, condition 3C) 상의제 2 소구치도함입양상을나타낸반면, 대부분의대구치는정출소 242

7 Vol. 41, No. 4, Korean J Orthod 연속호선과분절호선의유한요소분석 Table 2. Amount of tooth displacement for the continuous arch with miniscrews in the palatal slope (mm) X axis Condition 1A Condition 2A Condition 3A C.I Cusp tip 8.53E E E-01 Apex -2.68E E E-02 L.I Cusp tip 6.37E E E-01 Apex -2.02E E E-02 C Cusp tip 3.13E E E-02 Apex -9.30E E E-02 PM2 Cusp tip 1.43E E E-02 Apex -7.64E E E-02 M1 Cusp tip 6.17E E E-02 Apex -2.49E E E-02 M2 Cusp tip 2.07E E E-02 Apex -8.85E E E-03 Y axis Condition 1A Condition 2A Condition 3A C.I Cusp tip -1.40E E E-02 Apex 3.20E E E-02 L.I Cusp tip -1.23E E E-03 Apex 4.51E E E-04 C Cusp tip -1.20E E E-02 Apex 3.58E E E-02 PM2 Cusp tip 1.47E E E-03 Apex -7.94E E E-03 M1 Cusp tip 1.47E E E-02 Apex -1.39E E E-02 M2 Cusp tip -1.44E E E-02 Apex -4.43E E E-03 Z axis Condition 1A Condition 2A Condition 3A C.I Cusp tip -7.72E E E-03 Apex 5.51E E E-02 L.I Cusp tip -7.10E E E-02 Apex 3.67E E E-02 C Cusp tip -4.12E E E-02 Apex 3.85E E E-02 PM2 Cusp tip 3.49E E E-02 Apex 3.71E E E-03 M1 Cusp tip -6.33E E E-04 Apex 1.59E E E-02 M2 Cusp tip -4.96E E E-03 Apex 9.14E E E-04 C.I, Central incisor; L.I, lateral incisor; C, canine; PM2, second premolar; M1, first molar; M2, second molar; condition 1A, lever arm length of 0 mm with continuous arch; condition 2A, lever arm length of 10 mm with continuous arch; condition 3A, lever arm length of 20 mm with continuous arch. 243

8 이언화, 유형석, 이기준, 박영철 대치교정지 41 권 4 호, 2011 년 Table 3. Amount of tooth displacement for the segmented arch with miniscrews in the palatal slope (mm) X axis Condition 1B Condition 2B Condition 3B C.I Cusp tip 8.32E E E-01 Apex -2.61E E E-02 L.I Cusp tip 6.29E E E-01 Apex -1.97E E E-02 C Cusp tip 3.20E E E-01 Apex -8.68E E E-02 PM2 Cusp tip 5.21E E E-05 Apex -1.52E E E-05 M1 Cusp tip -1.52E E E-05 Apex -7.39E E E-06 M2 Cusp tip -1.23E E E-05 Apex -1.93E E E-06 Y axis Condition 1B Condition 2B Condition 3B C.I Cusp tip -1.45E E E-01 Apex 3.41E E E-02 L.I Cusp tip -1.30E E E-03 Apex 4.77E E E-03 C Cusp tip -1.30E E E-01 Apex 4.01E E E-02 PM2 Cusp tip -2.23E E E-06 Apex -5.63E E E-06 M1 Cusp tip -3.13E E E-06 Apex -2.05E E E-06 M2 Cusp tip -3.33E E E-06 Apex -8.87E E E-06 Z axis Condition 1B Condition 2B Condition 3B C.I Cusp tip -8.04E E E-02 Apex 5.69E E E-02 L.I Cusp tip -7.33E E E-02 Apex 3.96E E E-02 C Cusp tip -4.18E E E-02 Apex 4.38E E E-02 PM2 Cusp tip -3.39E E E-06 Apex -5.78E E E-06 M1 Cusp tip -5.02E E E-06 Apex -3.58E E E-06 M2 Cusp tip 1.71E E E-06 Apex 1.10E E E-06 C.I, Central incisor; L.I, lateral incisor; C, canine; PM2, second premolar; M1, first molar; M2, second molar; condition 1B, lever arm length of 0 mm with segmented arch; condition 2B, lever arm length of 10 mm with segmented arch; condition 3B, lever arm length of 20 mm with segmented arch. 244

9 Vol. 41, No. 4, Korean J Orthod 연속호선과분절호선의유한요소분석 Table 4. Amount of tooth displacement for the continuous arch with miniscrew in the midpalatal suture area (mm) X axis Condition 1C Condition 2C Condition 3C C.I Cusp tip 6.10E E E-01 Apex -1.82E E E-02 L.I Cusp tip 5.27E E E-02 Apex -1.48E E E-02 C Cusp tip 3.54E E E-02 Apex -9.68E E E-02 PM2 Cusp tip 1.96E E E-02 Apex -9.44E E E-02 M1 Cusp tip 8.13E E E-02 Apex -3.30E E E-02 M2 Cusp tip 3.11E E E-02 Apex -1.30E E E-03 Y axis Condition 1C Condition2C Condition3C C.I Cusp tip -1.10E E E-02 Apex 2.53E E E-02 L.I Cusp tip -1.10E E E-03 Apex 3.85E E E-02 C Cusp tip -1.18E E E-02 Apex 3.20E E E-02 PM2 Cusp tip 1.72E E E-03 Apex -8.04E E E-02 M1 Cusp tip 1.35E E E-03 Apex -1.69E E E-02 M2 Cusp tip -3.72E E E-02 Apex -5.95E E E-03 Z axis Condition 1C Condition 2C Condition 3C C.I Cusp tip -5.61E E E-03 Apex 4.76E E E-02 L.I Cusp tip -5.73E E E-04 Apex 3.69E E E-02 C Cusp tip -3.74E E E-02 Apex 4.06E E E-02 PM2 Cusp tip 2.46E E E-02 Apex 3.72E E E-03 M1 Cusp tip -1.17E E E-04 Apex 2.06E E E-02 M2 Cusp tip -1.99E E E-03 Apex 1.36E E E-04 C.I, Central incisor; L.I, lateral incisor; C, canine; PM2, second premolar; M1, first molar; M2, second molar; condition 1C, lever arm length of 0 mm with continuous arch; condition 2C, lever arm legnth of 10 mm with continuous arch; condition 3C, lever arm length of 20 mm with continuous arch. 245

10 이언화, 유형석, 이기준, 박영철 대치교정지 41 권 4 호, 2011 년 Table 5. Amount of tooth displacement for the segmented arch with miniscrew in the midpalatal suture area (mm) X axis Condition 1D Condition 2D Condition 3D C.I Cusp tip 5.76E E E-01 Apex -1.70E E E-02 L.I Cusp tip 5.17E E E-02 Apex -1.48E E E-02 C Cusp tip 3.75E E E-02 Apex -8.75E E E-02 PM2 Cusp tip 8.81E E E-05 Apex -1.11E E E-05 M1 Cusp tip -9.76E E E-05 Apex -6.03E E E-06 M2 Cusp tip -8.47E E E-05 Apex -2.47E E E-06 Y axis Condition 1D Condition 2D Condition 3D C.I Cusp tip -1.14E E E-02 Apex 2.69E E E-02 L.I Cusp tip -1.18E E E-03 Apex 4.22E E E-02 C Cusp tip -1.29E E E-01 Apex 3.62E E E-02 PM2 Cusp tip -2.06E E E-07 Apex -5.04E E E-05 M1 Cusp tip -2.84E E E-06 Apex -1.89E E E-06 M2 Cusp tip -3.01E E E-06 Apex -8.26E E E-07 Z axis Condition 1D Condition 2D Condition 3D C.I Cusp tip -5.82E E E-02 Apex 4.93E E E-02 L.I Cusp tip -6.01E E E-03 Apex 4.03E E E-02 C Cusp tip -3.94E E E-02 Apex 4.59E E E-02 PM2 Cusp tip -3.92E E E-06 Apex -5.59E E E-07 M1 Cusp tip -5.32E E E-06 Apex -2.85E E E-06 M2 Cusp tip 1.01E E E-06 Apex 1.05E E E-06 C.I, Central incisor; L.I, lateral incisor; C, canine; PM2, second premolar; M1, irst molar; M2, second molar; condition 1D, lever arm legnth of 0 mm with segmented arch; condition 2D, lever arm length of 10 mm with segmented arch; condition 3D, lever arm length of 20 mm with segmented arch. 246

11 Vol. 41, No. 4, Korean J Orthod 연속호선과분절호선의유한요소분석 Fig 4. Contour plot of vertical displacement of the continuous and segmented arches with miniscrews in the palatal slope. Condition 1C, Lever arm length of 0 mm with contitnuous arch; condition 2C, lever arm length of 10 mm with continuous arch; condition 3C, lever arm length of 20 mm with continuous arch; condition 1D, lever arm length of 0 mm with segmented arch; condition 2D, lever arm length of 10 mm with segmented arch; condition 3D, lever arm length of 20 mm with segmented arch. 견을보였으나구개경사면견인시보다정출량이적었다. 또한, 분절호선상의구치부변위는미약하였다. 치아의측방이동양상 (Lateral displacement) (Figs 6 and 7) 미니스크류의식립위치가구개경사면인경우 (Fig 6, Table 2 and 3) 연속호선과분절호선 (condition 1A, condition 2A, 247

12 이언화, 유형석, 이기준, 박영철 대치교정지 41 권 4 호, 2011 년 Fig 5. Contour plot of vertical displacement of continuous and segmented arches with miniscrew in the midpalatal suture area. Condition 1C, Lever arm length of 0 mm with contitnuous arch; condition 2C, lever arm length of 10 mm with continuous arch; condition 3C, lever arm length of 20 mm with continuous arch; condition 1D, lever arm length of 0 mm with segmented arch; condition 2D, lever arm length of 10 mm with segmented arch; condition 3D, lever arm length of 20 mm with segmented arch. condition 3A, condition 1B, condition 2B, condition 3B) 에서절치는치관의내측변위소견을나타냈으나, 레버암이길어질수록 (condition 2A, condition 3A, condition 2B, condition 3B) 견치와구치부는치관의협측변위양상을보였으며, 견치의변위량은분절호선에서더많았다. 또한, 분절호선상의구치부협측변위는연속호선에비해미약하였다. 미니스크류의식립위치가정중구개봉합부인경우 (Fig 7, Tables 4 and 5) 전치부변위양상은구개경사면견인시와유사 하였으나, 견치의협측변위량이미니스크류위치가구개경사면인경우보다적은것으로나타났다. 연속호선상의구치부는레버암이길어질수록 (condition 2C, condition 3C) 치관의협측변위가증가하였으나, 구개경사면견인에비해서는변위량이적었다. 분절호선상의구치부변위역시연속호선에비해미약하였다. 고찰 일반적으로발치를동반한교정치료의경우다양한메카닉과장치를이용하여치료효율성을높일 248

13 Vol. 41, No. 4, Korean J Orthod 연속호선과분절호선의유한요소분석 Fig 6. Contour plot of lateral displacement of continuous and segmented arches with miniscrews in the palatal slope. Condition 1C, Lever arm length of 0 mm with contitnuous arch; condition 2C, lever arm length of 10 mm with continuous arch; condition 3C, lever arm length of 20 mm with continuous arch; condition 1D, lever arm length of 0 mm with segmented arch; condition 2D, lever arm length of 10 mm with segmented arch; condition 3D, lever arm length of 20 mm with segmented arch. 수있는데, 36,37 Upadhyay 등 38 은치조성전돌환자에서 en-masse 로전치부견인시미니스크류의효과에대해보고하였고, Park 등 7 은설측교정에서의레버암을소개하였다. 순측교정과설측교정은힘의작 용점과저항중심과의관계로인해치아이동양상에차이가발생하므로 39 견인력을부여시교정력의조절이나부가적인 bend 등을이용할수있겠으나, 본연구의경우호선의보상만곡 1 없이미니스크류 249

14 이언화, 유형석, 이기준, 박영철 대치교정지 41 권 4 호, 2011 년 Fig 7. Contour plot of lateral displacement of continuous and segmented arches with miniscrew in the midpalatal suture area. Condition 1C, Lever arm length of 0 mm with contitnuous arch; condition 2C, lever arm length of 10 mm with continuous arch; condition 3C, lever arm length of 20 mm with continuous arch; condition 1D, lever arm length of 0 mm with segmented arch; condition 2D, lever arm length of 10 mm with segmented arch; condition 3D, lever arm length of 20 mm with segmented arch. 와레버암만을사용하여후방견인하였다. 연속호선과분절호선에서미니스크류의위치에관계없이레버암이짧을수록전치부의치관의설측경사이동및정출양상이나타났는데, 이는후방 견인력의작용점이상악 6 전치 40 및상악전치열의저항중심하방에서적용되었기때문이다. 반면레버암이길어질수록절치의정출은감소하였고견치는압하현상을보였는데, 이는상악전치열의저항 250

15 Vol. 41, No. 4, Korean J Orthod 연속호선과분절호선의유한요소분석 중심에대해전치부치근방향의모멘트의발생뿐만아니라, 상악 6 전치저항중심 11 에가장근접한치아인견치에서레버암효과가뚜렷이발현되었기때문인것으로생각된다. 또한, 연속호선상의제 2 소구치는레버암이짧을수록근심경사이동하였고, 길수록함입및협측변위를나타낸반면, 대구치는레버암이길어질수록원심이동및협측변위소견을보였는데, 이처럼연속호선상의구치부변위양상이악궁내구치부에서전치부를견인할때나타나는전형적인 vertical bowing 및 transeverse bowing 41 현상과차이를나타낸것은견인력의고정원이주호선상으로부터독립적으로위치한미니스크류에서견인 42 하였기때문에구치부에직접적인반작용이일어나지않은것으로보이며, 전치부견인초기시는악궁폭경조절을위한호선의부가적인구부림없이제 2 소구치와의악궁조화 (arch coordination) 가이루어질것으로생각된다. 분절호선상의구치부역시변위량은미미하나후방변위를비롯한 3 차원적이동소견을보였으나, 이는본실험모델이하나의연속된탄성체로가정한것에기인한것으로써실제임상결과와는차이가있을것이다. 구개경사면의미니스크류에서견인시정중구개봉합부에비해레버암이길어질수록견치의협측변위가두드러졌는데, 이는상악 6 전치의저항중심에대한모멘트의증가뿐만아니라, 기준평면중 x 분력을기준시힘의작용방향이정중구개봉합부에비해내측에서외측으로적용되었기때문인것으로보인다. 상악전치부의저항중심이중절치절단연으로부터후방으로 14 mm, 치근쪽으로 13.5 mm 에위치한다고보고한 Jeong 등 11 의연구에근거하면, 본실험에서의레버암의길이를 15 mm 라고가정할경우, 교합평면에대해레버암이 45 o 로위치하므로중절치에서브라켓 slot 까지의수직거리를통상적으로약 4 mm 로계산시실제수직적길이는중절치절단연으로부터치근첨으로약 14.6 mm 가된다. 따라서, 후방견인력벡터가거의전치부저항중심부위를통과하게되고궁극적으로는치체이동양상을예상할수있다. 또한, 정중구개봉합부에서 20 mm 의레버암으로견인시, 적용된레버암의수직적길이는약 18 mm 가되어전치부의치근이동양상을예상했으나, 결과상두호선공히중절치와측절치는치체이동을, 견치는치근이동양상을나타냈는데, 주요인으로주호선의변형 (deformation) 현 Fig 8. Deformation of main arch wire (meshed, before deformation; colored, after deformation; 1, central incisor; 2, lateral incisor; 3, canine). 상 (Fig 8) 43 을고려해야할것이다. 이는측절치와견치사이에위치한레버암의 cantilever 효과에의해발생한 bending 모멘트로인한것이며, 실제견인력의작용선이예측한위치보다하방으로이동하였기때문인것으로생각된다. 실험결과, 구개경사면견인시는분절호선의경우레버암이 10 mm 이상에서, 연속호선은 20 mm인경우에견치및절치의치체이동양상에근접했으므로, 짧은레버암을사용시에는분절호선이전치부 torque 조절 44 등에유리할수있으며, 연속호선에서는레버암길이의증가가필요할것이나전치부가가장치체이동에근접한조합은두호선공히레버암의길이가 20 mm이면서정중구개봉합부에서의견인이었으므로, 적어도 15 mm 이상의레버암을사용하는것이치체조절에바람직할것으로보인다. 또한, Kim 29 의연속호선에서의치열변위양상과비교시, 전치부의전후방및수직변위의방향은본연구결과와유사하였으나, 절대적인변위량에있어미니스크류를사용한본실험의분절호선이가장많았고, transpalatal arch (TPA) 29 를고정원으로사용한연속호선에서가장적은것으로나타났다. 후방분절의변위양상은미니스크류를사용한본실험모델과 TPA를사용한연속호선 29 에서다르게나타났으며, 대구치의후방변위량은 TPA 고정원 29 의연속호선에서가장많았고, 미니스크류를사용한분절호선이가장적은것으로나타나, 호선과고정원의종류에따라전방분절과후방분절에서의변위양상과변위량에차이가있음을알수있었다. 실제임상에적용시전치부조절을위해서는변위 251

16 이언화, 유형석, 이기준, 박영철 대치교정지 41 권 4 호, 2011 년 량이적은연속호선을선택하는것이치료결과의안전 (fail-safe) 한측면이있을것으로생각되나구치부의이동양상등을고려해야할것이다. 이상의결과를토대로, 초진시환자의상악전치경사도와수직적위치및악궁의폭경등을고려해서호선의종류와레버암의길이, 고정원및미니스크류의식립위치를선택하는것이최적의치료결과를위한고려사항이될것이며또한, 본연구에서밝힌치열변위양상은교정영역의치아이동을컴퓨터시뮬레이션을통해해석한것으로 3 차원모델을원하는형태로쉽게변형하여결과를도출할수있는장점 45 이있으나개개인의해부학적, 생물학적변이를완벽히재현하지못하고, 외력을부여시치아와치근막에나타나는초기변위양상이기때문에실제치아이동이시간에따른지속적인골조직등의반응인점에서추후생물학적, 생화학적연구가뒷받침된다면임상에많은도움을줄수있을것이다. 결론 설측의연속호선과분절호선상에서레버암의길이와교정용미니스크류의위치를달리하여상악전치부를후방견인시, 치열에나타나는변위양상을유한요소법으로비교분석하고자하였다. 1. 구개경사면에서견인시, 연속호선과분절호선은레버암이짧을수록전치부치관의설측경사이동및정출소견을나타냈고, 20 mm 인두호선에서중절치는치체이동양상을, 견치는치관의순측변위및함입, 치근의설측변위를나타냈으며, 변위량은분절호선에서많았다. 2. 정중구개봉합부견인시의전치부변위양상은구개경사면의경우와유사하였으나, 레버암의길이가 20 mm 인두호선에서절치의치체이동및견치의치근이동양상이나타났으며, 연속호선에서전치부치관의함입소견을보였다. 3. 두호선공히레버암이길어질수록절치의정출은감소하였고, 미니스크류위치가정중구개봉합부에비해외측인구개경사면견인의경우와함께견치의협측변위가증가하였으며, 변위량은분절호선에서많았다. 4. 구치부이동양상및변위량은연속호선의경우제 2 소구치의치관근심경사이동및함입소견을나타낸반면, 대구치는레버암이길수록원심 이동및협측변위를나타냈다. 분절호선상의구치부도후방이동을비롯한 3 차원적이동소견을나타냈으나, 변위량은연속호선에비해미미하였다. 설측에서상악전치부후방견인시전방분절의레버암작용에의해절치의경사이동과견치의측방이동이일어나는경향이있었으며, 전치부의치체이동을위해서는약 20 mm 의레버암을추천할수있다. 또한연속호선및분절호선의여부가치열변위양상및변위량에차이를나타냈다. 참고문헌 1. Sung SJ, Baik HS, Moon YS, Yu HS, Cho YS. A comparative evaluation of different compensating curves in the lingual and labial techniques using 3D FEM. Am J Orthod Dentofacial Orthop 2003;123: Vásquez M, Calao E, Becerra F, Ossa J, Enríquez C, Fresneda E. Initial stress differences between sliding and sectional mechanics with an endosseous implant as anchorage: a 3-dimensional finite element analysis. Angle Orthod 2001;71: Sia S, Shibazaki T, Koga Y, Yoshida N. Experimental determination of optimal force system required for control of anterior tooth movement in sliding mechanics. Am J Orthod Dentofacial Orthop 2009;135: Chung AJ, Kim US, Lee SH, Kang SS, Choi HI, Jo JH, et al. The pattern of movement and stress distribution during retraction of maxillary incisors using a 3-D finite element method. Korean J Orthod 2007;37: Jang HJ, Roh WJ, Joo BH, Park KH, Kim SJ, Park YG. Locating the center of resistance of maxillary anterior teeth retracted by Double J Retractor with palatal miniscrews. Angle Orthod 2010;80: Kucher G, Weiland FJ, Bantleon HP. Modified lingual lever arm technique. J Clin Orthod 1993;27: Park YC, Choy K, Lee JS, Kim TK. Lever-arm mechanics in lingual orthodontics. J Clin Orthod 2000;34: Nägerl H, Kubein-Meesenburg D. A FEM (Finite-Element- Measurement) study for the biomechanical comparison of labial and palatal force application on the upper incisors. Fortschr Kieferorthop 1993;54: Vanden Bulcke MM, Burstone CJ, Sachdeva RC, Dermaut LR. Location of the centers of resistance for anterior teeth during retraction using the laser reflection technique. Am J Orthod Dentofacial Orthop 1987;91: Sia S, Koga Y, Yoshida N. Determining the center of resistance of maxillary anterior teeth subjected to retraction forces in sliding mechanics. An in vivo study. Angle Orthod 2007; 77: Jeong GM, Sung SJ, Lee KJ, Chun YS, Mo SS. Finite-element investigation of the center of resistance of the maxillary dentition. Korean J Orthod 2009;39: Sung SJ, Kim IT, Kook YA, Chun YS, Kim SH, Mo SS. 252

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18 ORIGINAL ARTICLE Three dimensional finite element analysis of continuous and segmented arches with use of orthodontic miniscrews Eon-Hwa Lee, DDS, MSD, a,b Hyung-Seog Yu, DDS, MSD, PhD, c Kee-Joon Lee, DDS, MSD, PhD, d Young-Chel Park, DDS, MSD, PhD c Objective: The purpose of this study was to compare the displacement patterns shown by finite element analysis when the maxillary anterior segment was retracted from different orthodontic miniscrew positions and different lengths of lever arms in lingual continuous and segmented arch techniques. Methods: A three dimensional model was produced, the translation of teeth in both models was measured and individual displacement was calculated. Results: When traction was carried out from miniscrews in the palatal slope, lingual tipping of crowns and extrusion of the maxillary anterior segment were found in both continuous and segmented arches as the lever arms were made shorter. With miniscrews in the midpalatal suture area, the displacement patterns were similar to the palatal slope, but bodily movement of the upper incisors was observed in both continuous and segmented arches with the lever arm at 20 mm. When lever arms were longer, there was less extrusion of the incisors and more buccal displacement of the canines. Such displacement was shown less in the continuous arch than the segmented arch. The second premolar showed crown mesial tipping and intrusion, and the molars showed distal tipping in the continuous arch. The posterior segment was displaced three dimensionally in the segmented arch, but the amount of displacement was less than the continuous arch. Conclusions: It is recommended that lever arms of 20 mm in length be used for bodily movement of the anterior segment. Use of continuous or segmented arches affect the displacement patterns and induce differences in the amount of displacement. (Korean J Orthod 2011;41(4): ) Key words: Finite element analysis, Lever arm, Continuous arch, Segmented arch a Medical Professor, Department of Dentistry, College of Medicine, Inha University. b Graduate Student, c Professor, d Associate Professor, Department of Orthodontics, College of Dentisrty, Yonsei University. Corresponding author: Young-Chel Park. Department of Orthodontics, College of Dentistry, Yonsei University, 250 Seongsanno, Seodaemun-gu, Seoul , Korea. *Supported by the grant of Craniofacial Deformity Research Institute at College of Dentistry, Yonsei University ; , ypark@yuhs.ac. Received March 7, 2011; Last Revision June 22, 2011; Accepted June 24,