즉시부하시, 임플란트디자인이 주위골의응력분포에미치는영향 : 3 차원적유한요소분석 연세대학교대학원치의학과배정윤

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1 즉시부하시, 임플란트디자인이 주위골의응력분포에미치는영향 : 3 차원적유한요소분석 연세대학교대학원치의학과배정윤

2 즉시부하시, 임플란트디자인이 주위골의응력분포에미치는영향 : 3 차원적유한요소분석 지도한종현교수 이논문을박사학위논문으로제출함 2009 년 7 월일 연세대학교대학원치의학과배정윤

3 감사의글 논문을마무리하는시점에와서지나간시간을뒤돌아보며, 처음시작할때의 의욕과열정이얼마나남아있나생각해보면, 많이부끄러워집니다. 그러나, 저의 주위에많은분들이있었기에여기까지올수있었던것같습니다. 이논문이완성되는데있어부족한저에게처음부터지금까지끊임없는가르 침을주시고, 격려를보내주신한종현교수님께진심으로감사드립니다. 그리고, 바쁘신와중에도귀중한조언을해주시고, 논문의심사를해주신심준성교수님, 류인철교수님, 허성주교수님, 김선재교수님께도감사를드립니다. 또한, 이논문의실험을도와주시고, 많은조언을아끼지않으신전흥재교수님과강경탁, 주민진선생님에게도마음깊이감사를드립니다. 논문을준비하는동안힘들때마다옆에서많은도움이되어준분당제생병 원치과선생님들과저의지인들에게도감사의마음을전합니다. 그리고, 제가여기에있게해주신사랑하는아버지, 어머니, 항상격려해주시는 오빠와언니에게도감사의마음을표합니다 년 7 월 배정윤드림

4 차 례 그림및표차례 ⅱ 국문요약 ⅴ I. 서론 1 II. 재료및방법 4 1. 유한요소모델링 4 2. 임플란트-골계면디자인 5 3. 경계, 하중조건과물질의성질 5 III. 연구결과 8 1. 지연부하에서임플란트길이, 직경, 바디형태에따른골최대응력변화 즉시부하에서임플란트길이, 직경, 바디형태에따른골최대응력과변위변화 15 IV. 총괄및고찰 21 V. 결론 28 참고문헌 30 영문요약 39 i

5 그림차례 Fig.1. The 3-dimensional model including the crown, the implant. 7 Fig.2. Schematic presentation of a) tapered type b) straight type dental implant. 7 Fig.3. The distribution of cortical & trabecular bone stresses around a) delayed loaded (bonded) implants and b) immediately loaded (contact) implants 8 Fig.4. The distribution of cortical & trabecular bone stresses around a) tapered, b) straight 4.3 X 8.5, 4.3 X 10 and 4.3 X 11.5 mm delayed loaded (bonded) implants. 11 Fig.5. The distribution of cortical & trabecular bone stresses around a) tapered, b) straight 5.3 X 8.5, 5.3 X 10 and 5.3 X 11.5 mm delayed loaded (bonded) implants. 12 Fig.6. The maximum von-mises stress (EQV) of the bone among three implant length (8, 10, 11.5 mm) of diameter 4.3 mm and 5.3 mm delayed loaded (bonded) a) tapered and b) straight implants. 13 Fig.7. The maximum von-mises stress (EQV) of the bone among two implant diameter (4.3, 5.3mm) of length 8.5 mm, 10 mm, and 11.5 mm delayed loaded (bonded ) a) tapered and b) straight implants. 13 Fig.8. The maximum von-mises stress (EQV) of the bone among two implant body designs (tapered, straight form) of length 8.5 mm, 10 mm, and 11.5 mm delayed loaded (bonded ) a) diameter 4.3 mm and b) 5.3 mm implants. 14 ii

6 Fig.9. The distribution of cortical & trabecular bone stresses around a) tapered, b) straight 4.3 X 8.5, 4.3 X 10 and 4.3 X 11.5 mm immediately loaded (contact) implants. 17 Fig.10. The distribution of cortical & trabecular bone stresses around a) tapered, b) straight 5.3 x 8.5, 5.3 X 10 and 5.3 x 11.5 mm immediately loaded (contact) implants. 18 Fig.11. The maximum von-mises stress (EQV) of the bone among three implant length (8, 10, 11.5 mm) of diameter 4.3 mm and 5.3 mm immediately loaded (contact) a) tapered and b) straight implants. 19 Fig.12. The maximum von-mises stress (EQV) of the bone among two implant diameter (4.3, 5.3 mm) of length 8.5 mm, 10 mm, and 11.5 mm immediately loaded (contact) a) tapered and b) straight implants. 19 Fig.13. The maximum von-mises stress (EQV) of the bone among two implant body designs (tapered, straight form) of length 8.5 mm, 10 mm, and 11.5 mm immediately loaded (contact) a) diameter 4.3 mm and b) 5.3 mm implants. 20 iii

7 표차례 Table I. Mechanical properties of the materials. 6 Table II. The maximum von-mises stress (maximum equivalent stress or Max EQV stress) of the bone around different implant length, diameter and body design (tapered and straight) with bonded and contact interface condition. 9 Table III. The maximum sliding distance of model of contact implant-bone interfaces. 20 iv

8 국문요약 즉시부하시, 임플란트디자인이 주위골의응력분포에미치는영향 : 3 차원적유한요소분석 최근에는임플란트를식립한후보철물을장착하기까지소요하는치유기간을점차줄이고있는추세이며, 심지어는치유기간없이바로기능부하를가하는즉시부하치료도많이시행하는추세이다. 이러한즉시부하의성공에가장중요한요소는임플란트의초기안정성이며, 즉시부하결과에영향을주는요인들중임플란트디자인요인들의변화에의해서교합압을적용할때골에서지지하는표면적을늘일수있어, 발생하는응력을감소시킬수있다. 임플란트의즉시부하에서이들의영향은최근에연구하기시작했으며, 지연부하시와비교해서다른영향을미칠수있을것이다. 이번연구의목적은임플란트의즉시부하상황을유한요소방법으로재현하고, 임플란트주위골의응력분포에대한임플란트의디자인의영향을분석하여, 즉시부하시술을위한적절한임플란트선택에도움을주기위함이다. 실험방법은유한요소분석방법을선택했으며, 임플란트로지지하는하악제 1 소구치치관을 3차원적모델로재현하였다. Tapered, straight 형의, 4.3 mm의직경과 8, 10, 11.5 mm의길이를가진임플란트들과 5.3mm의직경과 8, 10, 11.5 mm의길이를가진임플란트들을즉시부하와지연부하상황에놓이게하여, 등가응력을분석했다. 임플란트의즉시부하시임플란트디자인이주위골의응력분포에미치는영향을연구한결과는다음과같다. v

9 1. 지연부하와비교해서즉시부하에서는응력이임플란트경부피질골뿐만 아니라, 임플란트 - 골계면을따라임플란트근단까지해면골에도광범위하게 분포하며, 최대등가응력도더높게나타났다. 2. 지연부하에서는 tapered 형직경 4.3 mm 의임플란트모델이 10 mm 에서 11.5 mm 로길이가증가할때최대응력이다소증가하는양상을보인것을제외하고는, 임플란트의길이가길어질수록최대응력이감소했다. 또한임플란트직경이커지면최대응력이감소했으며, tapered 형임플란트가 straight 형임플란트보다최대응력이더높았다. 3. 즉시부하에서는 tapered 형의임플란트에서는, 같은직경일때길이가 8.5 mm 에서 10 mm 로증가시에는최대응력이감소하나, 10 mm 에서 11.5 mm 로증가시에는최대응력이증가했으며, 같은길이일때는직경이증가할수록최대응력이감소했다. 바디형태에서는 4.3 X 8.5 mm 의임플란트모델을제외하고, tapered 형임플란트가 straight 형임플란트보다최대응력이더낮게나타났다. 즉시부하시임플란트-골계면의최대변위거리는허용되는미세동요도인 50 μm 이하의값을나타냄으로써, 골형성을방해하지않는것으로보인다. 4. 지연부하에서는길이, 직경, 바디형태들의변화에따른최대응력에대한영향이비교적규칙적인양상을보였으나, 즉시부하에서는이들의영향이다양하게나타나는모습을보여주었다. 즉지연부하에서의디자인변수들의영향과일치하지않을수있다는것을보여주었다 핵심되는말 : 즉시부하, 유한요소분석, 치과임플란트, 길이, 직경, 디자인, 응력 vi

10 I. 서론 임플란트를 Brånemark 이처음임상에도입했을때, 성공적인골유착을 위해서는임플란트를치은하방에위치시킨후부하를가하지않는 3-6 개월의 치유기간이필요하다고제시했다. 1-2 그러나, 최근임플란트를식립한후 보철물을장착하기까지소요하는치유기간을점차줄이고있는추세이며, 심지어는치유기간없이바로기능부하를가하는즉시부하에대한연구도보고되고있다. 3-6 즉시임플란트부하란임플란트를식립한후즉시또는몇시간후부하를 가하는것으로정의할수있다. 7 최근에 Wang 등 8 은즉시부하의정의를 임플란트를식립한후적어도 48시간내에, 임플란트지지수복물에교합력을가하는것으로제안했다. 이러한즉시부하는환자에게내원기간단축, 빠른저작기능과심미성의회복등으로편안함을제공해주지만, 임플란트의미세동요로인한더높은실패율, 최종결과예측의불확실성등을포함하는많은위험성을가지고있다. 7 초기즉 1970년대의임플란트의즉시부하는섬유피막화, 동요, 최종적으로 임플란트의소실로이어졌다 최근 10 년동안환자의조심스런선택, 교합과 보철물설계의적절한계획, 임플란트재료와표면, 디자인의개선으로성공률이 높아짐에따라즉시부하치료는점차확대되어가고있는추세이다. 7 통계상으로도 96% 이상의성공률을보고하고있고, 골흡수에서도지연부하와 즉시부하간에큰차이를보이지않고있다 이와같이다수의임상연구는진행되었으나, 즉시부하프로토콜에대한 - 1 -

11 연구와즉시부하의근거가될만한임상연구는부족한형편이다. 13 이러한즉시부하의성공에가장중요한요소는임플란트의초기안정성으로서, 골유착을위해서는기간이아니라, 교합압을전달할때골과임플란트계면사이에발생되는미세동요가대략 μm 정도의, 수용가능한역치이하에 존재하도록하는것이필요하다. 이를위해서 Gapski 등 20 은즉시부하결과에 영향을주는요인들을수술시초기임플란트안정성, 환자의골량과골질, 임플란트디자인, 교합과보철물디자인등이라고했다. 이중에서임플란트디자인요인으로는임플란트길이, 직경, 바디형태등이있으며, 이들을적절하게선택함에의해교합압을작용할때골에서지지하는 표면적을늘일수있어발생하는응력을감소시킬수있다. 21 바디형태중현재 가장대표적인디자인으로는 tapered 형과 straight 형이있다. 이런디자인요인들은지연부하에서도폭넓게연구하여왔으며, 이들의변화에의해임플란트치료의성공률을높일수있다는것을발견했다 그러나, 임플란트의즉시부하에서이들의영향은최근에연구하기시작했으며, 또한지연부하시와비교해서다른영향을미칠수도있을것이다 즉시부하에영향을주는변수들과골에서발생하는응력과의상관관계를좀더상세하게밝히기위한연구방법중의하나가유한요소분석법이다. 유한요소분석은지난 2세기동안임플란트주위골의응력의예측을위한 유용한방법으로이용해왔으며, 29 즉시부하상황을유한요소방법으로재현한 연구도몇몇논문에서볼수있다 Riger 등 31 과 Palomar 등 32 은완전한골유착전에는임플란트 - 골계면에서 전면적인활주운동이일어난다고생각했으므로, frictionless interface( 마찰이 - 2 -

12 없는계면 ) 으로재현했다. 그러나, Mellal 등 33 은치유기간동안특정한순간을 대표하는마찰계수를임플란트-골계면에서추정할수있으므로, 골유착전계면을임플란트와골사이의작은변위를허락하는마찰계면으로, 비선형 frictional contact( 마찰접촉 ) 요소를사용하여재현했다. 이번연구에서는즉시부하시임플란트-골계면을후자와같이재현하였다. 이번연구의목적은임플란트의즉시부하상황을유한요소방법으로재현하고, 임플란트주위골의응력분포에대한임플란트의디자인의영향을분석하여, 즉시부하시술을위한적절한임플란트선택에도움을주기위함이다

13 II. 재료및방법 1. 유한요소모델링 실험단계는 Pro/Engineer Wildfire 2.0으로모델링하고, Hypermesh 8.0 (Altair Co., USA) 으로 preprocessing, postprocessing 한후, ABAQUS 6.6 (HKS, Inc.) 으로해석하였다. 임플란트로지지하는하악제 1 소구치치관을 3차원적모델로재현하였다. 치관은 castable abutment (warantec, Seoul, Korea) 로제작한시멘트유지형금관이며, 지대주의높이는 5 mm로하였다. 임플란트주위의골은, Lekholm와 Zarb 34 의분류중 type 2 골을참고로해서, 2mm 두께의피질골하방에조밀한해면골로구성된하악골로 3차원적으로형성했다 (Fig.1). 골의높이는 23.4mm 직경은 16mm로하였다. 임플란트는 tapered, straight 형의내부연결형의임플란트 (Oneplant, warantec, Seoul, Korea) 를모델로하였다 (Fig.2). 4.3 mm의직경과 8, 10, 11.5 mm의길이를가진임플란트들과 5.3mm의직경과 8, 10, 11.5 mm의길이를가진임플란트들을즉시부하와지연부하상황에놓이게했다. 요소는 C3D10m (A 10-node modified quadratic tetrahedron), C3D4 (A 4- node linear tetrahedron) 를사용하였다. 요소크기는임플란트는 0.5, 골은 0.4로하였다

14 2. 임플란트 - 골계면디자인 임플란트의즉시부하와지연부하의상황은골과임플란트사이계면에서의서로다른상황을추정해서재현했다. 즉즉시부하시의골-임플란트계면은임플란트와골사이마찰이있는마찰접촉상황으로, 지연부하시의계면은임플란트와골이완전히고정된결합으로재현했다. 전자의구조는비선형마찰접촉요소를사용하여재현하였으며, 임플란트와골사이의약간의변위를허용한다. 33 골-임플란트간마찰계수는 0.3 으로추정하였다. 35,36 3. 경계, 하중조건과물질의성질 골조직주위로움직임이전혀발생하지않는다고가정하여, 골의바깥쪽가장자리를완전구속하였고, 하중은치관의장축방향으로 110N의수직부하를가했다. 37 유한요소분석결과는 von-mises stress( 등가응력 ) 으로계산하였으며, 상대적인비교의편리성을도모하기위해계산된등가응력을특정한값으로 선정하여색상으로표시하였다. 등가응력은연성물질에대한항복기준을 평가하기위한것으로, 2차원또는 3차원에서의스트레스들을결합함에의해계산되며, 유한요소분석결과는전형적으로등가응력으로나타낸다. 그리고, 즉시부하시임플란트-골계면에서의최대변위거리도해석하였다. 본연구에사용된임플란트, 피질골, 해면골, 금관은등방성, 동질성, 선형탄성재료로가정하였다. 상대적인기계적성질은물질에따라달라지며, 유한요소분석으로실험한기존의논문과제조회사자료에기초를두고결정하었다

15 구조적분석에서요구되는물리적성질은 Young s modulus 와 Poisson s ratio 이었다 (Table I). Table I. Mechanical properties of the materials. Materials Young s modulus (GPa) Poisson s ratio(v) Dental implant (Ti-Grade 4) Cortical bone Trabecular bone Gold

16 Fig.1. The 3-dimensional model including the crown, the implant. a) b) Fig.2. Schematic presentation of a) tapered type and b) straight type dental implant

17 III. 연구결과 골의응력분포형상을보면, 지연부하에비해즉시부하시응력이임플란트경부피질골뿐만아니라해면골에서임플란트-골계면을따라임플란트근단까지더광범위하게분포하는것을보여준다 (Fig.3). 또한최대등가응력은지연부하에비해즉시부하에서더높으며, 지연부하시는해면골보다피질골에서더높으며, 즉시부하에서도 tapered 형 4.3 X 10 mm, 4.3 X 11.5 mm, straight 형 4.3 X 8.5 mm 임플란트모델들을제외하고는피질골에서더높았다 (Table II). a) b) Fig.3. The distribution of cortical & trabecular bone stresses around a) delayed loaded (bonded) implants and b) immediately loaded (contact) implants - 8 -

18 Table II. The maximum von-mises stress (maximum equivalent stress or Max EQV stress) of the bone around different implant length, diameter and body design (tapered and straight) with bonded and contact interface condition. Interface Implant body Implant Implant Cortical EQV Trabecular EQV Design Diameter (mm) Length (mm) (MPa) (MPa) Bonded Tapered Straight Contact Tapered Straight

19 1. 지연부하에서임플란트길이, 직경, 바디형태에따른골최대 응력변화 지연부하에서는 tapered 형 4.3 X 8.5 mm 임플란트모델이다른모델보다더높은최대등가응력을보였다. 반면 straight 형 5.3 X 11.5 mm 임플란트모델이다른모델보다더낮은최대등가응력을보였다 (Fig.6). 지연부하에서는 tapered 형직경 4.3 mm의임플란트모델들은길이가 8.5 mm에서 10 mm로증가시에는최대응력이감소하나, 10 mm에서 11.5 mm로증가시 7.4% 증가한것을제외하고는, 같은직경과바디형태일때길이가길어질수록최대응력이감소하였다 (Fig.6). 특히 Tapered 형직경 4.3 mm의임플란트에서길이가 8.5 mm에서 10 mm로증가시최대응력이 66.3% 만큼감소했다. 한편같은바디형태와길이를가진임플란트모델들에서는직경이커지면최대응력이감소하였다 (Fig.7). 그리고, 같은직경과길이를가진임플란트모델들에서는 tapered 형이 straight 형보다최대응력값이더높았다 (Fig.8)

20 a) 4.3 X x X 11.5 b) 4.3 X X X 11.5 Fig.4. The distribution of cortical & trabecular bone stresses around a) tapered, b) straight 4.3 X 8.5, 4.3 X 10 and 4.3 X 11.5 mm delayed loaded (bonded) implants

21 a) 5.3 X X X 11.5 b) 5.3 X X X 11.5 Fig.5. The distribution of cortical & trabecular bone stresses around a) tapered, b) straight 5.3 X 8.5, 5.3 X 10 and 5.3 X 11.5 mm delayed loaded (bonded) implants

22 20 20 EQV(MPa) EQV(MPa) Implant Length Implant Length a) b) Fig.6. The maximum von-mises stress (EQV) of the bone among three implant length (8, 10, 11.5 mm) of diameter 4.3 mm and 5.3 mm delayed loaded (bonded) a) tapered and b) straight implants EQV(MPa) Implant Diameter EQ V(M P a) Implant Diameter a) b) Fig.7. The maximum von-mises stress (EQV) of the bone among two implant diameter (4.3, 5.3 mm) of length 8.5 mm, 10 mm, and 11.5 mm delayed loaded (bonded ) a) tapered and b) straight implants

23 20 20 EQV(MPa) EQV(MPa) Tapered Straight 0 Tapered Straight Implant Designs Implant Designs a) b) Fig.8. The maximum von-mises stress(eqv) of the bone among two implant body designs (tapered, straight form) of length 8.5 mm, 10 mm, and 11.5 mm delayed loaded (bonded ) a) diameter 4.3mm and b) 5.3mm implants

24 2. 즉시부하에서임플란트길이, 직경, 바디형태에따른골최대 응력과변위변화 즉시부하에서는 straight 형 4.3 X 11.5 mm 모델이다른모델보다더높은최대등가응력을보였다. 반면 tapered 형 5.3 X 10 mm 모델이다른모델보다더낮은최대등가응력을보였다 (Fig.11). Straight 형직경 4.3 mm 임플란트모델들을제외하고는, 같은직경과같은바디형태일때 8.5 mm에서 10 mm로증가시에는최대응력이감소하나, 10 mm 에서 11.5 mm로증가시에는최대응력이증가하였으며, 10 mm의길이일때, 가장낮은최대응력을보였다. 따라서 tapered 형의임플란트에서는같은직경일때길이가 8.5 mm에서 10 mm로증가시에는최대응력이감소하나, 10 mm에서 11.5 mm로증가시에는최대응력이증가하였다 (Fig.11). 즉 tapered 형직경 5.3 mm 임플란트모델들에서길이가 8.5 mm에서 10 mm 로증가시최대응력이 48.5% 만큼감소했으며, straight 형직경 5.3 mm 임플란트모델에서는최대응력이 53% 만큼감소했다. 반면 tapered 형직경 4.3 mm 임플란트모델에서길이가 10 mm에서 11.5 mm로증가시최대응력이 77.5% 만큼증가했다. 그러나, straight 형직경 4.3 mm 임플란트모델들에서는길이가길어질수록최대응력이증가하였다. 8.5 mm에서 10 mm 로증가시엔 70%, 특히 10 mm 에서 11.5 mm 증가시엔 314% 증가했다 (Fig.11). Straight 형길이 8.5, 10 mm 임플란트모델들을제외하고는, 같은바디형태와길이를가진임플란트모델들에서는직경이증가할수록최대응력이감소했다

25 (Fig.12). Straight 형길이 8.5, 10 mm 임플란트모델들에서는직경이 4.3 mm에서 5.3 mm로증가시최대응력이각각 313%, 14% 증가했다. 4.3 X 8.5 mm의임플란트모델을제외하고, 같은직경과길이일때, tapered 형이 straight 형보다최대응력이더낮았다 (Fig.13). 한편, 즉시부하시임플란트-골계면의최대변위거리는, tapered 형 4.3 X 11.5 mm 모델이다른모델보다더높은값을보인반면 tapered 형 5.3 X 11.5 mm 모델이다른모델보다더낮은값을보였다 (Table III). Tapered 형직경 4.3 mm 임플란트모델들을제외하고는, 같은직경과같은바디형태를가진임플란트모델들에서는길이가증가시에최대변위거리가감소했다. Tapered 형의길이 11.5 mm 임플란트모델들을제외하고는같은바디형태와길이를가진임플란트모델들에서는직경이감소할수록최대변위거리가감소했다. 4.3 X 10 mm, 4.3 X 11.5 mm의임플란트모델을제외하고, 같은직경과길이일때, tapered 형이 straight 형보다최대변위거리가더낮았다 (Table III)

26 a) 4.3 X X X 11.5 b) 4.3 X X X 11.5 Fig.9. The distribution of cortical & trabecular bone stresses around a) tapered, b) straight 4.3 X 8.5, 4.3 X 10 and 4.3 X 11.5 mm immediately loaded (contact) implants

27 a) 5.3 X X X 11.5 b) 5.3 X X X 11.5 Fig.10. The distribution of cortical & trabecular bone stresses around a) tapered, b) straight 5.3 x 8.5, 5.3 X 10 and 5.3 x 11.5 mm immediately loaded (contact) implants

28 EQV(MPa) EQV(MPa) Implant length Implant length a) b) Fig.11. The maximum von-mises stress (EQV) of the bone among three implant length (8, 10, 11.5 mm) of diameter 4.3 mm and 5.3 mm immediately loaded (contact) a) tapered and b) straight implants EQV(MPa) Implant Diameter EQV(MPa) Implant Diameter a) b) Fig.12. The maximum von-mises stress (EQV) of the bone among two implant diameter (4.3, 5.3 mm) of length 8.5 mm, 10 mm, and 11.5 mm immediately loaded (contact) a) tapered and b) straight implants

29 EQV(MPa) Tapered Straight Implant Designs EQV(MPa) Tapered Straight Implant Designs a) b) Fig. 13. The maximum von-mises stress (EQV) of the bone among two implant body designs (tapered, straight form) of length 8.5mm, 10mm, and 11.5mm immediately loaded (contact) a) diameter 4.3mm and b) 5.3mm implants. Table III. The maximum sliding distance of model of contact implant-bone interfaces. Interface Implant bodyimplant Implant Maximal sliding distance Design Diameter (mm) Length (mm) (μm) Contact Tapered Straight

30 IV. 총괄및고찰 지연부하에서는이전의연구결과와같이, 본연구에서도부하시응력이주로임플란트경부피질골에집중되어분포했다. 38 그러나, 지연부하시와비교해서즉시부하에서는응력이피질골뿐만아니라, 임플란트-골계면을따라임플란트근단까지해면골에도광범위하게분포했다. 또한, 최대응력도즉시부하에서더높게나타났다. 이것은전의실험결과들 28, 39 과일치한다. 이같이지연부하에비해더높은골응력이발생하는즉시부하의성공을위해서는적절한임플란트의선택을통하여골응력을줄이는것이필요할것이다. 따라서본연구는즉시부하시술을위한적절한임플란트선택에도움을주기위해, 즉시부하상황에서골응력분포에대한임플란트디자인의영향을유한요소분석을이용하여연구했다. 즉시부하시임플란트-골계면은임플란트의식립즉시골이직접적으로임플란트표면과접촉하여, 일차골접촉 을이루며, 시간이지남에따라골조직이리모델링되어, 이부위도새로운골로대체되어, 이차골형성 이일어난다. 40 Berglundh 등 41 에의하면개에서임플란트를식립후두시간후의 ground section을보면, 임플란트가골과밀접하게접촉하고있으며, 초기에빈 wound chamber 는육아조직과혈병으로이루어져있다. 즉시부하시의임플란트-골계면은전과정을유한요소방법으로재현하기어려우므로, 이러한식립초기같은특정한순간을재현하여, 임프란트와골사이에작은변위를허락하는마찰계면으로재현하기로했다. 이차골형성이

31 일어나면서부터는지연부하시와비슷한상황에놓이기때문이다. 골-임플란트접촉의물리적모델은마찰이없는접촉, 마찰접촉등이있으며, 가장간단한모델은마찰이없는접촉이고, 마찰접촉은더복잡한재현을하며, 비가역적이며, 경로-의존적이다. 42 이런마찰접촉계면을설명하는면대면 모델이정형외과에서발달해왔으며, 치과임플란트에도동일하게적용된다. 마찰 운동은 Elastic Coulomb 마찰모델로모델링되며, 42 금속과골의마찰계수는 사이에존재한다. 35 본실험에서는즉시부하상황을재현하기위한임플란트 - 골계면간의마찰 계수를임플란트모델의실제값이아닌, 기존의연구들 35,36 에서사용한값을 이용하여, 마찰접촉모델로재현했다. 0.3 과 1 사이에서마찰계수가 증가하더라도, 골응력을감소시키지는않는다는실험결과가있었다. 27, 28 지연부하에서의같은바디형태와직경을가진임플란트의길이의변화에따른최대등가응력의변화를보면, tapered형직경 4.3 mm의임플란트모델이 10 mm에서 11.5 mm로길이증가시최대응력이다소증가하는양상을보인것을제외하고는, 전반적으로같은직경과바디형태일때길이가길어질수록최대응력이감소했다. 이것은임플란트길이가길어질수록골응력이감소한다는전의연구결과들과일치한다. 13, 22 임플란트의증가된길이는초기고정력과임플란트-골접촉면적을늘이므로의미가있다. 38 지연부하에서의직경에대해영향을살펴보면, 같은바디형태와길이를가진임플란트모델들에서는직경이커지면최대응력이감소했다. 이것은기존의연구 결과들 24, 25 과 일치하는결과로서, 더넓은임플란트는증가된골접촉부위

32 때문에유사한높이와디자인을가진좁은임플란트보다더큰골접촉부위를 가지므로, 38 더호의적인응력분배가이루어진다. 43 또한, 임플란트에가해지는 교합하중의대부분이치조정에가해지며, 이치조정이조기골소실이일어나는곳이므로, 초기고정과토크에대한최소길이가얻어졌다면직경이길이보다더중요하다. 38 바디형태에대해서는, Mailat, 43 Siegele and Soltesz, 44 Patra 등 45 의연구결과들과같이지연부하에서같은길이와직경을가진임플란트모델들에서는 tapered 형임플란트가 straight 형임플란트보다최대응력이더높았다. Tapered 형임플란트는같은길이, 너비, 나선수의평행형나사임플란트에비해전반적인표면적이더적으며, 이특징은초기고정을감소시킬수있다. 21 한편, 즉시부하에서현재까지의논문들을고찰해보면, 직경 4 mm 이상, 길이 10 mm 이상의 tapered 형나사나선디자인의임플란트를추천하고있다. 7, 8, 46 즉시부하시길이, 직경, 바디형태에따른최대등가응력과변위의변화를분석해보았다. Straight 형직경 4.3 mm 임플란트모델들을제외하고는, 같은직경과같은바디형태일때길이가 8.5 mm에서 10 mm로증가시에는최대응력이감소하나, 10 mm에서 11.5 mm로증가시에는최대응력이증가했으며, 길이가 10 mm 일때, 가장낮은골응력을보였다. 전의실험결과들 13, 26, 28 은길이가길어질수록골응력이감소한다고보고했으므로, 이번실험결과와는다르다. 임상연구에서 Schnitman 등 47 은길이가 10 mm 보다짧은경우즉시부하임플란트에서 50% 의실패율을보였다고했다. 또많은논문들 에서즉시

33 부하에서는길이 10 mm 이상의임플란트를식립할것을추천하고있다. 그러나, straight형직경 4.3 mm 임플란트모델들에서는길이가길어질수록최대응력이증가하였다. Straight 형의직경 4.3 mm 임플란트에서는길이를증가시키는것이전혀최대응력감소에도움을주지않았다. 직경에대한결과를보면, straight 형길이 8.5, 10 mm 임플란트모델들을제외하고는, 같은바디형태와길이를가진임플란트모델들에서는직경이증가할수록최대응력이감소했다. 이것은지연부하시의실험결과와일치하는모습을보여주며, 다른즉시부하상황의유한요소분석실험에서의결과와도 일치한다. 26, 28 O stman 51 은더넓은임플란트는협측과구개측치밀골에더쉽게삽입되어골-금속표면접촉을크게한다고했다. 그의다른연구에서도 narrow/regular 임플란트에비해 wide 임플란트가공진주파수분석에서더높은초기임플란트안정성을보였다. 또한, 단일치관수복물을지지하는 wide body 임플란트의즉시하중에대한성공적인연구결과들이발표되었다 그러나, straight 형길이 8.5, 10 mm 임플란트모델들에서는직경이 4.3 mm에서 5.3 mm로증가시, 최대응력이증가했다. 이것은 5mm보다더큰직경의임플란트는골에서더큰응력을보여주므로, 즉시부하프로토콜에서선택해서는안된다고주장한 Georgiopoulas 등 13 의결과와일치한다. Degidi 등 55 는임상연구결과직경이 5.25 mm을넘는임플란트는즉시부하시위험성이증가한다고발표하였다. 즉지연부하와달리즉시부하에서는직경이증가할때반드시최대응력이감소하는것은아니었다

34 바디형태에서는 4.3 X 8.5 mm의임플란트모델을제외하고, tapered 형임플란트가 straight 형임플란트보다최대응력값이더낮게나타남으로써, 지연부하와가장대조적인모습을보여주었다. 임플란트바디형태는지연부하에서도중요한요인이지만, 즉시부하에서더특별한중요성을가진다. 그이유는즉시부하에서는임플란트를식립하자마자최대의안전성을얻어야하며, 교합력적용전에골이임플란트바디의요철부위로자라거나, 표면에부착할시간이없기때문이다. 21 Huang 등 23 은 tapered 형임플란트는 square straight 디자인에비해 피질골에서응력을방출시켜망상골로더많이응력을이동시켜피질골과망상골에서응력을감소시킨다고했다. Tapered 형임플란트의나선의증가된깊이는골-임플란트접촉면적를깊게증가시켜서이런생역학적효과에기여했을수도있다. 피질골부위에응력이집중되어있는지연부하에비해, 즉시부하에서는피질골뿐만아니라해면골에도응력이광범위하게분포하며, 골응력이더높으므로, 이러한 tapered 형의임플란트가 straight 형임플란트보다더낮은최대응력값을보일수있을것이다. 즉시부하에서는 tapered 형임플란트가 straight 형보다추천된다는연구결과들이있다. 8, 21, 56, 57 O stman 등 58 과 Glauser 등 59 은부드러운골질을가진부위에서 tapered 형임플란트의즉시부하시술시의높은생존율을발표했다. Tapered 형의임플란트의성공은골질, 수술기법과관계있으며, taper 각과나선깊이에따라다양한결과를가져올수있다. 한편, 즉시부하에서임플란트길이, 직경, 바디형태의, 최대응력과최대변위

35 거리에대한영향은서로일치하지는않았지만, tapered형 4.3 X 11.5 mm 임플란트는, tapered 형임플란트중에서, 최대변위거리도최대응력과같이가장높은값을보였다. 그러나, 모든모델에서최대변위거리는, 즉시부하에서허용되는미세동요도인 50 μm 이하의값을나타냄으로써, 골형성을방해하지않는것으로보인다. 이렇게지연부하에서는길이, 직경, 바디형태들의변화에따른최대응력에대한영향이비교적규칙적인양상을보였으나, 즉시부하에서는이들의영향이다양하게나타나는모습을보여주었다. 즉지연부하에서의이들의최대응력에대한영향과일치하지않을수있다는것을보여주었다. 본실험에서는유한요소분석에의해변수들에따른최대응력에대한영향의전반적인경향만살펴보았다. 따라서, 앞으로변수들의최대응력에대한영향과변수들간의영향을분석하기위한통계적결과처리가가능한실험이요구된다. 즉시부하의성공에는여러가지요인들이복합적으로영향을끼치기때문에, 최대응력의감소가임플란트성공률과반드시일치하지않을수도있다. 따라서, 근거가될만한임상연구가같이동반되어야할것이다. 그밖에실험조건에서본연구는교합력으로 110N 크기의, 수직부하만재현해서, 모델에정적하중을가했다. Morneburg와 Proshchel 37 등은단일임플란트의평균최대교합력은구치부에서 129N 정도라고했으며, 그밖의연구 61 에서도임플란트지지보철물에서 112.9N 정도라고했으므로, 이에근거해 교합력의크기를재현했다. 그리고, 사선방향의힘이나측방력이작용시응력이 증가할뿐만아니라, 응력의형태도전단력같이골에위험한형태로바뀌어, 골소실이나골재성장에손상을가져오므로, 지연부하에서뿐만아니라, 완전한

36 골유착이이루어지지않은조건을가진즉시부하에서는더욱이작용되지않아야한다. 38 또한, 기존의지연부하상황에서이같은하중을가하는많은실험을하여, 이미위와같은결과들을얻었다. 따라서, 본실험에서는수직방향이외의힘들을재현하지않았다. 그러나, 정적하중모델에비해동적하중모델에서임플란트-골계면에서더높은최대응력의결과를보여준다는연구결과 60 도있으며, 실제구강내상황과더일치하므로, 즉시부하의동적하중모델에서의유한요소분석에대해서도좀더연구해볼필요가있을것이다

37 V. 결론 유한요소분석을이용해, 임플란트의즉시부하상황을재현해서임플란트 주위골의응력분포에대한임플란트디자인의영향을연구한결과는다음과 같다. 1. 지연부하와비교해서즉시부하에서는응력이피질골뿐만아니라, 임플란트 - 골계면을따라임플란트근단까지해면골에도광범위하게분포하며, 최대등가 응력도더높게나타났다. 2. 지연부하에서는, tapered 형직경 4.3 mm 의임플란트모델이 10 mm 에서 11.5 mm 로길이가증가시최대응력이다소증가하는양상을보인것을제외하고는, 임플란트의길이가길어질수록최대응력이감소했다. 또한임플란트직경이커지면최대응력이감소했으며, tapered 형임플란트가 straight 형임플란트보다최대응력이더높았다. 3. 즉시부하에서, tapered 형의임플란트는길이가 8.5 mm 에서 10 mm 로증가 시에는최대응력이감소하나, 10 mm 에서 11.5 mm 로증가시에는최대응력이 증가했으며, 직경이증가할수록최대응력이감소했다. 바디형태에서는 4.3 X 8.5 mm 의임플란트모델을제외하고, tapered 형임플란트가 straight 형 임플란트보다최대응력이더낮게나타났다. 즉시부하시임플란트 - 골계면의 최대변위거리는허용되는미세동요도인 50 μm 이하의값을나타냄으로써, 골형성을방해하지않는것으로보인다

38 4. 지연부하에서는길이, 직경, 바디형태들의변화에따른최대응력에대한영향이비교적규칙적인양상을보였으나, 즉시부하에서는이들의영향이다양하게나타나는모습을보여주었다. 즉지연부하에서의변수들의영향과일치하지않을수있다는것을보여주었다

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48 Abstract The effect of implant designs on stress distribution of the bone around immediate loading implants : A 3-dimensional finite element analysis Jung Yoon Bae Department of Dentistry The Graduate School, Yonsei University (Directed by Professor Chong Hyun Han) Until recently, the healing period from dental implant placement to the prosthesis delivery has become shorter and even immediate loading procedure become popular. Implant primary stability is the most important clinical factor influencing success of immediate loading. The surface area of implant support may be increased by modifications in implant designs, so the stress in the bone be decreased. But, the effect of implant designs in immediately loaded implants has recently been investigated and will affect different compared to in delayed loaded implants. The purpose of this study was to investigate the effect of implant designs on stress distribution of the bone around immediate loading implants by a 3-dimensional finite element analysis and to help to select proper implant for immediate loading treatment

49 A 3-dimensional model of a single implant supported crown substituting a lower first premolar was simulated. The von-mises stresses of the bone around different implant length (8, 10, 11.5 mm), diameter (4.3, 5.3 mm) and body design (tapered, straight) with delayed loaded and immediately loaded condition were analyzed. The results were as followings; 1. Compared to the delayed loaded implants, in immediately loaded implants, the stresses were widely distributed in trabecular bone to the implant apex along implant-bone interfaces as well as in cortical bone surrounding the implant neck and the maximum von-mises stresses were higher. 2. For the delayed loaded implants, except that increasing implant length from 10 mm to 11.5 mm resulted in the maximum stress increasing, in diameter 4.3 mm tapered implants, increasing implant length resulted in the maximum stress reduction. And increasing implant diameter decreased the maximum stress, tapered implants showed higher maximum stresses than straight implants. 3. For the immediately loaded implants, increasing implant length from 8.5 mm to 10 mm resulted in the maximum stress reduction, but increasing implant length from 10 mm to 11.5 mm resulted in the maximum stress increasing and increasing implant diameter resulted in the maximum stress reduction in tapered implants. Except for 4.3 X 8.5 mm implant, tapered implants showed

50 lower maximum stresses than straight implants. The maximum sliding distance of model of contact implant-bone interfaces was less than accepted micromotion value (50 μm), so did not disturb osseointegration. 4. For the delayed loaded implants, the effects of the implant length, diameter, and body design on maximum stresses showed relatively regular appearance, but the effect of implant designs in immediately loaded implants showed various appearances, in other words, did not accord in delayed loaded implant Key word : immediate loading, finite element analysis, dental implant, length, diameter, design, stress