Stress analysis according to various retrograde cavity preparation … · 2020. 2. 13. · Stress analysis according to various retrograde cavity preparation designs for surgical

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Stress analysis according to various

retrograde cavity preparation designs

for surgical endodontics in the mesial root

of mandibular molar

: Finite element analysis

So Young Park

Department of Dentistry

The Graduate School, Yonsei University




of mandibular molar


Directed by Professor Euiseong Kim

A Dissertation

Submitted to the Department of Dentistry

and the Graduate School of Yonsei University

in a partial fulfillment of the

requirements for the degree of

Doctor of Philosophy

So Young Park

June 2017

Acknowledgements

감사의 글을 쓰고 있는 이 순간이 믿기지 않을 정도로 정말 행복합니다. 4 년 전, 막연한 꿈만

가지고 박사과정을 시작했는데, 고마운 분들의 도움으로 무사히 졸업을 하게 되었습니다. 한

편의 논문을 완성하기 까지, 한 발 그리고 또 한발, 그 어떤 걸음도 힘들지 않았던 걸음이

없었지만, 견디고 나니 참 많은 것을 배웠구나 하는 생각과 함께 제 자신이 한 뼘 더

성장했다는 것이 뿌듯합니다.

먼저 논문의 시작부터 끝까지 저를 가르쳐주시고 이끌어 주신 김의성 교수님께 진심으로

감사드립니다. 교수님이 계시지않았다면 이 논문은 시작되지도 못했을 것입니다 교수님의

열정으로 이렇게 박사 논문을 마무리 할 수 있었습니다. 정말 감사합니다.

대학원 수업 때 열정적인 강의로 저의 부족함을 일깨워주신 박성호 교수님, 박정원 교수님

감사합니다. 깊이 있는 지식과 쉼 없는 연구로 늘 타의 모범이 되시는 신촌 보존과 이승종

교수님, 이찬영 교수님, 노병덕 교수님, 정일영 교수님, 신유석 교수님께도 감사드립니다.

수련의들이 가장 좋아하고 의지하는 강남 보존과 신수정 교수님께도 감사 말씀 드립니다.

병마와 싸우시다 안타깝게 돌아가셨지만 늘 환자를 생각하는 마음을 가르쳐 주셨던

유재하교수님, 끝이 없는 연구 열정을 가지신 최병호 교수님, 늘 따뜻하게 제 손을 잡아

주시는 정승미 교수님, 유머러스 하지만 날카로운 지적과 깨어있는 이성으로 긴장하게

만드시는 이정섭 교수님, 따뜻한 눈빛과 부드러운 카리스마를 가지신 김지훈교수님 그리고 철

모르던 인턴 시절 저로 하여금 ‘교수님처럼 되고 싶다’ 라는 꿈을 갖게 해주시고 지금의 저를

있게 해주신 이윤 교수님 정말 감사합니다.

실험에 대해 많은 조언과 가르침을 주신 김현철 교수님, 궂은 일을 도맡아 해주시고 실험

과정 내내 제게 큰 도움을 주신 이찬주 박사님, 논문 구성을 꼼꼼히 살펴 주신 김선일

교수님께도 깊은 감사를 드립니다.

바쁘신 와중에도 격려해주시고 도움을 주신 이석준 선생님, 여상호 선생님, 정민선

선생님께도 감사를 드립니다.

마지막으로, 늦은 나이에 학구열에 불타는 저의 꿈을 곁에서 응원해주고 묵묵히 뒷바라지

해준 착하디 착한, 다시 태어나도 또 만나고 싶은 사랑하는 나의 신랑 김대식과 눈에 넣으면

아프겠지만 그 아픔까지 견딜 수 있을 것만 같은 내 전부인 사랑하는 딸 김은아 그리고

일하느라 공부하느라 바쁜 저를 대신해 가사와 육아를 도맡아 해주신 미안하고 고마운 엄마와

‘무슨 공부를 또 하느냐’ 며 구박하시지만 친구분들 만나면 은근히 딸 자랑하시는 아빠,

사랑하는 나의 가족 모두와 함께 이 기쁨을 나누고 싶습니다.

2017 년 6 월

박 소 영

i

Table of Contents

List of Tables ···················································································· iii

List of Figures ··················································································· iv

Abstract (English) ·············································································· vi

I. Introduction ···················································································· 1

II. Materials and Methods ····································································· 5

1. Construction of a 3-dimensional (3D) finite element (FE) root model ·················· 5

2. Apical preparation group designs ···························································· 7

3. Mathematical simulation of apical restoration and mechanical loading ·············· 15

4. Modification of apical preparation design from sub-group 4 in Group III ··········· 19

III. Results ······················································································· 20

IV. Discussion ···················································································· 32

V. Conclusion ···················································································· 39

ii

References ························································································ 40

Abstract (Korean) ·············································································· 56

iii

List of Tables

Table 1. The numbers of elements and node for each model ································· 16

Table 2. Mechanical properties of materials used in the study ······························· 17

Table 3. Maximum Principle and von Mises stress values from experimental groups ···· 21

iv

List of Figures

Figure 1. Diagram of mesial root of mandibular molar after canal shaping ················· 6

Figure 2. Summary of the preparation design ··················································· 8

Figure 3. Experimental details of the preparation design of Group I ························ 11

Figure 4. Experimental details of the preparation design of Group II ······················· 12

Figure 5. Experimental details of the preparation design of Group III ······················ 13

Figure 6. Experimental details of the preparation design of Group IV ····················· 14

Figure 7. Solid models of mesial root of mandibular first molar in the study ·············· 18

Figure 8. von Mises and max. Principle stress results from Group I ························ 19

Figure 9. von Mises and max. Principle stress results from Group II ······················· 23

v

Figure 10. von Mises and max. Principle stress results from Group III ···················· 24

Figure 11. von Mises and max. principle stress results from Group IV ····················· 25

Figure 12. von Mises and max. principle stress results from Group III, sub-group 4 ····· 26

Figure 13. Original and modification test set up from Group III, sub-group 4 ············ 27




vi

Abstract




of mandibular molar


So Young Park



(Directed by Prof. Euiseoung Kim, D.D.S., M.S.D., Ph.D.)

The aim of this study was to evaluate the effect of various designs of apical preparation

for surgical endodontics in the mesial root of a mandibular molar, with or without the

presence of alveolar bone, based on finite element analysis (FEA).

Three-dimensional FEA models were created and adapted using computer software

based on the mesial root canal anatomy of a mandibular first molar. To exclude the

interference of variation in the tooth coronal portion, the tooth model was bisected at the

vii

cementoenamel junction (CEJ), the coronal part was removed, and only the mesial root

was used. The experimental designs were classified depending on apical preparation size,

with or without isthmus, at a level of 3 mm from the apex; a 150-N load was applied

vertically, and von Mises stress and maximum principle stress were plotted. The results

were as follows:

1. As the amount of apical preparation increased in tested sub-groups, von Mises

stress and maximum principle stress were gradually reduced. This tendency was

the same in experimental conditions with or without the presence of the alveolar

bone.

2. In the isthmus preparation group (Group III and IV), where little root dentin

remained (sub-group 4), the situation was reversed, i.e., both von Mises stress and

maximum principle stress increased, especially in the distal concave area.

3. As the maximum principal stress had a positive value in the distal concave area,

root fracture initiation or detachment of the filling material (MTA) could occur at

this site.

4. As the amount of apical preparation increased, von Mises stress increased in roots

without MTA retrograde filling.

5. In the experimental condition without alveolar bone present, the vertical force was

transmitted directly to the tooth, concentrating stress mainly on the bucco-lingual

side, regardless of the experimental group.

viii

6. The apical preparation of sub-group 4 in Group III was modified. Following the

outline of the root, the cavity was prepared more mesially than the original design,

and an effort was made to retain the same root dentin thickness on both the mesial

and distal sides if possible. Stress values were lower than those in the original

preparation, especially the maximum principle stress, which reduced drastically in

the distal concave area.

7. A low stress field was formed on the mesial side of the mandibular molar mesial

root, and is thought to be due to the increased concavity of the distal side compared

to that of the mesial side.

Key words: FEA, stress distribution, apical preparation design, surgical endodontics

1




of mandibular molar


So Young Park, D.D.S., M.S.D



(Directed by Prof. Euiseong Kim, D.D.S., M.S.D., Ph.D.)

I. Introduction

Conventional root canal therapy is a treatment option that has been studied extensively

and has highly predictable success rate; the main goal of this treatment is to prevent or

heal apical periodontitis. (Friedman, Abitbol, and Lawrence 2003). From a biomechanical

perspective, this means cleaning, shaping, and disinfecting the root canal system to allow

three-dimensional obturation. However, anatomical complexities— including lateral or

2

accessary canals, apical delta, fin, and isthmus— limit the action of the instruments,

irrigant substances, and intracanal medications, and may result in endodontic failure.

(Siqueira 2001).

One of the main anatomical complexities in molars is the isthmus, which is defined as a

narrow, ribbon-shaped communication between two root canals, containing pulp tissue

(Teixeira et al. 2003; Weller, Niemczyk, and Kim 1995). Any root possessing more than

one canal has the potential to contain an isthmus. It has been reported that there are

diverse shapes (Hsu and Kim 1997), and there is a high incidence of isthmus in the

mesial-buccal root of maxillary first molars and the mesial root of mandibular first molars.

The incidence of isthmus ranges from 76 % to 100 % in maxillary first molars, and

from 54 % to 89 % in mandibular first molars (Cleghorn, Christie, and Dong 2006; von

Arx 2005). An isthmus, which contains necrotic debris, acts as a reservoir for organic

matter and microorganisms to grow and multiply, ultimately causing failure of the

nonsurgical root canal treatment(Nair et al. 2005). (Nair et al. 2005). Unfortunately, the

perfect method for cleaning and shaping an isthmus has yet to be devised. (Johnson et al.

2012; Lloyd et al. 2014).

Surgical endodontic treatment is an option when nonsurgical treatment or retreatment

fails to resolve the periapical infection because of anatomical complexities. With the

advent of microsurgical principles using microinstruments and magnification devices, the

success rate of surgical endodontics can be improved (Tsesis et al. 2009; Tsesis et al.

3

2006). The recognition and management of complex apical anatomy, including a canal

isthmus, is a crucial factor that could affect treatment outcome, and is especially

important in posterior teeth. Despite the improvement of equipment, anatomical

complexity makes the procedure more technically difficult. A study (Song, Shin, and Kim

2011) found that the major cause of surgical endodontic failure is poor technique, for two

reasons: incorrect apical preparation and lack of apical filling.

In the case of the isthmus, additional preparation for a retrograde filling is unavoidable

and this could weaken the root structure. A study (Kim et al. 2016) has reported that teeth

with a prepared isthmus recorded a significantly lower cumulative survival rate than teeth

with no isthmus; the reason is most likely that root dentin was weakened by apical

preparation of the isthmus during surgery. Many FEA or histological studies have also

reported that a root with an isthmus is more likely to be susceptible to fracture than a root

without an isthmus (Abedi et al. 1995; Chai and Tamse 2015; Sathorn et al. 2005). Stress

analysis studies through finite element analysis (FEA) are generally used for the

prediction of tooth fracture because concentrations of stress, from a biomechanical

perspective, indicate regions of potential failure. Finite element analysis has the following

advantages: control of variable factors for the standardization of experimental conditions

and direct measurement of stress in complex structures (Toksavul et al. 2006).

Despite the many clinical studies on the treatment outcomes of endodontic microsurgery,

studies regarding the effect of remaining root dentin on surgical outcome— according to

different apical preparation designs— have been rare.

4

Therefore, the purpose of this study was to investigate the influence of various designs

of apical preparation, for surgical endodontics in the mesial root of a mandibular molar,

on stress concentration, under different experimental conditions. Furthermore,

modification of the apical preparation was conducted to confirm the hypothesis that an

apical preparation design that follows the root outline, allowing similar remaining root

thickness on the mesial and distal side, showed favorable stress distribution. The

following factors were investigated:

1. The influence of apical preparation design

2. The influence of alveolar bone

3. The influence of the presence or absence of filling material

4. The influence of modification in apical preparation design

Under these experimental conditions, I investigated how the stress concentration of a

surgically treated mandibular molar mesial root changed, using an FEA.

5

II. Material and Methods

1. Construction of a 3-dimensional (3D) finite element (FE) root model

One mandibular first molar with associated periodontitis was extracted, with a resultant

normal morphology and no dental caries. The tooth was scanned at 2-µm intervals in a

micro–computed tomography machine (HMX; X-Tek Group, Santa Clara, CA, USA) to

obtain a real-size, geometric configuration of the root in three dimensions (3D). The

literature was searched to obtain a generalized size and dimension of the root (Ballullaya,

Vemuri, and Kumar 2013; de Pablo et al. 2010; Wolf et al. 2016) and, based on this

information, a standard 3D model of a mandibular first molar mesial root was reproduced

using 3D software (IDEAS 11 NX; UGS, Plano, TX, USA).

To exclude the interference of the coronal portion, the tooth model was bisected at the

cementoenamel junction (CEJ) and only the mesial root was used. The mesio-buccal (MB)

and mesio-lingual (ML) canals of the mesial root were enlarged and shaped to #30 file

size at the apex (Fig. 1). The solid models consisted of the root, the periodontal ligament

(PDL), and the surrounding alveolar bone. A mesh of linear, 8-noded, hexahedral

elements was laid over the tooth and surrounding structures in the software to produce a

3D root model for FEA.

6

Fig. 1. The diagram and dimension (mm) of mesial root of mandibular molar after canal shaping.

(A) mesio-distal view (B) cross sectional view at CEJ (C) cross sectional view at 3mm (D) cross

sectional view at apex, respectively.

Buccal

side

Lingual

side

(A)

(B)

(

(C)

(D)

1

0 . 0

1 1 . 0

D1 . 0

1 . 2

R2 . 5

0 . 5

0 . 31

3 . 2

5 . 5

D0 . 6

1 . 60

2

D0 . 3 R0 . 5

0 . 60

2

1

0 . 0

1 1 . 0

3 . 0

7

2. Apical preparation group designs

Various simulated root models were designed according to the type of apical preparation,

and the surgical technique from a previous article was followed: a 3 mm root tip with a 0°

bevel angle was resected, the root-end cavity was prepared, and the apical cavities were

filled using ProRoot MTA (Dentsply, Tulsa, OK, USA). The surgical procedures were

simulated in the models (Degerness and Bowles 2008).

The cutting plane of apical resection for the mesial root was simulated at a 3 mm level

from the apex, having MB and ML canals with or without isthmus. The resected cross-

section had two concavities (dumbbell shape) on both the mesial and distal sides; the

concavity of the distal side was deeper than that of the mesial side and more buccally

situated (Wolf et al. 2016) (de Pablo et al. 2010) (Ferrario et al. 1999).

Four types of apical preparation groups were designed, with each group having four sub-

groups, according to the size of apical preparation. The main contributing factor was the

amount of preparation, with or without isthmus (Fig. 2).

8

Fig. 2. The summary of the preparation design. (A) Group I: the tooth had no isthmus. 2 separated

MB and ML canals were prepared circularly with gradual enlargement. (B) Group II: the tooth had

no isthmus. 2 separated MB and ML canals were prepared in the bucco-lingual direction, and not

circularly, with gradual enlargement. (C) Group III: the tooth had isthmus. The preparation

included MB, ML canals and isthmus with circular enlargement. (D) Group IV: the tooth had

isthmus. The preparation included MB, ML canals and isthmus increasing in only the bucco-

lingual direction.

3.2

5.5

1.95

0.2

0.95 1.35

0.5R 1.0

R 1.8

0.15

D 0.6

D 1.0D 1.4

D 1.8

3.2

5.5

0.2

0.95 1.35

0.5R 1.0

R 1.8

D 0.6

D 1.0D 1.4

D 1.8 1.95

Lingual

side

Buccal

side

Distal side Distal side

Mesial side Mesial side

Buccal

side

Lingual

side

(A) Group I (B) Group II

(C) Group III (D) Group IV

Distal side

Distal side


Lingual

side

Lingual

side

Buccal

side

Buccal

side 3 . 2

5 . 5 0 . 2

0 . 95

1 . 35

0 . 5 R

1 . 0

R

1 . 8

0 . 3 0 . 3 0 . 3

0 . 95

D

1 . 0

3 . 2

5 . 5 0 . 2

0 . 95

1 . 35

0 . 5 R

1 . 0

R

1 . 8

0 . 3 0 . 3 0 . 3 1 . 95

R

0 . 5

9

Group I: the tooth had no isthmus. Two separated MB and ML canals were prepared

circularly with gradual enlargement (Fig. 3). The black line seen in Fig. 3A simulated the

shaped and filled apex with a diameter of 0.6 mm (sub-group 1). The apical preparation

was then enlarged circularly in diameter by 0.4 mm and, thus the diameter in sub-group 2

was 1.0 mm (red line), 1.4 mm in sub-group 3 (blue line), and 1.8 mm in sub-group 4

(green line).

Group II: the tooth had no isthmus. Two separated MB and ML canals were prepared

only in a bucco-lingual direction, with gradual enlargement (Fig. 4). The red line seen in

Fig. 4A simulated the surgically prepared apex with 1.0-mm diameter (sub-group 1). The

apical preparation was then enlarged only in a bucco-lingual direction by 0.3 mm, and

thus sub-group 2 (blue line), sub-group 3 (green line), and sub-group 4 (purple line) were

expanded in increasing 0.3-mm increments.

Group III: the tooth had an isthmus. The preparation included the MB canal, ML canal,

and isthmus with circular enlargement (Fig. 5). The black line seen in Fig. 5A simulated

the connection of sub-group 1 in Group I through isthmus preparation. Similarly, sub-

group 2 (red line), sub-group 3 (blue line), and sub-group 4 (green line) had simulated

isthmus preparation with connection of the MB canal and ML canal in Group I.

Group IV: the tooth had an isthmus. The preparation included the MB canal, ML canal,

and isthmus increasing only in a bucco-lingual direction (Fig. 6). The red line seen in Fig.

6A simulated the connection of sub-group 1 in Group II through isthmus preparation.

10

Similarly, sub-group 2 (blue line), sub-group 3 (green line), and sub-group 4 (purple line)

had simulated isthmus preparation with connection of the MB canal and ML canal in

Group II.

11

Fig. 3. Group I (A) sub-group 1: black line simulated the shaped and filled apex with diameter

0.6mm (B) sub-group 2: the diameter is 1.0 mm (C) sub-group 3: the diameter is 1.4 mm (D) sub-

group 4: the diameter is 1.8 mm respectively.

3.2

5.5

0.2

0.95 1.35

0.5R 1.0

R 1.8

D 0.61.95

3.2

5.5

0.2

0.95 1.35

0.5R 1.0

R 1.8

D 1.01.95

3.2

5.5

1.95

0.2

0.95 1.35

0.5R 1.0

R 1.8

D 1.41.95

3.2

5.5

0.2

0.95 1.35

0.5R 1.0

R 1.80.15

D 1.8

1.95

(A) sub-group 1

Mesial side

Distal side

(B) sub-group 2

(C) sub-group 3 (D) sub-group 4

Buccal

side

Buccal

side

Lingual

side

Lingual

side

Mesial side

Distal side


Lingual

side


Lingual

side

Buccal

side

Buccal

side

12

3.2

5.5

0.2

0.95 1.35

0.5R 1.0

R 1.8

0.95

D 1.0

3.2

5.5

0.2

0.95 1.35

0.5R 1.0

R 1.8

0.95

D 1.00.6

Fig. 4. Group II (A) sub-group 1: black line simulated the surgically prepared apex with diameter

1.0mm (B) sub-group 2: extended 0.3 mm more (C) sub-group 3: extended 0.6 mm more (D) sub-

group 4: extended 0.9 mm more from sub-group 1, respectively.

3.2

5.5

0.2

0.95 1.35

0.5R 1.0

R 1.8

0.3

0.95

D 1.0

3.2

5.5

0.2

0.95 1.35

0.5R 1.0

R 1.8

0.9

0.95

D 1.0

Lingual

side

Lingual

side

(A) sub-group 1 (B) sub-group 2


Buccal

side


Buccal

side


Buccal

side


Lingual

side


Buccal

side

Lingual

side

13

Fig. 5. Group III (A) sub-group 1: the connection of MB and ML canals in sub-group 1 of Group I

through isthmus preparation. (B) sub-group 2, (C) sub-group 3, and (D) sub-group 4 simulated

isthmus preparation with connection of MB and ML in corresponding sub-groups from Group I,

respectively.

3.2

5.5

0.2

0.95 1.35

0.5R 1.0

R 1.8

D 0.61.95

3.2

5.5

0.2

0.95 1.35

0.5R 1.0

R 1.8

D 1.01.95

3.2

5.5

0.2

0.95 1.35

0.5R 1.0

R 1.8

D 1.41.95

3.2

5.5

0.2

0.95 1.35

0.5R 1.0

R 1.8D 1.8 1.95

Distal side


Distal side

Buccal

side

Buccal

side



Lingual

side

Lingual

side


Distal side

Distal side

Buccal

side

Buccal

side

Lingual

side

Lingual

side

14

3.2

5.5

0.2

0.95 1.35

0.5R 1.0

R 1.8

1.95 R 0.5

3.2

5.5

0.2

0.95 1.35

0.5R 1.0

R 1.8

3.75 R 0.5

Fig. 6. Group IV (A) sub-group 1: the connection of MB and ML canals in sub-group 1 of Group

III through isthmus preparation. Along the same way, (B) sub-group 2, (C) sub-group 3, and (D)

sub-group 4 simulated isthmus preparation with connection of MB and ML in corresponding sub-

groups from Group I, respectively.

3.2

5.5

0.2

0.95 1.35

0.5R 1.0

R 1.8

2.55R 0.5

3.2

5.5

0.2

0.95 1.35

0.5R 1.0

R 1.8

3.15 R 0.5


Lingual

side

Lingual

side

Buccal

side

Buccal

side






Buccal

side

Buccal

side

Lingual

side

Lingual

side

15

3. Mathematical simulation of apical restoration and mechanical loading

Each model was further processed using a 3-dimensional (3D) modeling program to

make solid model. The final FE models were meshed in IDEAS using linear, 8-noded

hexahedral elements. The number of elements and nodes for each model are summarized

in Table 1, with the applied material properties summarized in Table 2 (Belli et al. 2011;

Carter and Hayes 1977; Peyton, Mahler, and Hershenov 1952; Rubin et al. 1983;

Weinstein, Klawitter, and Cook 1980). Displacement of all nodes on the base of the

supporting bone was constrained, and a force of 150 N was applied to the vertical axis,

according to literature data (Fig. 7) (Crispian Scully 2003; Koc, Dogan, and Bek 2011).

Stress generation and concentration according to the groups and sub-groups were

analyzed numerically using an FE package (ABAQUS V6.13-1; SIMULIA, Providence,

RI, USA). Roots without bony structure were also simulated to determine the sole effect

of the apical cavity design (Fig. 7C), while investigation of the influence of the retrograde

filling material was conducted under two conditions, i.e., with or without MTA retrograde

filling.

For simulated loading, von Mises and maximum principle stresses in the root dentin at

the resected level of 3 mm were extracted numerically according to the following:

preparation design, isthmus presence, and preparation size. Three sites were intensively

checked: site A— buccal surface of mesial root at resection level 3 mm from apex, site

B— prepared buccal margin; changed according to sub-groups, site C— maximum values

of von Mises stress under the experimental conditions.

16

Table 1. The numbers of elements and nodes of the Finite Element models.

Group Sub-group Node Element

I 1 11640 8436

I 2 14690 10340

I 3 13197 9994

I 4 15227 11480

II 1 14690 10340

II 2 12703 9108

II 3 13649 9180

II 4 13988 9328

III 1 12493 9560

III 2 12099 8316

III 3 17815 12920

III 4 14372 10146

IV 1 12099 8316

IV 2 13383 8988

IV 3 15383 10416

IV 4 13737 8988

17

Table 2. Mechanical properties of materials used in the study.

Material Modulus of elasticity

(GPa) Poisson ratio

Dentin 14.7 0.31

Periodontal ligament 0.0689 0.45

Cortical bone 13.7 0.26

Cancellous bone 1.37 0.3

Mineral trioxide aggregate

(MTA) 22.4 0.314

18

Fig. 7. Solid models of mesial root of mandibular first molar. (A) before (white canal) and after

(blue canal) canal shaping (B) after 3-mm apical resection (C) after 3-mm retrograde filling and

150N applied to vertical axis without alveolar bone. (D) with alveolar bone. (triangle form indicate

fixed point)

(A) (B)

(D) (C)

19

4. Modification of apical preparation design from sub-group 4 in Group III

Modification of the apical preparation was conducted to confirm the hypothesis that

when the preparation is conducted during a surgical procedure, it is advantageous to

prepare in a mesial direction, within the mesial root dentin. Among the experimental

groups, sub-group 4 in Group III was selected and tested with this modification because

this case had the largest apical preparation: representing the highest stress value. The

apical preparation design was modified as seen in Fig. 8, while maintaining a similar area

of MTA filling, and extending the preparation in a mesial direction. A 150-N vertical

force was then applied, in keeping with the original experiment setup.

3.2

5.5

0.2

0.95 1.35

0.5R 1.0

1.95

D 1.8

R 1.8

0.17

0.5

3.2

5.5

0.2

0.95 1.35

0.34

R 1.0

R 1.8D 1.8

1.95

0.34

Fig. 8. The original test set-up and modification of sub-group 4 in Group III. (A) the original

experimental details and (B) the modification details of the preparation design.

Mesial side

Buccal

side

Mesial side

Buccal

side


Lingual

side

Lingual

side

(A) (B)

20

III. Results

The maximum principle stress and von Mises stress values from the experimental

groups with alveolar bone are shown in Table 3. According to the enlargement of

preparation cavity in the tested sub-groups, the von Mises and maximum principle

stresses were reduced gradually (Fig. 9 - 12); this tendency was the same in both

conditions, with or without alveolar bone.

However, when the preparation was extended excessively in the isthmus preparation

groups (sub-group 4 in Groups III and IV), the situation reversed, i.e., both maximum

principle stress and von Mises stress increased (Fig. 11 and 12). The maximum principle

stress had positive values on the distal concavity (site C), which is tensile in nature, in

contrast with sites A and B.

Without alveolar bone, the vertical force was transmited directly to the tooth,

concentrating stress mainly on the bucco-lingual side (Fig. 13).

Another interesting finding was the low stress field that was formed on the mesial side,

with or without the presence of alveolar bone. Von Mises stress distribution diagram is

represented in Fig. 9A–12A and Fig. 13.

Von Mises stress results according to the distance from site C to the prepared canal in a

straight line with or without the presence of MTA retrograde filling, is shown in Fig. 14.

Preparations without MTA retrograde fillings in Group I and III (Fig. 14B, 14F) displayed

21

Table 3. Maximum Principle and von Mises stress values from experimental groups (MPa).

Group

Sub-

group

Maximum Principle stress Von Mises stress

A B C A B C

I 1 -0.441 -0.809 0.546 5.727 2.554 7.514

2 -0.578 -0.632 0.455 5.123 2.632 7.349

3 -0.603 -0.659 0.386 4.95 2.709 6.252

4 -0.744 -0.74 0.716 5.626 2.516 7.7

II 1 -0.578 -0.632 0.455 5.123 2.632 7.349

2 -0.404 -0.468 0.507 5.515 3.203 7.3

3 -0.878 -0.624 0.43 5.208 2.586 6.973

4 -0.58 -0.158 0.606 4.619 3.805 7.047

III 1 -0.51 -0.95 0.664 5.971 2.445 7.615

2 -0.441 -0.656 0.675 5.719 2.738 7.434

3 -0.634 -0.875 0.306 5.33 2.514 7.105

4 -0.608 -0.678 0.298 4.861 4.032 6.537

IV 1 -0.441 -0.656 0.675 5.719 2.738 7.434

2 -0.648 -0.667 0.629 5.35 2.867 7.408

3 -0.665 -0.61 0.651 5.256 2.72 7.342

4 -0.307 -0.667 0.519 5.567 3.45 7.28

22

an increased von Mises stress as the preparation cavity enlarged. Sub-group 4 in Group

III (Fig. 14F, green line) especially, indicated the highest stress value, i.e., 25 MPa, which

is about three times higher than that in the other sub-groups. In the bucco-lingual

enlargement groups (Group II and IV), the results were similar among the sub-groups

because the straight distance from site C to the prepared canal was identical (Fig. 14C,

14D, 14G, 14H). Von Mises stress results without an MTA retrograde filling in sub-group

4 of Groups I to IV is shown in Fig. 15. Excessive preparation in sub-group 4 in Group III

(Fig. 15C) represented the highest value (red and gray color) on the prepared plane at the

3-mm resection level.

23

Fig. 9. (A) von Mises stress distribution diagram calculated from Group I (sub-group 4)

corresponded finite models with alveolar bone condition. Color coding that blue to red colors

represenst stress values from low to high, respectively. A: buccal side of the mesial root at 3mm

resected level from apex B: prepared buccal margin which changed according to sub-groups C:

point of max. stress value (mainly located in buccal slop on distal concavity) (B) von Mises stress

results in sub-groups, (C) Maximum principle stress results in sub-groups.

7.80

7.15

7.65

5.83

5.00

4.55

3.90

0.25

0.261.95

1.30

6.52

0.00

von Mises

(MPa)

A B C0

1

2

3

4

5

6

7

8

9

von

Mis

es s

tres

s (M

Pa)

sub-group 1

sub-group 2

sub-group 3

sub-group 4A

B

C

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

Max. p

rin

cip

al

stre

ss (

MP

a)

A B C

sub-group 1

sub-group 2

sub-group 3

sub-group 4A

B

C

A B

C (A)

Buccal

side

Mesial side

Distal side

Lingual

side

(B) (C)

24

.

A B C

0

1

2

3

4

5

6

7

8

9

vo

n M

ises

str

ess

(MP

a)

sub-group 1

sub-group 2

sub-group 3

sub-group 4A

B

C

Fig. 10. (A) von Mises stress distribution diagram calculated from Group II (sub-group 4)






7.80

7.15

7.65

5.83

5.00

4.55

3.90

0.25

0.261.95

1.30

6.52

0.00

von Mises

(MPa)

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

Max. p

rin

cip

al

stre

ss (

MP

a)

A B C

sub-group 1

sub-group 2

sub-group 3

sub-group 4A

B

C

A B

C

Mesial side

Distal side

Buccal

side Lingual

side

(A)

(B) (C)

25

A B C0

1

2

3

4

5

6

7

8

9

vo

n M

ises

str

ess

(MP

a)

A

B

C

sub-group 1

sub-group 2

sub-group 3

sub-group 4

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

Ma

x.

pri

nci

pa

l st

ress

(M

Pa

)

A B C

sub-group 1

sub-group 2

sub-group 3

sub-group 4A

B

C

Fig. 11. (A) von Mises stress distribution diagram calculated from Group III (sub-group 4)






7.80

7.15

7.65

5.83

5.00

4.55

3.90

0.25

0.261.95

1.30

6.52

0.00

von Mises

(MPa)

A B

C

Mesial side

Buccal

side

Lingual

side

Distal side

(C)

(A)

(B)

26

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

Max. p

rin

cip

al

stre

ss (

MP

a)

A B C

sub-group 1

sub-group 2

sub-group 3

sub-group 4A

B

C

Fig. 12. (A) von Mises stress distribution diagram calculated from Group II (sub-group 4)






7.80

7.15

7.65

5.83

5.00

4.55

3.90

0.25

0.261.95

1.30

6.52

0.00

von Mises

(MPa)

A B C0

1

2

3

4

5

6

7

8

9

vo

n M

ises

str

ess

(MP

a)

sub-group 1

sub-group 2

sub-group 3

sub-group 4A

B

C

B

C

A

Mesial side

Buccal

side

Lingual

side

(C) (B)

Distal side

(A)

27

Fig. 13. (A) von Mises stress distributions calculated from Group III, sub-group 4 without alveolar

bone condition.

Mesial side

Distal side

(A) (B)

Buccal

side

Lingual

side

Distal side

Buccal

side

Lingual

side

(C) (D)

Distal side


Buccal

side

Buccal

side

Distal side

Lingual

side

Lingual

side

Mesial side

28

0.0 0.1 0.2 0.3 0.4 0.52

3

4

5

6

7

8

9

vo

n M

ises

str

ess

(MP

a)

Distance (mm)

sub-group 1

sub-group 3

sub-group 2

sub-group 4

C

0.0 0.1 0.2 0.3 0.4 0.52

3

4

5

6

7

8

9

von

Mis

es s

tres

s (M

Pa

)

Distance (mm)

sub-group 1

sub-group 3

sub-group 2

sub-group 4

C

0.0 0.1 0.2 0.3 0.4

4

5

6

7

8

9

10

vo

n M

ises

str

ess

(MP

a)

Distance (mm)

sub-group 1

sub-group 3

sub-group 2

sub-group 4

C

0.0 0.1 0.2 0.3 0.4 0.5

3

4

5

6

7

8

9

10

vo

n M

ises

str

ess

(MP

a)

Distance (mm)

C

sub-group 1

sub-group 3

sub-group 2

sub-group 4

(B) (A)

(D) (C)

29

0.0 0.1 0.2 0.3 0.4 0.52

3

4

5

6

7

8

9

von

Mis

es s

tres

s (M

Pa

)

Distance (mm)

sub-group 1

sub-group 3

sub-group 2

sub-group 4

C

0.0 0.1 0.2 0.3 0.4 0.5

5

6

7

8

9

10

11

vo

n M

ises

str

ess

(MP

a)

Distance (mm)

sub-group 1

sub-group 3

sub-group 2

sub-group 4

C

Fig. 14. von Mises stress results accorrding to the distance from C point to prepared canal with or

without MTA retro-grade filling. (A) Group I with MTA (B) Group I without MTA (C) Group II

with MTA (D) Group II without MTA (E) Group III with MTA (F) Group I without MTA (G)

Group IV with MTA (H) Group IV without MTA.

0.0 0.1 0.2 0.3 0.4 0.52

3

4

5

6

7

8

9

vo

n M

ises

str

ess

(MP

a)

Distance (mm)

C

sub-group 1

sub-group 3

sub-group 2

sub-group 4

0.0 0.1 0.2 0.3 0.4 0.5

5

10

15

20

25

vo

n M

ises

str

ess

(MP

a)

Distance (mm)

C

sub-group 1

sub-group 3

sub-group 2

sub-group 4

(E)

(G)

(F)

(H)

30

Fig. 15. Diagrams of von Mises stress results without MTA retro-grade filling condition. (A) sub-

group 4 in Group I (B) sub-group 4 in Group II (C) sub-group 4 in Group III (D) sub-group 4 in

Group IV.

(B) (A)

(C) (D)

Mesial side


Lingual

side

Lingual

side

Buccal

side

Buccal

side



Buccal

side

Buccal

side

Lingual

side

Lingual

side

Mesial side

31

The modification of apical preparation was carried out in a mesial direction, on the mesial

root dentin, in sub-group 4 of Group III. The resultant stress values changed drastically;

the maximum value of von Mises stress reduced from 7.7 MPa (A) to 6.6 MPa (B), while

the maximum principle stress reduced from 1.066 MPa (C) to 0.467 MPa (D) on the

distal concave aspect (Fig. 16).

Fig. 16. The modification of sub-group 4 in Group III. (A) von Mises stress distributions of the

original one and (B) the modifiction. (C) max. principle stress distributions of the original one and

(D) the modification.

7.80

7.15

7.65

5.83

5.00

4.55

3.90

0.25

0.261.95

1.30

6.52

0.00

von Mises

(MPa)

(B) (A)

(C) (D)

Lingual

side

Distal side

Lingual

side

Lingual

side

Buccal

side

Buccal

side


Distal side

Mesial side

Mesial side


Lingual

side Buccal

side

Buccal

side

32

IV. Discussion

An advantage of using an FEA method in stress concentration is the control of all

conditions through standardization (Belli et al. 2011). Furthermore, the effects of various

factors can be evaluated accurately in a short time using computer software (Eraslan et al.

2011; Toparli, Gokay, and Aksoy 1999), which would be impossible to achieve through a

clinical study in human teeth. In vitro testing using natural teeth is impossible because

other factors including canal length, canal diameter, canal curvature, and canal outline

cannot be controlled (Sathorn et al. 2005).

In this experiment, two stress values were measured, i.e., von Mises stress and

maximum principle stress. Von Mises stress is the net stress value combined from several

directions (x, y, and z directional axes) and is widely used as an indicator of the

possibility of damage occurrence (Pegoretti et al. 2002). Conversely, the maximum

principle stress has a directional nature: positive (tensile) or negative (compressive).

Therefore, von Mises stress values are used to evaluate the magnitude of stress that the

object is under, and the maximum principle stress is used to determine whether the stress

is tensile or compressive. In clinical situations, if tensile stress is concentrated on a

certain point, material dislodgement or root fracture may occur.

In this FEA simulation, a 150-N force was applied to the vertical axis; this usually

represents the maximum bite force in FEA studies. Studies have reported that the

maximum bite force varies, ranging from 70 to 500 or 700 N (Ferrario et al. 2004; Koc,

33

Dogan, and Bek 2011), and it may be affected by many factors such as gender, age,

restorations, oral habits, muscle tension, general condition, emotional stress, and

measurement method (Fernandes et al. 2003; Miura et al. 2001). Therefore, it is difficult

to determine the bite force value accurately. In this test, because the coronal portion of the

tooth was removed, the force was directly transmitted to the root, and because the force

was applied to only one mesial root, a force of 150 N was thought to be sufficient to

simulate the maximum bite force in clinical conditions. However, if a patient has a

maximum bite force higher than 150 N, especially due to oral habits like clenching or

bruxism, a higher clinical stress would have been exerted on the tooth than in this study.

I assumed that a large apical preparation might result in high stress concentration in the

apical root dentin; however, the experimental results were quite the contrary. Generally,

when the preparation amount was increased in experimental groups, von Mises stress and

maximum principle stress gradually decreased in both experimental conditions, with or

without the presence of alveolar bone. This stress reduction might be due to the modulus

of elasticity of MTA, which is higher than that of root dentin (Belli et al. 2011). In the

experimental condition without retrograde MTA filling, the von Mises stress increased as

the amount of apical preparation increased (Fig. 14B, 14F); in the analysis with

retrograde MTA filling present, as the size of apical preparation increased, the stress

decreased, thereby confirming the effect of the modulus of elasticity of MTA. Therefore,

the amount of preparation itself does not influence the outcome of a surgically treated

tooth when MTA is used for retrograde filling. Consequently, the rationale for preparation

34

design in a tooth containing an isthmus is valid, especially in a molar with multiple canals.

However, this FEA was performed under the assumption that the retrograde cavity was

uniformly filled with MTA without any voids, but in clinical situations, this requires

advanced clinical skill of the operator. Moreover, this further supports the conclusion of a

previous study that most failure of surgical endodontics is related to poor technique.

Therefore, as the FEA and clinical situation are not identical, direct application of an FEA

study result to a clinical scenario is not advisable. In addition, if the cavity is filled with a

different material with a lower modulus of elasticity than MTA, although the result may

not be as high as the stress without any filling material present, the stress value would be

higher than that measured when the cavity is filled with MTA. Higher stress values mean

a higher chance of distortion

This study was conducted in conditions with or without the presence of alveolar bone to

investigate the effect of supporting bone. In the experimental condition without alveolar

bone present, the vertical force is transmited directly to the tooth, concentrating stress

mainly on bucco-lingual side, regardless of experimental groups (Fig. 13); the mesial root

has a dumbbell shaped cross-section with longer bucco-lingual length, and decreasing

cross-sectional area from the CEJ to the apex. To summarize, the stress concentration is

influenced by tooth shape, not apical preparation amount (Sathorn et al. 2005).

In the experimental condition with alveolar bone present, the vertical force is influenced

by other factors such as resilience or alveolar bone support. It is more comparable with

clinical situations, and the result is also affected by the characteristics of individual bone

35

quality. In this situation, the stress is mainly concentrated on the buccal slope of the distal

concave area (Fig. 9-12); the distal concave area of the mesial root has the thinnest root

dentin, and is referred to as the danger zone, as precaution is required during non-surgical

endodontics..

One valuable finding was that when the minimum amount of root dentin remained in the

isthmus preparation group (sub-group 4 in Groups III and IV), the tendency was reversed;

both von Mises stress and maximum principle stress increased (Fig. 11, 12). The stress

was the highest in sub-group 4 of Group III where the remaining root dentin thickness

was 0.17 mm on the distal concave area. In summary, according to the enlargement of

apical preparation, the stress reduced gradually. However, when minimal amounts of root

dentin remained, the tendency reversed and stress concentrated; the maximum principle

stress had a positive value at the distal concave area, meaning the stress was tensile in

nature. Therefore, root fracture initiation and the detachment of the retrograde filling

material (MTA) may occur at this point (Eltit, Ebacher, and Wang 2013).

This speculation may provide a biomechanical explanation for failure of the surgically

treated molar. Kim et al. (Kim et al. 2016) have reported that teeth with a prepared

isthmus recorded a significantly lower cumulative survival rate than those without an

isthmus; they proposed the weakened root dentin caused by larger apical preparation to

prepare the isthmus as a possible reason. However, according to this study, the amount of

apical preparation itself is not a critical factor affecting the stress concentration, when a

standard amount of apical preparation is performed. It is supported by the result that as

36

the size of preparation increases, the von Mises stress and maximum principle stress

gradually decreases, in experimental conditions with or without alveolar bone present

(sub-groups 1-3). However, when very thin root dentin remains, as seen in sub-group 4 in

Group III, the root is susceptible to fracture, which can have serious clinical repercussions.

Modification of the apical preparation was conducted in sub-group 4 of Group III, which

had the largest apical preparation amount, representing the highest stress value. While

maintaining a constant cross-sectional area of the MTA filling, the preparation design was

modified so that both the mesial and distal outlines of the cavity preparation followed the

outline of the root, and the remaining dentin thickness was the same for both the mesial

and distal side. The resulting stress values were lower than that of the previous

preparation design, especially the value of maximum principle stress, which changed

drastically from 1.066 MPa to 0.467 MPa on the distal concave area (Fig. 16). Therefore,

the cavity preparation design, which follows the root outline, allowing a similar dentin

thickness to remain on the mesial and distal side, shows favorable stress distribution.

Since this modified design has almost an identical amount of preparation, the conclusion

can be drawn that the root outline has more influence on stress concentration and

distribution than does the amount of apical preparation. Therefore, my hypothesis, i.e.,

when preparation is conducted during the surgical procedure, it is advantageous to

prepare the cavity in a mesial direction and follow the outline of root, was confirmed.

Another interesting finding is that a low stress field is formed on the mesial side. It is

probably because the distal side is more concave than the mesial side of the mandibular

37

molar mesial root, in cross-sectional view. Thus, this preparation modification balances

the remaining root dentin on both sides, and creates a low stress field.

Finite element analysis studies produce results where outcomes are controlled and

experimental conditions simplified; it must be applied to a clinical situation with caution.

In clinical situations, many factors affect stress concentration, thereby increasing the

susceptibility of failure of the surgically treated tooth. Root morphology including canal

shape, number of canals, canal direction, degree of curvature, and isthmus presence are

natural tooth components that are unchangeable by the operator. The only element that

the operator can alter is the design of the apical preparation affecting the remaining root

dentin thickness. This study therefore focused on apical preparation design; studies

regarding the relationship between apical preparation design during surgical endodontic

procedures and stress concentration are scarce. This study is worthy in the respect that it

addresses the effect of apical preparation design on stress concentration, which is

significant in the success of the surgically treated tooth.

The main limitation of this study is that fatigue fracture concept was inapplicable to the

FEA study. In FEA simulation, when the load is removed, the stress is recovered

completely. However, a natural tooth exhibits fatigue fracture; a repetitive stress lower

than tensile strength causes plastic deformation, and finally causes tooth fracture.

Therefore, although the stress values in this study result are not high, it is supposed that

the effect can be more significant in real clinical situations.

38

To date, many studies have suggested that the amount of apical preparation is the cause of

surgical endodontic failure, especially in molar teeth. Similarly, the hypothesis of this

study was that stress increased according to apical preparation enlargement. However, the

results of this study show that the stress level is influenced more by the root outline than

the amount of apical preparation.

This FEA was performed in a well-controlled environment with simplified factors.

However, it is thought that the conclusion of this study is also worthy in a clinical

scenario. During surgical endodontic procedures, the operator should have a thorough

understanding of the root morphology, including the degree, location, and dentin

thickness of the distal concave area. The root should be prepared to follow the root

outline to ensure there is no point with very little dentin thickness remaining. Finally, the

retrograde cavity should be evenly filled with a material that has a similar modulus of

elasticity to that of dentin.

For further clinical applications, future studies should investigate the critical amount of

remaining dentin thickness that affects the outcome of surgically treated tooth, and the

effect of voids or defects of apical filling material on stress concentration.

39

V. Conclusion

The amount of apical preparation is of little importance to stress concentration, whereas

configuration of the root affects stress concentration. Therefore, the preparation design

containing an isthmus is reasonable, especially in multiple canal roots, but a little

remaining root dentin must be preserved; the operator must recognize the specific

configuration of the root under appropriate magnification, and it is advantageous to

perform retrograde preparation in a mesial direction within the mesial root dentin. This

preparation modification balances the remaining root dentin on both sides and creates a

low stress field.

40

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46

Oxford. ISBN 9780198510963.


"Root anatomy and canal configuration of the permanent mandibular first

molar: a systematic review". J Endod, 36(12): 1919-31.






restoration of severely damaged endodontically treated premolar teeth: a

FEM study". Clin Oral Investig, 15(3): 403-8.




"Single tooth bite forces in healthy young adults". J Oral Rehabil, 31(1): 18-

22.


endodontics: the Toronto Study. Phase 1: initial treatment". J Endod, 29(12):

787-93.


47



"Canal and isthmus debridement efficacy using a sonic irrigation technique in

a closed-canal system". J Endod, 38(9): 1265-8.

Kim, E., J. S. Song, I. Y. Jung, S. J. Lee and S. Kim. 2008. "Prospective clinical

study evaluating endodontic microsurgery outcomes for cases with lesions of

endodontic origin compared with cases with lesions of combined periodontal-

endodontic origin". J Endod, 34(5): 546-51.


Isthmus on the Outcomes of Surgically Treated Molars: A Retrospective

Study". J Endod, 42(7): 1029-34.


mass index and type of functional occlusion on bite force". J Appl Oral Sci,

19(3): 274-9.


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using high-resolution micro-computed tomography: a pilot study". J Endod,

40(4): 584-7.


bite force and dentate status between healthy and frail elderly persons". J

48

Oral Rehabil, 28(6): 592-5.


canal system of human mandibular first molars with primary apical

periodontitis after "one-visit" endodontic treatment". Oral Surg Oral Med

Oral Pathol Oral Radiol Endod, 99(2): 231-52.



23(13): 2667-82.




human tooth using a three-dimensional finite element model". J Dent Res,

62(2): 82-6.








49


Filho. 2003. "A preliminary in vitro study of the incidence and position of the

root canal isthmus in maxillary and mandibular first molars". Int Endod J,

36(4): 276-80.


"Analysis of dentinal stress distribution of maxillary central incisors

subjected to various post-and-core applications". Oper Dent, 31(1): 89-96.


second premolar tooth by using three-dimensional finite element method". J

Oral Rehabil, 26(2): 157-64.





evaluation of surgical endodontic treatment: traditional versus modern

technique". J Endod, 32(5): 412-6.


by endoscopic inspection during periradicular surgery". Int Endod J, 38(3):

160-8.


50




21(7): 380-3.



Molars by Means of Micro-Computed Tomography: An Ex Vivo Study". J

Endod, 42(4): 610-4.


"Effects of ultrasonic root-end cavity preparation on the root apex". Oral Surg

Oral Med Oral Pathol Oral Radiol Endod, 80(2): 207-13.









51


morphology of the human permanent maxillary first molar: a literature review". J

Endod, 32(9): 813-21.


Oxford. ISBN 9780198510963.


"Root anatomy and canal configuration of the permanent mandibular first molar: a

systematic review". J Endod, 36(12): 1919-31.






restoration of severely damaged endodontically treated premolar teeth: a FEM

study". Clin Oral Investig, 15(3): 403-8.




"Single tooth bite forces in healthy young adults". J Oral Rehabil, 31(1): 18-22.


52

endodontics: the Toronto Study. Phase 1: initial treatment". J Endod, 29(12): 787-

93.




"Canal and isthmus debridement efficacy using a sonic irrigation technique in a

closed-canal system". J Endod, 38(9): 1265-8.

Kim, E., J. S. Song, I. Y. Jung, S. J. Lee and S. Kim. 2008. "Prospective clinical

study evaluating endodontic microsurgery outcomes for cases with lesions of

endodontic origin compared with cases with lesions of combined periodontal-

endodontic origin". J Endod, 34(5): 546-51.


Isthmus on the Outcomes of Surgically Treated Molars: A Retrospective Study". J

Endod, 42(7): 1029-34.


mass index and type of functional occlusion on bite force". J Appl Oral Sci, 19(3):

274-9.


intracanal tissue and debris through a novel laser-activated system assessed using

high-resolution micro-computed tomography: a pilot study". J Endod, 40(4): 584-

53

7.


bite force and dentate status between healthy and frail elderly persons". J Oral

Rehabil, 28(6): 592-5.


canal system of human mandibular first molars with primary apical periodontitis

after "one-visit" endodontic treatment". Oral Surg Oral Med Oral Pathol Oral

Radiol Endod, 99(2): 231-52.



23(13): 2667-82.




human tooth using a three-dimensional finite element model". J Dent Res, 62(2):

82-6.





54





Filho. 2003. "A preliminary in vitro study of the incidence and position of the root

canal isthmus in maxillary and mandibular first molars". Int Endod J, 36(4): 276-

80.


"Analysis of dentinal stress distribution of maxillary central incisors subjected to

various post-and-core applications". Oper Dent, 31(1): 89-96.


second premolar tooth by using three-dimensional finite element method". J Oral

Rehabil, 26(2): 157-64.





evaluation of surgical endodontic treatment: traditional versus modern technique".

J Endod, 32(5): 412-6.


55

by endoscopic inspection during periradicular surgery". Int Endod J, 38(3): 160-8.





21(7): 380-3.



Molars by Means of Micro-Computed Tomography: An Ex Vivo Study". J Endod,

42(4): 610-4.

56

국문 요약

하악대구치 근심치근의 외과적 근관치료에서

역충전 와동 형성 디자인에 따른 응력 변화연구

: 유한요소 분석

연세대학교 대학원 치의학과

(지도교수 김 의 성)

박 소 영

본 연구는 하악 대구치 근심치근의 외과적 근관치료에서 다양한 치근단 삭제

디자인이 다양한 실험 조건에서 치근의 스트레스에 미치는 영향을 유한요소

방법을 이용하여 평가하였다.

발치된 하악 제 1대구치를 CT 스캔한 뒤 문헌고찰을 통해 크기를

표준화하고 이를 이용하여 유한요소 분석 모델을 제작하였다. 치관부 변이에

57

따른 실험의 변수를 제거하기 위해 치관부를 백악법랑 경계에서 제거한 뒤

근심 치근만 실험에 사용하였다.

하악 제 1대구치 근심치근의 유한요소 모델상에서 외과적 근관치료를

시뮬레이션 한 뒤 수직 방향으로 150N 힘을 가하였다. 치근단 삭제의

디자인에 따른 본 미세스 응력과 주응력의 수치를 측정하였다.

하악 대구치 근심치근의 외과적 근관치료시 치근단 삭제 디자인에 따른

영향을 조사하여 다음과 같은 결과를 얻었다.

1. 치조골이 있는 실험조건에서 치근단의 삭제량이 증가함에 따라서 폰

미제스와 주응력의 값은 반대로 점진적으로 감소되었다. 이러한 경향은

치조골이 있는 조건과 없는 조건에서 유사하였다.

2. Isthmus 를 치근단 삭제 디자인에 포함시켰던 실험군 III과 IV 에서,

특히 가장 많은 양의 치근단 삭제가 진행되어 적은 치질이 남게 되는

경우 (sub-group 4)에서는 앞선 응력 값의 경향이 반전되어 스트레스가

증가되었다.

3. 이때의 치근단 단면의 원심측으로 주응력이 양의 값을 가지므로

인장력을 나타내고 이는 이 부위에서 높은 스트레스가 걸릴 경우

치근의 크랙이 진행되거나 또는 충전재료 (MTA)의 탈락이 발생할 수

있는 임상적 상황과 연관된다.

58

4. MTA로 치근단 역충전을 시행하지 않은 실험 조건에서는 치근단

삭제량이 커짐에 따라 본 미제스 스트레스 값이 증가되었다. 따라서

치근단 삭제량이 증가하여도 스트레스 값이 소폭 감소하는 경향을

보였던 앞선 실험결과는 치근 상아질이 탄성계수보다 더 큰 탄성계수를

가지는 MTA 역충전때문이라는 것이 확인되었다.

5. 치조골이 없는 조건에서는 수직으로 가한 힘이 치근에 직접적으로

전달되어 협설측 방향으로 높은 스트레스 집중을 나타내었다. 이것은

근심치근의 외형이 백악법랑부위에서 보다 치근단쪽에서 더 좁은

면적을 가지고 협설측으로 더 긴 단면을 가지는 것과 연관되는 것으로

생각된다. 따라서 스트레스의 집중은 치아의 외형에 영향을 받는다는

것을 알 수 있다.

6. 치근의 외형을 따라가면서 단면에서 근원심측으로 비슷한 정도의 치근

두께가 남도록 치근단 삭제 디자인을 변경하여 실험한 결과 스트레스

값이 감소되었다. 특히 원심측의 오목한 외형을 가지는 부위에서

주응력의 크기가 크게 감소하였다.

7. 치근의 근심측에 치우쳐서 낮은 스트레스 영역이 났는데 이것은 하악

대구치의 근심치근에서 근심측보다 원심측에서 더 오목한 단면을

가지기 때문인 것으로 생각된다.

59

결론적으로, 외과적 근관치료 시 치근단 삭제량 자체는 스트레스 집중에

미치는 영향이 크지 않다고 할 수 있다. 그러므로 여러 개의 근관을 가지는

경우 isthmus를 포함하는 삭제디자인은 타당하다고 하겠다. 다만 치근의

단면에서 특정부위로의 과잉 치질 삭제가 일어나지 않도록 주의해야한다.

이를 위한 제안으로 외과적 근관치료 시, 치근삭제가 치근이 외형을

따라가면서 근심쪽으로 치우치도록 하는 것은 남는 치근의 양을 근원심면에서

비슷하게 한다는 점에서 뿐만아니라 더 낮은 스트레스 영역이 형성되는

쪽이라는 면에서 이점이 있다. 그러기 위해서는 술자는 술 전에 치근의

특징적인 외형에 대해 숙지하고 있어야 하고 탄성계수가 치근의 상아질과

비슷한 재료를 이용하여 역충전 와동을 빈틈없이 잘 채워 넣는 고도로 훈련된

임상 스킬이 요구된다.

핵심 되는 말: 유한요소, 스트레스분포, 치근단 삭제 디자인, 외과적 근관치료

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Stress analysis according to various retrograde cavity preparation … · 2020. 2. 13. · Stress analysis according to various retrograde cavity preparation designs for surgical