Factors Affecting Fracture Susceptibility of Tooth Root: A Laboratory and Finite Element Analysis (FEA) Study

Chankhrit Sathorn

Doctor of Clinical Dentistry

November 2004

Endodontic Unit School of Dental Science, Faculty of Medicine, Dentistry and Health Sciences

Submitted in partial fulfillment of the requirements of the degree of Doctor of Clinical Dentistry

ii

Abstract

From a fracture mechanics viewpoint, structural defects, cracks or canal

irregularities are likely to play a major role in fracture susceptibility of the roots,

because stresses can be exponentially amplified at these sites. By incorporating

defects into a smooth round canal using rotary NiTi, theoretically the roots

could be strengthened. The aims of the study were to determine whether rotary

NiTi canal preparation strengthens roots, and whether the fracture pattern can

be predicted by finite element analysis (FEA) models. 25 teeth were prepared

using hand file and another 25 using rotary NiTi. After obturation, all teeth

were subject to loading until fracture; load and patterns were recorded. Four

FEA models were created from fractured roots. No significant difference of

fracture load between the two techniques was found. Mesio-distal fracture

occurred more often in the rotary NiTi group. Stress patterns in three of the

four FEA models correlated well with the observed fracture patterns.

The aim of the subsequent study was to determine the extent to which canal

size, radius of curvature and proximal root concavity influence fracture

susceptibility and pattern. A standardized cross-section of the mid-root region

of a mandibular incisor was created by averaging the dimensions of ten

extracted teeth, and the basic FEA model was created. By varying canal

diameter, shape and proximal concavity, these factors could be examined for

roles in fracture susceptibility and pattern. The factors all interact in

influencing fracture susceptibility and pattern, with dentine thickness not the

iii

only determining factor. The removal of dentine does not always result in

increased fracture susceptibility.

iv

Declaration

This is to certify that the thesis comprises only my original work except where indicated in the preface; due acknowledgement has been made in the text to all other material used; the thesis is 12,858 words in length, inclusive of footnotes, but exclusive of tables, maps, appendices and bibliography.

Dr Chankhrit Sathorn

v

Acknowledgements

Mr Dariusz Walter, a PhD candidate in engineering, for his expertise in LUSAS

software.

Dr Michael Swain, Professor of Aerospace Mechanical, and Mechatronic

Engineering at University of Sydney, for his invaluable suggestions and

insights in biomechanical properties of dentin.

Dr Sabu John, Associate Professor of Engineering at RMIT, for his in depth

understanding of engineering aspects of this research project.

Dedication

To my family, I couldn’t have done all this, without you.

To my high school teacher, Ms Poonsup Mitsumpun, who has always inspired

me with her endless enthusiasm and innate curiosity. A great example of how

one fine teacher could shape many more student lives.

To my mentor, Prof Harold H Messer, a wonderful scientist and a great human

being.

vi

Preface

This thesis is a part of ongoing research at the University of Melbourne into

different aspects of vertical root fractures and endodontics. It consists of four

chapters; the first two chapters are introduction and literature review, the latter

two are manuscripts that have already been accepted for publication in the

Journal of Endodontics. Spelling and referencing formats differ in Chapters 3-4

according to the requirements of the Journal of Endodontics. References are

included at the end of Chapters 2-4 because of the structure of the thesis.

vii

Table of Contents Chapter 1: Introduction ............................................................................................. 1 Chapter 2: Literature review ..................................................................................... 2 Vertical Root Fracture (VRF) ................................................................................. 2 Clinical problems................................................................................................ 2 Prevalence ........................................................................................................... 2 Prognosis............................................................................................................. 3 Etiology ............................................................................................................... 4 Endodontic procedures.................................................................................. 4 CO2 test ........................................................................................................ 4 Access opening ........................................................................................... 5 Calcium hydroxide medication ................................................................. 5 Effects of NaOCl ......................................................................................... 6 Canal preparation....................................................................................... 6 Obturation ................................................................................................... 8 Retropreparation......................................................................................... 9 Bleaching ..................................................................................................... 9

Restorative procedures ................................................................................ 10 Management ..................................................................................................... 13

Fracture related biomechanical properties of dentine ...................................... 14 Moisture content............................................................................................... 15 Hardness ........................................................................................................... 15 Young’s modulus ............................................................................................. 16 Ultimate strength.............................................................................................. 17

Fracture mechanics .............................................................................................. 18 Stress.................................................................................................................. 18 Stress vs. Strength......................................................................................... 19

Strain.................................................................................................................. 20 Young’s modulus ............................................................................................. 20 Fracture toughness ........................................................................................... 21 Mode of Fracture .............................................................................................. 21 Brittle fracture ............................................................................................... 21 Ductile fracture ............................................................................................. 22

Why do fractures occur below a material’s ultimate tensile strength?........ 22 Fatigue failure............................................................................................... 23 Crack, flaw size concept............................................................................... 23 Crack arrest ................................................................................................... 27

Fracture prediction........................................................................................... 28 The study of stress and fracture...................................................................... 28 Experimental method................................................................................... 28 Theoretical method....................................................................................... 28 Numerical method ....................................................................................... 29

Aims ...................................................................................................................... 30 References ............................................................................................................. 31

Chapter 3: Article I Laboratory study and FEA verification ................................ 38

viii

Abstract ................................................................................................................. 39 Introduction.......................................................................................................... 40 Materials and Methods ........................................................................................ 41 Results ................................................................................................................... 46 Discussion ............................................................................................................. 48 References ............................................................................................................. 52 Figure legends ...................................................................................................... 54 Figure 1 ................................................................................................................. 55 Figure 2 ................................................................................................................. 56 Figure 3 ................................................................................................................. 57

Chapter 4: Article II an FEA study of factors affecting fracture strength ........... 58 Abstract ................................................................................................................. 59 Introduction.......................................................................................................... 60 Materials and Methods ........................................................................................ 61 Results ................................................................................................................... 65 Discussion ............................................................................................................. 68 References ............................................................................................................. 72 Figure legends ...................................................................................................... 75 Figure 1 ................................................................................................................. 76 Figure 2 ................................................................................................................. 77 Figure 3 ................................................................................................................. 78

1

Chapter 1: Introduction

A vertical root fracture (VRF) is defined as a longitudinal fracture confined to

the root that usually begins on the internal wall and extends outward to the

root surface (Walton 2002). VRF poses a serious diagnostic challenge; it often

presents without any specific signs and symptoms, and it can radiographically

and clinically mimic lesions of endodontic and periodontal origin. Complete

management is also troublesome involving complicated, costly and time-

consuming procedures, yet the prognosis is generally poor. As a result, VRF

can be a very costly problem for society, in the form of direct costs (including

labour and material) and indirect costs to the patient (loss of income for patients

who miss work). Prevention is therefore the key to avoiding unfavourable

events after root fracture. However, before preventive measures against VRF

can be undertaken, etiological factors of root fractures need to be fully

understood, and factors affecting fracture susceptibility need to be more clearly

identified. A better understanding of VRF might then enable the practitioner to

create biologically and mechanically sound preventive strategies and/or

management. This study aimed to validate one of the assumed etiological

factors of VRF i.e. canal preparation, as well as three factors potentially

influencing fracture susceptibility i.e. dentine thickness, canal shape, and

external root morphology.

2

Chapter 2: Literature review

Vertical Root Fracture (VRF)

Clinical problems

Root fracture is an undesirable clinical entity for several reasons. First and

foremost, definitive diagnosis is often difficult, particularly in its early stages

(Fuss et al. 2001; Testori et al. 1993). Second, even after root fracture has been

diagnosed, predictable management involves rather aggressive approaches i.e.

extraction or root amputation. A conservative approach has been suggested,

but without long-term outcomes (Kawai et al. 2002; Trope et al. 1992). Third, if

root fractures are not treated promptly and properly, pulpal infection and loss

of the tooth are inevitable; masticatory function will then be compromised.

Finally, complex and costly restorations are needed after extraction or root

amputation, and, of course, economic losses are unavoidable.

Prevalence

Survival analysis of endodontically treated teeth showed that 15% of those

would be extracted in ten years (Dammaschke et al. 2003). In endodontically

treated teeth that had been scheduled for extraction, it has been reported that

VRF was responsible for 11% (Fuss et al. 1999) to 13% (Vire 1991). Thus around

0.2% per year of root filled teeth would be lost directly because of VRF (13% of

15%=1.95% in ten years, therefore ~0.2% per year). Based on an average

number of 2.2 root fillings per adult (Eriksen 1991), it can be estimated from

census data that there are 132, 25 and 420 million root filled teeth in patients in

3

Thailand, Australia and the USA. Extrapolation from these data indicates that

264,000, 50,000, and 840,000 teeth in Thailand, Australia and the USA,

respectively would be lost each year because of VRF. A problem of this

magnitude would warrant studies to identify its etiological factors, in order to

improve its prevention and management.

There has been an increasing recognition of VRF in non-endodontically treated

teeth since 1995. A preliminary report of the phenomenon was first made by

Yang et al (1995). They reported 12 teeth with VRF in non-endodontically

treated molars. The majority were severely attrited mandibular molars in

males. All had clinically intact crowns with no or minimal restorations (Yang et

al. 1995). Subsequent reports were made with increasing numbers of affected

teeth identified (Chan et al. 1998; Yeh 1997). In the most recent study of 315

teeth that had been scheduled for extraction because of VRF, 40% of such teeth

were non-endodontically treated (Chan et al. 1999). Apparently, VRF in non-

endodontically treated teeth is not as uncommon as might usually be

anticipated. This surprisingly high number of VRF in non-endodontically

treated teeth is another reason that a better understanding of VRF is required.

Prognosis

At present, prognosis is virtually hopeless for a tooth with a VRF (Walton 2002).

4

Etiology

Endodontic treatment has been suggested as a cause of VRF by several studies.

These clinical studies (Bender et al. 1983; Gher et al. 1987) and review article

(Tamse 1988) documented the presence of root canal fillings in fractured teeth

but did not determine the incidence of fractures in teeth with root canal fillings

and without. Therefore, odds ratio-a figure that quantifies the strength of

association (Silman et al. 2002)-could not be calculated. As a result, their

proposed association between endodontic treatment and VRF was questionable;

a causative relationship was even more difficult to demonstrate. Even though

their claims of association were questionable, many subsequent works have

been done to investigate biological and mechanical consequences of endodontic

and restorative procedures on VRF. Factors contributing to VRF were classified

into predisposing and precipitating factors (Maxwell et al. 1986). Predisposing

factors are factors that clinicians have no influence over such as tooth natural

anatomy, attrition, moisture content, and brittleness. Precipitating factors or

factors resulting from dental procedure can be sub-classified into endodontic

and restorative procedures:

Endodontic procedures

CO2 test

Carbon dioxide ice is an irreplaceable endodontic tool for pulp testing. Since its

temperature is extremely low (-78οC), it was implicated in crack initiation,

however, studies have shown otherwise (Peters et al. 1983; Peters et al. 1986).

5

Scanning electron microscopy and surface analysis were utilized; no new cracks

were detected after carbon dioxide ice application for up to two minutes.

Access opening

The access opening is one component of the endodontic procedures involving

tooth structure removal. It was thought to contribute, in part, to increased

prevalence of root fracture in endodontically treated teeth. The reduction in

tooth stiffness after various endodontic and restorative procedures has been

studied using strain gauge techniques. The results indicated that endodontic

procedures have only a small effect on the tooth, reducing the relative stiffness

by 5%. This was less than that of an occlusal cavity preparation (20%). The

largest losses in stiffness were related to the loss of marginal ridge integrity.

MOD cavity preparation resulted in an average of a 63% loss in relative cuspal

stiffness (Reeh et al. 1989).

Calcium hydroxide medication

A retrospective study reported a high prevalence of cervical fracture in

endodontically treated immature teeth (Cvek 1992). Besides thin dentine, long-

term calcium hydroxide medication has also been alluded to as a cause of root

weakening (Andreasen et al. 2002). The authors pointed out that calcium

hydroxide may, due to its alkaline nature, neutralize, dissolve, or denature

some of the acidic protein components in dentine and thereby weaken it. Their

results showed a marked decrease in fracture strength with increasing storage

time. Their specimens, however, were immature sheep teeth; extrapolation to

6

human teeth would not be entirely accurate. Moreover, there was no control

group, making their results even more questionable, that is, the decrease in

fracture strength might well be the result of storage time and/or conditions.

Effects of NaOCl

One in vitro study (Sim et al. 2001) showed that irrigation with 5.25% NaOCl

could significantly reduce flexural strength, and alter strain characteristics of

root dentine, which resulted in a reduction of Young’s modulus i.e. the teeth

were more brittle, and more susceptible to fracture. Even though this study

showed statistically significant reduction of certain mechanical properties of

dentine, a clinically significant reduction was not necessarily ensured. In

addition, enamel was removed from all samples to accentuate the differences in

tested properties. As a result, this was not a good representative of the clinical

situation.

Canal preparation

It is widely accepted that the removal of excessive amounts of radicular dentine

compromises root strength (Gutmann 1992). Canal preparation involves

dentine removal, and therefore, may compromise the fracture strength of the

roots. Canal preparation has been repeatedly suggested (Bender & Freedland

1983; Gher et al. 1987; Tamse 1988) as a cause of VRF, however, very little

scientific information is available to substantiate the claim. One in vitro study

showed that the more dentine removed, the more likely the tooth is to fracture

(Wilcox et al. 1997). The study, however, used the same tooth as its own

7

comparison, i.e. the tooth was gradually enlarged then load was applied if no

fracture occurred, it would be enlarged further then subject to loading again.

This process was repeated until fracture occurred. The higher fracture

susceptibility in larger canals, therefore, might be the result of stress

accumulation from the previous loading procedure. Another in vitro study

showed that hand instrumented mandibular premolars were more susceptible

to fracture than uninstrumented counterparts, while canal preparation in canine

teeth had no effects whatsoever (Wu et al. 2004). The authors concluded that

canal shape and remaining dentine thickness must play an important role in

determining fracture strength.

With technological advancements, canal preparation techniques have evolved

rapidly in recent years. The introduction of rotary nickel-titanium (NiTi)

instruments for canal preparation has changed canal shape, size and taper

compared to hand instrumentation. Canal shape after preparation with hand

files can be quite irregular (Portenier et al. 1998; Tan et al. 2002). From a fracture

mechanics point of view, the presence of structural defects, cracks or canal

irregularities is likely to play a major role in determining fracture strength

(Gdoutos 1993), because an applied stress may be exponentially amplified at the

tip of those defects (Callister 2003). With rotary NiTi preparation, canal shapes

are more likely to be rounder and smoother (Bryant et al. 1998; Glossen et al.

1995; Thompson et al. 1997); canal irregularities are likely to be incorporated

into the preparation and eliminated. Theoretically, smoothly tapering canals

8

prepared using rotary NiTi should result in lower fracture susceptibility. It is

part of this study objective to determine whether rotary NiTi canal preparations

reduce fracture susceptibility compared to hand instrumentation (Chapter 3).

Obturation

Obturation, both vertical and lateral condensation techniques, involve load

application through spreaders and pluggers to the root canal wall and radicular

dentine. It is another step in the root canal treatment procedure that has been

implicated as a cause of VRF (Tamse 1988). Stresses are closely associated with

structural failure or fracture, because structural failure will occur once the

applied load produces a stress that exceeds the ultimate strength of material

(Callister 2003). Stresses in roots as a result of obturation have been studied

utilizing finite element analysis (FEA) (This method will be discussed in detail

later in this review). These studies have shown that the likelihood of root

fractures as a result of root canal obturation-either lateral or vertical

condensation-is a remote possibility (Telli et al. 1998; Yaman et al. 1995). Similar

studies have also been conducted using different measurement techniques.

Several obturation techniques (lateral condensation, Obtura, and Thermafil)

have been studied in regard to their effects on VRF using strain gauges (Saw et

al. 1995). The Obtura technique and lateral condensation involved greater loads

during obturation, more than double that of Thermafil technique. However, the

mean load required to cause VRF was five to six times higher than the load

used in obturation. Another two studies directly measured the load generated

during lateral condensation, and found that the load generated was generally

9

far lower than the load required to fracture the roots (Lertchirakarn et al. 1999;

Lindauer et al. 1989). Thus, obturation should not be regarded as a major cause

of VRF except in very weak roots.

Retropreparation

Ultrasonic cavity preparations in endodontic surgery have become a common

procedure. Concern has been raised that cracks have appeared in some

instances when ultrasonic instruments have been used (Saunders et al. 1994).

Laboratory studies showed contradictory results, some reported a strong

association between ultrasonic retropreparation and the presence of cracks

(Frank et al. 1996; Layton et al. 1996), while some reported otherwise (Beling et

al. 1997; Lin et al. 1999; Navarre et al. 2002). One issue these authors seem to

agree upon is that the power setting of the ultrasonic unit plays an important

role in crack initiation i.e. a low power setting reduces the likelihood of crack

initiation.

Bleaching

One in vitro study evaluated the effects of different bleaching procedures (vital

bleaching) on the fracture toughness and microhardness of bovine teeth. All six

bleaching regimens (Opalescence Xtra, Opalescence Quick, Rapid White,

Whitestrips, Opalescence 10%, and Opalescence PF 15%) resulted in a

statistically significant percentage loss of microhardness (Knoop hardness).

Only one bleaching regimen (Opalescence 10%) resulted in a statistically

significant reduction in fracture toughness. In the remaining five regimens,

10

changes in fracture toughness were not statistically significant. In this study,

bovine tooth sections were immersed entirely in bleaching agents; this is never

the case in clinical conditions. If the results had shown a significant reduction

in fracture toughness, the results would have been questioned because the test

conditions were too severe. However, since the results showed non-significant

reduction in fracture toughness, then in clinical conditions we would be more

confident that the bleaching procedures were unlikely to affect fracture

toughness. It is, however, the nature of laboratory and animal studies that

extrapolation to clinical conditions in humans would not be entirely

appropriate (Attin et al. 2004). Another in vitro study with more clinically

simulated conditions also substantiated the non-significant effect of bleaching

on fracture toughness (White et al. 2003). Regarding non-vital bleaching and

fractures, up to the present there has not been any literature available.

Restorative procedures

Historically, endodontically treated teeth were indiscriminately restored with a

crown to prevent subsequent fractures, and a post to reinforce root strength.

This rationale has been challenged by the study of Sorensen and Martinoff in

1984. It was a retrospective cohort study that demonstrated non-significant

differences in failure rate (as measured by the number of fractured teeth,

restoration dislodgement, and teeth with symptoms) of endodontically treated

teeth with and without post placement. The studied also showed the non-

significant difference in failure rate of endodontically treated incisors with and

11

without a crown. In other words, a post did not reduce the chance of fracture

(did not reinforce roots); a crown reduced the chance of fractures but only in

posterior teeth. A review article of contemporary endodontic and

prosthodontic literature concluded that 1) preservation of tooth structure was a

key of fracture resistance; 2) posts should not be used with the intention of

reinforcing the tooth; 3) review of functional and parafunctional forces must be

undertaken before restoring the tooth, as these will influence the prognosis

(Fernandes et al. 2001; Stockton et al. 1998).

Posts could not reinforce the roots, not only that, they even have been

implicated as a cause of VRF in contemporary endodontic literature (Fuss et al.

2001; Morfis 1990). One hundred and fifty four endodontically treated teeth

that had been extracted because of VRF have been studied (Fuss et al. 2001). In

their subjects, a post was present in the canal more frequently (1.5 times) than

without. The authors concluded that post placement and root canal treatment

are the major etiological factors for root fractures. The fact that posts were

present more frequently did not necessarily mean that posts cause fractures.

40% of their subjects demonstrated VRF even though post was not present.

This study is a cross sectional survey, which is lower than Sorensen and

Martinoff’s study (Sorensen et al. 1984) in the hierarchy of quality of evidence

(Sackett 2000). Therefore, the notion that “posts cause fracture” should be

balanced with Sorensen and Martinoff’s study that showed a non-significant

difference in failure rate of teeth restored with and without a post. It would

12

have strengthened the study of Fuss et al in 2001, if the control group (root

treated teeth without VRF) had been included and exposure (post placement)

had been examined, then an odds ratio could have been calculated. An

association of post placement and VRF, if any were found, would then be more

convincing.

Since 1984 numerous materials and designs of post have been introduced; some

systems utilizing a dentine-bonding system to reinforce the roots were of

interest. Most of the studies regarding these new materials and designs in

relation to VRF are laboratory experiments; therefore, quality of the evidence is

not as good as a clinical study. One retrospective cohort study was conducted

on teeth restored with Composipost system (carbon fiber post cemented with

resin cement) and cast post and cores as a control group (Ferrari et al. 2000).

Two hundred patients were selected and divided equally into two groups. The

patients were recalled after 6 months, 1, 2 and 4 yrs and clinical and

radiographic examinations were completed. The results showed no root

fracture in the Composipost group, whereas cast post showed 9% root fracture.

This study indicated that the Composipost system was superior to the

conventional cast post and core system after 4 yrs of clinical service. Another

two case series studies (n=180, 59) also substantiated the abovementioned study

by reporting the low clinical failure rate of carbon fiber posts (2-8%), though

their follow up periods were quite short (30 months) (Glazer 2000; Malferrari et

al. 2003).

13

Preparation of a post space adds a certain risk of VRF to a tooth, especially if an

oversized post channel is prepared. It is generally accepted, though without

any scientific verification, that post space preparation should not leave the

dentinal canal wall thinner than 1mm (Gutmann 1992; Raiden et al. 1999),

otherwise the tooth might be notoriously prone to VRF. It is logical to expect

that the thinner the dentine, the more likely the tooth is to fracture (Wilcox et al.

1997). Remaining dentine thickness attracts much interest but with little clinical

value because dentine thickness is difficult to determine clinically. Besides

dentine thickness, two more factors have also been proposed to potentially

influence fracture susceptibility i.e. radius of canal curvature and external root

morphology (Lertchirakarn et al. 2003). A low radius of canal curvature can act

as a stress raiser area (Callister 2003), which makes the root more susceptible to

fracture. External root morphology has also been shown with finite element

analysis (FEA) to be a strong determinant of fracture direction (Lertchirakarn et

al. 2003). The effects of these three factors have been studied primarily on

geometrically simple FEA models, which do not necessarily reflect actual root

shape. The clinical picture is, however, probably much more complex. It is part

of this study objective to study the effects of those three factors (i.e. dentine

thickness, radius of canal curvature, and external proximal root surface

concavity) in FEA models that are much more clinically simulated (Chapter 4).

Management

Up to the present, the only predictable management of VRF has been extraction

or root amputation. There have been, however, efforts to manage VRF

14

conservatively. Two case reports have involved attempts to seal the fracture

line with adhesive resin then replanted and intentionally rotated the tooth 180

degrees in order to avoid contact with the area where the alveolar bone and

PDL of the root surface was lost along the fracture line. The tooth was still

functional after 18 months, the authors, however, did not report specific details

of periodontal status. (Kawai & Masaka 2002; Kudou et al. 2003). A variation of

conservative VRF management has also been attempted. Glass ionomer was

used to bond the fracture fragments instead of adhesive resin as in

abovementioned method; guided tissue regeneration technique was also

employed. The tooth was clinically and radiographically within normal limits

after one year (Trope & Rosenberg 1992). Heroic efforts were made in another

study (Selden 1996) involving complicated and multi-stepped procedures i.e.

surgical procedure incorporated ultrasonic fracture cleaning, bonding of the

fracture repair with silver glass-ionomer cement, placement of a bone graft

material, and application of guided-tissue regeneration. One-year review

showed a very unfavourable outcome.

Fracture related biomechanical properties of dentine

There are many technical difficulties in testing, measurement and comparison

of biomechanical properties of dentine. For example, storage media and storage

time have never been standardized. They can influence measurement, making

comparison between studies virtually impossible. Small sizes of specimens

obtainable and the shape complexity make them particularly difficult to be

tested. In some studies, a small number of samples were tested; meaningful

15

information was, therefore, unlikely because of the lack of statistical power. To

complicate the matter further, values of a single mechanical property are

different within various locations of a single tooth. Taking all these difficulties

together, it is not surprising to see a large range of values of mechanical

properties.

Moisture content

The reduction of moisture content in endodontically treated teeth is an often-

quoted reason for their increased fracture susceptibility (Johnson et al. 1976;

Wagnild et al. 2002). The moisture content of endodontically treated teeth was

studied and shown to be 9% less than vital teeth (Helfer et al. 1972). This study

is based on teeth obtained from only one dog, the 9% percent difference was

attributable to loss of free water. Their findings were questionable, since teeth

were stored in saliva before analysis of water content. Also, the study did not

show a progressive loss of moisture with increasing time after pulp extirpation.

A subsequent study has failed to confirm these Helfer et al’s results (Papa et al.

1994). Matched pairs of contralateral human teeth, endodontically treated teeth

and vital teeth, were compared. Their moisture contents were not statistically

significantly different.

Hardness

Hardness tests measure a material’s resistance to deformation caused by surface

indentation or abrasion (Anusavice 1996). It has been shown that the hardness

values decreased in dentine closer to the pulp (Pashley et al. 1985); the authors

16

concluded that the reduction in hardness was a result of the increased tubule

density or dentine porosity. This conclusion, however, was challenged by

subsequent study (Kinney et al. 1996). Using atomic force microscopy and

nano-indentation techniques, Kinney and coworkers were able to demonstrate

that most, if not all, of the decreased hardness is a result of decreased hardness

of intertubular dentine. They reported hardness of intertubular dentine in the

range of 0.51GPa near DEJ and 0.12GPa near the pulp whereas the higher value

of peritubular dentine (2.54GPa) was site-independent. Because dentine

hardness depends on mineral concentration (Featherstone et al. 1983), it is

highly likely that the intertubular dentine near the pulp is less mineralized. It is

very tempting to try to relate dentine hardness to other physical properties such

as tensile strength or Young’s modulus. In ductile materials, the tensile

strengths are often observed to scale with hardness, because they derived from

plasticity theory for materials that display significant yielding. However,

mineralized tissues are more brittle, showing little if any yielding prior to

failure.

Young’s modulus

Initially, Young’s modulus of dentine was not found to be affected by tooth

type and age (Tyldesley 1959). More recent reports showed that it is different

even in the same tooth at different distances from the DEJ. The Young’s

modulus of dentine tends to decrease with increasing distance from the DEJ

toward the pulp (Kinney et al. 1996; Meredith et al. 1996) i.e. site dependent.

Young’s modulus of vital and non-vital dentine has been investigated; a

17

statistically significant difference between those two has never been

demonstrated (Huang et al. 1992; Standford et al. 1960)

Ultimate strength

Information regarding ultimate strength of dentine consists of three types i.e.

tensile, compressive and shear. For dentine specimens failing in tension, the

ultimate strength is in the area of 52 MPa (Bowen et al. 1962) to 105 MPa (Sano et

al. 1994). These large differences are likely to be the result of flaws in

specimens, since surface smoothening can increase strength (Sano et al. 1994).

Furthermore, measurements of compressive strength, which are less likely to be

affected by flaws, were more consistent. Values of compressive strength

ranging from 275 to 300 MPa have been reported (Craig et al. 1958). The

compressive strength of root dentine was found to be lower than that of coronal

dentine (Standford et al. 1960). When dentine specimens are placed under

compressive load until fracture, dentine behaves in an isotropic manner

(Standford et al. 1960; Tyldesley 1959; Watts et al. 1987). That is, the fracture of

dentine under compressive forces occurs along the line of maximum stress and

is not related to tubule orientation, while fracture under tensile load appears to

be in an anisotropic manner (Lertchirakarn et al. 2001), with greater maximum

tensile strength in a direction parallel to tubule direction.

The values of shear strength of dentine are highly variable, reflecting

inconsistency and the lack of measurement standardization. A preliminary

study reported shear strength in the range of 69-147MPa (Roydhouse 1970).

18

Later on those results and measurement techniques have been questioned due

to differing punch sizes and specimen thickness (Marshall et al. 1997). A recent

study using more accurate single plane lap shear testing has reported the shear

strength of dentine at 36.2MPa (Gwinnett 1994); this low value may have been

due to the specimens having been from dentine closer to the pulp, or to

problems with the experimental design, or with bending of the specimen. The

more recent study showed that the disparity in reported values of the shear

strength could be attributed to tubule orientation and location within the tooth

(Watanabe et al. 1996) i.e. dentine behaves in an anisotropic manner under shear

force. The large standard deviations found in ultimate strength of dentine

imply that the strength might be controlled by some factors that could not be

detected in the tests.

Fracture mechanics

Fracture mechanics is an engineering discipline dealing with how and why

fractures occur, and ultimately, how to prevent or at least minimize the chance

of fracture occurring. To be able to understand this field, certain terms and

definitions need to be clarified.

Stress

It is a measure of how hard the atoms and molecules, which make up the

material are being pushed together or pulled apart as a result of external forces.

Numerically, the stress in any direction at a given point in a material is simply

the force or load which happens to be acting in that direction at the point,

19

divided by the area on which the force acts (Ashby et al. 1996).

Stress=load/area, s=P/A. Stress units are MN/m2.

Stress vs. Strength

The strength of a material is the stress required to break a piece of the material

itself. We are most often concerned with the tensile strength of materials, which

is sometimes called the ‘ultimate tensile strength’. It is the maximum stress that

can be sustained by a material in tension (Callister 2003). In the dental

literature, strength values are often heavily relied upon as predictors of

structural performance of materials. Strength, however, is more of a

“conditional” than an intrinsic material property, and strength data alone

cannot be directly extrapolated to predict structural performance. Strength data

are informative only when placed into context via knowledge of material

testing methodology, testing environment and failure mechanism. Structural

failure is determined by additional failure probability variables (in concert with

strength) that describe stress distributions and flaw size distributions in

specimens. Variations in the flaw size lead to variation in the failure strength.

Specimens with large flaws will fail at lower stresses than will specimens

containing smaller flaws. Grinding and polishing of many glasses and ceramics

can introduce a layer of compressive stress, which “strengthens” the material.

Such strengthening by grinding has also been demonstrated for a number of

dental ceramics (Giordano et al. 1995) removal of the outer 50-100 µm

“ceramming skin” has been shown to increase the strength of a glass-ceramic

crown material, due to removal of flaws unique to this layer of ceramic

20

(Campbell et al. 1989). Understanding of actual clinical failure modes is

absolutely necessary before results of in vitro strength testing can be considered

to have clinical validity.

Strain

Stress tells us how hard-that is, with how much force-the atoms at any point in

a solid are being pulled apart, while strain tells us how far they are being pulled

apart-that is, by what proportion the bonds between the atoms are stretched

(Gordon 1991b). Materials respond to stress by straining i.e. changing their

dimension, shape or length. Thus, if a rod which has an original length L is

caused to stretch by an amount l by the action of a force on it, strain in the rod

will be e, so e=l/L. Strain is a ratio, which is to say a number, and it has no units.

Young’s modulus

Young’s modulus is sometimes called ‘the elastic modulus, and is quite often

spoken of as ‘stiffness’. It provides information on the amount of deformation

that will occur in a material under load i.e. the more the deformation of the

material under a specified load is, the lower the value of Young’s modulus.

Low modulus materials are “floppy” and deflect a lot when they are loaded.

The formal equation for calculating Young’s modulus is stress/strain. As we

are dividing stress by a fraction, which is to say a number, which has no

dimensions, Young’s modulus has the same dimensions as a stress and is

expressed in stress units, i.e. MN/m2.

21

Fracture toughness

It expresses the ability of a material to resist fracture in the presence of cracks

(Gdoutos 1993). It can also be defined as the energy absorbed in making a unit

area of crack surface. Its units are energy m-2 or Jm-2. A high toughness means

that it is hard to make a crack propagate.

Mode of Fracture

The fracture may be roughly classified as brittle and ductile. The classification

is based on the ability of a material to experience plastic deformation (Callister

2003). Any fracture process involves two steps -crack formation and

propagation- in response to an imposed stress. The mode of fracture is highly

dependent on the mechanism of crack propagation (Ashby & Jones 1996).

Brittle fracture

Brittle fracture is associated with low energy and high fracture velocities

(Gdoutos 1993). Cracks may spread extremely rapidly, with very little

accompanying plastic deformation. Very little plastic deformation takes place

at crack tips in brittle materials. The direction of crack motion is nearly

perpendicular to the direction of the applied stress and yields a relatively flat

fracture surface. The fracture surface is rather featureless, with a flat surface

suggesting little or no plastic deformation. Such cracks may be said to be

unstable, and crack propagation, once started, will continue spontaneously

without an increase in magnitude of the applied stress (Callister 2003).

22

Ductile fracture

Ductile fracture is associated with large deformations, high-energy dissipation

rates and slow fracture velocities. (Gdoutos 1993). This mode of fracture is

characterized by extensive plastic deformation in the vicinity of an advancing

crack. The plastic flow at the crack tip naturally turns an initially sharp crack

into a blunt crack, and it turns out from the stress mathematics that this crack

blunting decreases local stresses so that, at the crack tip itself, local stress is just

sufficient to keep on plastically deforming. Furthermore, the process proceeds

relatively slowly as the crack length is extended. Crack growth in this way

consumes a lot of energy by plastic flow; the bigger the plastic zone, the more

energy is absorbed. Such a crack is often said to be stable. That is, it resists any

further extension unless there is an increase in the applied stress. In addition,

there will ordinarily be evidence of appreciable gross deformation at the

fracture surfaces (e.g., twisting and tearing). The fracture surface is extremely

rough, indicating that a great deal of plastic work has taken place (Callister

2003).

Why do fractures occur below a material’s ultimate tensile

strength?

It was realized that the results of laboratory tensile tests could not be

extrapolated to predict fracture behaviour (Anderson 1995).

23

Fatigue failure

It was first realized in the middle of the nineteenth century that engineering

components often fail when subjected to repeated fluctuating loads whose

magnitude is well below the critical load under monotonic loading. Early

investigation was primarily concerned with axle and bridge failures which

occurred at cyclic load levels less than half their corresponding monotonic load

magnitudes. Failure due to repeated loading was called “fatigue failure”

(Gdoutos 1993). This concept has recently been implemented in dental research

(Butz et al. 2001; Pontius et al. 2002; Strub et al. 2001) and has made a laboratory

experiment more clinically simulated, in contrast to monotonic loading or

“crunch crown” test (Kelly 1995), which gives very little information of clinical

performance of material.

Crack, flaw size concept

People put the grooves in slabs of chocolate, in order to separate them more

easily. Almost any geometrical irregularities, such as holes and cracks and

sharp corners in an otherwise continuous solid may raise the local stress very

dramatically. Holes and notches may cause the stress in their immediate

vicinity to be much higher than the breaking stress of the material, even when

the general level of stress in the surrounding neighborhood is low (Gordon

1991a).

It was demonstrated in experiments that the longer a metal wire, the lower the

load it could sustain. The plausible explanation to these results is that all

24

structural materials contain flaws, which have a deteriorating effect on the

strength of the material. The larger the volume of the material tested, the

higher the possibility that flaws exist, which reduce the material strength.

The fracture strength of a solid material is a function of the cohesive forces that

exist between atoms. On this basis, the theoretical cohesive strength of a brittle

elastic solid has been estimated to be approximately E/10, where E is the

modulus of elasticity. The experimental fracture strengths of most materials

normally lie between 10 and 1000 times below this theoretical value. In the

1920s, A. A. Griffith proposed that this discrepancy between theoretical

cohesive strength and observed fracture strength could be explained by the

presence of very small, microscopic flaws or cracks that always exist under

normal conditions at the surface and within the interior of a body of material

(Griffith 1920). These flaws are a detriment to the fracture strength because an

applied stress may be amplified or concentrated at the tip, the magnitude of this

amplification depending on crack orientation and geometry. This phenomenon

is demonstrated in the figures below.

25

(a) Showing geometry of flaw or crack in relation to material as a whole.

(b) Showing a stress profile across a cross section containing an internal crack.

As indicated by this profile, the magnitude of this localized stress diminishes

with distance away from the crack tip. At positions far removed, the stress is

equal to the nominal stress σ0 or the applied load divided by the specimen

cross-sectional area (perpendicular to this load). Due to their ability to amplify

an applied stress in their locale, these flaws are sometimes called stress raisers.

If it is assumed that a crack has an elliptical shape (or is circular) and is oriented

perpendicular to the applied stress, the maximum stress at the crack tip, σm is

equal to

+=

2/1

21

t

om

a

ρσσ

26

where σ0 is the magnitude of the nominal applied tensile stress, ρt is the radius

of curvature of the crack tip, and a represents the length of a surface crack, or

half of the length of an internal crack. For a relatively long microcrack that has

a small tip radius of curvature, the factor (a/ρt)1/2 may be very large (certainly

much greater than unity); under these circumstances takes the form

2/1

2

=

t

om

a

ρσσ

Furthermore, σm will be many times the value of σ0. Sometimes the ratio σm /σ0

is denoted as the stress concentration factor Kt:

2/1

0

2

==

t

m

t

aK

ρσσ

which is simply a measure of the degree to which an external stress is amplified

at the tip of a crack.

It should be noted that stress amplification is not restricted to these microscopic

defects; it may occur at macroscopic internal discontinuities (e.g., voids), at

sharp corners, and at notches in large structures. In relation to endodontics,

these defects could be canal irregularities, fins, or anything that interrupts the

smooth flow of structural geometry, even the oval shape of a canal cross section

of a premolar could be considered a mega-flaw.

27

The effect of a stress raiser is more significant in brittle than in ductile materials.

For a ductile material, plastic deformation ensues when the maximum stress

exceeds the yield strength. This leads to a more uniform distribution of stress

in the vicinity of the stress raiser and to the development of a maximum stress

concentration factor less than the theoretical value. Such yielding and stress

redistribution do not occur to any appreciable extent around flaws and

discontinuities in brittle materials; therefore, essentially the theoretical stress

concentration will result. It was proposed that all brittle materials contain a

population of small cracks and flaws that have a variety of sizes, geometries,

and orientations. Fracture will result when, upon application of a tensile stress,

the theoretical cohesive strength of the material is exceeded at the tip of one of

these flaws. This leads to the formation of a crack that then rapidly propagates.

If no flaws were present, the fracture strength would be equal to the cohesive

strength of the material. Very small and virtually defect-free metallic and

ceramic whiskers have been grown with fracture strengths that approach their

theoretical values.

Crack arrest

Crack in a uniform tensile stress field continues to move because the energy is

constantly supplied to crack tip region. On the other hand, crack growth under

constant displacement conditions eventually leads to crack arrest, since the

energy supplied to the crack tip region progressively decreases with time.

28

Fracture prediction

To predict fractures or structural failures, fracture toughness, applied load,

material strength, crack size and structural geometry are all essential pieces of

information. Strength of material is one of several fracture determining factors.

The study of stress and fracture

A number of techniques have been utilized to study stresses in the hope of

relating it to fracture susceptibility. These techniques consist of experimental,

theoretical and numerical methods (Darbar et al. 1994).

Experimental method

It involves loading roots to the point of fracture using a servohydraulic testing

machine. Given the large variation of root shape, size and also canal shape,

size, the information regarding fracture susceptibility can be very difficult to

detect statistically unless the sample size is unrealistically large. Furthermore,

effects of root shape, size and canal shape, size on fracture susceptibility would

be impossible to study unless roots and canals with an exact morphology that

we want to study are available.

Theoretical method

It uses engineering theory and eliminates the need for direct experimental

measurements. Photoelastic stress analysis is one of these methods and it can

provide visual evidence of stress concentration areas within the model.

Photoelastic method involves construction of a model of the structure to be

investigated from a photoelastic material. The model preparation for this

29

method is arduous since it is critical that the model is of uniform thickness.

Moreover, if a number of roots with different morphology were needed for the

study, it would be laborious and costly to create every single model needed for

analysis. Additionally, gathering magnitude of tensile stress can be lengthy and

demanding because special equipment and expertise are needed, yet data is not

very accurate.

Numerical method

Stress concentration area and magnitude of 3-dimensional geometrical shapes,

which are subjected to mechanical load, can be calculated using mathematical

methods. This calculation method cannot apply to complex structures, which

are usually found in nature. Finite element analysis (FEA) is a computerized

numerical method for solving complex problems by dividing complex

structures (non-geometrical shape e.g. tooth) into many small-interconnected

simple structures (geometrical shape), which are called finite elements. The

stress concentration area and magnitude of each element that subject to

mechanical load are then calculated and are hooked together afterward. The

results are the estimated calculation of thousands and thousands of small

elements. In essence, it gives us an idea of where stress concentration areas are

located and how high the stress is. The FEA results can then be used to predict

fracture patterns and also fracture susceptibility. Changes of relevant

parameters such as root shape and loads can be easily incorporated into the

calculation and hence conducting the analysis and assimilating the results is

quicker than the photoelastic analysis. With this method, we can concentrate on

30

the objective of the analysis, specifying the different loads and conditions, and

then obtain answers that normally would have required a prototype or real

model (Brauer 1988). Because computer models are the result of estimation of

many parameters, it is a nature of this method that validation is necessary to

make computer models more convincing. It is also part of this study objective

to validate FEA models (Chapter 3).

Aims

The objectives of this study were (a) to determine whether rotary NiTi canal

preparations strengthen roots; (b) to determine whether the observed fracture

load and pattern could be predicted from the FEA models; (c) to determine to

what extent the prepared root canal diameter will influence fracture

susceptibility and pattern or fracture; (d) to determine the extent to which a

concavity on the external proximal root surface will change fracture

susceptibility and pattern.

31

References

Anderson TL (1995) Fracture mechanics : fundamentals and applications, 2nd edn. Boca Raton: CRC Press.

Andreasen JO, Farik B, Munksgaard EC (2002) Long-term calcium hydroxide as a root canal dressing may increase risk of root fracture Dental Traumatology. 18, 134-7.

Anusavice KJ (1996) Physical properties of dental materials. In KJ Anusavice, RW Phillips eds. Phillips' Science of Dental Materials., 10th edn; pp. 33-74. Philadelphia: W.B.Saunders.

Ashby MF, Jones DRH (1996) Engineering materials, 2nd edn. Oxford:

Butterworth-Heinemann.

Attin T, Muller T, Patyk A, Lennon AM (2004) Influence of different bleaching systems on fracture toughness and hardness of enamel Operative Dentistry 29, 188-95.

Beling KL, Marshall JG, Morgan LA, Baumgartner JC (1997) Evaluation for cracks associated with ultrasonic root-end preparation of gutta-percha filled canals Journal of Endodontics 23, 323-6.

Bender IB, Freedland JB (1983) Adult root fracture Journal of American Dental

Association 107, 413-9.

Bowen RL, Rodriguez MM (1962) Tensile strength and modulus of elasticity of tooth structure and several restorative materials. Journal of American Dental

Association 64, 378-87.

Brauer JR (1988) What every engineer should know about finite element analysis New York: M. Dekker.

Bryant ST, Thompson SA, al-Omari MA, Dummer PM (1998) Shaping ability of Profile rotary nickel-titanium instruments with ISO sized tips in simulated root canals: Part 1 International Endodontic Journal 31, 275-81.

Butz F, Lennon AM, Heydecke G, Strub JR (2001) Survival rate and fracture strength of endodontically treated maxillary incisors with moderate defects restored with different post-and-core systems: an in vitro study International Journal of Prosthodontics 14, 58-64.

Callister WD (2003) Failure. In WD Callister ed. Materials science and engineering : an introduction, 6th edn; pp. 192-245. New York ; [Chichester]: Wiley.

Campbell SD, Kelly JR (1989) Influence of surface preparation on the strength and surface microstructure of a cast dental ceramic International Journal of Prosthodontics 2, 459-66.

32

Chan CP, Lin CP, Tseng SC, Jeng JH (1999) Vertical root fracture in endodontically versus nonendodontically treated teeth: a survey of 315 cases in Chinese patients. Oral Surgery, Oral Medicine, Oral Pathology, Oral Radiology and Endodontics 87, 504-7.

Chan CP, Tseng SC, Lin CP, Huang CC, Tsai TP, Chen CC (1998) Vertical root fracture in nonendodontically treated teeth--a clinical report of 64 cases in Chinese patients Journal of Endodontics 24, 678-81.

Craig RG, Peyton FA (1958) Elastic and mechanical properties of human dentin. Journal of Dental Research 37, 710-8.

Cvek M (1992) Prognosis of luxated non-vital maxillary incisors treated with calcium hydroxide and filled with gutta-percha. A retrospective clinical study Endodontics & Dental Traumatology 8, 45-55.

Dammaschke T, Steven D, Kaup M, Ott KH (2003) Long-term survival of root-canal-treated teeth: a retrospective study over 10 years Journal of Endodontics. 29,

638-43.

Darbar UR, Huggett R, Harrison A (1994) Stress analysis techniques in complete dentures Journal of Dentistry 22, 259-64.

Eriksen HM (1991) Endodontology--epidemiologic considerations Endodontics & Dental Traumatology 7, 189-95.

Featherstone JD, ten Cate JM, Shariati M, Arends J (1983) Comparison of artificial caries-like lesions by quantitative microradiography and microhardness profiles Caries Research 17, 385-91.

Fernandes AS, Dessai GS (2001) Factors affecting the fracture resistance of post-core reconstructed teeth: a review International Journal of Prosthodontics 14, 355-63.

Ferrari M, Vichi A, Garcia-Godoy F (2000) Clinical evaluation of fiber-reinforced epoxy resin posts and cast post and cores American Journal of Dentistry 13, 15B-8B.

Frank RJ, Antrim DD, Bakland LK (1996) Effect of retrograde cavity preparations on root apexes Endodontics & Dental Traumatology 12, 100-3.

Fuss Z, Lustig J, Katz A, Tamse A (2001) An evaluation of endodontically treated vertical root fractured teeth: impact of operative procedures. Journal of Endodontics 27, 46-8.

Fuss Z, Lustig J, Tamse A (1999) Prevalence of vertical root fractures in extracted endodontically treated teeth. International Endodontic Journal 32, 283-6.

33

Gdoutos EE (1993) Fracture mechanics : an introduction Dordrecht ; Boston: Kluwer Academic Publishers.

Gher ME, Jr., Dunlap RM, Anderson MH, Kuhl LV (1987) Clinical survey of fractured teeth [published erratum appears in J Am Dent Assoc 1987 May;114(5):584] Journal of the American Dental Association 114, 174-7.

Giordano R, Cima M, Pober R (1995) Effect of surface finish on the flexural strength of feldspathic and aluminous dental ceramics International Journal of Prosthodontics 8, 311-9.

Glazer B (2000) Restoration of endodontically treated teeth with carbon fibre posts--a prospective study Journal of the Canadian Dental Association 66, 613-8.

Glossen CR, Haller RH, Dove SB, del Rio CE (1995) A comparison of root canal preparations using Ni-Ti hand, Ni-Ti engine-driven, and K-Flex endodontic instruments Journal of Endodontics 21, 146-51.

Gordon JE (1991a) Designing for safety. In JE Gordon ed. Structures or Why

things don't fall down.; pp. 60-9. London: Penguin Book.

Gordon JE (1991b) The invention of stress and strain. In JE Gordon ed. Structures or Why things don't fall down.; pp. 45-59. London: Penguin Book.

Griffith AA (1920) The Phenomena of Rupture and Flow in Solids. Philosophical Transactions 221, 163-98.

Gutmann JL (1992) The dentin-root complex: anatomic and biologic considerations in restoring endodontically treated teeth Journal of Prosthetic Dentistry 67, 458-67.

Gwinnett AJ (1994) A new method to test the cohesive strength of dentin Quintessence International 25, 215-8.

Helfer AR, Melnick S, Schilder H (1972) Determination of the moisture content of vital and pulpless teeth Oral Surgery, Oral Medicine, Oral Pathology 34, 661-70.

Huang TJ, Schilder H, Nathanson D (1992) Effects of moisture content and endodontic treatment on some mechanical properties of human dentin Journal of Endodontics 18, 209-15.

Johnson JK, Schwartz NL, Blackwell RT (1976) Evaluation and restoration of endodontically treated posterior teeth Journal of the American Dental Association 93, 597-605.

Kawai K, Masaka N (2002) Vertical root fracture treated by bonding fragments and rotational replantation Dental Traumatology. 18, 42-5.

Kelly JR (1995) Perspectives on strength Dental Materials 11, 103-10.

34

Kinney JH, Balooch M, Marshall SJ, Marshall GW, Jr., Weihs TP (1996) Hardness and Young's modulus of human peritubular and intertubular dentine Archives of Oral Biology 41, 9-13.

Kudou Y, Kubota M (2003) Replantation with intentional rotation of a complete vertically fractured root using adhesive resin cement Dental Traumatology. 19, 115-7.

Layton CA, Marshall JG, Morgan LA, Baumgartner JC (1996) Evaluation of cracks associated with ultrasonic root-end preparation Journal of Endodontics 22, 157-60.

Lertchirakarn V, Palamara JE, Messer HH (1999) Load and strain during lateral condensation and vertical root fracture Journal of Endodontics 25, 99-104.

Lertchirakarn V, Palamara JE, Messer HH (2001) Anisotropy of tensile strength of root dentin Journal of Dental Research 80, 453-6.

Lertchirakarn V, Palamara JE, Messer HH (2003) Patterns of vertical root fracture: factors affecting stress distribution in the root canal Journal of Endodontics 29, 523-8.

Lin CP, Chou HG, Chen RS, Lan WH, Hsieh CC (1999) Root deformation during root-end preparation. Journal of Endodontics 25, 668-71.

Lindauer PA, Campbell AD, Hicks ML, Pelleu GB (1989) Vertical root fractures in curved roots under simulated clinical conditions Journal of Endodontics 15, 345-9.

Malferrari S, Monaco C, Scotti R (2003) Clinical evaluation of teeth restored with quartz fiber-reinforced epoxy resin posts International Journal of Prosthodontics 16, 39-44.

Marshall GW, Jr., Marshall SJ, Kinney JH, Balooch M (1997) The dentin substrate: structure and properties related to bonding Journal of Dentistry 25, 441-58.

Maxwell EH, Braly BV, Eakle WS (1986) Incompletely fractured teeth--a survey of endodontists Oral Surgery, Oral Medicine, Oral Pathology 61, 113-7.

Meredith N, Sherriff M, Setchell DJ, Swanson SA (1996) Measurement of the microhardness and Young's modulus of human enamel and dentine using an indentation technique Archives of Oral Biology 41, 539-45.

Morfis AS (1990) Vertical root fractures Oral Surgery, Oral Medicine, Oral Pathology 69, 631-5.

35

Navarre SW, Steiman HR (2002) Root-end fracture during retropreparation: a comparison between zirconium nitride-coated and stainless steel microsurgical ultrasonic instruments Journal of Endodontics. 28, 330-2.

Papa J, Cain C, Messer HH (1994) Moisture content of vital vs endodontically treated teeth Endodontics & Dental Traumatology 10, 91-3.

Pashley D, Okabe A, Parham P (1985) The relationship between dentin microhardness and tubule density Endodontics & Dental Traumatology 1, 176-9.

Peters DD, Lorton L, Mader CL, Augsburger RA, Ingram TA (1983) Evaluation of the effects of carbon dioxide used as a pulpal test. 1. In vitro effect on human enamel Journal of Endodontics 9, 219-27.

Peters DD, Mader CL, Donnelly JC (1986) Evaluation of the effects of carbon dioxide used as a pulpal test. 3. In vivo effect on human enamel Journal of Endodontics 12, 13-20.

Pontius O, Hutter JW (2002) Survival rate and fracture strength of incisors restored with different post and core systems and endodontically treated incisors without coronoradicular reinforcement Journal of Endodontics. 28, 710-5.

Portenier I, Lutz F, Barbakow F (1998) Preparation of the apical part of the root canal by the Lightspeed and step-back techniques International Endodontic Journal 31, 103-11.

Raiden G, Costa L, Koss S, Hernandez JL, Acenolaza V (1999) Residual thickness of root in first maxillary premolars with post space preparation. Journal of Endodontics 25, 502-5.

Reeh ES, Messer HH, Douglas WH (1989) Reduction in tooth stiffness as a result of endodontic and restorative procedures Journal of Endodontics 15, 512-6.

Roydhouse RH (1970) Punch-shear test for dental purposes Journal of Dental

Research 49, 131-6.

Sackett D (2000) Evidence based medicine : how to practice and teach EBM, 2nd edn. Edinburgh: Churchill Livingstone.

Sano H, Ciucchi B, Matthews WG, Pashley DH (1994) Tensile properties of mineralized and demineralized human and bovine dentin Journal of Dental Research 73, 1205-11.

Saunders WP, Saunders EM, Gutmann JL (1994) Ultrasonic root-end preparation, Part 2. Microleakage of EBA root-end fillings International Endodontic Journal 27, 325-9.

Saw LH, Messer HH (1995) Root strains associated with different obturation techniques Journal of Endodontics 21, 314-20.

36

Selden HS (1996) Repair of incomplete vertical root fractures in endodontically treated teeth--in vivo trials Journal of Endodontics. 22, 426-9.

Silman AJ, Macfarlane GJ (2002) Epidemiological studies : a practical guide, 2nd / edn. Cambridge: Cambridge University Press.

Sim TP, Knowles JC, Ng YL, Shelton J, Gulabivala K (2001) Effect of sodium hypochlorite on mechanical properties of dentine and tooth surface strain. International Endodontic Journal 34, 120-32.

Sorensen JA, Martinoff JT (1984) Intracoronal reinforcement and coronal coverage: a study of endodontically treated teeth Journal of Prosthetic Dentistry 51, 780-4.

Standford JW, Weigel KV, Paffenbarger GC, Sweeney WT (1960) Compressive properties of hard tooth tissues and some restorative materials. Journal of American Dental Association 60, 746-56.

Stockton L, Lavelle CL, Suzuki M (1998) Are posts mandatory for the restoration of endodontically treated teeth? Endodontics & Dental Traumatology 14, 59-63.

Strub JR, Pontius O, Koutayas S (2001) Survival rate and fracture strength of incisors restored with different post and core systems after exposure in the artificial mouth Journal of Oral Rehabilitation 28, 120-4.

Tamse A (1988) Iatrogenic vertical root fractures in endodontically treated teeth Endodontics & Dental Traumatology 4, 190-6.

Tan BT, Messer HH (2002) The quality of apical canal preparation using hand and rotary instruments with specific criteria for enlargement based on initial apical file size Journal of Endodontics. 28, 658-64.

Telli C, Gulkan P (1998) Stress analysis during root canal filling by vertical and lateral condensation procedures: a three-dimensional finite element model of a maxillary canine tooth British Dental Journal 185, 79-86.

Testori T, Badino M, Castagnola M (1993) Vertical root fractures in endodontically treated teeth: a clinical survey of 36 cases Journal of Endodontics 19, 87-91.

Thompson SA, Dummer PM (1997) Shaping ability of ProFile.04 Taper Series 29 rotary nickel-titanium instruments in simulated root canals. Part 1 International Endodontic Journal 30, 1-7.

Trope M, Rosenberg ES (1992) Multidisciplinary approach to the repair of vertically fractured teeth Journal of Endodontics 18, 460-3.

37

Tyldesley WR (1959) The mechanical properties of human enamel and dentine. British Dental Journal 106, 269-78.

Vire DE (1991) Failure of endodontically treated teeth: classification and evaluation Journal of Endodontics 17, 338-42.

Wagnild GW, Mueller KI (2002) Restoration of the Endodontically Treated Tooth. In S Cohen, RC Burns eds. Pathways of the pulp, 8th edn; pp. 765-95. St. Louis ; London: Mosby.

Walton RE (2002) Longitudinal Tooth Fractures. In RE Walton, M Torabinejad eds. Principles and practice of endodontics, 3th edn; pp. 513-18. Philadelphia: Saunders.

Watanabe LG, Marshall GW, Jr., Marshall SJ (1996) Dentin shear strength: effects of tubule orientation and intratooth location Dental Materials 12, 109-15.

Watts DC, el Mowafy OM, Grant AA (1987) Temperature-dependence of compressive properties of human dentin Journal of Dental Research 66, 29-32.

White DJ, Kozak KM, Zoladz JR, Duschner HJ, Gotz H (2003) Effects of Crest Whitestrips bleaching on surface morphology and fracture susceptibility of teeth in vitro Journal of Clinical Dentistry 14, 82-7.

Wilcox LR, Roskelley C, Sutton T (1997) The relationship of root canal enlargement to finger-spreader induced vertical root fracture Journal of Endodontics 23, 533-4.

Wu MK, van der Sluis LW, Wesselink PR (2004) Comparison of mandibular premolars and canines with respect to their resistance to vertical root fracture Journal of Dentistry 32, 265-8.

Yaman SD, Alacam T, Yaman Y (1995) Analysis of stress distribution in a vertically condensed maxillary central incisor root canal Journal of Endodontics

21, 321-5.

Yang SF, Rivera EM, Walton RE (1995) Vertical root fracture in nonendodontically treated teeth Journal of Endodontics 21, 337-9.

Yeh CJ (1997) Fatigue root fracture: a spontaneous root fracture in non-endodontically treated teeth British Dental Journal 182, 261-6.

38

Chapter 3: Article I Laboratory study and FEA verification

A Comparison of the Effects of Two Canal Preparation Techniques on Root Fracture Susceptibility and Fracture Pattern.

(A manuscript accepted for publication in the Journal of Endodontics)

39

Abstract

The aims of the study were to determine whether rotary NiTi canal preparation

strengthens roots, and whether the fracture pattern can be predicted by finite

element analysis (FEA) models. From a fracture mechanics viewpoint,

structural defects, cracks or canal irregularities are likely to play a major role in

fracture susceptibility of the roots, because stresses can be exponentially

amplified at these sites. By incorporating defects into a smooth round canal

using rotary NiTi, theoretically the roots could be strengthened. 25 teeth were

prepared using hand file and another 25 using rotary NiTi. After obturation, all

teeth were subject to loading until fracture; load and patterns were recorded.

Four FEA models were created from fractured roots. No significant difference

of fracture load between the two techniques was found. Mesio-distal fracture

occurred more often in the rotary NiTi group. Stress patterns in three of the

four FEA models correlated well with the observed fracture patterns.

40

Introduction

Vertical root fracture (VRF) is an important clinical problem leading to

extraction or root amputation. As its effects are catastrophic, many studies have

sought to identify the etiological factors of VRF, in an endeavor to improve its

prevention and management. It has been observed clinically that VRF occurs

commonly in endodontically treated teeth (1-3), and as a result, endodontic

procedures have been blamed as a frequent cause of VRF. Numerous

experimental studies have challenged this conclusion. Dentin of endodontically

treated teeth does not exhibit mechanical properties that are significantly

different from those of vital teeth; that is, dentin does not appear to become

more brittle (4, 5). It has been shown that access cavity preparation has non-

significant effects on tooth stiffness (6). The load generated during lateral

condensation is generally far lower than the load required to fracture the roots

(7, 8). Thus, obturation should not be regarded as a major cause of VRF except

in very weak roots. Canal preparation involves dentin removal and may

compromise the fracture strength of the roots; it is, therefore, another area that

has been studied as a potential cause of VRF (9).

With technological advancements, canal preparation techniques have evolved

rapidly in recent years. The introduction of rotary nickel-titanium (Ni-Ti)

instruments for canal preparation has changed canal shape, size and taper

compared to hand instrumentation. Canal shape after preparation with hand

files can be quite irregular (10, 11). From a fracture mechanics point of view,

41

the presence of structural defects, cracks or canal irregularities is likely to play a

major role in determining fracture strength (12), because an applied stress may

be exponentially amplified at the tip of those defects (13). With rotary NiTi

preparation, canal shapes are more likely to be rounder and smoother (14-16);

canal irregularities are likely to be incorporated into the preparation and

eliminated. Theoretically, smoothly tapering canals prepared using rotary Ni-

Ti should result in higher fracture strength. Patterns of VRF might also be

different with this new canal preparation technique. The aim of this study was

to determine whether rotary NiTi canal preparations strengthen the roots.

Finite element analysis (FEA) of stresses in the canal walls of selected fractured

roots was also undertaken to determine whether the observed fracture load and

pattern could be predicted from the prepared canal shape.

Materials and Methods

Extracted human mandibular incisor teeth were stored in 10% buffered

formalin until canal preparation. All teeth were examined macroscopically for

gross caries, second canals, open apices and anatomical irregularities or

fractures, and teeth with those characteristics were excluded from the study.

Fifty included teeth were stored in distilled water throughout the study.

42

Tooth preparation

All teeth were decoronated 2mm above the approximal CEJ, and straight-line

access was prepared using high-speed flat-fissure diamond burs. Canal

patency was established with a size 10 K-file. All teeth with canal obliteration

or where canal patency could not be established were excluded from the study.

Teeth were randomly distributed into two experimental groups, each with a

sample size of 25: A. Rotary NiTi canal preparation using ProFile (PF)

(Maillefer, Dentsply, Tulsa Dental Tulsa, OK) and B. Hand preparation using

stainless steel K-files (SS) (Maillefer, Dentsply, Tulsa Dental Tulsa, OK).

Cleaning and shaping

Rotary NiTi ProFile instrumentation (PF)

The length of the root canal was determined with a #10 K-file; the working

length was set at 1 mm short of the apical foramen. A crown-down technique

was utilized. The torque-control motor (ATR Technika Dentsply, Tulsa Dental

Tulsa, OK) was set at the recommended rotational speed and torque according

to the manufacturer’s recommendation for each instrument. The teeth were

irrigated with 1% sodium hypochlorite solution and EDTA after each file

change, and all canals were enlarged to size 40, 0.04 taper. Instrumented teeth

were then kept moist in water until the obturation phase.

43

Hand instrumentation (SS)

Working length was defined as 1 mm short of the apical foramen. Coronal

flaring was achieved with Gates Glidden drills (sizes 1, 2, 3) and shaping

achieved with stainless steel K-files (Dentsply, Tulsa Dental Tulsa, OK). These

teeth were instrumented using the step-back technique utilizing a balanced

force concept (17). The teeth were irrigated with 1% sodium hypochlorite

solution and EDTA after each file change, and all canals were enlarged to size

40 (MAF). Files were stepped back in 1 mm increments for three additional file

sizes and recapitulated using the MAF between files. Instrumented teeth were

kept in the same condition as in the PF group.

Obturation

Canals were thoroughly dried with paper points before insertion of gutta

percha. Lateral condensation was employed using 0.04 taper gutta percha

(Dentsply, Tulsa Dental Tulsa, OK) in both PF and SS groups. AH 26 (Dentsply,

De Trey, Konstanz, Germany) root canal sealer was used for all canals. Once

obturation was completed, excess gutta percha was removed to 1-2mm below

the CEJ. Completed teeth were wrapped in moist gauze and stored in separate

jars in a 37°C incubator for 1 week to ensure the proper setting of the sealer

cement.

44

Loading

All teeth were mounted vertically in a putty mix impression material

(Formasil® Xact, Heraeus Kulzer, Wehrheim, Germany). Loading was applied

using a spreader tip (D11) mounted in an Instron testing machine (model 5544

series Instron Corp. Canton MA). The spreader tip was initially placed into the

canal of each tooth, advanced manually until it contacted the gutta percha, and

then advanced vertically and automatically at a constant rate (2 mm per

minute). Root fracture was noted by listening for a distinctive crack, in

conjunction with the observation of a sudden deflection in the running graph.

Load at fracture was then recorded in Newton (N).

The fractured roots were later examined under a light microscope with 20x

magnification to determine the fracture pattern, which was categorized into

bucco-lingual, mesio-distal and compound fracture.

Statistical analysis

Unpaired t test and one-way ANOVA were performed using the SPSS/PC

version 10 (SPSS Inc. Chicago, IL) to compare load at fracture in association

with the two preparation techniques and three different fracture patterns

respectively. The Tukey post hoc test was also carried out to test differences

45

among groups according to fracture pattern. All statistical analysis was

performed at the 95% level of confidence.

Development of FEA models based on fractured roots (MODEL I-IV)

Four experimentally fractured roots were randomly selected from within each

fracture pattern, and were sectioned horizontally at the mid root. FEA models

were developed by digitizing a single cross-section of each root at the mid root

level.

Linear elastic isotropic analysis and eight-node hexahedral elements were

chosen, as in a previous study (18). All nodes in all models were given three

degree of freedom. Poisson’s ratio and Young’s modulus of dentin were

textbook values (19). All models were 3 mm thick. A structural face load was

applied to each model in a perpendicular direction around the root canal

surface. Tensile stress contours were plotted.

46

Results

Fracture susceptibility

Fracture loads are shown in Figure 1 and 2. The mean fracture load for teeth

prepared by hand and rotary Ni-Ti was almost identical (113.5+20.2N vs

114.9+37.1N). The range of loads required to fracture teeth was greater in the

rotary NiTi group (95% CI: 100.4 to 129.5N) than in the hand-prepared group

(95% CI: 105.6 to 121.4N), but there was no statistically significant difference in

the fracture loads for the two preparation techniques (p=0.866).

Fracture pattern

Bucco-lingual and mesio-distal fractures were observed in almost the same

frequency (36%, 38% respectively), and compound fracture was found in 26%.

The highest fracture load was associated with mesio-distal fracture

(127.6+27.5N; 95% CI: 115.2 to 139.9N), followed by bucco-lingual fracture

(108.8+30.2N; 95% CI: 94.9 to 122.7N) and compound fracture (102.1+25.8N;

95% CI: 88.1 to 116.1N). One-way ANOVA showed a statistically significant

difference in load at fracture among the three fracture patterns (p=0.03). The

Tukey post hoc test was then carried out and showed the fracture load of mesio-

distal fracture to be significantly greater than compound fracture (p=0.04), but

not significantly different from bucco-lingual fracture (p=0.116).

47

In the hand instrumentation group, bucco-lingual fracture occurred more often

(44%) than mesio-distal and compound fracture (32%, 24% respectively). In the

rotary NiTi group, on the contrary, mesio-distal fracture occurred more often

(44%) than bucco-lingual and compound fracture (28%, 28% respectively).

FEA model predictability (Figure 3)

The four teeth sectioned in the mid root region showed variable external root

cross sectioned shape, a small canal diameter in relation to dentin thickness,

and an approximately round canal profile except for the ribbon-shaped canal in

figure 3D. Overall, stress patterns in three of the four FEA models correlated

very well with the observed fracture pattern, while the fourth could not be

predicted reliably because of the uniform stress distribution.

Figure 3A shows an unusual root form with a bulge on one of the proximal

surfaces. The cross-sectioned canal shape was round. The root split

completely, with the fracture in a diagonal, mesio-distal direction. FEA model I

showed the highest tensile stresses localized in the proximal area of the canal

wall. The observed fracture pattern in the tooth correlated reasonably well with

the predominantly proximal stress pattern in the FEA model.

Figure 3B shows a slight concavity on one of the proximal surfaces of the root,

with a round canal profile. The fracture was incomplete and located on one

proximal surface and also in a bucco-lingual direction (compound fracture).

48

The corresponding FEA model showed a relatively uniform stress distribution,

without any highly localized tensile stress area. It was, therefore, difficult to

predict the fracture pattern in the tooth from the stress pattern derived using

FEA.

Figure 3C shows an ovoid root shape without any proximal concavity. Canal

irregularities were clearly present as a result of using hand preparation. The

fracture was in a bucco-lingual direction. The FEA model showed highly

localized tensile stresses on the canal surface specifically concentrated at sites of

canal wall irregularities. The FEA model closely mimicked the actual fracture

pattern for this tooth.

Figure 3D shows an ovoid root shape with a significant concavity at one of the

proximal surfaces. The canal was ribbon-shaped, and canal preparation

appeared to remove dentin only in the middle of the canal, with buccal and

lingual extremities of the canal wall untouched. Gutta percha filled the entire

canal space. The fracture was in a bucco-lingual direction. The corresponding

FEA model showed highly localized stresses on both buccal and lingual canal

walls, correlating very well with the observed fracture pattern.

Discussion

Rotary NiTi canal preparation did not reduce fracture susceptibility of the roots

tested in the study. No significant difference in the fracture load of hand and

49

rotary NiTi canal preparations could be demonstrated, in part owing to the fact

that there was a wide range of fracture loads in both groups. Root and canal

morphology vary widely among teeth, and the age and restorative history of

the teeth were not known. It would be difficult to demonstrate statistically

significant differences with this wide range of randomly collected extracted

teeth. It has been suggested that this variability could be reduced by using

match-paired contralateral teeth from the same subject, such as cadaver teeth

(20).

Bucco-lingual fracture did not predominate in the present study, in contrast to

previous root fracture studies. Both clinical (21, 22) and experimental (7, 23)

studies of VRF have consistently shown predominantly bucco-lingual fracture.

These studies, however, were all from the pre-rotary NiTi era. Smoothly

tapering round canals created by rotary NiTi preparation might have changed

the fracture pattern toward mesio-distal.

The mechanism of bucco-lingual fracture was proposed by Lertchirakarn et al.

(18). When pressure is applied in a thick-walled vessel, stresses are of two

types: tensile stress in a circumferential direction and compressive stress in the

radial direction. The thin (proximal) part of the wall will be forced to expand

more readily than the thick (bucco-lingual) part of the wall in a radial direction.

The asymmetrical expansion creates additional circumferential tensile stresses

on the inner surface of the thicker areas, resulting from the outward bending of

50

the thinner part of the dentin wall (24). This explanation might not be

applicable in the present study because in the study by Lertchirakarn et al. (18),

the proximal dentin of their models was much thinner compared to canal

diameter. The proximal dentin in the present study, on the contrary, is much

thicker in comparison to canal diameter. The outward expansion of the

proximal walls might not occur because of the greater thickness of dentin.

The predictability of the pattern of fracture was reduced when the canal shape

was round, because of the lack of a highly localized tensile stress area. Crack

initiation can occur anywhere around a smooth, round canal surface unless the

external root morphology leads to highly localized stress. In this scenario,

localized defects such as canal irregularities, which were not detected here, may

have been the major determinant of crack initiation. These irregularities

increase fracture susceptibility, because stress may be amplified and

concentrated at the tip of these defects (13).

Attempts to reduce fracture susceptibility of the roots clinically are limited

because many factors interact in influencing fracture susceptibility, and most of

them are beyond the control of clinicians e.g. root shape, proximal concavity.

The clinician can, however, reduce fracture susceptibility by maintaining the

canal size as small as practical, and by striving for a smooth round canal

without irregularities. In addition, clinicians can identify susceptible teeth prior

to commencement of endodontic treatment, based on root size and taper.

51

Acknowledgements

The authors are deeply indebted to Dr Sabu John, Associate Professor of

Engineering at RMIT, and Dr Michel Swain, Professor of Aerospace Mechanical

and Mechatronic Engineering, University of Sydney, for their invaluable

suggestions.

52

References

1. Testori T, Badino M, Castagnola M. Vertical root fractures in endodontically treated teeth: a clinical survey of 36 cases. Journal of Endodontics 1993;19:87-91.

2. Fuss Z, Lustig J, Tamse A. Prevalence of vertical root fractures in extracted endodontically treated teeth. International Endodontic Journal 1999;32:283-6.

3. Bender IB, Freedland JB. Adult root fracture. Journal of American Dental Association 1983;107:413-9.

4. Sedgley CM, Messer HH. Are endodontically treated teeth more brittle? Journal of Endodontics 1992;18:332-5.

5. Huang TJ, Schilder H, Nathanson D. Effects of moisture content and endodontic treatment on some mechanical properties of human dentin. Journal of Endodontics 1992;18:209-15.

6. Reeh ES, Messer HH, Douglas WH. Reduction in tooth stiffness as a result of endodontic and restorative procedures. Journal of Endodontics 1989;15:512-6.

7. Lertchirakarn V, Palamara JE, Messer HH. Load and strain during lateral condensation and vertical root fracture. Journal of Endodontics 1999;25:99-104.

8. Lindauer PA, Campbell AD, Hicks ML et al. Vertical root fractures in curved roots under simulated clinical conditions. Journal of Endodontics 1989;15:345-9.

9. Wilcox LR, Roskelley C, Sutton T. The relationship of root canal enlargement to finger-spreader induced vertical root fracture. Journal of Endodontics 1997;23:533-4.

10. Tan BT, Messer HH. The quality of apical canal preparation using hand and rotary instruments with specific criteria for enlargement based on initial apical file size. Journal of Endodontics. 2002;28:658-64.

11. Portenier I, Lutz F, Barbakow F. Preparation of the apical part of the root canal by the Lightspeed and step-back techniques. International Endodontic Journal 1998;31:103-11.

12. Gdoutos EE. Fracture mechanics : an introduction. Dordrecht ; Boston: Kluwer Academic Publishers, 1993. xiii, 307 p. (Solid mechanics and its applications ; v. 14.).

13. Callister WD. Failure. In: WD Callister, editor Materials science and engineering : an introduction. 6th edn. New York ; [Chichester]: Wiley, 2003:192-245.

53

14. Bryant ST, Thompson SA, al-Omari MA et al. Shaping ability of Profile rotary nickel-titanium instruments with ISO sized tips in simulated root canals: Part 1. International Endodontic Journal 1998;31:275-81.

15. Thompson SA, Dummer PM. Shaping ability of ProFile.04 Taper Series 29 rotary nickel-titanium instruments in simulated root canals. Part 1. International Endodontic Journal 1997;30:1-7.

16. Glossen CR, Haller RH, Dove SB et al. A comparison of root canal preparations using Ni-Ti hand, Ni-Ti engine-driven, and K-Flex endodontic instruments. Journal of Endodontics 1995;21:146-51.

17. Roane JB, Sabala CL, Duncanson MG, Jr. The "balanced force" concept for instrumentation of curved canals. Journal of Endodontics 1985;11:203-11.

18. Lertchirakarn V, Palamara JE, Messer HH. Patterns of vertical root fracture: factors affecting stress distribution in the root canal. Journal of Endodontics 2003;29:523-8.

19. Craig RG, Hanks CT. Restorative dental materials. 9th ed. St. Louis: Mosby, 1993. xix, 581 p.

20. Usman N, Baumgartner JC, Marshall JG. Influence of instrument size on root canal debridement. Journal of Endodontics 2004;30:110-2.

21. Selden HS. Repair of incomplete vertical root fractures in endodontically treated teeth--in vivo trials. Journal of Endodontics. 1996;22:426-9.

22. Walton RE, Michelich RJ, Smith GN. The histopathogenesis of vertical root fractures. Journal of Endodontics 1984;10:48-56.

23. Saw LH, Messer HH. Root strains associated with different obturation techniques. Journal of Endodontics 1995;21:314-20.

24. Muvdi BB, McNabb JW. Engineering mechanics of materials. 3rd ed. New York: Springer-Verlag, 1991. 693 p.

54

Figure legends

Fig 1 Box and whisker plots of fracture loads in hand instrumentation, and

ProFile group (Upper and lower end of (whisker) line are highest and lowest

load at fracture, respectively. Upper and lower end of the box are 75 and 25

percentile, respectively. Horizontal line is median.)

Fig 2 Box and whisker plots of fracture loads in bucco-lingual, mesio-distal, and

compound fracture pattern (Upper and lower end of (whisker) line are highest

and lowest load at fracture, respectively. Upper and lower end of the box are 75

and 25 percentile, respectively. Horizontal line is median.)

Fig 3 Cross section at mid root level of selected teeth and their FEA model

counterparts (arrows indicate fracture lines)

55

Figure 1

0

50

100

150

200

Hand ProfileHand ProfileHand Profile

56

Figure 2

0

50

100

150

200

Bucco

Lingual

Mesio

Distal

CompoundBucco

Lingual

Mesio

Distal

CompoundBucco

Lingual

Mesio

Distal

CompoundBucco

Lingual

Mesio

Distal

CompoundBucco

Lingual

Mesio

Distal

CompoundBucco

Lingual

Mesio

Distal

CompoundBucco

Lingual

Mesio

Distal

CompoundBucco

Lingual

Mesio

Distal

Compound

57

Figure 3

I II III IV

A B C D

58

Chapter 4: Article II an FEA study of factors affecting fracture strength Effects of Root Canal Size and External Root Surface Morphology on Fracture

Susceptibility and Pattern: A Finite Element Analysis

(A manuscript accepted for publication in the Journal of Endodontics)

59

Abstract

The aim of the study was to determine the extent to which canal size, radius of

curvature and proximal root concavity influence fracture susceptibility and

pattern. A standardized cross-section of the mid-root region of a mandibular

incisor was created by averaging the dimensions of ten extracted teeth, and then

the basic finite element analysis (FEA) model was created. By varying canal

diameter, shape and proximal concavity, these factors could be examined for

roles in fracture susceptibility and pattern. The factors all interact in

influencing fracture susceptibility and pattern, with dentin thickness not the

only determining factor. The removal of dentin does not always result in an

increased fracture susceptibility.

60

Introduction

Vertical root fracture (VRF) is an important clinical problem; it is the second

most frequent identifiable reason for loss of endodontically treated teeth (1).

Once VRF occurs little can be done to rectify the situation, yet factors that

predispose to fracture remain largely unknown. A better understanding of

factors related to VRF might open the possibility of better prevention and/or

management of this catastrophic entity.

Dentin thickness, radius of canal curvature and external root morphology have

been proposed as factors potentially influencing fracture susceptibility (2). The

thinner the dentin, the more likely the tooth is to fracture (3). A low radius of

canal curvature can act as a stress raiser area (4), which makes the root more

susceptible to fracture. External root morphology has also been shown with

finite element analysis (FEA) to be a strong determinant of fracture direction (2).

The effects of these three factors have been studied primarily on geometrically

simple FEA models, which do not necessarily reflect actual root shape. The

clinical picture is probably much more complex. The FEA modeling technique

in the present study attempted to obtain a more realistic root cross-sectional

shape based on actual mandibular incisors.

Clinical and experimental studies have shown that root fractures occur

predominantly in a bucco-lingual direction (5-8). Root cross-sections are

usually ovoid in shape, especially in roots that are more prone to fracture such

61

as mandibular incisors and mesio-buccal roots of molars. Dentin thickness in

the bucco-lingual direction, particularly in mandibular incisors, is often double

that of proximal dentin, yet fracture usually runs through this thick region (8).

The mechanism of bucco-lingual fracture has been thoroughly explained using

FEA modeling (2, 9). An explanation of mesio-distal fracture, however, has not

been clarified. In this study, canal size and external root morphology

(specifically a proximal concavity) were modeled to examine for roles in mesio-

distal fracture susceptibility.

The objectives of this study were: (a) to determine to what extent the prepared

root canal diameter will influence fracture susceptibility and pattern of fracture;

(b) to determine the extent to which a concavity on the external proximal root

surface will change fracture susceptibility and pattern.

Materials and Methods

Development of the Basic Model of Root Dentin and Canal

A standardized cross-section of the mid-root region of a mandibular incisor was

created by averaging the dimensions of ten extracted teeth (10). Ten extracted

human mandibular incisors with a single canal (both right and left side teeth)

were selected from the previous study (11) on the basis of their uniform,

62

symmetrical root morphology and straight roots. All teeth had previously been

stored in 10% buffered formalin for at least two weeks and were cleaned using

an ultrasonic scaler and scalpel. Roots were sectioned horizontally at the mid

root level using a diamond saw. The buccal and lingual surfaces were

identified and all ten roots were aligned in the same orientation. Digital

photographs were taken using an intra oral camera (Acucam Concept IV

Dentsply/Gendex, Des Plaines, IL), and the images were converted to JPEG

files. The mid-point of every root canal and the mid-point on the buccal root

surface were identified using image management software (ACDsee version 3.1,

ACD Systems Inc. Arlington, TX). Radii were drawn from the center point

through the buccal mid-point, and new radii were drawn every 10 degrees from

this reference line, using Corel Draw version 9 (Corel Corp, Ottawa, Ontario,

Canada). Thirty-six coordinates of the root surfaces were obtained from the

intercept points of the radii with the external root surface for each tooth using

UTHSCSA Image Tool for Windows version 3.00 (The University of Texas

Health Sciences Center at San Antonio, TX) A composite external root shape

was generated by deriving the means for each intercept in the 10 teeth. The 36

coordinates of the points defining the composite root shape were transferred

into finite element analysis software LUSAS 13.3-2 (FEA Ltd. Kingston Upon

Thames, Surrey, U.K.) and the basic FEA model was generated. No attempt

was made to create a composite canal space. Canal shape and size were very

variable among the ten teeth selected. Instead, the center point of each canal

was used to create canals of varying diameter. The canal for the basic model

63

was made round, with a diameter of 0.5 mm, corresponding to the canal shape

and size typically prepared using rotary instruments in the mid-root region.

For the experimental models, canal size was kept round and was increased

systematically in 0.5 mm increments. Cementum was not included in the

model. Once roots had been cleaned with an ultrasonic scaler and scalpel,

remaining cementum was very thin compared to the entire root structure and

could not be modeled reliably.

Basic model (MODEL I)

This model served as the basic model for systematic modification of root canal

size and external root surface morphology. A round root canal with diameter

0.5 mm was created, and the thinnest part of dentin (on the proximal surface)

was 1.0 mm.

Effect of increasing canal diameter (MODEL II-IV)

The canal diameter was gradually increased and dentin thickness was reduced

accordingly. Canal diameters of 1.0, 1.5 and 2.0 mm were created and the

corresponding thinnest part of dentin was 0.75, 0.5, and 0.25 mm respectively.

The external root surface remained the same as in the basic model. These canal

diameters are larger than would normally be created during canal preparation,

64

and are more representative of large post spaces. The sizes were chosen to

result in a progressive decrease in proximal dentin thickness.

Effect of increased proximal root concavity (MODEL V-VIII)

To create a proximal concavity on the mesial and distal root surfaces, the basic

model (MODEL I) was modified. Both mesial and distal external root surfaces

were reduced by 0.2 mm at the mid proximal area, and the resulting root profile

was then smoothed to incorporate the concavity into the overall root outline.

Up to 0.2 mm dentin was removed from the proximal root surface, while the

root canal diameters remained unchanged at 0.5, 1.0, 1.5 and 2.0 mm; the

thinnest part of dentin was 0.8, 0.55, 0.3 and 0.05 mm respectively.

Effect of circumferential filing in a ribbon shaped canal (MODEL IX-X)

A modification of one root cross section (ribbon-shaped canal MODEL IV in the

previous study) was made to create MODEL X by changing the canal shape

from the actual prepared ribbon-shaped canal. A preparation of a smooth

ovoid shaped canal was created simulating the use of rotary instruments in a

“circumferential filing” action.

Linear elastic isotropic analysis and eight-node hexahedral elements were

chosen, as in a previous study (2). All nodes in all models were given three

65

degree of freedom. Poisson’s ratio and Young’s modulus of dentin were

textbook values (12). All models were 3 mm thick. A structural face load was

applied to each model in a perpendicular direction around the root canal

surface. Tensile stress contours were plotted. The notional load at fracture was

also calculated, based on the computed face load required to yield a maximum

tensile stress of 60 MPa. This stress corresponds approximately to the ultimate

tensile stress of dentin in a direction parallel to tubule orientation (12, 13). This

approach provided a comparison of fracture susceptibilities with the different

canal and root morphologies.

Results

Effects of increasing canal diameter (MODEL I-IV)(figure 1)

Base model (I): The notional fracture load was 80N, with the highest stress

located on the canal wall, and concentrated specifically on the mesial and distal

surfaces. Based on the stress distribution, a crack would initiate on the internal

surface (canal wall) and propagate to the external root surface, resulting in

mesio-distal fracture.

As canal diameters were increased in models (II-IV), the notional fracture load

was lower accordingly (48N, 28N, and 11.5N, respectively). In models II and

III, maximal stresses were located on the internal canal wall, but were

66

concentrated specifically on the buccal and lingual aspects. Hence a crack

would initiate in the canal wall first and propagate to the external root surface

in bucco-lingual fracture mode. High external surface stresses in the proximal

area were noted in all models, and increased progressively from model I to IV.

With a dentin thickness of 0.25 mm (model IV), the crack would initiate on the

external proximal surface, where stress was highest, and propagate inward to

the canal wall (mesio-distal fracture).

Effects of increased proximal root concavity (MODEL V-VIII) (figure 1)

The internal stress patterns were quite similar to their counterparts in previous

models (models I-IV), but with greater external proximal stresses. The highest

stresses were located on the external proximal surface when dentin thickness

was less than 0.3 mm (models VII and VIII). The crack would initiate on the

external proximal surface and propagate inward to the canal wall in those

models (mesio-distal fracture). The proximal concavity increased fracture

susceptibility in the models with the same canal diameter as in the first part of

the study (reduction of dentin thickness). In terms of fracture susceptibility in

relation to remaining proximal dentin thickness, the concavity had very little

effect (figure 3).

Overall, models I-VIII showed a highly non-uniform tensile stress distribution.

The magnitude of stresses in a bucco-lingual direction declined sharply from

67

greatest on canal surfaces to very low throughout most buccal and lingual

dentin. On the contrary, approximal dentin showed some degree of stresses

throughout the entire thickness.

Effect of circumferential filing in a ribbon shaped canal (MODEL IX and X)

(figure 2)

No circumferential filing (model IX): The notional fracture load was 21.5N, the

highest stress was located on the canal wall, and concentrated at the buccal and

lingual extremities. The stress distribution pattern was non-uniform, with

highly localized stress areas in addition to the buccal and lingual canal wall.

Based on stress patterns, a crack would initiate internally at the canal

extremities and propagate outward, resulting in bucco-lingual fracture, which

actually correlated very well with the fractured tooth. Circumferential filing

(model X): The notional fracture load was 40N, almost double that of the

previous model. The highest stress was located and concentrated in the same

area as in model IX. Thus the fracture pattern would occur in a similar fashion.

However, the stress pattern distribution was much more uniform than in model

IX, and highly localized stress was not found in any area other than the buccal

and lingual canal walls.

68

Discussion

Stresses are closely associated with structural failure or fracture, because

structural failure will generally occur once the applied load produces a stress

that exceeds the ultimate strength of the material (4). Tensile stresses were used

in this study to predict fracture susceptibility and pattern because the stresses

predisposing to fracture are tensile (in a circumferential direction around the

canal wall). The direction of crack propagation is generally perpendicular to

the stress direction (4) and also perpendicular to the surface. Tensile stress

contour plots in FEA models thus can be used to predict fracture patterns.

Once the maximum tensile stress in the FEA model is located, the site of

potential crack initiation is identified and the direction of crack propagation

will be perpendicular to the surface in that location.

Although FEA is a very useful technique, it possesses certain limitations. The

FEA technique is based on several assumptions. Firstly, it assumes that dentin

is a uniform, isotropic material: its properties are not different when tested in

different areas or directions. In reality, dentin is a biomaterial created and

changed over time; different areas may have different Poisson’s ratio and

Young’s modulus, which are two of many parameters in the FEA calculation,

depending on factors such as mineral content. Using atomic force microscopy,

Kinney et al demonstrated a decrease in hardness where dentin is closer to the

pulp (14). Young’s modulus, compressive and shear strength of dentin have

been shown to differ greatly depending on distance from the pulp (15, 16).

69

However, variability in ultimate tensile strength has not been verified.

Secondly, a structural face load around the entire root canal surface was

selected as the load case in the FEA calculations based on the assumption that

the spreader, which was used experimentally to apply the load to fracture (17),

did not touch the canal wall. Thus gutta percha was assumed to behave like a

perfect fluid, which equally and uniformly distributed the load around the

canal wall. This may not apply clinically. Had the spreader touched the canal

wall, a point load would be more appropriate. Despite these limitations and

assumptions, previous studies have shown that the FEA technique is

reasonably reliable in prediction of fracture patterns (2, 11). FEA offers the

advantage that individual variables and combinations of variables can be tested

systematically in a way that is not possible experimentally. The wide variation

in results using extracted teeth (as much as a fourfold range in fracture

susceptibility in several previous studies) (8, 11) reflects the large natural

variation in extracted teeth. This natural variability may mask smaller effects of

individual variables such as proximal root concavity, which can only be

investigated using approaches such as FEA.

Ultimate tensile strength of dentin may not correlate directly with crack

initiation and propagation. Tensile strength is not an intrinsic material

property; rather it is a conditional material property. Tensile strength can be

greatly affected by structural defects, cracks or canal irregularities, which are

always present in any material. These may be much more influential in crack

70

initiation and strength because an applied stress may be exponentially

amplified or concentrated at the tips of those defects (4). It is, however, not

possible to incorporate small structural defects, cracks or canal irregularities

with the present FEA modeling technique.

Two types of mesio-distal fracture were found; inward and outward crack

propagation. Outward crack propagation in mesio-distal fracture occurs in

thick proximal dentin (≥ 0.3mm) and a high degree of canal curvature.

Propagation in an inward direction from the external root surface occurs in thin

proximal dentin (≤ 0.3mm). This thin wall must have expanded radially

resulting in outward bending of external proximal surfaces.

The more dentin is removed, the greater the fracture susceptibility, as shown in

MODELS I-IV. These results coincide with the study by Wilcox et al in 1997 (3).

The present study, however, indicates that reduction of dentin thickness is only

one factor in increased fracture susceptibility. In fact, our study showed that

dentin thickness, curvature of the external proximal root surface, canal size and

shape all interact in influencing fracture susceptibility and pattern of fracture.

Location of crack initiation and direction of crack propagation vary greatly and

are difficult to predict. A proximal concavity did not significantly reduce

fracture susceptibility as we first expected; it rather heightened stresses at

external proximal surfaces.

71

Lertchirakarn et al logically speculated that the reduction of the degree of the

curvature inside the root canal could reduce fracture susceptibility (9). Model X

shows that their speculation was valid. This model has a significant clinical

implication especially in ribbon shaped canal preparation. The preparation of a

smooth ovoid shaped canal results in the reduction of degree of curvature,

giving a better result in term of fracture susceptibility reduction. Thus removal

of dentin does not always result in an increased fracture susceptibility.

Elimination of stress raiser areas as in buccal and lingual extremities of ribbon

shaped canals makes it less susceptible to fracture.

This study has shown that fracture is unpredictable, and can occur anywhere in

the root. Many factors interact in influencing fracture susceptibility and

pattern, and any one variable can easily predominate over the others.

However, certain clinical principles remain valid. Canal preparation should be

as conservative as practical, consistent with adequate cleaning and shaping. A

smoothly rounded canal shape is favorable and can eliminate stress

concentration sites, which inevitably result in higher fracture susceptibility.

Much of the fracture susceptibility, however, is intrinsic to the root and canal

morphology (dentin thickness, canal shape and size, external root shape) and is

beyond the influence of the clinician.

72

References

1. Caplan DJ, Weintraub JA. Factors related to loss of root canal filled teeth. Journal of Public Health Dentistry 1997;57:31-9.

2. Lertchirakarn V, Palamara JE, Messer HH. Patterns of vertical root fracture: factors affecting stress distribution in the root canal. Journal of Endodontics 2003;29:523-8.

3. Wilcox LR, Roskelley C, Sutton T. The relationship of root canal enlargement to finger-spreader induced vertical root fracture. Journal of Endodontics 1997;23:533-4.

4. Callister WD. Failure. In: WD Callister, editor Materials science and engineering : an introduction. 6th edn. New York ; [Chichester]: Wiley, 2003:192-245.

5. Pitts DL, Natkin E. Diagnosis and treatment of vertical root fractures. Journal of Endodontics 1983;9:338-46.

6. Walton RE, Michelich RJ, Smith GN. The histopathogenesis of vertical root fractures. Journal of Endodontics 1984;10:48-56.

7. Selden HS. Repair of incomplete vertical root fractures in endodontically treated teeth--in vivo trials. Journal of Endodontics. 1996;22:426-9.

8. Lertchirakarn V, Palamara JE, Messer HH. Load and strain during lateral condensation and vertical root fracture. Journal of Endodontics 1999;25:99-104.

9. Lertchirakarn V, Palamara JE, Messer HH. Finite element analysis and strain-gauge studies of vertical root fracture. Journal of Endodontics 2003;29:529-34.

10. Bellucci C, Perrini N. A study on the thickness of radicular dentine and cementum in anterior and premolar teeth. International Endodontic Journal 2002;35:594-606.

11. Sathorn C, Palamara JE, Messer HH. A Comparison of the Effects of Two Canal Preparation Techniques on Root Fracture Susceptibility and Fracture Pattern. Journal of Endodontics (in press).

12. Craig RG, Hanks CT. Restorative dental materials. 9th ed. St. Louis: Mosby, 1993. xix, 581 p.

13. Lertchirakarn V, Palamara JE, Messer HH. Anisotropy of tensile strength of root dentin. Journal of Dental Research 2001;80:453-6.

73

14. Kinney JH, Balooch M, Marshall SJ et al. Hardness and Young's modulus of human peritubular and intertubular dentine. Archives of Oral Biology 1996;41:9-13.

15. Smith DC, Cooper WE. The determination of shear strength. A method using a micro-punch apparatus. British Dental Journal 1971;130:333-7.

16. Konishi N, Watanabe LG, Hilton JF et al. Dentin shear strength: effect of distance from the pulp. Dental Materials 2002;18:516-20.

17. Monaghan P, Bajalcaliev JG, Kaminski EJ et al. A method for producing experimental simple vertical root fractures in dog teeth. Journal of Endodontics 1993;19:512-5.

74

Table 1. Summary of canal diameter, minimum dentine thickness, maximum tensile stress area, and notional fracture load of model I-VIII

MODEL Root outline Canal

diameter (mm)

Proximal dentin thickness (mm)

Maximum stress internal (MPa)

Maximum stress external (MPa)

Notional fracture load

(N)

I Normal ovoid

0.5 1.0 60 35 80

II Normal ovoid 1 0.75 60 35 48

III Normal ovoid 1.5 0.50 60 55 28

IV Normal ovoid

2 0.25 44 60 11.5

V Proximal concavity 0.5 0.80 60 35 58

VI Proximal concavity 1 0.55 60 52 48

VII Proximal concavity 1.5 0.30 45 60 16

VIII Proximal concavity 2 0.05 40 60 2.5

75

Figure legends

Fig 1 FEA models showing the effects of increasingly larger canal diameter, and

proximal concavity

Fig 2 FEA models showing the effects of circumferential filing

Fig 3 Graph showing the effects of proximal concavity and relationship of

notional load at fracture and dentin thickness

76

Figure 1

I II III IV

V VI VII VIII

80N 1mm

48N 0.75mm

28N 0.5mm

11.5N 0.25mm

58N 0.8mm

48N 0.55mm

16N 0.3mm

2.5N 0.05mm

77

Figure 2

IX X

40N 21.5N

78

Figure 3

Minerva Access is the Institutional Repository of The University of Melbourne

Author/s:SATHORN, CHANKHRIT

Title:Factors affecting fracture susceptibility of tooth root: a laboratory and finite element analysis(FEA) study

Date:2004-11

Citation:Sathorn, C. (2004). Factors affecting fracture susceptibility of tooth root: a laboratory andfinite element analysis (FEA) study. Doctorate thesis, Endodontic Unit, School of DentalScience, Faculty of Medicine, Dentistry and Health Sciences, The University of Melbourne.

Publication Status:Unpublished

Persistent Link:http://hdl.handle.net/11343/39034

Terms and Conditions:Terms and Conditions: Copyright in works deposited in Minerva Access is retained by thecopyright owner. The work may not be altered without permission from the copyright owner.Readers may only download, print and save electronic copies of whole works for their ownpersonal non-commercial use. Any use that exceeds these limits requires permission fromthe copyright owner. Attribution is essential when quoting or paraphrasing from these works.