Additional studies on the distribution of stresses during ... - Nature

RESEARCH

endodontics

Additional studies on the distribution of stresses during vertical compaction of gutta-percha in the root canal C. Telli,1 P. Gülkan,2 and W. Raab,3 Objective This study was designed to investigate the effect of certain pathological alterations of the dental structures (diminishing bone support, internal resorption, root perforation, periapical lesion) on stress distribution during root canal filling procedures by the warm vertical compaction technique. Design The computer stress analyses were done for a maxillary canine tooth model which was based on dimensions recovered from a human cadaveric maxilla scanned by CT. Methods The finite element method was used to calculate the stresses generated during root canal filling procedures by warm vertical compaction technique. Patterns of stress distribution associated with various alterations in dental structures were investigated. For this purpose 60 cases were simulated. The hypothetical force of 10 N is taken as a unit representation. For other magnitudes of applied force, the corresponding stresses would be scaled directly because the calculations were made for linear materials. Results and Conclusion It is found that, when diminishing bone support and internal resorption are concurrently simulated, a marked increase in stress magnitudes occur (maximum von Mises stress 5.37 N/mm2). However, these values still remain much below the most frequently reported tensile strength of dentine (50–100 N/mm2). If dentist’s handwork is transformed into equivalent edge tractions on gutta-percha, then stresses in dentine, even when they are corrected for 3-kg applied force, appear to remain below fracture strengths of this material. This result leads us to conclude that when warm vertical compaction technique is skilfully performed and inadvertent undue force is not applied, a premature root fracture in a large rooted maxillary anterior tooth with straight root canal anatomy is not likely to occur, even for the unfavourable conditions simulated in our model. This result, like all results derived from modelling applications, is of course contingent upon agreement between the way in which the clinical operations are performed and the way in which they are mirrored for computer representation. We believe that the approach described here avoids the spurious stresses that have been reported in similar investigations.

1Associate Professor, Department of Endodontics, Hacettepe University, Faculty of

Dentistry, Ankara, Turkey, currently on leave at Department of Operative Dentistry, Heinrich-Heine University, 40225 Düsseldorf, FRG 2Professor, Department of Civil Engineering, Middle East Technical, University, 06531 Ankara, Turkey 3Professor and Chairman, Department of Operative Dentistry, Heinrich-Heine University, 40225 Düsseldorf, FRG REFEREED PAPER

Received 01.12.98; accepted 04.05.99 © British Dental Journal 1999; 187: 32–37

32

Root fractures reported as being caused by the compaction procedures of gutta-percha within the root canal by different techniques have been the subject of lengthy debate since their introduction to endodontic therapy. It has been speculated that excessive application of pressure during gutta-percha compaction process within the root canal could lead to root fractures.1 There have been efforts to understand the nature and magnitude of stresses distributed throughout the root during the application of different gutta-percha compaction techniques. These methods include mechanical testing systems,2–4 strain gauge techniques,5–6 and photoelastic modelling.7 Reported mean spreader loads required to cause vertical root fractures during lateral compaction in these investigations vary between 7–16 kg depending on many parameters such as tooth type, root canal flare, spreader design, root curvature, remaining dentine thickness after root canal preparation.2–6 Recently finite element method (FEM) has been employed to estimate the stresses that occur during vertical and lateral compaction procedures. The reported values in these investigations appear to be in great contradiction. One group of investigators, eg RicksWilliamson et al.8 like Gimlin et al.9 reported to have calculated maximum stresses of the order of 50–60 N/mm2 in the apical or coronal sections of the root canal, whereas we10 and Yaman et al.,11 Table 1 Material properties1

Enamel14 Dentine15 Periodontal ligament16 Alveolar bone17 Gutta-percha (cold)18 Gutta-percha (warm)18 Special element

Modulus of elasticity N/mm2

Poisson’s ratio

8.41 x 104 2.00 x 104 5.00 x 101 1.40 x 104 3.00 x 102 3.00 x 100 1.50 x 100

0.300 0.310 0.490 0.150 0.485 0.485 0.499

1Every

material, including biological ones, possesses certain intrinsic mechanical properties that are used in performing stress analyses of situations in which they are involved. One of these is a measure of their stiffness, or resistance to becoming deformed. This property is expressed through the elastic modulus, also called Young’s modulus, which, in the case of a linear material, is the ratio of the stress (force per unit area) to the strain (change of length per unit length). When stresses and strains are directly proportional, the material is said to be linear. (For every biological material this may not be the case.) The word ‘modulus’ means ‘a small measure’ in Latin. The other particular property characterising every material is the so-called Poisson’s ratio. This is a dimensionless number that characterises how much a given material will deform in a direction perpendicular to the direction in which it is loaded. For example, if a piece of putty is shaped like a cylindrical object, and then stretched, ie made longer, its diameter will shrink. Conversely, if the putty is placed inside a rigidwalled container, and then pressed from its open end, it will press against the walls of the container because it will want to expand laterally. For most common materials this ratio lies in the range 0.1–0.45

BRITISH DENTAL JOURNAL, VOLUME 187, NO. 1, JULY 10 1999

RESEARCH

endodontics Table 2 Parameter variations in vertical condensation Case no:

1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41. 42. 43. 44. 45. 46. 47. 48. 49. 50. 51. 52. 53. 54. 55. 56. 57. 58. 59. 60.

Changes in tooth structure

— — — — — — — — — — — — — — — — — — Internal resorption Internal resorption Internal resorption Internal resorption Internal resorption Internal resorption Internal resorption Internal resorption Internal resorption Internal resorption Internal resorption Internal resorption Internal resorption Internal resorption Internal resorption Internal resorption Internal resorption Internal resorption Internal resorption + perforation Internal resorption + perforation Internal resorption + perforation Internal resorption + perforation Internal resorption + perforation Internal resorption + perforation Internal resorption + perforation Internal resorption + perforation Internal resorption + perforation Internal resorption + perforation Internal resorption + perforation Internal resorption + perforation Internal resorption + perforation Internal resorption + perforation Internal resorption + perforation Internal resorption + perforation Internal resorption + perforation Internal resorption + perforation — — — — — —

Changes in bone structure

Load on

Pressure at section

— — — — — — DBS (1/3) DBS (1/3) DBS (1/3) DBS (1/3) DBS (1/3) DBS (1/3) DBS (2/3) DBS (2/3) DBS (2/3) DBS (2/3) DBS (2/3) DBS (2/3) — — — — — — DBS (1/3) DBS (1/3) DBS (1/3) DBS (1/3) DBS (1/3) DBS (1/3) DBS (2/3) DBS (2/3) DBS (2/3) DBS (2/3) DBS (2/3) DBS (2/3) — — — — — — DBS (1/3) DBS (1/3) DBS (1/3) DBS (1/3) DBS (1/3) DBS (1/3) DBS (2/3) DBS (2/3) DBS (2/3) DBS (2/3) DBS (2/3) DBS (2/3) Periapical lesion Periapical lesion Periapical lesion Periapical lesion Periapical lesion Periapical lesion

A A M M C C A A M M C C A A M M C C A A M M C C A A M M C C A A M M C C A A M M C C A A M M C C A A M M C C A A M M C C

1-1 1-1 1-1,2-2 1-1,2-2 1-1,2-2,3-3 1-1,2-2,3-3 1-1 1-1 1-1,2-2 1-1,2-2 1-1,2-2,3-3 1-1,2-2,3-3 1-1 1-1 1-1,2-2 1-1,2-2 1-1,2-2,3-3 1-1,2-2,3-3 1-1 1-1 1-1,2-2 1-1,2-2 1-1,2-2,3-3 1-1,2-2,3-3 1-1 1-1 1-1,2-2 1-1,2-2 1-1,2-2,3-3 1-1,2-2,3-3 1-1 1-1 1-1,2-2 1-1,2-2 1-1,2-2,3-3 1-1,2-2,3-3 1-1 1-1 1-1,2-2 1-1,2-2 1-1,2-2,3-3 1-1,2-2,3-3 1-1 1-1 1-1,2-2 1-1,2-2 1-1,2-2,3-3 1-1,2-2,3-3 1-1 1-1 1-1,2-2 1-1,2-2 1-1,2-2,3-3 1-1,2-2,3-3 1-1 1-1 1-1,2-2 1-1,2-2 1-1,2-2,3-3 1-1,2-2,3-3

Magnitude (N/mm2)

2.85 2.85 0.285,1.65 0.285,1.65 0.285,0.165,1.29 0.285,0.165,1.29 2.85 2.85 0.285,1.65 0.285,1.65 0.285,0.165,1.29 0.285,0.165,1.29 2.85 2.85 0.285,1.65 0.285,1.65 0.285,0.165,1.29 0.285,0.165,1.29 2.85 2.85 0.285,1.65 0.285,1.65 0.285,0.165,1.29 0.285,0.165,1.29 2.85 2.85 0.285,1.65 0.285,1.65 0.285,0.165,1.29 0.285,0.165,1.29 2.85 2.85 0.285,1.65 0.285,1.65 0.285,0.165,1.29 0.285,0.165,1.29 2.85 2.85 0.285,1.65 0.285,1.65 0.285,0.165,1.29 0.285,0.165,1.29 2.85 2.85 0.285,1.65 0.285,1.65 0.285,0.165,1.29 0.285,0.165,1.29 2.85 2.85 0.285,1.65 0.285,1.65 0.285,0.165,1.29 0.285,0.165,1.29 2.85 2.85 0.285,1.65 0.285,1.65 0.285,0.165,1.29 0.285,0.165,1.29

Special element

Present Absent Present Absent Present Absent Present Absent Present Absent Present Absent Present Absent Present Absent Present Absent Present Absent Present Absent Present Absent Present Absent Present Absent Present Absent Present Absent Present Absent Present Absent Present Absent Present Absent Present Absent Present Absent Present Absent Present Absent Present Absent Present Absent Present Absent Present Absent Present Absent Present Absent

Maximum von Mises stress in dentine (N/mm2)

4.41 3.93 1.90 2.09 1.40 1.24 4.44 3.96 2.10 2.33 1.60 1.58 4.67 4.31 2.43 2.62 1.60 1.58 4.40 3.98 3.34 3.63 1.43 1.40 4.42 4.61 3.45 3.99 1.63 1.59 5.25 4.37 5.27 5.26 1.64 1.59 4.40 3.96 3.34 3.63 1.43 1.18 4.42 4.61 3.43 3.97 1.63 1.59 5.25 4.37 5.23 5.22 1.59 1.59 5.17 4.22 1.91 2.08 1.60 1.58

Maximum tensile stress in dentine (N/mm2)

3.78 3.13 1.49 1.56 0.95 0.86 3.88 3.15 1.75 1.84 1.25 1.22 4.03 3.64 2.16 2.22 1.27 1.23 3.79 3.15 2.00 2.19 0.97 0.90 3.90 4.12 2.65 2.89 1.37 1.23 4.50 3.67 4.51 4.64 1.45 1.23 3.79 3.14 1.99 2.18 0.97 0.55 3.88 4.12 2.68 2.91 1.36 1.23 4.50 3.67 4.48 4.59 1.23 1.23 4.32 3.47 1.49 1.56 1.25 1.22

DBS (1/3) = diminishing bone support of the coronal 1/3 root structure DBS (2/3) = diminishing bone support of the coronal 1/3 + middle 1/3 root structure A = load on apical 1/3 M = load on middle 1/3 + apical 1/3 (%10) C = load on coronal 1/3 + middle 1/3 (%10) + apical 1/3 (%10)

following different modelling procedures, have calculated maximum stresses which are about an order of magnitude smaller of that, even when corrections are introduced to take into account the differences of the applied force. The orders of magnitude for the stresses reported in References 8 and 9 are so high as to cause frac-


ture in most materials encountered in ordinary engineering practice. These values are even above some of the most frequently reported tensile strength for dentine (50–100 N/mm2).12–13 In our earlier work we have calculated the stresses generated during lateral and vertical compaction of gutta-percha within the root

33

RESEARCH

endodontics

I

III V

II IV

Fig. 1 Standard body on which the FEM analysis performed and the elements used for representing the pathological changes in dental structures. ( I ) One-third diminishing bone support of the root structure, ( II ) Two-thirds diminishing bone support of the root structure, ( III ) Internal resorption, ( IV ) Periapical lesion, ( V) Perforation in dentine

canal on a 3-Dimensional (3D) maxillary canine tooth model which was crafted by using the dimensions of computer tomographic scans of a cadaveric maxilla.10 In the present study, certain pathological conditions which cause some degree of weakness of the dental structures will be investigated. The objective for this attempt is to investigate whether these parametrically varied conditions may lead to premature root fractures under vertical compaction forces.

resenting diminishing bone support (DBS), internal resorption (IR), root perforation (RP) and periapical lesion (PL) are graphically represented in figure1. DBS was evaluated at two levels. We apportioned the DBS to the root length as being 1/3rd and 2/3rd loss of alveolar bone (fig. 1). IR is simulated as being a symmetrical dentine resorption on the middle one-third of the root, as usually observed in the clinic. The complete set of parametric variations included in this study can be summarised succinctly as follows, with reference to Table 2. • Normal dental structures (Cases 1–6) • 1/3 DBS (1/3rd loss of alveolar bone support) (Cases 7–12) • 2/3 DBS (2/3rd loss of alveolar bone support) (Cases 13–18) • IR + normal bone support (NBS) (Cases 19–24) • IR + 1/3 DBS (Cases 25–30) • IR + 2/3 DBS (Cases 31–36) • IR + RP + NBS (Cases 37–42) • IR + RP + 1/3 DBS (Cases 43–48) • IR + RP + 2/3 DBS (Cases 49–54) • PL + NBS (Cases 55–60) All simulated conditions were evaluated at three levels (apical, middle and coronal) as seen in figure 2 and Table 2. Elements used for representing DBS, IR, RP and PL were simply assigned diminishingly small material properties. This represents the absence of the corresponding material. For the representation of IR the assigned elements shown in figure 1 were considered either as having the gutta-percha characteristics alone or a gutta-percha layer that is surrounded by a thin layer of special elements. A description for the special element is provided in the next section. Description of the endodontist’s hand operations during warm vertical compaction procedure to the computer

The finite element representation of the model used in this study is shown in figure 1. Figure 2 is used as a descriptive tool for the explanation of each special case. For the representation of warm vertical compaction (WVC) loads, it is assumed that the force is evenly distributed between the tip of the plugger and the gutta-percha and the

Materials and methods

The model The standard body for which the stress analysis was performed, as well as the parametric modifications designed for this study is shown in figure 1. This model represents a maxillary canine tooth and its adjacent supporting structures. The material properties of the components in the model were defined based on previous studies as given in Table 1.14–18 The tooth was represented primarily as an assemblage of 8-noded solid brick elements. The model in figure1 has 3,680 nodes and 2,514 elements. Details of the modelling procedure were described in a previous article.10 The fineness of the model was primarily governed by the scans obtained from a cadeveric maxilla. In finite element work, finer subdivisions generally lead to more accurate results. The basic model has been kept unchanged because the primary objective here is to ascertain whether the systematic parameter variations that will be introduced in it will in fact lead to stresses that might test the capacity of the dentine. The previous conclusion had been that undetected imperfections in the tooth structure or other irregularities for which no provision was made during the modelling phase and the misapplication of the technique (ie extreme levering action done by spreader, or an inadvertent transmission of undue forces on dentine through the tip of a plugger or spreader) were the likely culprits in causing the root fractures. It is now time to test that hypothesis.10 Pathological changes in dental structures simulated in this study are summarised in Table 2, whereas elements used for rep-

34

3

3

2

2

1

1 Gutta-percha Periodontal ligament Bone Special element Dentine-enamel

Fig. 2 Schematic representation of the investigated levels subjected to loading during vertical compaction. (Level 1-1 is apical, Level 2-2 is middle and Level 3-3 is coronal in a sequential compaction process. Special elements enable the downward movement of gutta-percha without being bonded to dentine)


RESEARCH

endodontics

x 10–2 300 240 180 120 60 0

Fig.3 von Mises Stresses in N/mm2 (Case 16 in Table 2)

pressure is found by dividing the force by the contact area. WVC stresses evaluated at three levels (apical, middle and coronal) are shown in figure 2 and Table 2. When the apical layer is compacted the upper part of the canal is empty and when a new layer is compacted a fraction of the previously applied pressure is considered to be still effective on the formerly compacted layers. This is put into effect as follows: First a force of 10N is applied along Section 1-1 in the canal, with the rest of the canal assumed to be empty. This pressure is applied over the central gutta-percha elements excluding the thin layer which is in contact with the canal wall (fig. 2). In the first case a special element is employed and the thin layer between the dentinal wall and the gutta-percha were considered as an assemblage of these elements. These elements act like an incompressible fluid, capable of pressing against the surface it touches, but not able to distort it in shear, and in our opinion are necessary to simulate WVC of the thermally softened gutta-percha without being bonded to the root canal wall. In the second case, all the elements inside the root canal at the apical section are considered as guttapercha elements. In this respect our modelling differs from similar studies,8,9 and may be the reason of why the corresponding results are different. A similar operation was repeated for the middle one-third over Section 2-2, with the proviso that while the full normal pressure was applied over that section, one-tenth of the previously applied stress continued to act along Section 1-1. The same loading scenario was repeated for the coronal Section 3-3 with reduced stresses now existing over the previously loaded Sections 1-1 and 2-2. We wish to stress that this scenario is one of several possible ways in which the obturation procedure is simulated in a numerical experiment. When judgement is based on how well the stresses or strains recovered by this simulation as well as the previous studies8–11 match experimental results19 it becomes apparent that an acceptable imitation of reality has been achieved. In the WVC cases the layer which was being compacted was considered to have the Young’s modulus of warm gutta-percha while the rest of the layers were assigned the Young’s modulus of cold gutta-percha. For this purpose Young’s modulus of gutta-percha


was decreased by a factor of 100 as recognised by previous research.18 All simulated pathological conditions were also evaluated at three levels (apical, middle and coronal), and the loading area was kept similar for both normal and pathological cases (fig. 2 and Table 2). The hypothetical force of 10 N (about 1 kg force) is taken as a unit representation. For other magnitudes the corresponding stresses would be scaled directly. For all cases, principal, shear, tensile, compression and, a special combined representation called von Mises10 values were recovered. The software we used is a widely tested commercially available tool called SAP 90. Results

The results of the numerical experiments are summarised in Table 2. An additional table showing all analysed stress components (Table 3) is also supplied for the most critical cases in order to provide an impression of the full stress picture. Table 3 requires some clarification for clinical readers, and it needs to be examined in conjunction with Table 2. An examination of the latter shows that cases 33 and 34 are the most critical because the maximum von Mises (5.27 N/mm2) and tensile stress (4.67 N/mm2) values were calculated in cases 33 and 34, respectively (figure 5, Table 2). These cases represent the tooth having IR and 2/3 DBS of its root structure being compacted on middle one-third. With the residual pressure of 0.285 N/mm2 still effective along the previously loaded section along line 1-1, the application of an additional 1.65 N/mm2 along 2-2 creates this critical state of stress in the domain. The peak stresses are confined to the immediate vicinity of loaded section. The subscripts for the various stress components in Table 3 indicate the direction in which they act, and are in themselves of no particular relevance. The magnitude of a given stress is of course relevant, as is the critical combination of various types of stress called the von Mises stress. The von Mises stress is a good indication of that state of loading when brittle fracture of the dentine may occur. Both DBS (fig. 3) and IR (fig. 4) simulations created some increase in stress magnitudes especially in the middle-third loading cases as would expected (Table 2). This increase was more pronounced for the latter case (Table 2). When cases having both DBS as well as IR are concerned, the maximum calculated von Mises

x 10–2 400 320 240 160 80 0


35

RESEARCH

endodontics Table 3 The stress components of the critical cases (in N/mm2). These cases represent middle-third loading scenarios having internal resorption and two-thirds diminishing bone support of its root structure Case 33

min

max

Case 34

min

max

–1.71 –1.17 –0.98 –1.89 –0.89 –0.98 –0.14 –0.55 –1.92 —

3.15 3.94 2.94 2.35 0.95 0.87 4.51 2.59 0.27 5.27

SXX SYY SZZ SXY SXZ SYZ S1 S2 S3 SVM

–1.73 –1.26 –0.89 –2.12 –0.88 –0.92 –0.13 –0.50 –1.78 —

3.34 4.10 2.87 2.37 0.89 0.82 4.64 2.67 0.39 5.26

x 10–2 SXX SYY SZZ SXY SXZ SYZ S1 S2 S3 SVM

550 440 330 220 110

stress value was observed to be up to about three times greater (figure 5, Table 2).

0 Discussion

The stress patterns displayed in figures 3 to 6 must be interpreted as being qualitative. It must be noted that, the particular geometry of the model created for this study, as well as the description of the endodontist’s manual operation to the computer software are the major factors that govern the stresses. The calculated values are also dominated by the material properties used for each particular numerical investigation. Although there appears to be a consistency on the reported elastic properties of some dental structures such as enamel and dentine, the values reported for some others (eg periodontal ligament) may display great variation.12–18 The reported Young’s modulus values for periodontal ligament changes within a range of 7 ´ 10–2 MPa to 1.7 ´ 10+3 MPa and this wide range can by no means be considered as reasonable. The material properties used in this study are updated as recommended by recent research.14–18 Comparison of the results obtained from a previous investigation10 with the present effort reveals a difference on the calculated values (about 25% on the maximum) which seems to be mainly influenced by the different material properties used for periodontal ligament. But it is safe to say that different material properties used for this dental structure have no critical influence on the present investiga-

x 10–2 550 440 330 220 110 0

Fig. 6 von Mises Stresses in N/mm2 (Case 55 in Table 2)

tion as maximum calculated stress values still remain much below the reported median tensile strength of dentine. The 10 N force value was chosen for unit representation. The stresses desired for any other force than 10 N could be obtained by simple scaling of the tabulated values. The maximum tensile stress values calculated for vertical compaction cases remain below the median tensile strength of dentine even when they are scaled by a factor of three ( ie 30 N force). When all compaction levels were evaluated the apical 1/3 seems to be the most critical region during obturation where maximum stress values in dentine observed (Table 2 and figure 6). This finding is easy to justify as the stress, which is proportional to the force exerted by the endodontist is applied over a smaller area in this case. This finding is not in agreement with a previous study9 which reported to have calculated stress concentrations on coronal and middle thirds of the root. Fracture due to lateral compaction forces has been widely reported.1–5 In contrast, fractures caused by WVC forces have not been frequently reported. However, contrary to our results, the maximum tensile stress values calculated for WVC in some studies8,9 are surprisingly high so as to cause root fracture almost in all tooth samples. It is rational to think that an incomplete root fracture that is created during root canal therapy may develop into a complete root fracture under occlusal forces. Moreover, only a minority of cases develop vertical root fractures and in that respect, unless misapplication of the technique is concerned care must be exercised before condemning any root canal preparation20 or filling technique.8–11 It is known that even spontaneous root fractures (fatigue root fracture) could develop in non-endodontically treated teeth.21,22 Inadvertent levering action done by the hand instrument, remains as the main future line of research to investigate the maximum stress value that could be generated by an endodontist through either spreader or plugger. Conclusion


36

Within the limits of this study the following conclusion is drawn. The most frequently reported range of tensile strength of dentine is about 50–100 N/mm2.12,13 The maximum von Mises stress value calculated in this numerical study on the other hand is no more than


RESEARCH

endodontics 5.37 N/mm2 for a force of 10 N. This value is still below the median tensile strength of dentine even when it is scaled by a factor of three (under 30 N force). These results lead us to believe that warm vertical compaction technique when performed skilfully, does not likely create premature root fractures in a large rooted maxillary anterior tooth with straight root canal anatomy, even when it contains severe weaknesses in itself and its supporting structures. Skilful performance means the avoidance of the application of undue force through the tip of the plugger to the root canal wall (which is a prerequisite for this technique) and requires the existence of no extenuating circumstances which have not been described above.

9 10 11 12 13

The authors thank Dr Andy Rossiter for his constructive criticism of the manuscript. 14 1 2 3 4 5 6 7 8

Meister F, Tennyson L, Gerstein H. Diagnosis and possible causes of vertical root fractures. Oral Surg Oral Med Oral Pathol 1980; 49: 243-53. Pitts D L, Matheny H E, Nicholls J I. An in vitro study of spreader loads required to cause vertical root fracture during lateral condensation. J Endod 1983; 9: 544-550. Holcomb J Q, Pitts D L, Nicholls J I. Further investigation of spreader loads required to cause vertical root fracture during lateral condensation. J Endod 1987; 13: 277-284. Lindauer P A, Campbell A D, Hicks M L, Pelleu G B. Vertical root fractures in curved roots under simulated clinical conditions. J Endod 1989; 15: 345349. Dang D A, Walton R E. Vertical root fracture and root distortion: effect of spreader design. J Endod 1989; 15: 294-301. Murgel C A F, Walton R E. Vertical root fracture and dentin deformation: the influence of spreader design. Endod Dent Traumatol 1990; 6: 273-278. Martin H, Fischer E. Photoelastic stress comparison of warm (Endotec) versus cold lateral condensation technique. Oral Surg Oral Med Oral Pathol 1990; 70: 325-327. Ricks-Williamson L J, Fotos P G, Goel V K, Spivey J D, Rivera E M, Khera S.

15 16 17 18 19 20 21 22

A three-dimensional finite element stress analysis of an endodontically prepared maxillary central incisor. J Endod 1995; 21: 362-367. Gimlin D R, Parr C H, Aguirre-Ramirez G. A comparison of stresses produced during lateral and vertical condensation using engineering models. J Endod 1986; 12: 235-241. Telli C, Gülkan P. Stress analysis during root canal filling by vertical and lateral condensation procedures: a three-dimensional finite element model of a maxillary canine tooth. Br Dent J 1998; 185: 79-86. Yaman S D, Alaçam T, Yaman Y. Analysis of stress distribution in a vertically condensed maxillary central incisor root canal. J Endod 1995; 21: 321-325. Craig R G, O’Brien W J, Powers J M. Dental materials, properties and manipulation. 4th ed, pp 10-31. St. Louis: C.V. Mosby, 1987. Sano H, Ciucchi B, Matthews W G, Pashley D H. Tensile Properties of mineralized and demineralized human and bovine dentin. J Dent Res 1994; 73: 1205-1211. Williams K R, Edmundson J T. Orthodontic tooth movement analysed by the finite element method. Biomaterials 1984; 5: 347-351. Tanne K, Koenig H A, Burstone C. Moment to force ratios and center of rotation. Am J Orthod Dentofac Orthop 1988; 94: 426-431. Rees J S, Jacobsen P H. Elastic modulus of the periodontal ligament. Biomaterials 1997; 18: 995-999. Tanne K, Nagataki T, Inoue Y, Sakuda M, Burstone C. Patterns of initial tooth displacements associated with various root lengths and alveolar bone heights. Am J Orthod Dentofac Orthop 1991; 100: 66-71. Camps J J, Pertot W J, Escavy J Y, Pravaz M. Young’s modulus of warm and cold gutta-percha. Endod Dent Traumatol 1996; 12: 50-53. Lertchirakarn V, Palamara J E A, Messer H H. Load and strain during lateral condensation and vertical root fracture. J Endod 1999; 25: 99-104. Omnink P A, Davis R D, Wayman B E. An in vitro comparison of incomplete root fractures associated with three obturation techniques. J Endod 1994; 20: 32-37. Telli C, Gülkan P, Günel H. A critical reevaluation of stresses generated during vertical and lateral condensation of gutta-percha in the root canal. Endod Dent Traumatol 1994; 10: 1-10. Yeh C. Fatigue root fracture: a spontaneous root fracture in nonendodontically treated teeth. Br Dent J 1997; 182: 261-266.

BDA Information Centre Services Did you know? • As a BDA member you can gain access to one of the best dental information services in the world • You don’t have to be based in London to use the service • You can borrow books, videos and information packages • You can borrow up to eight items via the postal system The only cost to you is the cost of the return postage. If you’re not sure what to request then telephone us and we can advise you. • You are entitled to free MEDLINE searches Telephone us with a subject and we will send you a list of relevant references with abstracts. • You can request photocopies of journal articles There is a small charge for this service and you need to fill in a Photocopy Request Form first. Telephone us if you would like one of these forms. • You can register to receive free Current Dental Titles These are MEDLINE-based lists of references on eight areas of dentistry which are sent to you automatically twice a year. Phone us for a registration form. For further details of any of these services dial 0171 935 0875 x265. or contact us via e-mail at: [email protected] Visit the Information Centre web pages at: www.bda-dentistry.org.uk


37