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The Effect of Isthmus on Vertical Root Fracture in Endodontically Treated Teeth
Basic Research—Technology
The Effect of Isthmus on Vertical Root Fracture in Endodontically Treated Teeth Herzl Chai, PhD,* and Aviad Tamse, MD† Abstract Introduction: Vertical root fracture (VRF) from apical condensation of gutta-percha is a common failure mode in endodontically treated teeth. Virtually all previous studies of VRF are limited to 1-canal roots. In this study, we consider experimentally and analytically VRF in roots with 2 canals. Methods: The interior root morphology in mandibular molar teeth extracted from patients due to VRF or other reason was examined from a series of polished horizontal cross sections. A 2-dimensional fracture mechanics analysis was used to determine crack growth from the canal surface to the outer root surface and evaluate the apical load needed to cause VRF, Fmax. Results: From a mechanistic viewpoint, the isthmus connecting root canals can be regarded as a natural weak plane or crack. The results expose the prime role of isthmus in reducing Fmax, from z 50 N with no isthmus present to z 10 N. Conclusions: Two-canal mesial roots are much more prone to VRF than 1-canal distal roots. We suggest that VRF may occur during clinical condensation of gutta-percha in mesial roots of mandibular molars as well as other roots with canals connected by isthmus. (J Endod 2015;-:1–5)
Key Words Crack, gutta-percha, isthmus, root canal, vertical root fracture
From the *School of Mechanical Engineering, Faculty of Engineering, Tel-Aviv University, Tel-Aviv, Israel; and † Goldschleger School of Dental Medicine, Tel-Aviv University, Tel-Aviv, Israel. Address requests for reprints to Prof Herzl Chai, School of Mechanical Engineering, Faculty of Engineering, Tel-Aviv University, Tel-Aviv, Israel. E-mail address: [email protected] 0099-2399/$ - see front matter Copyright ª 2015 American Association of Endodontists. http://dx.doi.org/10.1016/j.joen.2015.04.003
V
ertical root fracture (VRF) is a major complication in endodontically treated teeth that often leads to tooth extraction. Wedging forces and pressure transmitted to the canal wall during condensation of gutta-percha (GP) are primary causes for VRF (1, 2). This form of VRF was studied in vitro by loading to fracture root canals filled with GP, with the load applied apically by a spreader (3–8). VRF was taken to occur once a noticeable drop in the machine’s load versus displacement curve occurred. As discussed in Figure 2 of the study by Chai and Tamse (9), the corresponding load Fmax was approximately 100 N for oval canals and somewhat greater for round ones. Similar tests but with the apical force applied repeatedly in increasing amplitudes (10–12) yielded similar Fmax values, a coincidence that points to the clinical relevance of the single-ramp loading case. Analytic studies of VRF caused by apical condensation of GP are generally limited to elucidating stresses in uncracked, 1-canal roots having circular or elliptic canal cross sections (4, 13–15). Although correctly identifying the location on the canal wall where the fracture initiates, such studies provide no information on the evolution of fracture or the apical force causing VRF. Recently, the process of crack growth in 1-canal roots was studied using a simplified 2-dimensional fracture configuration consisting of a horizontal root slice containing an elliptic canal section (9). Initial cracks placed on the inner canal wall were driven to the outer one by uniform pressure acting on the canal surface. This pressure was tied to the apical GP condensation force F using a simple formula. The predicted Fmax agreed quite well with the test data of several studies (3–8). Most studies on VRF are limited to teeth with a 1-canal root. The clinical relevance of such studies is somewhat muted by the fact that the corresponding VRF load well exceeds the 15- to 30-N range used by endodontists during root canal obturation (16). The purpose of this study was to explore VRF in 2-canal roots, for which clinical experience suggests that VRF is more common. This study had 2 major thrusts. The first was to gain information on the distribution of interior damage in mandibular molar teeth extracted because of VRF. This was achieved by observing horizontal sections of teeth using optical microscopy. The results of this part were then used to develop a fracture mechanics model for predicting VRF load Fmax.
Materials and Method Tests Twenty-five mandibular molar human teeth having 2 roots, distal with 1 canal and mesial with 2 canals, were used. The teeth were extracted from 30- to 50-year-old patients at the School of Dental Medicine at Tel-Aviv University. Eighteen of these teeth exhibited a visible fracture extending over a part or the entire root axis, whereas the rest had no VRF symptoms when extracted. The roots, embedded in an epoxy resin for support, were first ground and then polished perpendicularly to their axis on a rotating cloth to a mirror surface quality using a 1-mm grade diamond paste. The polished surface was cleansed for 15 minutes in an ultrasonic bath of distilled water before it was observed under an optical microscope. This process was repeated in 1- to 2-mm increments until the entire root length was covered. Analysis As shown in Figure 1, the fracture model used consists of a thin horizontal root slice containing 2 canals connected by an isthmus. The external root surface is attached to a bone via a 0.2-mm-thick periodontal ligament. In view of the geometric and
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The Effect of Isthmus on VRF
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Basic Research—Technology
Figure 1. (A) A 2-dimensional fracture mechanics model for VRF in 2-canal roots. The specimen consists of a thin horizontal root slice containing 2 canals having an elliptic cross section. The wall of 1 or both canals is subjected to a uniform pressure, q, which drives an initial crack c to the outer root surface to cause VRF. As shown in (B), the orientation of the canal section may vary.
material complexities posed by this fracture problem, the following simplifications were invoked: 1. The external root surface was taken to be oblong (rectangle length D = 5 mm and surface radius R = 1.5 mm), whereas the bone was assumed to be square (L = 10 mm). The canal section was assumed to be elliptic (axes a and b). As shown in Figure 1B, the orientation of the canal section may differ from that of the root section. 2. The isthmus connecting the canals was considered as an open crack. 3. All materials were assumed to be isotropic and linearly elastic as characterized by Young’s modulus E and Poisson’s ratio n (Table 1). In order to study root fracture, a small initial crack (length c) was placed at a given location on the canal wall(s), typically along the long axis of the canal section (Fig. 1B). The surface of 1 or both the canals was subjected to a uniform pressure q. The latter produces circumferential tensile stresses on the wall of the canal section, which may enlarge the initial crack. The growth behavior of the crack was determined using a commercial finite element (FEM) code (Version 11; ANSYS Inc, Cannonsburg, PA) specified to plane stress conditions. The calculations were similar to a previous study on 1-canal roots (9). Briefly, the crack was incremented gradually along the path where the tensile stress responsible for crack growth is maximized. During this growth, the wall pressure, q(c), was adjusted such that K(c) = KC, where K is the stress intensity factor at the crack tip and KC the fracture toughness of dentin. As done in the study by Chai and Tamse (9), KC was taken to increase linearly from 1 to 3 MPa m1/2 over the first 0.5 mm of crack TABLE 1. Material Data in This Study* Material
Young’s modulus E (GPa)
Poisson’s ratio n
Dentin Periodontal ligament Bone
18.0 0.05 1.4
0.31 0.45 0.30
*The material data used are taken from Chai and Tamse (9).
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growth while remaining fixed thereafter (17). VRF was taken to occur when the crack reached the external root wall. The analysis was completed by relating the wall pressure to apical force via F = Aq, where A = pab is the canal’s cross-sectional area (9). The FEM calculations were implemented in the fracture model by creating a fine grid near the crack tip. The grid was refined until the stress intensity factor converged to within 2%–3% (9).
Results Tests Figure 2 shows 3 micrograph sequences representing the root morphology and damage distribution observed in this study: an unobturated tooth (Fig. 2A) and obturated teeth extracted because of VRF (Fig. 2B and C). In the case of Figure 2A, the canals in the 2-canal root are nearly round with a diameter z 0.27 mm. These canals are connected by a ribbonlike material structure called an isthmus, which in a given section can be fully open or closed. The fine, straight dark lines noted by arrows in the print suggest that for mechanical modeling purposes the isthmus can be viewed as a weak plane or crack. No other forms of damage are seen in the 2-canal root. The canals in the obturated roots (Fig. 2B and C) are considerably larger than in Figure 2A, whereas the isthmus remains intact. The damage is conclusively limited to the 2-canal roots, attesting to the prime role of the isthmus in causing root failure. The fracture in Figure 2B is limited to the coronal part of the crown, whereas the isthmus is fully open throughout the root axis, again showing the material weakness of the isthmus. Other noteworthy observations from the sectioning study are as follows: 1. All teeth extracted because of VRF have been subjected to endodontic treatment with GP. 2. The shapes of the external surface in the 1-canal and 2-canal roots resemble oblong and hourglass shapes, respectively. 3. Although the intact canal sections are nearly round, obturated ones are ellipticlike with a size and orientation that may vary greatly along the root axis. JOE — Volume -, Number -, - 2015
Basic Research—Technology
Figure 2. Three sequences of cross-section micrographs from extracted mandibular molar teeth each having 2 roots, 1 with 2 canals and the other with 1 canal. (A) A tooth not treated endodontically that has been extracted from a patient for reasons other than VRF. (B and C) Endodontically treated teeth extracted from patients because of VRF. The distances from the root apex to the root section for the first, second, and third frames from left to right are (A) 4.5, 6.9, and 8.4; (B) 3.8, 5.2, and 7.0; and (C) 2.0, 3.9, and 5.4 mm. The marked fine cracks between the 2 canals in Figure 1A indicate that the isthmus is a loosely connected material that can be considered a planar crack. The fracture in B is limited to the coronal part while that in C occupies the entire root length. The damage noted by the arrow in B may have occurred during tooth extraction.
4. Cracks tend to initiate on the canal wall where the radius of curvature is smallest. (An exception to this occurs in the middle frame of Figure 2B. However, this departure likely reflects rapid changes in the canal orientation along the root axis.) 5. The crack path tends to reorient itself along the isthmus or buccolingual direction as the crack extends (Fig. 2C).
Analysis Figure 3A shows contours of maximum tensile stress normalized by pressure q for 4 illustrative cases, all having no initial crack, minor canal axis a = 0.3 mm, and canal pressure q = 1 MPa. Because of configurational symmetry, only part of the root section is shown. The JOE — Volume -, Number -, - 2015
canals in I and II are round (b/a = 1), whereas those in III and IV are elliptic, b/a = 2, with the major axis aligned along III or normal IV to the long axis of the root section. All canals except in I are connected by the isthmus (crack). As shown, the largest tensile stress where fracture would initiate conclusively occurs on the canal wall where the local radius of curvature is smallest. Comparing prints I and II, one observes that the presence of an isthmus dramatically increases the critical tensile stress (ie, by a factor z4). Figure 3B shows the variation of apical force needed to maintain crack growth Fcr with crack length c for 4 illustrative cases, all having minor canal axis a = 0.3 mm, for conditions specified in the print with reference to the canal geometry depicted in Figure 1B with coordinate x’ coincident with x. Results are given for 2 round canals and 2 The Effect of Isthmus on VRF
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Basic Research—Technology
Figure 3. FEM results for the specimen in Figure 1 with L, D, and R = 10, 5, and 1.5 mm. (A) Contours of first principal (maximum) tensile stress, s1, normalized by applied canal pressure q for canals with no initial cracks. (I and II) Circular canals a = b = 0.3 mm without the isthmus and with the isthmus present, respectively. (III and IV) Elliptic canals b = 2a = 0.6 mm connected by an isthmus with a major canal axis along and perpendicular to the isthmus direction, respectively. Because of symmetry, only part of the specimen is shown. (B) The apical force needed to maintain crack growth Fcr versus crack length for the specimen of Figure 1 with a = 0.3 mm and coordinates x’, y’ (B) coincident with x, y (A). Results are given for circular canal b/a = 1 and elliptic 1 b/a = 2 in each case with and without the isthmus present. All cracks propagate along the long axis of the root section where the crack driving force is maximized. Curves are smooth fits to the FEM data (symbols). Note that the load needed to initiate crack growth depends on the initial crack length cF; the latter was estimated as 0.07 mm (9). Fmax is the load needed to cause VRF, indicated in the print only for the round canals.
elliptic ones (b/a = 2) in each case with and without an isthmus present. The symbols and curves in the plot denote FEM data and smooth fits. The former were obtained by placing an initial crack on each 1 of the 2 canal walls, which renders the configuration fully symmetric. The cracks were conclusively made to propagate along the isthmus direction, for which the tensile stress at each crack tip is maximized. Figure 3B shows that the force needed to initiate fracture depends on the initial crack length cF. With cF estimated based on reported failure stress values for dentin as 0.07 mm (9), the following may be noted: 1. Fcr first increases before reaching a peak value (Fmax) a certain distance from the outer root surface. Accordingly, a crack would grow stably with load until Fmax is reached, at which time unstable fracture to the root surface or VRF commences. 2. The curves for the elliptic canals (b/a = 2) are conclusively below those of the round ones, consistent with the smaller canal radius of curvature. 3. The inclusion of an isthmus greatly reduces Fmax; in the case of the elliptic canal, this amounts to a factor of z5 (ie, from z50 N to z10 N).
Discussion Isthmi are narrow, ribbonlike structures between root canals that contain pulp tissue. Unfortunately, no study on their mechanical properties seems to be available. Micro–computed tomographic imaging has been used to observe the interior root morphology in teeth (18–20) and detect isthmi and cracks on cross sections in various 2-canal roots (20). However, the fine cracks in the polished sections of the untreated roots in Figure 2A may not be detected by micro–computed tomographic imaging. Such cracks as well as the clear separation of isthmus 4
Chai and Tamse
seen in such images as Figure 2B and C suggest that isthmi are loosely connected structures easily separable by tensile stresses generated during GP condensation or occlusal forces. Basic fracture mechanics theory dictates that once opened into a cracklike form, an isthmus would greatly enhance growth of collinear cracks in the canal wall; the more so, the longer it is (21). As shown in Figure 3B, the presence of an isthmus dramatically reduces the VRF force (in the case of the elliptic canal from z50 N to as little as z10 N). The latter is in the range of apical forces used by clinicians during root canal obturation (16). The VRF model in Figure 1 may equally apply to any 2-canal roots connected by isthmus. As shown in the studies by von Arx et al (22, 23), isthmus prevalence is greatest in single roots with 2 canals such as maxillary first premolars and mesial roots of mandibular molars. Accordingly, the model predicts that VRF in such roots should be much more common than in 1-canal roots. Although this was clearly apparent in the root sectioning study (eg, Fig. 2B and C), in vitro tests devoted to determining VRF in 2-canal roots as done for 1-canal roots (3–8) would be helpful. It is interesting to comment on the stresses that drive VRF. The pressure exerted on the canal wall during GP condensation is generally thought to be a leading cause for VRF (1, 4, 9, 13–15). According to linear fracture mechanics theory (21), this pressure would cause cracks to initiate on the canal wall where the radius of curvature is smallest and propagate in the general direction of the isthmus, traits that are consistent with experimental evidence (eg, Fig. 2C). VRF may also occur because of occlusal forces. Indeed, in vitro tests show that obturation alone in 1-canal roots may produce only small cracks (24–26), not the clinical VRF commonly reported in the literature. The role of occlusal forces on VRF is made apparent by the ex vivo study of Barreto et al (27) in which the crowns of single-rooted 1-canal teeth were subjected to cyclic loading (106 cycles at a 90-N JOE — Volume -, Number -, - 2015
Basic Research—Technology peak load) directed at 45 to the tooth axis. VRF occurred only in those roots that underwent obturation (eg, 13.3% for lateral and 33.3% for Tagger’s hybrid-type compactions of GP). However, the stresses responsible for VRF due to occlusal type loading are not well understood. There are other factors that may affect VRF. It was shown in the study by Chai and Tamse (9) that the VRF force Fmax is proportional to dentin toughness KC. The latter is known to decrease with patient age (17, 28), which is consistent with clinical studies showing that the likelihood of VRF tends to increase with patient age (29, 30). KC may also be adversely affected by foreign objects and bacteria accommodated in dentinal cracks (31); the latter tend to form during root canal preparation (24–26). Another case in which KC may reduce is in root sections exhibiting the butterfly effect in which the dentin is harder mesiodistally (32). This might explain the high prevalence of vertical root fractures that run buccolingually. Finally, VRF may be affected by such factors as the canal’s dimensions, taper, and remaining dentin wall thickness (4, 10, 14). The analysis of these effects is beyond the scope of this study.
Acknowledgments Supported by the Israeli Science Foundation (ISF) under grant no. 810/09 given to 1 of the authors (H. Chai). The authors deny any conflicts of interest related to this study.
References 1. Meister F, Lommel TJ, Gerstein H. Diagnosis and possible causes of vertical root fractures. Oral Surg Oral Med Oral Pathol Oral Radiol Endod 1980;49:243–53. 2. Tamse A. Vertical root fracture of endodontically treated teeth. In: J Ingle JI, Bakland LK, Baumgartner CJ, eds. Ingle’s Endodontics, 6th ed. Toronto: BC Decker; 2008. 3. Saw LH, Messer HH. Root strains associated with different obturation techniques. J Endod 1995;21:314–20. 4. Lertchirakarn V, Palamara JE, Messer HH. Load and strain during lateral condensation and vertical root fracture. J Endod 1999;25:99–104. 5. Sathorn C, Palamara JE, Messer HH. A comparison of the effects of two canal preparation techniques on root fracture susceptibility and fracture pattern. J Endod 2005;31:283–7. 6. Lam PP, Palamara JE, Messer HH. Fracture strength of tooth roots following canal preparation by hand and rotary instrumentation. J Endod 2005;31:529–32. 7. Hammad M, Qualtrough A, Silikas N. Effect of new obturating materials on vertical root fracture resistance of endodontically treated teeth. J Endod 2007;33:732–6. 8. Hegde MN, Shetty S, Godara N. Evaluation of fracture strength of tooth roots following canal preparation by hand and rotary instrumentation—an in vitro study. Endodontology 2008;20:22–9. 9. Chai H, Tamse A. Fracture mechanics analysis of vertical root fracture from condensation of gutta-percha. J Biomech 2012;45:1673–82.
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10. Pitts DL, Matheny HE, Nicholls JI. An in vitro study of spreader loads required to cause vertical root fracture during lateral condensation. J Endod 1983;9: 544–50. 11. Holcomb JQ, Pitts DL, Nicholls JI. Further investigation of spreader loads required to cause vertical root fracture during lateral condensation. J Endod 1987;13:277–84. 12. Soros C, Zinelis S, Lambrianidis T, Palaghias G. Spreader load required for vertical root fracture during lateral compaction ex vivo: evaluation of periodontal simulation and fracture load information. Oral Surg Oral Med Oral Pathol Oral Radiol Endod 2008;106:e64–70. 13. Lertchirakarn V, Palamara JE, Messer HH. Finite element analysis and strain gauge studies of vertical root fracture. J Endod 2003;29:529–34. 14. Sathorn C, Palamara JE, Messer HH, Palamara D. Effect of root canal size and external root surface morphology on fracture susceptibility and pattern: a Finite Element analysis. J Endod 2005;31:288–92. 15. Versluis A, Messer HH, Pintado MR. Changes in compaction stress distributions in roots resulting from canal preparation. Int Endod J 2006;39:931–9. 16. Harvey TE, White JT, Leeb IJ. Lateral condensation stress in root canals. J Endod 1981;7:151–5. 17. Koester KJ, Ager JW III, Ritchie RO. The effect of aging on crack-growth resistance and toughening mechanisms in human dentin. Biomaterials 2008;29:1318–28. 18. Susin L, Yoon JC, Liu Y, et al. Canal and isthmus debridement efficacies of two irrigant agitation techniques in a closed system. Int Endod J 2010;43:1077–90. 19. Sarno MU, Sidow SJ, Looney SW, et al. Canal and isthmus debridement efficacy of the VPro EndoSafe negative-pressure irrigation technique. J Endod 2012;38: 1631–4. 20. Huang CC, Chang YC, Chuang MC, et al. Analysis of the width of vertical root fracture in endodontically treated teeth by 2 micro–computed tomography systems. J Endod 2014;40:698–702. 21. Cherepanov GP. Mechanics of Brittle Fracture. New York: McGraw-Hill; 1979. 22. von Arx T. Frequency and type of canal isthmuses in first molars detected by endoscopic inspection during periradicular surgery. Int Endod J 2005;38:160–8. 23. von Arx T, Steiner RG, Tay FR. Apical surgery: endoscopic findings at the resection level of 168 consecutively treated roots. Int Endod J 2011;44:290–312. 24. Onnink PA, Davis RD, Wayman BE. An in vitro comparison of incomplete root fractures associated with three obturation techniques. J Endod 1994;20:32–7. 25. Shemesh H, Bier CA, Wu MK, et al. The effects of canal preparation and filling on the incidence of dentinal defects. Int Endod J 2009;42:208–13. 26. Adorno CG, Yoshioka T, Jindan P, et al. The effect of endodontic procedures on apical crack initiation and propagation ex vivo. Int Endod J 2013;46:763–8. 27. Barreto MS, Moraes RA, Da Rosa RA, et al. Vertical root fractures and dentin defects: effects of root canal preparation, filling, and mechanical cycling. J Endod 2012;38: 1135–9. 28. Nazari A, Bajaj D, Zhang D, et al. Aging and the reduction in fracture toughness of human dentin. J Mech Behav Biomed Mater 2009;2:550–9. 29. Tamse A, Fuss Z, Lustig J, Kaplavi J. An evaluation of endodontically treated vertically fractured teeth. J Endod 1999;25:506–8. 30. Cohen S, Berman LH, Blanco L, et al. Demographic analysis of vertical root fractures. J Endod 2006;32:1160–3. 31. Walton RE, Michelich RJ, Smith GN. The histopathogenesis of vertical root fractures. J Endod 1984;10:48–56. 32. Russel AA, Hong L, Chandler NP. Investigation of dentin hardness in roots exhibiting the butterfly effect. J Endod 2014;40:842–4.
The Effect of Isthmus on VRF
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The Effect of Isthmus on Vertical Root Fracture in Endodontically Treated Teeth Herzl Chai, PhD,* and Aviad Tamse, MD† Abstract Introduction: Vertical root fracture (VRF) from apical condensation of gutta-percha is a common failure mode in endodontically treated teeth. Virtually all previous studies of VRF are limited to 1-canal roots. In this study, we consider experimentally and analytically VRF in roots with 2 canals. Methods: The interior root morphology in mandibular molar teeth extracted from patients due to VRF or other reason was examined from a series of polished horizontal cross sections. A 2-dimensional fracture mechanics analysis was used to determine crack growth from the canal surface to the outer root surface and evaluate the apical load needed to cause VRF, Fmax. Results: From a mechanistic viewpoint, the isthmus connecting root canals can be regarded as a natural weak plane or crack. The results expose the prime role of isthmus in reducing Fmax, from z 50 N with no isthmus present to z 10 N. Conclusions: Two-canal mesial roots are much more prone to VRF than 1-canal distal roots. We suggest that VRF may occur during clinical condensation of gutta-percha in mesial roots of mandibular molars as well as other roots with canals connected by isthmus. (J Endod 2015;-:1–5)
Key Words Crack, gutta-percha, isthmus, root canal, vertical root fracture
From the *School of Mechanical Engineering, Faculty of Engineering, Tel-Aviv University, Tel-Aviv, Israel; and † Goldschleger School of Dental Medicine, Tel-Aviv University, Tel-Aviv, Israel. Address requests for reprints to Prof Herzl Chai, School of Mechanical Engineering, Faculty of Engineering, Tel-Aviv University, Tel-Aviv, Israel. E-mail address: [email protected] 0099-2399/$ - see front matter Copyright ª 2015 American Association of Endodontists. http://dx.doi.org/10.1016/j.joen.2015.04.003
V
ertical root fracture (VRF) is a major complication in endodontically treated teeth that often leads to tooth extraction. Wedging forces and pressure transmitted to the canal wall during condensation of gutta-percha (GP) are primary causes for VRF (1, 2). This form of VRF was studied in vitro by loading to fracture root canals filled with GP, with the load applied apically by a spreader (3–8). VRF was taken to occur once a noticeable drop in the machine’s load versus displacement curve occurred. As discussed in Figure 2 of the study by Chai and Tamse (9), the corresponding load Fmax was approximately 100 N for oval canals and somewhat greater for round ones. Similar tests but with the apical force applied repeatedly in increasing amplitudes (10–12) yielded similar Fmax values, a coincidence that points to the clinical relevance of the single-ramp loading case. Analytic studies of VRF caused by apical condensation of GP are generally limited to elucidating stresses in uncracked, 1-canal roots having circular or elliptic canal cross sections (4, 13–15). Although correctly identifying the location on the canal wall where the fracture initiates, such studies provide no information on the evolution of fracture or the apical force causing VRF. Recently, the process of crack growth in 1-canal roots was studied using a simplified 2-dimensional fracture configuration consisting of a horizontal root slice containing an elliptic canal section (9). Initial cracks placed on the inner canal wall were driven to the outer one by uniform pressure acting on the canal surface. This pressure was tied to the apical GP condensation force F using a simple formula. The predicted Fmax agreed quite well with the test data of several studies (3–8). Most studies on VRF are limited to teeth with a 1-canal root. The clinical relevance of such studies is somewhat muted by the fact that the corresponding VRF load well exceeds the 15- to 30-N range used by endodontists during root canal obturation (16). The purpose of this study was to explore VRF in 2-canal roots, for which clinical experience suggests that VRF is more common. This study had 2 major thrusts. The first was to gain information on the distribution of interior damage in mandibular molar teeth extracted because of VRF. This was achieved by observing horizontal sections of teeth using optical microscopy. The results of this part were then used to develop a fracture mechanics model for predicting VRF load Fmax.
Materials and Method Tests Twenty-five mandibular molar human teeth having 2 roots, distal with 1 canal and mesial with 2 canals, were used. The teeth were extracted from 30- to 50-year-old patients at the School of Dental Medicine at Tel-Aviv University. Eighteen of these teeth exhibited a visible fracture extending over a part or the entire root axis, whereas the rest had no VRF symptoms when extracted. The roots, embedded in an epoxy resin for support, were first ground and then polished perpendicularly to their axis on a rotating cloth to a mirror surface quality using a 1-mm grade diamond paste. The polished surface was cleansed for 15 minutes in an ultrasonic bath of distilled water before it was observed under an optical microscope. This process was repeated in 1- to 2-mm increments until the entire root length was covered. Analysis As shown in Figure 1, the fracture model used consists of a thin horizontal root slice containing 2 canals connected by an isthmus. The external root surface is attached to a bone via a 0.2-mm-thick periodontal ligament. In view of the geometric and
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Figure 1. (A) A 2-dimensional fracture mechanics model for VRF in 2-canal roots. The specimen consists of a thin horizontal root slice containing 2 canals having an elliptic cross section. The wall of 1 or both canals is subjected to a uniform pressure, q, which drives an initial crack c to the outer root surface to cause VRF. As shown in (B), the orientation of the canal section may vary.
material complexities posed by this fracture problem, the following simplifications were invoked: 1. The external root surface was taken to be oblong (rectangle length D = 5 mm and surface radius R = 1.5 mm), whereas the bone was assumed to be square (L = 10 mm). The canal section was assumed to be elliptic (axes a and b). As shown in Figure 1B, the orientation of the canal section may differ from that of the root section. 2. The isthmus connecting the canals was considered as an open crack. 3. All materials were assumed to be isotropic and linearly elastic as characterized by Young’s modulus E and Poisson’s ratio n (Table 1). In order to study root fracture, a small initial crack (length c) was placed at a given location on the canal wall(s), typically along the long axis of the canal section (Fig. 1B). The surface of 1 or both the canals was subjected to a uniform pressure q. The latter produces circumferential tensile stresses on the wall of the canal section, which may enlarge the initial crack. The growth behavior of the crack was determined using a commercial finite element (FEM) code (Version 11; ANSYS Inc, Cannonsburg, PA) specified to plane stress conditions. The calculations were similar to a previous study on 1-canal roots (9). Briefly, the crack was incremented gradually along the path where the tensile stress responsible for crack growth is maximized. During this growth, the wall pressure, q(c), was adjusted such that K(c) = KC, where K is the stress intensity factor at the crack tip and KC the fracture toughness of dentin. As done in the study by Chai and Tamse (9), KC was taken to increase linearly from 1 to 3 MPa m1/2 over the first 0.5 mm of crack TABLE 1. Material Data in This Study* Material
Young’s modulus E (GPa)
Poisson’s ratio n
Dentin Periodontal ligament Bone
18.0 0.05 1.4
0.31 0.45 0.30
*The material data used are taken from Chai and Tamse (9).
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growth while remaining fixed thereafter (17). VRF was taken to occur when the crack reached the external root wall. The analysis was completed by relating the wall pressure to apical force via F = Aq, where A = pab is the canal’s cross-sectional area (9). The FEM calculations were implemented in the fracture model by creating a fine grid near the crack tip. The grid was refined until the stress intensity factor converged to within 2%–3% (9).
Results Tests Figure 2 shows 3 micrograph sequences representing the root morphology and damage distribution observed in this study: an unobturated tooth (Fig. 2A) and obturated teeth extracted because of VRF (Fig. 2B and C). In the case of Figure 2A, the canals in the 2-canal root are nearly round with a diameter z 0.27 mm. These canals are connected by a ribbonlike material structure called an isthmus, which in a given section can be fully open or closed. The fine, straight dark lines noted by arrows in the print suggest that for mechanical modeling purposes the isthmus can be viewed as a weak plane or crack. No other forms of damage are seen in the 2-canal root. The canals in the obturated roots (Fig. 2B and C) are considerably larger than in Figure 2A, whereas the isthmus remains intact. The damage is conclusively limited to the 2-canal roots, attesting to the prime role of the isthmus in causing root failure. The fracture in Figure 2B is limited to the coronal part of the crown, whereas the isthmus is fully open throughout the root axis, again showing the material weakness of the isthmus. Other noteworthy observations from the sectioning study are as follows: 1. All teeth extracted because of VRF have been subjected to endodontic treatment with GP. 2. The shapes of the external surface in the 1-canal and 2-canal roots resemble oblong and hourglass shapes, respectively. 3. Although the intact canal sections are nearly round, obturated ones are ellipticlike with a size and orientation that may vary greatly along the root axis. JOE — Volume -, Number -, - 2015
Basic Research—Technology
Figure 2. Three sequences of cross-section micrographs from extracted mandibular molar teeth each having 2 roots, 1 with 2 canals and the other with 1 canal. (A) A tooth not treated endodontically that has been extracted from a patient for reasons other than VRF. (B and C) Endodontically treated teeth extracted from patients because of VRF. The distances from the root apex to the root section for the first, second, and third frames from left to right are (A) 4.5, 6.9, and 8.4; (B) 3.8, 5.2, and 7.0; and (C) 2.0, 3.9, and 5.4 mm. The marked fine cracks between the 2 canals in Figure 1A indicate that the isthmus is a loosely connected material that can be considered a planar crack. The fracture in B is limited to the coronal part while that in C occupies the entire root length. The damage noted by the arrow in B may have occurred during tooth extraction.
4. Cracks tend to initiate on the canal wall where the radius of curvature is smallest. (An exception to this occurs in the middle frame of Figure 2B. However, this departure likely reflects rapid changes in the canal orientation along the root axis.) 5. The crack path tends to reorient itself along the isthmus or buccolingual direction as the crack extends (Fig. 2C).
Analysis Figure 3A shows contours of maximum tensile stress normalized by pressure q for 4 illustrative cases, all having no initial crack, minor canal axis a = 0.3 mm, and canal pressure q = 1 MPa. Because of configurational symmetry, only part of the root section is shown. The JOE — Volume -, Number -, - 2015
canals in I and II are round (b/a = 1), whereas those in III and IV are elliptic, b/a = 2, with the major axis aligned along III or normal IV to the long axis of the root section. All canals except in I are connected by the isthmus (crack). As shown, the largest tensile stress where fracture would initiate conclusively occurs on the canal wall where the local radius of curvature is smallest. Comparing prints I and II, one observes that the presence of an isthmus dramatically increases the critical tensile stress (ie, by a factor z4). Figure 3B shows the variation of apical force needed to maintain crack growth Fcr with crack length c for 4 illustrative cases, all having minor canal axis a = 0.3 mm, for conditions specified in the print with reference to the canal geometry depicted in Figure 1B with coordinate x’ coincident with x. Results are given for 2 round canals and 2 The Effect of Isthmus on VRF
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Figure 3. FEM results for the specimen in Figure 1 with L, D, and R = 10, 5, and 1.5 mm. (A) Contours of first principal (maximum) tensile stress, s1, normalized by applied canal pressure q for canals with no initial cracks. (I and II) Circular canals a = b = 0.3 mm without the isthmus and with the isthmus present, respectively. (III and IV) Elliptic canals b = 2a = 0.6 mm connected by an isthmus with a major canal axis along and perpendicular to the isthmus direction, respectively. Because of symmetry, only part of the specimen is shown. (B) The apical force needed to maintain crack growth Fcr versus crack length for the specimen of Figure 1 with a = 0.3 mm and coordinates x’, y’ (B) coincident with x, y (A). Results are given for circular canal b/a = 1 and elliptic 1 b/a = 2 in each case with and without the isthmus present. All cracks propagate along the long axis of the root section where the crack driving force is maximized. Curves are smooth fits to the FEM data (symbols). Note that the load needed to initiate crack growth depends on the initial crack length cF; the latter was estimated as 0.07 mm (9). Fmax is the load needed to cause VRF, indicated in the print only for the round canals.
elliptic ones (b/a = 2) in each case with and without an isthmus present. The symbols and curves in the plot denote FEM data and smooth fits. The former were obtained by placing an initial crack on each 1 of the 2 canal walls, which renders the configuration fully symmetric. The cracks were conclusively made to propagate along the isthmus direction, for which the tensile stress at each crack tip is maximized. Figure 3B shows that the force needed to initiate fracture depends on the initial crack length cF. With cF estimated based on reported failure stress values for dentin as 0.07 mm (9), the following may be noted: 1. Fcr first increases before reaching a peak value (Fmax) a certain distance from the outer root surface. Accordingly, a crack would grow stably with load until Fmax is reached, at which time unstable fracture to the root surface or VRF commences. 2. The curves for the elliptic canals (b/a = 2) are conclusively below those of the round ones, consistent with the smaller canal radius of curvature. 3. The inclusion of an isthmus greatly reduces Fmax; in the case of the elliptic canal, this amounts to a factor of z5 (ie, from z50 N to z10 N).
Discussion Isthmi are narrow, ribbonlike structures between root canals that contain pulp tissue. Unfortunately, no study on their mechanical properties seems to be available. Micro–computed tomographic imaging has been used to observe the interior root morphology in teeth (18–20) and detect isthmi and cracks on cross sections in various 2-canal roots (20). However, the fine cracks in the polished sections of the untreated roots in Figure 2A may not be detected by micro–computed tomographic imaging. Such cracks as well as the clear separation of isthmus 4
Chai and Tamse
seen in such images as Figure 2B and C suggest that isthmi are loosely connected structures easily separable by tensile stresses generated during GP condensation or occlusal forces. Basic fracture mechanics theory dictates that once opened into a cracklike form, an isthmus would greatly enhance growth of collinear cracks in the canal wall; the more so, the longer it is (21). As shown in Figure 3B, the presence of an isthmus dramatically reduces the VRF force (in the case of the elliptic canal from z50 N to as little as z10 N). The latter is in the range of apical forces used by clinicians during root canal obturation (16). The VRF model in Figure 1 may equally apply to any 2-canal roots connected by isthmus. As shown in the studies by von Arx et al (22, 23), isthmus prevalence is greatest in single roots with 2 canals such as maxillary first premolars and mesial roots of mandibular molars. Accordingly, the model predicts that VRF in such roots should be much more common than in 1-canal roots. Although this was clearly apparent in the root sectioning study (eg, Fig. 2B and C), in vitro tests devoted to determining VRF in 2-canal roots as done for 1-canal roots (3–8) would be helpful. It is interesting to comment on the stresses that drive VRF. The pressure exerted on the canal wall during GP condensation is generally thought to be a leading cause for VRF (1, 4, 9, 13–15). According to linear fracture mechanics theory (21), this pressure would cause cracks to initiate on the canal wall where the radius of curvature is smallest and propagate in the general direction of the isthmus, traits that are consistent with experimental evidence (eg, Fig. 2C). VRF may also occur because of occlusal forces. Indeed, in vitro tests show that obturation alone in 1-canal roots may produce only small cracks (24–26), not the clinical VRF commonly reported in the literature. The role of occlusal forces on VRF is made apparent by the ex vivo study of Barreto et al (27) in which the crowns of single-rooted 1-canal teeth were subjected to cyclic loading (106 cycles at a 90-N JOE — Volume -, Number -, - 2015
Basic Research—Technology peak load) directed at 45 to the tooth axis. VRF occurred only in those roots that underwent obturation (eg, 13.3% for lateral and 33.3% for Tagger’s hybrid-type compactions of GP). However, the stresses responsible for VRF due to occlusal type loading are not well understood. There are other factors that may affect VRF. It was shown in the study by Chai and Tamse (9) that the VRF force Fmax is proportional to dentin toughness KC. The latter is known to decrease with patient age (17, 28), which is consistent with clinical studies showing that the likelihood of VRF tends to increase with patient age (29, 30). KC may also be adversely affected by foreign objects and bacteria accommodated in dentinal cracks (31); the latter tend to form during root canal preparation (24–26). Another case in which KC may reduce is in root sections exhibiting the butterfly effect in which the dentin is harder mesiodistally (32). This might explain the high prevalence of vertical root fractures that run buccolingually. Finally, VRF may be affected by such factors as the canal’s dimensions, taper, and remaining dentin wall thickness (4, 10, 14). The analysis of these effects is beyond the scope of this study.
Acknowledgments Supported by the Israeli Science Foundation (ISF) under grant no. 810/09 given to 1 of the authors (H. Chai). The authors deny any conflicts of interest related to this study.
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10. Pitts DL, Matheny HE, Nicholls JI. An in vitro study of spreader loads required to cause vertical root fracture during lateral condensation. J Endod 1983;9: 544–50. 11. Holcomb JQ, Pitts DL, Nicholls JI. Further investigation of spreader loads required to cause vertical root fracture during lateral condensation. J Endod 1987;13:277–84. 12. Soros C, Zinelis S, Lambrianidis T, Palaghias G. Spreader load required for vertical root fracture during lateral compaction ex vivo: evaluation of periodontal simulation and fracture load information. Oral Surg Oral Med Oral Pathol Oral Radiol Endod 2008;106:e64–70. 13. Lertchirakarn V, Palamara JE, Messer HH. Finite element analysis and strain gauge studies of vertical root fracture. J Endod 2003;29:529–34. 14. Sathorn C, Palamara JE, Messer HH, Palamara D. Effect of root canal size and external root surface morphology on fracture susceptibility and pattern: a Finite Element analysis. J Endod 2005;31:288–92. 15. Versluis A, Messer HH, Pintado MR. Changes in compaction stress distributions in roots resulting from canal preparation. Int Endod J 2006;39:931–9. 16. Harvey TE, White JT, Leeb IJ. Lateral condensation stress in root canals. J Endod 1981;7:151–5. 17. Koester KJ, Ager JW III, Ritchie RO. The effect of aging on crack-growth resistance and toughening mechanisms in human dentin. Biomaterials 2008;29:1318–28. 18. Susin L, Yoon JC, Liu Y, et al. Canal and isthmus debridement efficacies of two irrigant agitation techniques in a closed system. Int Endod J 2010;43:1077–90. 19. Sarno MU, Sidow SJ, Looney SW, et al. Canal and isthmus debridement efficacy of the VPro EndoSafe negative-pressure irrigation technique. J Endod 2012;38: 1631–4. 20. Huang CC, Chang YC, Chuang MC, et al. Analysis of the width of vertical root fracture in endodontically treated teeth by 2 micro–computed tomography systems. J Endod 2014;40:698–702. 21. Cherepanov GP. Mechanics of Brittle Fracture. New York: McGraw-Hill; 1979. 22. von Arx T. Frequency and type of canal isthmuses in first molars detected by endoscopic inspection during periradicular surgery. Int Endod J 2005;38:160–8. 23. von Arx T, Steiner RG, Tay FR. Apical surgery: endoscopic findings at the resection level of 168 consecutively treated roots. Int Endod J 2011;44:290–312. 24. Onnink PA, Davis RD, Wayman BE. An in vitro comparison of incomplete root fractures associated with three obturation techniques. J Endod 1994;20:32–7. 25. Shemesh H, Bier CA, Wu MK, et al. The effects of canal preparation and filling on the incidence of dentinal defects. Int Endod J 2009;42:208–13. 26. Adorno CG, Yoshioka T, Jindan P, et al. The effect of endodontic procedures on apical crack initiation and propagation ex vivo. Int Endod J 2013;46:763–8. 27. Barreto MS, Moraes RA, Da Rosa RA, et al. Vertical root fractures and dentin defects: effects of root canal preparation, filling, and mechanical cycling. J Endod 2012;38: 1135–9. 28. Nazari A, Bajaj D, Zhang D, et al. Aging and the reduction in fracture toughness of human dentin. J Mech Behav Biomed Mater 2009;2:550–9. 29. Tamse A, Fuss Z, Lustig J, Kaplavi J. An evaluation of endodontically treated vertically fractured teeth. J Endod 1999;25:506–8. 30. Cohen S, Berman LH, Blanco L, et al. Demographic analysis of vertical root fractures. J Endod 2006;32:1160–3. 31. Walton RE, Michelich RJ, Smith GN. The histopathogenesis of vertical root fractures. J Endod 1984;10:48–56. 32. Russel AA, Hong L, Chandler NP. Investigation of dentin hardness in roots exhibiting the butterfly effect. J Endod 2014;40:842–4.
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