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Polymerization shrinkage: effects of constraint and filling technique in composite restorations
Dental Materials (2004) 20, 236–243
http://www.intl.elsevierhealth.com/journals/dema
Polymerization shrinkage: effects of constraint and filling technique in composite restorations Alessandro D. Loguercioa,*, Alessandra Reisa, Rafael Y. Ballesterb a
´lio Vargas, School of Dentistry, University of Oeste de Santa Catarina, Campus Joac¸aba, R. Getu 2125, Bairro Flor da Serra, CEP Joac¸aba, SC 89600-000, Brazil b ˜o Paulo, Sa ˜o Paulo, SP, Brazil School of Dentistry, University of Sa Received 2 October 2002; received in revised form 24 January 2003; accepted 23 April 2003
KEYWORDS Adhesion; Composite resin; Polymerization shrinkage; Constraint; Cfactor; Filling technique; Microtensile bond strength
Summary Objectives. To evaluate the linear polymerization shrinkage (LPS) and its effect upon mean gap width, bond strength and cohesive strength of a composite placed under different constraints (C-factors—CF) and filling techniques. Methods. Composite was placed in cavities sized 4 £ 4 £ 2 mm3 (CF ¼ 3) or on flat dentin surfaces (CF ¼ 0.3) of bovine incisors, after adhesive application. They were inserted in one or three increments, and light cured (600 mW/cm2) for 80 s. The LPS was measured by placing a probe on the top surface of the composite in order to measure its dislodgment in the top– bottom direction. Half of the sample was sectioned to obtain composite resin sticks subjecting them to tensile forces at 0.5 mm/min. The other half of the sample was sectioned and the mean gap width was measured in both sides of the sections. Then the sections were sliced again to obtain composite/dentin sticks. The mean gap width in the sticks was performed before subjecting them to tensile forces at 0.5 mm/min. Data was analyzed by a two-way ANOVA and the correlation between the bond strength and gap width was analyzed by simple linear regression. Results. (1) Linear polymerization shrinkage: significant differences were observed for the interaction ðp , 0:05Þ: Under the low constraint, the LPS were similar for both filling techniques. Under higher constraint, polymerization shrinkage was lower for the incremental technique. (2) Gap width and bond strength: no difference was detected either for interaction, or for technique ðp . 0:05Þ: Under higher constraint, the gap width was higher and the bond strength lower. (3) The cohesive strength of composite resin was similar for all groups ðp . 0:05Þ: No correlation between bond strength and gap width was found ðp ¼ 0:17Þ: Significance. The effects of polymerization shrinkage were not reduced by the filling technique under the different cavity constraints tested. Q 2003 Academy of Dental Materials. Published by Elsevier Ltd. All rights reserved.
Introduction
*Corresponding author. Tel./fax: þ55-49-551-2000. E-mail address: [email protected]
Light cured composite resins are now widely used in clinical practice because of their esthetic advantages, ease of use, good bonding to tooth
0109-5641/$ 30.00 Q 2003 Academy of Dental Materials. Published by Elsevier Ltd. All rights reserved. doi:10.1016/S0109-5641(03)00098-8
Polymerization shrinkage
structure and improved mechanical properties. However, the polymerization reaction of light cured composites leads to the development of higher stresses when the composite resin is bonded to the cavity walls.7 The role of the bonded to unbonded surface area ratios (constraint or Cfactor index) on the development of polymerization stresses with composite resins was demonstrated by Feilzer et al.7 They described an in vitro model in which restorations with Cfactor , 1 are the only ones likely to survive polymerization shrinkage stresses. Thus, early bond strengths are crucial since they are responsible for preserving the adhesive interface during development of stress from polymerization. Haller et al.10 reported a reduction of the bond strength to dentin of some adhesive systems when applied to 3D cavities in comparison with flat surfaces. Yoshikawa et al.33 were the first to evaluate resin – dentin bond strength using the microtensile test in class I cavities and they found decreased bond strength for all adhesive systems tested under high C-factors. However, this study disregarded the role of the filling technique on the stress relief since different C-factor cavities were not filled under the same technique. Other studies have reached similar conclusions, regarding the reduction of bond strength values under high C-factor cavities.2,3,32 However, to the extent of our knowledge no study has effectively compared the effects of constraints restored under different filling techniques. It is of common belief that widespread incremental filling techniques are capable of reducing the concentration of stresses arising from the cure of resins at the tooth interface when light activated composite resin are employed.12,15 However, Versluis et al.27 reported in a theoretical study using Finite Element Analysis methods (FEA), that incremental filling techniques could produce higher polymerization stresses at the restoration interface compared with bulk filling. On the other hand, other laboratorial studies have not detected any difference among filling techniques,25,30 thus requiring further studies on this field. Bond strength tests and microleakage studies are used as in vitro indicators of the strength and integrity of the marginal seal of composite resin restorations. Several studies have attempted to correlate the results of these tests but none have succeeded.1,19,24 However, most of them were not performed in the same specimen and under the same C-factor. Therefore, the objective of this study was: (1) to measure the linear polymerization shrinkage, gap width, adhesive bond strength and the cohesive
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strength of the composite resin employed for restoration of different C-factor cavities under different filling techniques and; (2) the relationship between marginal adaptation and microtensile bond strength in the same specimen.
Materials and methods Selection and teeth preparation Twenty sound bovine incisors were used. Teeth free from cracks or any other kind of structural defect were selected under magnification of £ 20. The teeth were disinfected in 0.5% chloramine for 15 days and stored for less than 6 months in 0.9% saline solution. All buccal surfaces were ground and flattened under water refrigeration with a 180 grit SiC paper (Fig. 1a). On each tooth, two standardized cavities were prepared in the buccal surfaces with C-factor ¼ 3 (4 mm wide, 4 mm high and 2 mm deep) by means of carbide burs (ref. #330, Kg Sorensen, SP, Brazil) (Fig. 1b). Then, half of the teeth had the cavity walls eliminated by grinding, leaving only the cavity floor, in order to reduce the C-factor to 0.3. The roughness of the carbide bur was maintained.33
Restorative procedures All teeth were restored with Single Bond adhesive system (3M ESPE, St Paul, MN, USA) and Z-250 resin composite (3M ESPE). As the light tip could not be positioned near the composite surface because a probe was positioned on it, the composite material was light-cured by two light-curing units with a light output of 600 mW/cm2 (VIP, Bisco, Schaumburg, IL, USA) in order to provide an energy density of approximately 16 J/cm2 for increment. The calibration of the light unit was daily performed on the light curing radiometer and confirmed using a Demetron radiometer (mod. 100, Demetron, Danbury, CT, USA). The adhesive system was applied according to the manufacturer’s instructions. In each tooth, one of the cavities was bulk filled, and the other one was restored by an incremental technique—three layers, similar to the oblique technique.27 See Fig. 1c – g. The composite resin was inserted in the cavity by means of a Centrix syringe (Centrix Incorporated. Shelton, CT, USA). In the bulk technique, restorations were light-cured with two pulses of 40 s each. In the incremental technique, after placing two oblique layers, a pulse of 40 s was used with a delay of 45 s between them; then the third layer
238 A.D. Loguercio et al.
Figure 1 (a – n): Schematic description of the experimental design. The buccal surface was flat (a) before the preparation of two cavities (b). The cavities were kept in half of the sample (c0 and d0 ), while in the other half, the buccal surface was ground until the exposure of the cavity floor, leaving the same roughness of other half (c0 and d00 ). All cavities were filled (e0 and e00 ) in bulk (g0 and g00 ) or incrementally—3 layers (f0 and f00 ). After 24 h, all restorations were sectioned (h0 and h00 ) and in each slice the mean gap width was measured (i0 and i00 ). Thereafter, these slices were sectioned again in order to obtain either sticks from the adhesive interface (j0 , j00 and l) or from the composite resin (m0 , m00 and n). The mean gap Width was measured again in the resin/dentin sticks before the tension testing (k0 and k00 ).
Polymerization shrinkage
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was placed and light-cured with another pulse of 40 s. Therefore, the energy density supplied to each technique was standardized.
were finished and polished by means of Sof Lex PopOn (3M ESPE) in order to facilitate the posterior cutting procedures.
Linear polymerization shrinkage
Gap measurements
The development of the experimental design was based on the method of Watts and Cash;28 however the linear polymerization shrinkage of the composite resin was measured inside the cavity in all restorations. After the composite resin placement and before the light curing procedure, a device that consisted of a probe (model p 10, Sylvac, Crissier, Switzerland) able to record the dislodgment (mm) of the composite resin in the top – bottom direction was placed on the composite resin surface. The probe used was similar to linear variable differential transformer (LVDT) used by Watts and Cash,28 which has a sensitivity of approximately 0.1 mm. The calibration of the probe was ultimately performed by the Swiss Federal Office of Metrology, according to the Sylvac Standard of Quality. For intermediate calibration, the probe was lightly clamped in a vertical stand opposed by an Instron extensometer (2630-101 GL 10 mm, Canton MA, USA) assembled with a display accuracy superior to 0.1 mm. As the depth of each cavity was accurately recorded with the probe before the resin placement, the percentage of linear polymerization shrinkage could be obtained. The point of measurement was standardized at a distance of 2 mm from the bottom of the cavity (this distance was measured with the probe) in the center of the cavity. After, the specimens were stored in distilled water at 37 8C for 24 h and then the restorations
The teeth were longitudinally sectioned (Labcut 1010 machine, Extec Corp., Enfield, CT, USA) in order to obtain slices with a thickness of approximately 0.7 mm. Three slices were obtained for each cavity (Fig. 1h). In each side of the slices, the mean width of the gaps in the adhesive interface was measured under a magnification of £ 400 (Shimadzu HMV-2, Tokyo, Japan). Considering that the gap along the interface does not have any regular geometric shape, the measurement was performed in approximately rectangular sections (a; b; f; etc.). The area of each section was calculated based on the width and length, as it can be seen in Fig. 2. The ratio between the partial areas and the total length of the interface resulted in the mean gap width.
Microtensile bond strength Slices from five teeth of each experimental condition had their slices sectioned (Labcut 1010 machine, Extec Corp., Enfield, CT, USA) in order to obtain resin –dentin sticks from the cavity floor with a rectangular cross-sectional area of approximately 0.7 mm2 (Fig. 1i and j). Nine sticks were obtained for each restoration and again the same procedure of gap width measurement was repeated on the four sides of each stick, as described previously (Fig. 1k and l). The specimens were fixed with cyanoacrylate resin (Zapit, Corona, CA, USA) to a modified device
Figure 2 (A) Schematic drawing showing a slice of a restoration. (B) Higher magnification of the adhesive interface. In each of the approximately rectangular sections (a; b and f) it was measured the length ðlÞ and the respective width ðwÞ: The partial area of the section a; for instance, was obtained by the multiplication the length a ðla Þ by the width a ðwa Þ: In this case, it would be: 5 £ 2 ¼ 10 mm2.
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A.D. Loguercio et al.
Table 1 Means and standard deviations of the linear polymerization shrinkage (%), mean gap width in slices and sticks (mm) for each group. C-factor/filling technique
Linear Gap in Gap in polymerization slices (mm) sticks (mm) shrinkage (%)
0.3/Three layers 0.3/Bulk 3/Three layers 3/Bulk
1.05 (0.04)a 0.98 (0.05)a 1.57 (0.10)b 1.95 (0.08)c
5.1 4.7 12.4 13.9
(2.9)d (2.4)d (5.2)e (5.8)e
4.6 (2.8)f 4.5 (2.3)f 8.1 (3.9)g 9.4 (5.2)g
The results in the groups marked with the same letters show no statistical difference.
and subjected to a microtensile test in a universal machine with a load cell of 100 N (Kratos Dinamometros, Sa ˜o Paulo, Brazil) at a crosshead speed of 0.5 mm/min. The load at failure and the crosssectional area of each specimen was measured to calculate the bond strength in MPa. The analysis of the fractured surfaces was performed under a magnification of £ 400 (Shimadzu HMV-2). The sticks were classified according to the following patterns: cohesive (failure within resin or dentin), adhesive (failure in the interface between tooth and resin) and mixed fracture pattern. The sticks that showed a cohesive fracture pattern were not assigned for calculation of bond strength means.
summing three per restoration. For each group 15 sticks were tested. These sticks were tested under tensile load at a crosshead speed of 0.5 mm/min and the composite resin cohesive strength was calculated in the same way as described for the resin/ dentin sticks, in order to detect any possible damage to the composite resin due to the development of internal tension from shrinkage polymerization.
Statistical analysis Before performing the statistical analysis, a single mean was computed for the values of microtensile bond strength and composite resin cohesive strength (MPa) obtained from sticks originating from the same restoration ðn ¼ 5Þ: Similarly, the same was performed for mean gap width (mm) measured in slices from the same experimental unit (restoration). Thereafter, the means of microtensile bond strength, resin cohesive strength, gap width and linear polymerization shrinkage (%) were subjected to a two-way ANOVA and Tukey’s test ða ¼ 0:05Þ for comparison of the means. The frequency of sticks that debonded during specimen preparation were analysed by a chi-square test ða ¼ 0:05Þ: The correlation between the bond strength means and the gap width (mm) measured in the sticks was analyzed by simple linear regression. The strength of the association between these two variables was estimated with the Pearson productmoment correlation statistic.
Cohesive strength of composite resin measured by microtensile test
Results Slices from the other five teeth of each experimental condition were sectioned (Labcut 1010 machine, Extec Corp., Enfield, CT, USA) in order to obtain resin sticks with a rectangular cross-sectional area of approximately 0.7 mm2 (Fig. 1m and n). One stick near the cavity floor was obtained from each slice,
The results and their respective standard deviations are shown in Tables 1 and 2. Linear polymerization shrinkage. Two-way ANOVA (C-factor vs. filling technique) showed that significant differences were observed for
Table 2 Number of sticks for each fracture pattern and number of sticks debonded during specimen preparation, means and standard deviations of the cross-sectional area of sticks (mm2), microtensile bond strength (MPa) and cohesive strength of composite resin (MPa) for each experimental group. C-factor/filling technique
0.3/Three layers 0.3/Bulk 3/Three layers 3/Bulk
Number of sticks for each fracture pattern and debonded sticks C
A/M
Debonded
10 7 4 9
32 35 30 23
3 3 11 13
Area (mm2)
Microtensile bond strength (MPa)
Composite resin cohesive strength (MPa)
0.74(0.06)a 0.74(0.07)a 0.73(0.10)a 0.75(0.07)a
37.3(9)b 39.9(14)b 31.3(12)c 34.9(12)c
93.7(13.9)d 89.8(14.1)d 96.5(12.5)d 98.4(22.1)d
The results in the groups marked with the same letters show no statistical difference. C, cohesive fracture pattern; A/M, adhesive plus mixed fracture pattern.
Polymerization shrinkage
the interaction of the factors ðp , 0:05Þ: Under the low C-factor, linear polymerization shrinkage was similar for both filling techniques. Conversely, under the high C-factor, the incremental technique (1.57%) reduced the shrinkage compared to the bulk filling (1.95%). Gap width. The results suggest no significant interaction between the factors for the measurements made in the slices and in the sticks ðp . 0:05Þ: No significant difference was found regarding technique ðp . 0:05Þ: However, as seen in Table 1, the different C-factors influenced the results ðp , 0:05Þ: Bond strength. Only the C-factor was responsible for differences observed on microtensile bond strength values obtained from the adhesive interface ðp , 0:05Þ: Lower values were found under the high C-factor. The frequency of the fracture pattern was also different for the experimental groups. Table 2 shows that the frequency of premature debonding before testing was higher under the high C-factor. Conversely, the frequency of cohesive fracture pattern was higher under the low C-factor. Composite resin cohesive strength. The results suggest no significant differences for either the interaction or for the main factors ðp . 0:05Þ: Correlation. There was no statistically significant correlation between the microtensile bond strength and the mean gap width measured in the sticks ðp ¼ 0:17Þ:
Discussion The experimental design of this study was conducted in bovine teeth due to ethical concerns that are related to the use of human teeth. The histological features of human and bovine permanent dentin seem to be similar23 and no difference in bond strength values has been detected.22 Thus the bovine incisor dentin is a suitable substitute for human molar dentin.23 Although several studies on polymerization shrinkage and its harmful effects have been conducted, little attention was given to the development of a simple method capable of measuring the polymerization shrinkage inside a cavity and to verify its likely consequences in the adhesive interface and the internal structure of the composite restorative material under the same experimental unit, as the present one. The results from the linear polymerization shrinkage have confirmed that the higher the ratio of bonded to unbonded surface, the greater is
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the shrinkage in the top-bottom direction. The restriction caused by bonding to the cavity walls prevents the composite resin from reducing its length in the top – bottom direction during the polymerization process. Thus, one of the likely consequences of that, i.e. a higher deflection of the unbonded surface, could be distinguished by the higher linear polymerization shrinkage observed under the higher C-factor. One of the advantages of the incremental technique claimed by several authors is that the volume reduction of each increment could be compensated by the next, and thus the consequence of polymerization shrinkage would be less deleterious since only the volume reduction of the last layer would effectively damage the bond surface. Theoretically, if an infinite number of increments were used, the magnitude of polymerization shrinkage would be insignificant.12 Actually, this statement is only partially true, since all polymerization shrinkage does not occur immediately after light-activation. Sakaguchi et al.21 reported that right after activation only 70 – 85% of polymerization shrinkage occurred; after 5 min this event could reach somewhere around 93%. In a similar way, the achievement of adequate mechanical properties is not immediate. After 30 min of activation, only 60% of the elastic modulus and flexural strength are completed.26 The idea that the subsequent increment can compensate for the polymerization shrinkage would only be valid if the increment could be placed in all regions where volume reduction occurs. This seems to be possible only for the deflected surface but not for the volume reduction that occurs in the interface and leads to gap formation. On the contrary, the polymerization of additional layers tends to deform even more the previous increments, increasing the gap width. According to Carvalho et al.4 and Davidson and Feilzer5 the incremental technique should be used in order to reduce the C-factor of the cavity and therefore minimizes the harmful effects of stress development on the adhesive interface. In fact, the linear polymerization shrinkage, measured under high C-factor, was lower when the cavity was filled incrementally, albeit inferior to the values obtained under low C-factor. Other studies have also reached similar conclusions.6,29 Nonetheless, such reduction was unable to eliminate the consequences of stress development on the adhesive interface. According to the present results, for a given Cfactor, the microtensile bond strength and the mean gap width was similar for both filling techniques. Under the higher C-factor there was
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a reduction of the bond strength values and an increase in the mean gap width, independent of filling technique, which is in agreement with other studies.2,3,32,33 Probably during polymerization shrinkage of the last increment, a considerable strain from the polymerization shrinkage of the first layer can still be under development, leading to a concentration of stresses on the adhesive interface. In fact, this means that the polymerization shrinkage and the consequent stresses that arise may result in a combined effect of polymerization shrinkage from all increments.27,31 Other inherent variables in the present study must be taken into account to allow a comprehensive understanding of the similar results provided by the filling technique. The depth of the cavity in the present study was shallow, limited by the anatomical shape of the bovine teeth. Thus, this fact allowed the complete polymerization of the composite resin when this material was placed in bulk. As the depth of the cavity increases, the light intensity attenuation that occurs inside the composite restorative material prevents the bottom surface from being completely cured.13,20 So, the main drawback of the bulk technique was overcome in the present study. In deeper cavities one may not expect such similar results. For instance, Giannini et al.8 have shown that the bond strength of a composite resin to the cavity floor of a 4 mm deep cavity was low, apart from the activation mode used. Some factors like the properties of the restorative material and the likely tooth deformation under the stress development may interfere with the results and these aspects were not taken into consideration in this study.11,14 Thus, future studies should be conducted to elucidate these hypotheses. The stress development that arises from polymerization shrinkage may cause higher deflection of the unbonded surface, deformation of the tooth structure, gaps along the adhesive interface and also lead to cracks and failures inside the restorative material. The cohesive strength of the composite resin remained unaltered in the experimental groups. During hardening, if the bonding to the cavity walls was strong enough to avoid gap formation, no tooth deformation occurred, the stresses concentrated inside the composite material would produce micro-cracks before its completely hardening, reducing some mechanical properties of the restorative material, such as the hardness, tensile and flexural strength. Other studies have already demonstrated that when the composite resin completely adhered to the walls of a high C-factor cavity, the resin failed cohesively.7 However, the increase in the mean gap width and
A.D. Loguercio et al.
the consequent reduced bond strength under the high C-factor could have contributed to the stress relief from polymerization shrinkage preventing the reduction in the mechanical properties of the composite resin. Actually, the results of the present investigation suggest that in clinical situations the adhesive interface might fail since shrinkage stress surpasses the bond strength to dentin. Some studies have attempted to correlate the data from marginal sealing, micro and nanoleakage with bond strength values immediately or over time.9,16,18 Gu ´zman-Ruiz et al.9 measured the marginal leakage in sticks previously stained with silver nitrate. Pereira et al.18 and Okuda et al.16 tried to correlate the nanoleakage in the hybrid layer in ‘sticks’ stained with silver nitrate. However, as in the present study, none has succeeded in obtaining the correlation between bond strength and marginal sealing even with both tests performed in the same specimen. The explanation for this is still unclear. Some authors have detected that the kind of stain may influence the results obtained in the long term, making the evaluation of marginal sealing and/or nanoleakage difficult.16 – 18 Thus, it seems that the measurement of the mean gap width over time, along with bond strength tests, as a way to evaluate the adhesive, interface, may be a suitable alternative since it does not require any staining. However, this hypothesis still needs to be proved. Therefore, based on the limitations of this study we may conclude that despite the partial reduction of linear polymerization shrinkage under high constraint restored incrementally, the harmful effects from polymerization shrinkage stresses were not minimized.
Acknowledgements This study is part of the thesis of Alessandro Dourado Loguercio (University of Sa ˜o Paulo) for partial fulfillment of the PhD degree in Dental Materials. We thank Dr Ricardo M Carvalho and Dr Ma ´rio F. Go ´es for their expert advice. This investigation was supported in part by FAPESP 99/05124-0 (Fundac ¸˜ ao de Apoio a ` Pesquisa do Estado de Sa ˜o Paulo). The authors are also grateful to Paulo Eduardo dos Santos for graphic illustration support.
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2. Armstrong SR, Keller JC, Boyer DB. The influence of water storage and C-factor on the dentin—resin composite microtensile bond strength and debond pathway utilizing a filled and unfilled adhesive resin. Dent Mater 2001;17:268—76. 3. Bouillaguet S, Ciucchi B, Jacoby T, Wataha JC, Pashley DH. Bonding characteristics to dentin walls of class II cavities, in vitro. Dent Mater 2001;17:316—21. 4. Carvalho RM, Pereira JC, Yoshiyama M, Pashley DH. A review of polymerization contraction: the influence of stress development versus stress relief. Oper Dent 1996;21:17—24. 5. Davidson CL, Feilzer AJ. Polymerization shrinkage and polymerization shrinkage stress in polymer-based restoratives. J Dent 1997;25:435—40. 6. Feilzer AJ, De Gee AJ, Davidson CL. Increased wall-to-wall curing contraction in thin bonded resin layers. J Dent Res 1989;68:48—50. 7. Feilzer AJ, De Gee AJ, Davidson CL. Setting stress in composite resin in relation to configuration of the restoration. J Dent Res 1987;66:1636—9. 8. Giannini M, Santos AJS, Carvalho RM, Paulillo LAMS, Lovadino JR. Effects of irradiation mode and filling technique on resin/ dentin bond strength in Class I cavities. J Dent Res (Special Issue) 2002;81:A70. Abstract number 355. 9. Guzman-Ruiz S, Armstrong SR, Cobb DS, Vargas MA. Association between microtensile bond strength and leakage in the indirect resin composite/dentin adhesively bonded joint. J Dent 2001;29:145—53. 10. Haller B, Klaiber B, Betz T, Dobersch S. Shear bond strength to dentin by simulation of three-dimensional class V cavity configuration. Dent Mater 1991;7:206—10. 11. Huysmans MC, van der Varst PG, Lautenschlager EP, Monaghan P. The influence of simulated clinical handling on the flexural and compressive strength of posterior composite restorative materials. Dent Mater 1996;12:116—20. 12. Koenigsberg S, Fuks A, Grajower R. The effect of three filling techniques on marginal leakage around class II composite resin restorations in vitro. Quint Int 1989;20: 117—21. 13. Lo ¨sche GM. Marginal adaptation of class II composite fillings: guided polymerization vs reduced light intensity. J Adhes Dent 1999;1:31—9. 14. Miguel A, La Macorra JC. A predictive formula of the contraction stress in restorative and luting materials attending to free and adhered surfaces, volume and deformation. Dent Mater 2001;17:241—6. 15. Neiva IF, De Andrada MA, Baratieri LN, Monteiro Jr. S, Ritter AV. An in vitro study of the effect of restorative technique on marginal leakage in posterior composites. Oper Dent 1998; 23:282—9. 16. Okuda M, Pereira PN, Nakajima M, Tagami J. Relationship between nanoleakage and long-term durability of dentin bonds. Oper Dent 2001;26:482—90.
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17. Pereira PN, Dias WR, Nakajima M, Sidhu SK. Relationship between nanoleakage and bond strength. J Dent Res (Special Issue) 2002;81:A416. Abstract number 3372. 18. Pereira PN, Okuda M, Nakajima M, Sano H, Tagami J, Pashley DH. Relationship between bond strengths and nanoleakage: evaluation of a new assessment method. Am J Dent 2001;14: 100—4. 19. Retief DH, Mandras RS, Russell CM. Shear bond strength required to prevent microleakage of the dentin/restoration interface. Am J Dent 1994;7:44—6. 20. Rueggeberg FA, Caughman WF, Curtis Jr. JW, Davis HC. Factors affecting cure at depths within light-activated resin composites. Am J Dent 1993;6:91—5. 21. Sakaguchi RL, Peters MC, Nelson SR, Douglas WH, Poort HW. Effects of polymerization contraction in composite restorations. J Dent 1992;20:178—82. 22. Schilke R, Bauss O, Lisson JA, Schuckar M, Geurtsen W. Bovine dentin as a substitute for human dentin in shear bond strength measurements. Am J Dent 1999;12:92—6. 23. Schilke R, Lisson JA, Baub O, Geustsen W. Comparison of the number and diameter of dentinal tubules in human and bovine dentine by scanning electron microscopic investigation. Arch Oral Biol 2000;45:355—61. 24. Staninec M, Kawakami M. Adhesion and microleakage tests of a new dentin bonding system. Dent Mater 1993;9: 204—8. 25. Tjan AHL, Bergh BH, Lidner C. Effect of various incremental techniques on the marginal adaptation of class II composite resin restorations. J Prosthet Dent 1992;67:62—6. 26. Unterbrink GL, Muessner R. Influence of light intensity on two restorative systems. J Dent 1995;23:183—9. 27. Versluis A, Douglas WH, Cross M, Sakaguchi RL. Does an incremental filling technique reduce polymerization shrinkage stresses? J Dent Res 1996;75:871—8. 28. Watts DC, Cash AJ. Determination of polymerization shrinkage kinetics in visible-light-cured materials: methods development. Dent Mater 1991;7:281—7. 29. Watts DC, Marouf AS. Optimal specimen geometry in bonded-disk shrinkage-strain measurements on light-cured biomaterials. Dent Mater 2000;16:447—51. 30. Wilson J. Effect of design features and restorative techniques on marginal leakage of MO composites: an in vitro study. Oper Dent 1993;18:155—9. 31. Winkler MM, Katona TR, Paydar NH. Finite element stress analysis of three filling techniques for class V light-cured composite restorations. J Dent Res 1996;75:1477—83. 32. Yoshikawa T, Burrow MF, Tagami J. The effects of bonding system and light curing method on reducing stress of different C-factor cavities. J Adhes Dent 2001;3:177—83. 33. Yoshikawa T, Sano H, Burrow MF, Tagami J, Pashley DH. Effects of dentin depth and cavity configuration on bond strength. J Dent Res 1999;78:898—905.
http://www.intl.elsevierhealth.com/journals/dema
Polymerization shrinkage: effects of constraint and filling technique in composite restorations Alessandro D. Loguercioa,*, Alessandra Reisa, Rafael Y. Ballesterb a
´lio Vargas, School of Dentistry, University of Oeste de Santa Catarina, Campus Joac¸aba, R. Getu 2125, Bairro Flor da Serra, CEP Joac¸aba, SC 89600-000, Brazil b ˜o Paulo, Sa ˜o Paulo, SP, Brazil School of Dentistry, University of Sa Received 2 October 2002; received in revised form 24 January 2003; accepted 23 April 2003
KEYWORDS Adhesion; Composite resin; Polymerization shrinkage; Constraint; Cfactor; Filling technique; Microtensile bond strength
Summary Objectives. To evaluate the linear polymerization shrinkage (LPS) and its effect upon mean gap width, bond strength and cohesive strength of a composite placed under different constraints (C-factors—CF) and filling techniques. Methods. Composite was placed in cavities sized 4 £ 4 £ 2 mm3 (CF ¼ 3) or on flat dentin surfaces (CF ¼ 0.3) of bovine incisors, after adhesive application. They were inserted in one or three increments, and light cured (600 mW/cm2) for 80 s. The LPS was measured by placing a probe on the top surface of the composite in order to measure its dislodgment in the top– bottom direction. Half of the sample was sectioned to obtain composite resin sticks subjecting them to tensile forces at 0.5 mm/min. The other half of the sample was sectioned and the mean gap width was measured in both sides of the sections. Then the sections were sliced again to obtain composite/dentin sticks. The mean gap width in the sticks was performed before subjecting them to tensile forces at 0.5 mm/min. Data was analyzed by a two-way ANOVA and the correlation between the bond strength and gap width was analyzed by simple linear regression. Results. (1) Linear polymerization shrinkage: significant differences were observed for the interaction ðp , 0:05Þ: Under the low constraint, the LPS were similar for both filling techniques. Under higher constraint, polymerization shrinkage was lower for the incremental technique. (2) Gap width and bond strength: no difference was detected either for interaction, or for technique ðp . 0:05Þ: Under higher constraint, the gap width was higher and the bond strength lower. (3) The cohesive strength of composite resin was similar for all groups ðp . 0:05Þ: No correlation between bond strength and gap width was found ðp ¼ 0:17Þ: Significance. The effects of polymerization shrinkage were not reduced by the filling technique under the different cavity constraints tested. Q 2003 Academy of Dental Materials. Published by Elsevier Ltd. All rights reserved.
Introduction
*Corresponding author. Tel./fax: þ55-49-551-2000. E-mail address: [email protected]
Light cured composite resins are now widely used in clinical practice because of their esthetic advantages, ease of use, good bonding to tooth
0109-5641/$ 30.00 Q 2003 Academy of Dental Materials. Published by Elsevier Ltd. All rights reserved. doi:10.1016/S0109-5641(03)00098-8
Polymerization shrinkage
structure and improved mechanical properties. However, the polymerization reaction of light cured composites leads to the development of higher stresses when the composite resin is bonded to the cavity walls.7 The role of the bonded to unbonded surface area ratios (constraint or Cfactor index) on the development of polymerization stresses with composite resins was demonstrated by Feilzer et al.7 They described an in vitro model in which restorations with Cfactor , 1 are the only ones likely to survive polymerization shrinkage stresses. Thus, early bond strengths are crucial since they are responsible for preserving the adhesive interface during development of stress from polymerization. Haller et al.10 reported a reduction of the bond strength to dentin of some adhesive systems when applied to 3D cavities in comparison with flat surfaces. Yoshikawa et al.33 were the first to evaluate resin – dentin bond strength using the microtensile test in class I cavities and they found decreased bond strength for all adhesive systems tested under high C-factors. However, this study disregarded the role of the filling technique on the stress relief since different C-factor cavities were not filled under the same technique. Other studies have reached similar conclusions, regarding the reduction of bond strength values under high C-factor cavities.2,3,32 However, to the extent of our knowledge no study has effectively compared the effects of constraints restored under different filling techniques. It is of common belief that widespread incremental filling techniques are capable of reducing the concentration of stresses arising from the cure of resins at the tooth interface when light activated composite resin are employed.12,15 However, Versluis et al.27 reported in a theoretical study using Finite Element Analysis methods (FEA), that incremental filling techniques could produce higher polymerization stresses at the restoration interface compared with bulk filling. On the other hand, other laboratorial studies have not detected any difference among filling techniques,25,30 thus requiring further studies on this field. Bond strength tests and microleakage studies are used as in vitro indicators of the strength and integrity of the marginal seal of composite resin restorations. Several studies have attempted to correlate the results of these tests but none have succeeded.1,19,24 However, most of them were not performed in the same specimen and under the same C-factor. Therefore, the objective of this study was: (1) to measure the linear polymerization shrinkage, gap width, adhesive bond strength and the cohesive
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strength of the composite resin employed for restoration of different C-factor cavities under different filling techniques and; (2) the relationship between marginal adaptation and microtensile bond strength in the same specimen.
Materials and methods Selection and teeth preparation Twenty sound bovine incisors were used. Teeth free from cracks or any other kind of structural defect were selected under magnification of £ 20. The teeth were disinfected in 0.5% chloramine for 15 days and stored for less than 6 months in 0.9% saline solution. All buccal surfaces were ground and flattened under water refrigeration with a 180 grit SiC paper (Fig. 1a). On each tooth, two standardized cavities were prepared in the buccal surfaces with C-factor ¼ 3 (4 mm wide, 4 mm high and 2 mm deep) by means of carbide burs (ref. #330, Kg Sorensen, SP, Brazil) (Fig. 1b). Then, half of the teeth had the cavity walls eliminated by grinding, leaving only the cavity floor, in order to reduce the C-factor to 0.3. The roughness of the carbide bur was maintained.33
Restorative procedures All teeth were restored with Single Bond adhesive system (3M ESPE, St Paul, MN, USA) and Z-250 resin composite (3M ESPE). As the light tip could not be positioned near the composite surface because a probe was positioned on it, the composite material was light-cured by two light-curing units with a light output of 600 mW/cm2 (VIP, Bisco, Schaumburg, IL, USA) in order to provide an energy density of approximately 16 J/cm2 for increment. The calibration of the light unit was daily performed on the light curing radiometer and confirmed using a Demetron radiometer (mod. 100, Demetron, Danbury, CT, USA). The adhesive system was applied according to the manufacturer’s instructions. In each tooth, one of the cavities was bulk filled, and the other one was restored by an incremental technique—three layers, similar to the oblique technique.27 See Fig. 1c – g. The composite resin was inserted in the cavity by means of a Centrix syringe (Centrix Incorporated. Shelton, CT, USA). In the bulk technique, restorations were light-cured with two pulses of 40 s each. In the incremental technique, after placing two oblique layers, a pulse of 40 s was used with a delay of 45 s between them; then the third layer
238 A.D. Loguercio et al.
Figure 1 (a – n): Schematic description of the experimental design. The buccal surface was flat (a) before the preparation of two cavities (b). The cavities were kept in half of the sample (c0 and d0 ), while in the other half, the buccal surface was ground until the exposure of the cavity floor, leaving the same roughness of other half (c0 and d00 ). All cavities were filled (e0 and e00 ) in bulk (g0 and g00 ) or incrementally—3 layers (f0 and f00 ). After 24 h, all restorations were sectioned (h0 and h00 ) and in each slice the mean gap width was measured (i0 and i00 ). Thereafter, these slices were sectioned again in order to obtain either sticks from the adhesive interface (j0 , j00 and l) or from the composite resin (m0 , m00 and n). The mean gap Width was measured again in the resin/dentin sticks before the tension testing (k0 and k00 ).
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was placed and light-cured with another pulse of 40 s. Therefore, the energy density supplied to each technique was standardized.
were finished and polished by means of Sof Lex PopOn (3M ESPE) in order to facilitate the posterior cutting procedures.
Linear polymerization shrinkage
Gap measurements
The development of the experimental design was based on the method of Watts and Cash;28 however the linear polymerization shrinkage of the composite resin was measured inside the cavity in all restorations. After the composite resin placement and before the light curing procedure, a device that consisted of a probe (model p 10, Sylvac, Crissier, Switzerland) able to record the dislodgment (mm) of the composite resin in the top – bottom direction was placed on the composite resin surface. The probe used was similar to linear variable differential transformer (LVDT) used by Watts and Cash,28 which has a sensitivity of approximately 0.1 mm. The calibration of the probe was ultimately performed by the Swiss Federal Office of Metrology, according to the Sylvac Standard of Quality. For intermediate calibration, the probe was lightly clamped in a vertical stand opposed by an Instron extensometer (2630-101 GL 10 mm, Canton MA, USA) assembled with a display accuracy superior to 0.1 mm. As the depth of each cavity was accurately recorded with the probe before the resin placement, the percentage of linear polymerization shrinkage could be obtained. The point of measurement was standardized at a distance of 2 mm from the bottom of the cavity (this distance was measured with the probe) in the center of the cavity. After, the specimens were stored in distilled water at 37 8C for 24 h and then the restorations
The teeth were longitudinally sectioned (Labcut 1010 machine, Extec Corp., Enfield, CT, USA) in order to obtain slices with a thickness of approximately 0.7 mm. Three slices were obtained for each cavity (Fig. 1h). In each side of the slices, the mean width of the gaps in the adhesive interface was measured under a magnification of £ 400 (Shimadzu HMV-2, Tokyo, Japan). Considering that the gap along the interface does not have any regular geometric shape, the measurement was performed in approximately rectangular sections (a; b; f; etc.). The area of each section was calculated based on the width and length, as it can be seen in Fig. 2. The ratio between the partial areas and the total length of the interface resulted in the mean gap width.
Microtensile bond strength Slices from five teeth of each experimental condition had their slices sectioned (Labcut 1010 machine, Extec Corp., Enfield, CT, USA) in order to obtain resin –dentin sticks from the cavity floor with a rectangular cross-sectional area of approximately 0.7 mm2 (Fig. 1i and j). Nine sticks were obtained for each restoration and again the same procedure of gap width measurement was repeated on the four sides of each stick, as described previously (Fig. 1k and l). The specimens were fixed with cyanoacrylate resin (Zapit, Corona, CA, USA) to a modified device
Figure 2 (A) Schematic drawing showing a slice of a restoration. (B) Higher magnification of the adhesive interface. In each of the approximately rectangular sections (a; b and f) it was measured the length ðlÞ and the respective width ðwÞ: The partial area of the section a; for instance, was obtained by the multiplication the length a ðla Þ by the width a ðwa Þ: In this case, it would be: 5 £ 2 ¼ 10 mm2.
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Table 1 Means and standard deviations of the linear polymerization shrinkage (%), mean gap width in slices and sticks (mm) for each group. C-factor/filling technique
Linear Gap in Gap in polymerization slices (mm) sticks (mm) shrinkage (%)
0.3/Three layers 0.3/Bulk 3/Three layers 3/Bulk
1.05 (0.04)a 0.98 (0.05)a 1.57 (0.10)b 1.95 (0.08)c
5.1 4.7 12.4 13.9
(2.9)d (2.4)d (5.2)e (5.8)e
4.6 (2.8)f 4.5 (2.3)f 8.1 (3.9)g 9.4 (5.2)g
The results in the groups marked with the same letters show no statistical difference.
and subjected to a microtensile test in a universal machine with a load cell of 100 N (Kratos Dinamometros, Sa ˜o Paulo, Brazil) at a crosshead speed of 0.5 mm/min. The load at failure and the crosssectional area of each specimen was measured to calculate the bond strength in MPa. The analysis of the fractured surfaces was performed under a magnification of £ 400 (Shimadzu HMV-2). The sticks were classified according to the following patterns: cohesive (failure within resin or dentin), adhesive (failure in the interface between tooth and resin) and mixed fracture pattern. The sticks that showed a cohesive fracture pattern were not assigned for calculation of bond strength means.
summing three per restoration. For each group 15 sticks were tested. These sticks were tested under tensile load at a crosshead speed of 0.5 mm/min and the composite resin cohesive strength was calculated in the same way as described for the resin/ dentin sticks, in order to detect any possible damage to the composite resin due to the development of internal tension from shrinkage polymerization.
Statistical analysis Before performing the statistical analysis, a single mean was computed for the values of microtensile bond strength and composite resin cohesive strength (MPa) obtained from sticks originating from the same restoration ðn ¼ 5Þ: Similarly, the same was performed for mean gap width (mm) measured in slices from the same experimental unit (restoration). Thereafter, the means of microtensile bond strength, resin cohesive strength, gap width and linear polymerization shrinkage (%) were subjected to a two-way ANOVA and Tukey’s test ða ¼ 0:05Þ for comparison of the means. The frequency of sticks that debonded during specimen preparation were analysed by a chi-square test ða ¼ 0:05Þ: The correlation between the bond strength means and the gap width (mm) measured in the sticks was analyzed by simple linear regression. The strength of the association between these two variables was estimated with the Pearson productmoment correlation statistic.
Cohesive strength of composite resin measured by microtensile test
Results Slices from the other five teeth of each experimental condition were sectioned (Labcut 1010 machine, Extec Corp., Enfield, CT, USA) in order to obtain resin sticks with a rectangular cross-sectional area of approximately 0.7 mm2 (Fig. 1m and n). One stick near the cavity floor was obtained from each slice,
The results and their respective standard deviations are shown in Tables 1 and 2. Linear polymerization shrinkage. Two-way ANOVA (C-factor vs. filling technique) showed that significant differences were observed for
Table 2 Number of sticks for each fracture pattern and number of sticks debonded during specimen preparation, means and standard deviations of the cross-sectional area of sticks (mm2), microtensile bond strength (MPa) and cohesive strength of composite resin (MPa) for each experimental group. C-factor/filling technique
0.3/Three layers 0.3/Bulk 3/Three layers 3/Bulk
Number of sticks for each fracture pattern and debonded sticks C
A/M
Debonded
10 7 4 9
32 35 30 23
3 3 11 13
Area (mm2)
Microtensile bond strength (MPa)
Composite resin cohesive strength (MPa)
0.74(0.06)a 0.74(0.07)a 0.73(0.10)a 0.75(0.07)a
37.3(9)b 39.9(14)b 31.3(12)c 34.9(12)c
93.7(13.9)d 89.8(14.1)d 96.5(12.5)d 98.4(22.1)d
The results in the groups marked with the same letters show no statistical difference. C, cohesive fracture pattern; A/M, adhesive plus mixed fracture pattern.
Polymerization shrinkage
the interaction of the factors ðp , 0:05Þ: Under the low C-factor, linear polymerization shrinkage was similar for both filling techniques. Conversely, under the high C-factor, the incremental technique (1.57%) reduced the shrinkage compared to the bulk filling (1.95%). Gap width. The results suggest no significant interaction between the factors for the measurements made in the slices and in the sticks ðp . 0:05Þ: No significant difference was found regarding technique ðp . 0:05Þ: However, as seen in Table 1, the different C-factors influenced the results ðp , 0:05Þ: Bond strength. Only the C-factor was responsible for differences observed on microtensile bond strength values obtained from the adhesive interface ðp , 0:05Þ: Lower values were found under the high C-factor. The frequency of the fracture pattern was also different for the experimental groups. Table 2 shows that the frequency of premature debonding before testing was higher under the high C-factor. Conversely, the frequency of cohesive fracture pattern was higher under the low C-factor. Composite resin cohesive strength. The results suggest no significant differences for either the interaction or for the main factors ðp . 0:05Þ: Correlation. There was no statistically significant correlation between the microtensile bond strength and the mean gap width measured in the sticks ðp ¼ 0:17Þ:
Discussion The experimental design of this study was conducted in bovine teeth due to ethical concerns that are related to the use of human teeth. The histological features of human and bovine permanent dentin seem to be similar23 and no difference in bond strength values has been detected.22 Thus the bovine incisor dentin is a suitable substitute for human molar dentin.23 Although several studies on polymerization shrinkage and its harmful effects have been conducted, little attention was given to the development of a simple method capable of measuring the polymerization shrinkage inside a cavity and to verify its likely consequences in the adhesive interface and the internal structure of the composite restorative material under the same experimental unit, as the present one. The results from the linear polymerization shrinkage have confirmed that the higher the ratio of bonded to unbonded surface, the greater is
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the shrinkage in the top-bottom direction. The restriction caused by bonding to the cavity walls prevents the composite resin from reducing its length in the top – bottom direction during the polymerization process. Thus, one of the likely consequences of that, i.e. a higher deflection of the unbonded surface, could be distinguished by the higher linear polymerization shrinkage observed under the higher C-factor. One of the advantages of the incremental technique claimed by several authors is that the volume reduction of each increment could be compensated by the next, and thus the consequence of polymerization shrinkage would be less deleterious since only the volume reduction of the last layer would effectively damage the bond surface. Theoretically, if an infinite number of increments were used, the magnitude of polymerization shrinkage would be insignificant.12 Actually, this statement is only partially true, since all polymerization shrinkage does not occur immediately after light-activation. Sakaguchi et al.21 reported that right after activation only 70 – 85% of polymerization shrinkage occurred; after 5 min this event could reach somewhere around 93%. In a similar way, the achievement of adequate mechanical properties is not immediate. After 30 min of activation, only 60% of the elastic modulus and flexural strength are completed.26 The idea that the subsequent increment can compensate for the polymerization shrinkage would only be valid if the increment could be placed in all regions where volume reduction occurs. This seems to be possible only for the deflected surface but not for the volume reduction that occurs in the interface and leads to gap formation. On the contrary, the polymerization of additional layers tends to deform even more the previous increments, increasing the gap width. According to Carvalho et al.4 and Davidson and Feilzer5 the incremental technique should be used in order to reduce the C-factor of the cavity and therefore minimizes the harmful effects of stress development on the adhesive interface. In fact, the linear polymerization shrinkage, measured under high C-factor, was lower when the cavity was filled incrementally, albeit inferior to the values obtained under low C-factor. Other studies have also reached similar conclusions.6,29 Nonetheless, such reduction was unable to eliminate the consequences of stress development on the adhesive interface. According to the present results, for a given Cfactor, the microtensile bond strength and the mean gap width was similar for both filling techniques. Under the higher C-factor there was
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a reduction of the bond strength values and an increase in the mean gap width, independent of filling technique, which is in agreement with other studies.2,3,32,33 Probably during polymerization shrinkage of the last increment, a considerable strain from the polymerization shrinkage of the first layer can still be under development, leading to a concentration of stresses on the adhesive interface. In fact, this means that the polymerization shrinkage and the consequent stresses that arise may result in a combined effect of polymerization shrinkage from all increments.27,31 Other inherent variables in the present study must be taken into account to allow a comprehensive understanding of the similar results provided by the filling technique. The depth of the cavity in the present study was shallow, limited by the anatomical shape of the bovine teeth. Thus, this fact allowed the complete polymerization of the composite resin when this material was placed in bulk. As the depth of the cavity increases, the light intensity attenuation that occurs inside the composite restorative material prevents the bottom surface from being completely cured.13,20 So, the main drawback of the bulk technique was overcome in the present study. In deeper cavities one may not expect such similar results. For instance, Giannini et al.8 have shown that the bond strength of a composite resin to the cavity floor of a 4 mm deep cavity was low, apart from the activation mode used. Some factors like the properties of the restorative material and the likely tooth deformation under the stress development may interfere with the results and these aspects were not taken into consideration in this study.11,14 Thus, future studies should be conducted to elucidate these hypotheses. The stress development that arises from polymerization shrinkage may cause higher deflection of the unbonded surface, deformation of the tooth structure, gaps along the adhesive interface and also lead to cracks and failures inside the restorative material. The cohesive strength of the composite resin remained unaltered in the experimental groups. During hardening, if the bonding to the cavity walls was strong enough to avoid gap formation, no tooth deformation occurred, the stresses concentrated inside the composite material would produce micro-cracks before its completely hardening, reducing some mechanical properties of the restorative material, such as the hardness, tensile and flexural strength. Other studies have already demonstrated that when the composite resin completely adhered to the walls of a high C-factor cavity, the resin failed cohesively.7 However, the increase in the mean gap width and
A.D. Loguercio et al.
the consequent reduced bond strength under the high C-factor could have contributed to the stress relief from polymerization shrinkage preventing the reduction in the mechanical properties of the composite resin. Actually, the results of the present investigation suggest that in clinical situations the adhesive interface might fail since shrinkage stress surpasses the bond strength to dentin. Some studies have attempted to correlate the data from marginal sealing, micro and nanoleakage with bond strength values immediately or over time.9,16,18 Gu ´zman-Ruiz et al.9 measured the marginal leakage in sticks previously stained with silver nitrate. Pereira et al.18 and Okuda et al.16 tried to correlate the nanoleakage in the hybrid layer in ‘sticks’ stained with silver nitrate. However, as in the present study, none has succeeded in obtaining the correlation between bond strength and marginal sealing even with both tests performed in the same specimen. The explanation for this is still unclear. Some authors have detected that the kind of stain may influence the results obtained in the long term, making the evaluation of marginal sealing and/or nanoleakage difficult.16 – 18 Thus, it seems that the measurement of the mean gap width over time, along with bond strength tests, as a way to evaluate the adhesive, interface, may be a suitable alternative since it does not require any staining. However, this hypothesis still needs to be proved. Therefore, based on the limitations of this study we may conclude that despite the partial reduction of linear polymerization shrinkage under high constraint restored incrementally, the harmful effects from polymerization shrinkage stresses were not minimized.
Acknowledgements This study is part of the thesis of Alessandro Dourado Loguercio (University of Sa ˜o Paulo) for partial fulfillment of the PhD degree in Dental Materials. We thank Dr Ricardo M Carvalho and Dr Ma ´rio F. Go ´es for their expert advice. This investigation was supported in part by FAPESP 99/05124-0 (Fundac ¸˜ ao de Apoio a ` Pesquisa do Estado de Sa ˜o Paulo). The authors are also grateful to Paulo Eduardo dos Santos for graphic illustration support.
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