Demineralization of caries-affected transparent dentin by citric acid: an atomic force microscopy study

Demineralization of caries-affected transparent dentin by citric acid: an atomic force microscopy study

dental materials Dental Materials 17 (2001) 45±52 www.elsevier.com/locate/dental Demineralization of caries-affected transparent dentin by citric ac...

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dental materials Dental Materials 17 (2001) 45±52

www.elsevier.com/locate/dental

Demineralization of caries-affected transparent dentin by citric acid: an atomic force microscopy study G.W. Marshall Jr. a,*, Y.J. Chang a, S.A. Gansky b, S.J. Marshall a a

Division of Biomaterials and Bioengineering, Department of Preventive and Restorative Sciences, University of California, San Francisco, CA 94143-0758, USA b Division of Oral Epidemiology and Dental Public Health, Department of Preventive and Restorative Sciences, University of California, San Francisco, CA 94143-0758, USA Received 28 October 1999; accepted 8 March 2000

Abstract Objectives: This study determined recession rates of peritubular dentin and intertubular dentin in citric acid solution (0.018 M, pH ˆ 2.5) for caries-affected transparent dentin, one of the major components of dentin substrate as altered by caries, with comparisons made with noncarious dentin. Methods: Transparent dentin was identi®ed by sagittally sectioning ®ve obviously carious teeth. Sections were then cut through the transparent dentin area perpendicular to the course of the dentinal tubules. Polished dentin samples of the transparent dentin and non-carious dentin were prepared with an internal reference layer and studied at speci®c intervals for citric acid etching in an atomic force microscope (AFM). Results: At baseline, transparent dentin was identi®ed by dentinal tubules that were largely occluded with mineral deposits that on etching proved to be acid resistant. Peritubular dentin etched rapidly and linearly over time until it could no longer be measured, yielding etching rates for transparent dentin that could not be distinguished from normal dentin. The normal and transparent intertubular dentin surfaces began etching at nearly the same rate, but then surface recession stabilized after less than 1 mm depth change for both dentin types. Signi®cance: Most previous studies have focused on demineralization and bonding to normal dentin, although many bonding procedures involve altered dentin substrates, such as those modi®ed by caries. In this study, peritubular and intertubular dentin from normal and cariesaffected dentin exhibited similar behavior. The major difference was the presence of acid resistant mineral in most of tubule lumens in the transparent dentin. q 2001 Academy of Dental Materials. Published by Elsevier Science Ltd. All rights reserved. Keywords: Dentin; Caries; Transparent dentin; Demineralization; Etching; Atomic force microscopy

1. Introduction Most current methods of dentin bonding rely on demineralization treatments of the dentin surface [1,2], that remove the smear layer and establish a microporous surface which bonding agents may penetrate to create a hybrid structure composed of partially demineralized dentin in intimate association with the bonding polymer [3]. However, most previous studies have focused on demineralization and bonding to normal dentin, even though most bonding procedures actually involve altered dentin substrates. Dentin caries results in a lesion often described as being composed * Corresponding author. Department of Preventive and Restorative Dental Sciences, University of California, San Francisco, 707 Parnassus Avenue, P.O. Box 0758, San Francisco, CA 94143-0758, USA. Tel.: 11415-476-9119; fax: 11-415-476-0858. E-mail address: [email protected] (G.W. Marshall Jr.).

of infected and affected dentin layers [4±6]. Conservative dental treatment seeks to preserve and often bond to affected dentin, which can be divided into a number of altered regions that include, in order of depth, the discolored or turbid layer, the transparent layer, subtransparent layer, and perhaps unaltered dentin [6±8]. Nakabayashi et al. [9] suggested that there may be important differences in the demineralization of caries-affected dentin that could affect bonding. Nakajima et al. [10] have reported that cariesaffected dentin has lower bond strength as compared with normal dentin for some bonding systems. However, determining the zones involved in the bonding procedures in these studies was not possible. Therefore, it is important to clarify the behavior of each of the caries-affected zones. Recent studies have demonstrated that the atomic force microscope (AFM) offers a powerful tool for directly observing demineralization, drying, bonding processes, and mechanical properties of calci®ed tissues, since it offers

0109-5641/01/$20.00 + 0.00 q 2001 Academy of Dental Materials. Published by Elsevier Science Ltd. All rights reserved. PII: S 0109-564 1(00)00056-7

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Fig. 1. Optical micrograph of cross-section through carious molar showing areas of caries-affected transparent dentin below dark/discolored caries region.

advantages of high resolution and the potential to operate in air or solution [11±14]. In earlier AFM studies, normal dentin etching characteristics in a variety of acids have been assessed and methods to establish a reference layer for accurate depth change measurements have been explored [15±18]. When such samples were demineralized in dilute acid solutions, preferential attack on the peritubular dentin with a linear etching rate was found over time. Intertubular dentin etching resulted in surface recession which quickly reached a plateau after less than 1 mm, after which no further depth changes in the intertubular dentin could be detected as long as the samples remained hydrated [11,15]. Acceptable reference layers for height measurements have included evaporated gold [15], photoresist or acid resistant varnish [18], and most recently the incorporation of a cyanoacrylate layer within the sample [16,17]. This study sought to apply these methods to test the hypothesis that the caries-affected transparent zone etches differently than normal dentin. In order to do this, an AFM study of etching dentin in citric acid was conducted. Such a study provides insight into the demineralization process, and therefore, enhances our understanding of differences in cariesaffected transparent dentin and normal dentin and should contribute to improved dentin bonding. 2. Materials and methods This study determined recession rates of peritubular dentin and intertubular dentin in citric acid solution (0.018 M, pH ˆ 2.5) for caries-affected transparent dentin, one of the major components of the dentin substrate as altered by caries, with comparisons made with non-carious dentin. In this investigation, a Digital Instruments Nanoscope III AFM (Digital Instruments, Santa Barbara, CA, USA) was utilized with a wet cell so that fully hydrated samples could be studied. The basic AFM operating principles have been described elsewhere [11,15,19]. For this study we used the contact mode in which the sample is scanned by the sharp

AFM tip with a constant light force. This provides a representation of the surface morphology with an in-plane resolution dictated by the radius of curvature of the tip (about 20 nm as measured by SEM), while the vertical resolution is about 0.1 nm. Carious teeth and third molars, which served as the control group, were obtained from research subjects requiring such extractions as part of their dental treatment. All subjects enrolled in this research provided informed consent for the protocol which had been approved by the UCSF Institutional Committee on Human Research. The extracted teeth were sterilized by gamma radiation [20] and stored in puri®ed and ®ltered water at 48C until prepared. The teeth were sectioned longitudinally. The carious teeth were examined at low power in an optical microscope to determine areas that contained caries-affected transparent dentin (Fig. 1). Fifty consecutively obtained teeth with obvious carious lesions were examined; nearly all teeth had areas that could be readily identi®ed as transparent. Cuts parallel to the occlusal surface were made to expose the areas of transparent dentin to be examined. Control samples were disks cut parallel to the occlusal surface from non-carious third molars. The cut surfaces were then metallographically polished through 0.05 mm alumina-aqueous slurry and ultrasonically cleaned. A cyanoacrylate (Adhesive QX-4; MDS Products Inc., Anaheim, California, USA) reference layer was prepared prior to ®nal polishing as previously described [16,17]. 2.1. AFM study Dentin disks (n ˆ 10 for short-term and n ˆ 8 for longterm characterization, minimum of n ˆ 5† were etched with citric acid solution prepared from reagent grade citric acid at a concentration of 0.018 M that gave a pH value of 2.5 using a TIM 900 pH meter (Titra Lab. Radiometer, Copenhagen, Denmark). Etching was carried out for various intervals up to a cumulative time of 30 min. Initially, the intervals were 5 s in length for the ®rst 20 s, while subsequent intervals were of longer duration as little change could be detected in the specimens. Initially, a baseline image of the area to be studied was obtained under water. A small glass ¯uid chamber specially ®tted for the AFM was used for imaging. The standard AFM optical head with laser beam de¯ection and standard AFM controller electronics were used. The silicone o-ring was not used for sealing the ¯uid. A small volume of liquid (approx. 50 ml) was contained in the chamber and air bubbles were avoided since they interfere with the laser beam. The AFM cantilever and tip, cantilever substrate, and sample surface were submerged in the ¯uid. After baseline imaging, the sample was removed and acid was applied for speci®ed intervals ranging from 5 s to several minutes. At the end of each interval, the acid solution on the sample was thoroughly washed away with puri®ed and ®ltered water and the sample was imaged again in the liquid cell. The same central

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3. Results

Fig. 2. Schematic diagram of AFM depth measurements relative to reference layer for region of dentin containing one tubule surrounded by peritubular (P) and intertubular (Inter) dentin. At baseline (top) the reference layer (Ref), peritubular and intertubular dentin are at the same height. After etching (middle), the AFM tip measures height difference between the reference layer, peritubular dentin which has been etched, and the collagen rich surface of the partially demineralized intertubular dentin surface. After further etching (bottom), the peritubular dentin continues to recede, but intertubular dentin surface location changes only slightly. The AFM tip does not measure the location of the demineralized±mineralized intertubular dentin interface.

area (50 £ 50 mm 2) of each disk including a portion of the reference layer was examined in the liquid cell at each interval. The AFM measurements relative to the reference layer were made as illustrated schematically in Fig. 2 and as previously reported [16]. The sample was never desiccated during these procedures. Vertical distance between a selected area of the dentin surface and the reference layer was measured at six points (three each for intertubular and peritubular dentin) on each sample at each time in a processed image. Dentin recession, based on the difference in vertical distance relative to the reference layer (Fig. 2), was averaged separately for intertubular and peritubular dentin. Since the same area was observed for each sample over time, initial etching rates for peritubular and intertubular dentin were determined from the slopes of the regression lines of recession over time separately for intertubular and peritubular dentin. The prolonged etching characteristics of intertubular dentin were characterized by the recession versus time curves. Long-term etching characteristics of peritubular dentin could not be measured because the surface of the peritubular dentin receded beyond the reach of the AFM tip. The same method was used in attempting to determine the etching rate of the mineral deposits found in the tubule lumens of the caries-affected transparent dentin. However, the irregular contour of these deposits did not allow returning to the same exact point at each etching interval and therefore, accurate measurements could not be made. Etching characteristics for the peritubular and intertubular areas of the transparent and normal dentin were statistically compared using general linear mixed regression models with a random disk effect and 95% con®dence intervals [21], for early etching rates of peritubular and intertubular dentin, while a cell mean mixed regression model of the depth of intertubular recession was used for comparison of the longterm etching characteristics of the intertubular dentin.

Fig. 3 shows images at baseline and after 5 s of etching for citric acid at pH ˆ 2.5 for transparent and normal dentin. In the baseline images, the reference layer (top left) is barely apparent since gray shade differences re¯ect height differences in the AFM image; and it is at nearly the same height as the polished dentin. Transparent dentin had most of the lumens of the dentin tubules ®lled with an apparent mineral deposit, while normal dentin showed patent tubules throughout. On etching several changes were noted, including rapid recession of the peritubular dentin, and recession of the intertubular dentin in both the transparent and normal dentin samples. The mineral deposits within the tubule lumens (luminal deposits) also underwent etching at a slower rate than either the peritubular or intertubular dentin, as indicated by the lighter shading of the deposits and the similar shading to the reference layer. This became more clearly delineated as the other surfaces receded. Fig. 4 shows a sequence of images of the same area of transparent dentin from baseline through 60 s of etching. In the images following etching at 5, 10, and 15 s, the presence of luminal deposits can be seen, although there are slight changes in appearance. The deposits appeared to be rather loosely packed into the lumen and completely disappeared after 20 s. This disappearance has been interpreted as wash-out of the loose deposits, rather than a result of a sudden increase in dissolution rate. The irregular surface of the luminal deposits and their sudden disappearance prevented us from obtaining an accurate etching rate for these deposits. The peritubular dentin quickly receded below the surface and could not be easily seen after 20 s of etching. The intertubular dentin initially appeared to undergo recession, but little change was apparent after 15±20 s. Note that the same area is re-imaged at each interval throughout this etching sequence and therefore allows for longitudinal study of the changes in the same area of the sample. These experiments demonstrate that as etching proceeded the peritubular dentin was etched rapidly and the intertubular dentin surface decreased in height only a very limited amount relative to the reference layer, while the luminal deposits appeared to etch at a slow rate initially and then disappeared over one etching interval, probably due to wash-out of the loose deposit. Fig. 5 shows the recession for the peritubular dentin and the intertubular dentin for the ®rst 30 s for all samples of normal and transparent dentin. The initial peritubular and intertubular dentin recession rates appeared linear for both forms of dentin but had different rates, with the slope of the peritubular dentin much higher than that of the intertubular dentin. After 20±30 s, accurately measuring the rate of the peritubular dentin was not possible, as noted above. The intertubular dentin could be followed for extended periods. Comparison of the short-term slopes for both the peritubular transparent and normal dentin and intertubular normal and transparent dentin shows no signi®cant differences between

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Fig. 3. AFM comparison images of etching caries-affected transparent (top) and normal dentin (bottom). Baseline and 5 s images for citric acid etching at pH 2.5 (0.018 M). Reference layer is at top left side of each image. Transparent dentin contained luminal deposits that were not present in normal dentin. Tubule number differences in the images re¯ect slightly different dentin depths.

the transparent and normal dentin as indicated by the overlapping 95% con®dence intervals. Table 1 shows the etching rates derived from the linear regression for the peritubular dentin and intertubular dentin from the initial recession shown in Fig. 5. The average values of 29.8 and 26.5 nm/s for transparent peritubular dentin and normal peritubular dentin, respectively, were not signi®cantly different …p ˆ 0:17†: Similarly, the initial apparent etching rates for the intertubular dentin were 2.0 and 5.5 nm/s for carious transparent and normal intertubular dentin and were not signi®cantly different …p ˆ 0:15†: Fig. 6 shows the recession curves for transparent and normal intertubular

dentin for experiments carried out for a cumulative etching time of 30 min. The intertubular dentin of both types etched at a similar initial rate, but then recession slowed and the depth change plateaued. Table 1 also shows the depth of recession at which plateaus in the recession curves were reached for the intertubular dentin. The depth changes at the plateau occurred at nearly the same time and gave values of 541 nm for transparent and 589 nm for normal intertubular dentin. Overall the curves of Fig. 6 showed no signi®cant differences in the long-term recession behavior of the normal and transparent intertubular dentin …p ˆ 0:56†:

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Fig. 4. Etch sequence of caries-affected transparent dentin at times up to 60 s. Reference layer at top left side. Tubules were mostly occluded at the start of etching, and peritubular dentin etched around the deposits that were more acid resistant, as the intertubular dentin receded slightly. After 20 s, most deposits were no longer observed in the tubule lumens, probably as a result of wash-out.

4. Discussion Transparent dentin forms as one consequence of caries and results from partial occlusion of the tubule lumen with mineral deposits. A number of workers have demonstrated that these deposits are acid resistant and it has been suggested that many such deposits are composed of whitlockite [7,22]. Whether such deposits are the result of an active defense mechanism or are a result of a dissolution and reprecipitation phenomena is still unclear. However, their presence is believed to reduce ingress of acid, bacteria, and/or bacterial byproducts and therefore, serves as protection for the pulp tissue. Since the transparent layer is apparently protective and does not contain bacteria, it is believed that it should be retained in conservative cavity preparations and, therefore, may form a substantial portion of cavity preparations. There is little or con¯icting evidence concerning the mechanical and demineralization characteristics of this zone, and even its prevalence is uncertain. During our optical identi®cation of transparent dentin, we found a very high prevalence of transparent dentin in large carious lesions, although both large areas and intermittent areas of transparent dentin were often present (Fig. 1) in sections from different teeth. The results show that the peritubular dentin and intertubular dentin of transparent carious and normal dentin have

etching characteristics that were very similar in these experiments. The initial etching rates were slightly, but not signi®cantly, higher for the carious transparent dentin. With the sample size and variation in our study, we had 80% power to detect a difference in etching rate of 2.5 nm/s. This suggests that the presence of the deposits in the lumen does not decrease the etching behavior of either dentin component. The mineral deposits within the tubule lumens are well known to be acid resistant [6,7], as qualitatively determined by SEM. Efforts to quantitatively measure their etching rates proved to be dif®cult in the current studies because the deposits appeared to be relatively loosely packed into the tubules and were irregular in their surface contour. This made it dif®cult to return to the same point to measure recession relative to the reference layer during the initial intervals of etching, and subsequent periods resulted in loss of all or portions of the deposits. This loss of material was probably a result of wash-out of the deposits after minimal etching. With more completely packed mineral deposits and a continuous etching technique [18], it may be possible to overcome this limitation in future studies and determine the etching rate of the deposits. It may, therefore, be considered that the main difference in the etching characteristics of caries transparent dentin and normal dentin is the presence of the luminal deposits. However, other workers have shown bond strength test

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Fig. 5. Plots of recession vs. time for the peritubular and intertubular dentin surface for all transparent and normal dentin samples etched 0±30 s in citric acid at pH 2.5 (0.018 M). Bars ˆ 95% con®dence intervals and show no difference in recession characteristics between transparent and normal dentin in peritubular and intertubular dentin. Mixed effect linear regressions were used to estimate etching rates.

results that suggest that bond strengths to carious dentin that are likely to contain transparent dentin regions are lower than bond strengths to normal dentin [10]. This suggests that there may be differences in transparent dentin that were not detectable by this study. In addition, Ogawa et al. [7] reported that the microhardness of transparent dentin is generally lower than normal dentin despite the increased mineral in the tubule lumen. This suggests that the mineral level in the intertubular portion of the transparent dentin is likely to be lower than in normal dentin. These results raise

the question of whether or not such a presumed lower mineral content would result in differences in etching rates of the peritubular dentin or intertubular recession as determined in the current study. A partially demineralized intertubular dentin would have no effect on the peritubular dentin, and it is therefore reasonable to expect no difference in the etching rates of peritubular dentin from transparent and normal forms of dentin. The response of the intertubular dentin as determined by the AFM method utilized in these experiments measures the location of the surface relative to

Table 1 Average values of etch-rate measurements are shown. P-values at which the measurements were not signi®cantly different are also shown Type

Location

Etch rate (nm/s)

95% CI

Short-term characteristics Carious Peritubular Normal Peritubular Carious Intertubular Normal Intertubular

29.8 26.5 2.0 5.5

[26.2,33.3] [23.5,29.5] [±1.5,5.6] [2.4,8.5]

Long-term characteristics Carious Intertubular Normal Intertubular

± ±

[476,616] [514,663]

Recession at plateau (nm) ± ± ± ± 541 589

Carious vs. normal P-value 0.17 0.15

0.56

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Fig. 6. Recession curves for transparent and normal intertubular dentin samples for etching times up to 1800 s. Bars ˆ 95% con®dence intervals and showed no difference in recession characteristics which after rapid initial change, slowed and appeared to plateau after depth changes of less than 1 mm.

the reference layer. It is important to understand that this determination is not the same as determining the location of the demineralization front in the intertubular dentin, since this front moves inward as demineralization occurs and leaves a demineralized collagen layer on the surface [8]. This point is emphasized in the schematic diagram of Fig. 2 that shows the measurement of the surface location of the intertubular dentin, which is measured relative to the position of the reference layer, as well as the location of the demineralization front, which is not detectable with this method. Thus, as a result of the rapid plateau in the recession curve for both hydrated transparent and normal dentin, any difference in the location of the front is not detectable. Other methods, such as drying and collapsing this layer [8], or non-invasive methods such as X-ray tomographic microscopy that reveal the location of the demineralization front [8,18], will have to be used to determine if there are differences in the location and rate of progression of the front. Several other speculations may be made to account for work showing decreased bond strength to carious dentin as shown by others, and similar etching rates for peritubular and intertubular dentin from transparent and normal dentin as shown in this work. The collagen in the carious dentin

tested for bond strength may have been altered by either the carious process or subsequent etching for bonding. A second possibility is that the carious dentin might be more deeply demineralized and therefore, bonding agents may not have penetrated as completely in the carious samples as in normal samples. A third possibility is that the presence of luminal deposits in transparent dentin restricts penetration of bonding agents, creating a less than ideal hybrid layer. Finally, the tests with carious dentin may have been carried out in samples containing other altered zones of caries-affected dentin. Determination of which of these mechanisms are more likely will have to await additional studies of both bond strength and etching characteristics of various zones of caries-affected dentin. 5. Conclusions This work demonstrated that peritubular dentin of cariesaffected transparent dentin is rapidly etched at a rate that was indistinguishable from normal dentin. In contrast with behavior of the peritubular dentin, the recession of the intertubular dentin was extremely limited for citric acid at pH of

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2.5 and was indistinguishable from the intertubular dentin of caries-affected transparent dentin. The major distinguishing characteristic of the carious transparent dentin was the presence of acid resistant mineral deposits in the lumen of the tubules. However, in the current samples these deposits were relatively loosely packed and their etching rate could not be accurately determined. Their presence appeared to have no effect on either peritubular etching rate or intertubular dentin recession. Acknowledgements This study was supported by the US Public Health Service through National Institutes of Health/National Institute of Dental Research Grants P01 DE09859 and R01 DE11526. Grateful acknowledgment is made of manuscript preparation by M. Ashton Ponce. References [1] Bertolotti RL. Conditioning of the dentin substrate. Oper Dent 1992(Suppl 5):131±6. [2] Pashley DH. The effects of acid etching on the pulpodentin complex. Oper Dent 1992;17:229±42. [3] Nakabayashi N, Kojima K, Masuhara E. The promotion of adhesion by the in®ltration of monomers into tooth substrates. J Biomed Mater Res 1982;16:265±73. [4] Shafer WG, Hine MK, Levy BM. A textbook of oral pathology. Philadelphia: W.B. Saunders, 1974 (p. 290, 291, 399±404). [5] Hoffman S. Histopathology of caries lesions. In: Menaker L, editor. The biologic basis of dental caries, Hagerstown: Harper and Row, 1980. p. 226±46. [6] Fusayama T. A simple pain-free adhesive restorative system by minimal reduction and total etching. Tokyo: Ishiyaku EuroAmerica, 1993 (p. 1±22, 73, 74). [7] Ogawa K, Yamashita Y, Ichijo T, Fusayama T. The ultrastructure and hardness of the transparent layer of human carious dentin. J Dent Res 1983;62:7±10.

[8] Marshall GW, Marshall SJ, Kinney JH, Balooch M. The dentin substrate: structure and properties related to bonding. J Dent 1997;25:441±58. [9] Nakabayashi N, Ashizawa M, Nakamura M. Identi®cation of a resin± dentin hybrid layer in vital human dentin created in vivo: durable bonding to vital dentin. Quintessence Int 1992;23:135±41. [10] Nakajima M, Sano H, Burrow MF, Tagami J, Yoshiyama M, Ebisu S, Ciucchi B, Russell CM, Pashley DH. Tensile bond strength and SEM evaluation of caries-affected dentin using dentin adhesives. J Dent Res 1995;74:1679±88. [11] Marshall GW, Balooch M, Tench R, Kinney JH, Marshall SJ. Atomic force microscopy of acid effects on dentin. Dent Mater 1993;9:265±8. [12] Cassinelli C, Morra M. Atomic force microscopy studies of the interaction of a dentin adhesive with tooth hard tissue. J Biomed Mater Res 1994;28:1427±31. [13] Kinney JH, Balooch M, Marshall SJ, Marshall GW, Weihs TP. Hardness and Young's modulus of human peritubular and intertubular dentine. Arch Oral Biol 1996;41:9±13. [14] Balooch M, Wu-Magidi I-C, Lundkvist AS, Balazs A, Marshall SJ, Marshall GW, Seikhaus WJ, Kinney JH. Viscoelastic properties of demineralized human dentin in water with atomic force microscopy (AFM)-based indentation. J Biomed Mater Res 1998;40:539±44. [15] Marshall GW, Balooch M, Kinney JH, Marshall SJ. Atomic force microscopy of conditioning agents on dentin. J Biomed Mater Res 1995;29:1381±7. [16] Marshall GW, Inai N, Wu-Magidi I-C, Balooch M, Kinney JH, Tagami J, Marshall SJ. Dentin demineralization: effects of dentin depth, pH and different acids. Dent Mater 1997;13:338±43. [17] Marshall Jr. GW, Wu-Magidi I-C, Watanabe LG, Inai N, Balooch M, Kinney JH, Marshall SJ. Effect of citric acid concentration on dentin demineralization, dehydration and rehydration: an atomic force microscopy study. J Biomed Mater Res 1998;42:500±7. [18] Kinney JH, Balooch M, Haupt DL, Marshall SJ, Marshall GW. Mineral distribution and dimensional changes in human dentin during demineralization. J Dent Res 1995;74:1179±84. [19] Jahanmir J, Haggar BG, Haynes JB. The scanning probe microscope. Scanning Microsc 1992;6:625±60. [20] White JM, Goodis HE, Marshall SJ, Marshall GW. Sterilization of teeth by gamma radiation. J Dent Res 1994;73:1560±7. [21] McLean RA, Sanders WL, Stroup WW. A uni®ed approach to mixed linear models. American Statistician 1991;45:54±64. [22] Daculsi G, LeGeros RZ, Jean A, Kerebel B. Possible physicochemical processes in human dentin caries. J Dent Res 1987;66:1356±9.