pH-cycling models for in vitro evaluation of the efficacy of fluoridated dentifrices for caries control: strengths and limitations

Despite a plethora of in situ studies and clinical trials evaluating the efficacy of fluoridated dentifrices on caries control, in vitro pH cycling models are still broadly used because they mimic the dynamics of mineral loss and gain involved in caries formation. This paper critically reviews the current literature on existing pH-cycling models for the in vitro evaluation of the efficacy of fluoridated dentifrices for caries control, focusing on their strengths and limitations. A search was undertaken in the MEDLINE electronic journal database using the keywords "pH-cycling", "demineralization", "remineralization", "in vitro", "fluoride", "dentifrice". The primary outcome was the decrease of demineralization or the increase of remineralization as measured by different methods (e.g.: transverse microradiography) or tooth fluoride uptake. Inclusion of studies, data extraction and quality assessment were undertaken independently and in duplicate by two members of the review team. Disagreements were solved by discussion and consensus or by a third party. One hundred and sixteen studies were included, of which 42 addressed specifically the comparison of dentifrices using different pH-cycling models. The other studies included meta-analysis or reviews, data about the effect of different fluoride sources on de-remineralization, different methods for analysis de-remineralization and chemical variables and characteristics of dental hard tissues that might have influence on de-remineralization processes. Generally, the studies presented ability to detect known results established by clinical trials, to demonstrate dose-related responses in the fluoride content of the dentifrices, and to provide repeatability and reproducibility between tests. In order to accomplish these features satisfactorily, it is mandatory to take into account the type of substrate and baseline artificial lesion, as well as the adequate response variables and statistical approaches to be used. This critical review of literature showed that the currently available pH-cycling models are appropriate to detect dose-response and pH-response of fluoride dentifrices, and to evaluate the impact of new active principles on the effect of fluoridated dentifrices, as well as their association with other anti-caries treatments.

the high level of scientific control and the resulting lower variability intrinsic to in vitro models, as well as the smaller sample size required. Additionally, the response variables that can be employed in pH-cycling models are more sensitive than those available for use in the clinical situation. Due to these key advantages, pH-cycling models have helped improving the understanding of the caries process and the possible mechanisms by which fluoride exerts its anti-caries effect. Furthermore, they are broadly used in profile studies for rapid and inexpensive testing of developing and recently marketed products 106,116 . The role of pH-cycling models is therefore to facilitate the generation of sufficient quantitative data to give investigators the confidence to appropriately design clinical trials 18 .
However, pH-cycling models as all in vitro protocols have important limitations: (1) they are unable to completely simulate the complex intraoral conditions leading to caries development, even when "artificial mouth" systems, bacterial biofilms and saliva are employed. This is particularly relevant for testing fluoridated dentifrices with monofluorophosphate (MFP), since the enzyme systems required for MFP hydrolysis are present in saliva and plaque in vivo, but are absent in most in vitro test methods; (2) they cannot mimic solid surface area/solution ratios or the saliva/plaque fluid composition encountered in vivo 107 , since different oral surfaces are bathed in different volumes and source combinations of saliva, (3) there are artifacts associated with the choice of substrate and test conditions, particularly the time periods of de-and remineralization, which are much faster than those expected to occur in in vivo conditions 106 ; and (4) they are not able to adequately simulate topical use and clearance of products from the oral cavity. While dentifrices are typically slurried to simulate dilution during brushing, the uptake and reactivity of fluoride are consistently lower in vivo than in vitro, which may result in inaccurate assessments of the anti-caries potential of formulations directed toward enhancement of fluoride delivery 107 . All these limitations must be kept in mind when data from pH-cycling studies are intended to be extrapolated for the clinical situations. This paper critically reviews the current literature on existing pH-cycling models for the in vitro evaluation of the efficacy of fluoridated dentifrices for caries control, focusing on their strengths and limitations. Additionally, the impact of the characteristics of previous artificial caries lesions on subsequent de-remineralization, the response variables usually chosen, and the American Dental Association (ADA) guidelines 1,2 for this kind of tests are considered. Finally, studies involving different pH-cycling protocols are compared, considering separately those focusing on fluoride dose-response or pH-response of the dentifrices, type of fluoride compound present in the dentifrice, the impact of new active principles on the effect of fluoridated dentifrices, as well as their association with other anti-caries treatments. The validity of the pH-cycling protocols is discussed in the light of data from clinical studies, whenever possible. Based on the currently available literature, future perspectives in pH-cycling protocols are also included in the discussion.

METhODS
A search was undertaken in the MeDLINe electronic journal database using the keywords "pHcycling", "demineralization", "remineralization", "in vitro", "fluoride", "dentifrice". The primary outcome was the decrease of demineralization or the increase of remineralization as measured by different methods (e.g.: microhardness, microradiography, polarized light microscopy) or tooth fluoride uptake.
One hundred and sixteen papers referring to the following issues were retrieved: 1) the comparison of dentifrices using different pH-cycling models; 2) meta-analysis/reviews about methods or the effect of fluoride on dental de-remineralization; 3) the effect of different fluoride sources on deremineralization in vitro; 4) different methods to analysis de-remineralization and; 5) chemical variables and characteristics of dental hard tissues that might have influence on de-remineralization process.
Inclusion of studies, data extraction and quality assessment were undertaken independently and in duplicate by two members of the review team. Disagreements were resolved by discussion and consensus or by a third party.

RESULTS AND LITERATURE REVIEW
The genesis of modern pH-cycling models was produced by ten Cate and Duijsters 87 (1982). In typical pH-cycling studies for testing the efficacy of fluoridated dentifrices, a dental substrate (enamel or dentin, from permanent or primary teeth, from human or bovine origin) is sequentially exposed to demineralizing and remineralizing solutions with intermediary treatments with the dentifrices.
In vitro pH-cycling models can generally be classified into progression (demineralizing) or reversal (remineralizing) models depending on the flux of mineral from or to the dental substrate, respectively 106 , as shown in Figure 1. The demineralizing models usually employ an initially sound substrate and the response variable will analyze the potential of the dentifrice to reduce the loss of mineral from the substrate to the demineralizing solution or the gain of mineral pH-cycling models for in vitro evaluation of the efficacy of fluoridated dentifrices for caries control: strengths and limitations 2010;18(4):316-34 from the remineralizing solution. Demineralizing models can also employ substrates with artificial caries lesion to measure the extent of further demineralization. In remineralizing models, dental substrates with artificial caries lesions are used and the response variables will measure the mineral gain in the lesions as a consequence of the treatment with the dentifrices.
Some important methodological aspects have been found in the literature review. They will be presented and discussed below in order to make easier the choice for appropriate protocols for the incoming studies as well as the adequate interpretation of the results of existing publications by the readers. Finally, the data from studies about the effect of fluoride dentifrices on deremineralization will be presented in tables and discussed in the text. The future perspectives for studies using pH-cycling as an in vitro model will also be addressed.
Type of dental substrates that can be used in ph-cycling models excellent reviews to guide the choice of dental substrates for in vitro and in situ studies have been presented by Mellberg 60 (1992) and Ogaard and Rolla 68 (1992). Regarding the origin of the substrates, human teeth can be regarded as the most appropriate source from the perspective of clinical relevance. However, their composition is variable, due to genetic influences, environmental conditions (diet, fluoride exposure, previous caries challenge) and age (post-eruptive maturation and dentin sclerosis). These differences lead to large variations in their response under acidic challenges.
Among the different types of human teeth, permanent molars and premolars are the most often employed teeth. Primary teeth are only occasionally used because it is difficult to obtain them and they have a small surface for experimental manipulation. When primary teeth are used, it must be taken into account that the progression of lesions in vitro is faster than would occur for permanent teeth 114 . Regarding the age, impacted or partially erupted teeth are more porous than teeth that have been exposed to the oral cavity for a longer time and caries progression should be expected to occur in a faster rate 10 . In addition, dentin sclerosis, which occurs with age, can alter the dentin susceptibility to caries development since a gradual mineralization of the peritubular dentin occurs, eventually resulting in complete obliteration of the tubules 79 .
On the other hand, bovine teeth are more readily available and have a more uniform composition when compared to human teeth, thus providing a less variable response to both cariogenic challenge and anti-caries treatments, such as fluoridated dentifrices 60 . Additionally, bovine teeth have a bigger surface area which makes easier experimental manipulation. Furthermore, bovine teeth present higher porosity, which allows a faster diffusion of ions to the demineralized area 26,28,55 . Thus, longer experimental periods might compromise the ability of the model to show fluoride dose-response. Although bovine enamel is more porous than human enamel, which leads to faster demineralization and remineralization, these differences result in quantitative and not qualitative differences in behavior. Additionally, the artificial caries lesions produced from bovine teeth have a mineral distribution and structure that resembles lesions produced from human teeth, both for enamel and dentin 20,28,37,60 . Thus, bovine tooth can be considered an acceptable alternative to human tooth in Cariology research and may offer advantages to human tooth by decreasing the response time and variability of the hard tissue substrate in the model 60 .
Considering the different types of mineralized dental tissues, enamel and dentin have very different structures and compositions, which interfere in their susceptibilities to dental caries. Basically, permanent enamel is composed by mineral (85% volume) in the form of hydroxy-or fluorapatite crystals organized in prisms. Upon a cariogenic challenge (4.5<pH<5.5), hydroxyapatite crystals are dissolved from the subsurface, while fluorapatite crystals are deposited at the surface, originating a subsurface lesion. The dissolution process is merely a chemical event.
Permanent dentin, however, contains 47% apatite, 33% organic components (90% collagen and 10% non-collagenous proteins) and 20% water by volume. The mineral phase is hydroxyapatite, similar to enamel, but the crystallites have much smaller dimensions. The hexagonal dentinal crystallites are 3-30 nm in cross-section and about 50 nm in length. This results in a much larger surface area to crystallite volume ratio and therefore a more reactive mineral phase. The organic matrix is mainly composed of collagen. It is present as a very structured triple helix of three intertwined polypeptide chains. In addition, there are many non-collagenous (phosphoproteins, phospholipids and proteoglycans) components that determine the matrix properties. These compounds play a role in the nucleation and regulation of mineral formation during odontogenesis 90 . Then they may interfere with demineralization and remineralization processes by a similar mechanism of action. There is a synergism between matrix and apatite. The mineral phase can only be partially dissolved during an acid attack, while the matrix cannot be digested by enzymatic action while its surface is protected by apatite. Dentin caries is therefore a biochemical process characterized initially by the dissolution of the mineral part thus exposing the organic matrix to breakdown 50,66,79 by bacteria-derived enzymes and host-derived enzymes, such as the matrix metalloproteinases (MMPs) present in dentin and saliva 15,100 . The dentin demineralization rate decreases when the amount of degradable collagen increases, whereby the demineralized matrix is attributed to hamper ionic diffusion into and out of the demineralizing area 49,50 . However, it should be remembered that during caries lesion formation in vivo, teeth with a vital pulpo-dentinal organ will respond to most exogenous stimuli through the apposition of minerals along and within the dentinal tubules 32 . This phenomenon, together with the outward flow of dentinal fluid from the pulp, may be expected to significantly reduce the rate of in vivo lesion progression in dentin compared to in vitro situation 80 .
It has been shown that MMPs get activated when the pH drops in the presence of acids from cariogenic challenges. The subsequent neutralization by salivary buffer systems enhances the degrading activity of the organic matrix 100 (Figure 2). It is noteworthy that dentin matrix degradation occurs when bacterial collagenase is added to remineralizing solution but not to demineralizing solution in pH-cycling models 47 , i.e. the activity of bacterial collagenase added to demineralization solution is lost, while the activity of host MMPs is enhanced at low pH, emphasizing the importance of host collagenases 100 . Thus, pH-cycling models without the addition of collagenases or gelatinases can only simulate the chemical events involved in root dentin caries, since they do not take into consideration the biochemical role of salivary MMPs in the degradation of the demineralized organic matrix. Additionally, when simulating dentin caries in vitro, it is also important to use freshly extracted teeth and store these teeth properly (0.02% NaN 3 , 0.9% NaCl solution, at 4 o C) 70 in order to assure that the activity of dentin MMPs is preserved.
In addition to the necessity of degradation of the organic matrix for dentin caries progression, dentin de-and remineralization has many other characteristics that differ from enamel de-and remineralization: (1) dentin is more susceptible to caries attack than is enamel, with a critical pH more than one pH-unit higher than that for enamel 41 ; (2) dentin demineralizes faster and remineralizes slower than enamel under the same experimental conditions 4,86 ; (3) more concentrated fluoride is needed for remineralization of dentin than for enamel 38 ; (4) dentin contact area with cariogenic acids is bigger than that of enamel and hence dentin is apparently much more permeable to acids, with demineralization taking place at a relatively large depth, while mineral deposition is restricted to the outer layers. If the crystallites surrounding the diffusion channels (tubules) are coated with a fluoride-rich mineral (due to the use of fluoride dentifrice), the acids will bypass these relatively resistant minerals, while mineral and fluoride ions will readily be deposited. Thus, the lesion front in dentin moves deeper, while the surface layer becomes broader. In enamel, on the other hand, diffusion is much slower and allows acids to "sidestep" into smaller intraprismatic porosities and dissolve crystallites that are still unaffected by either acid or fluoride. Thus, mineral uptake and loss occur at similar depths for enamel lesions, while pH-cycling models for in vitro evaluation of the efficacy of fluoridated dentifrices for caries control: strengths and limitations 2010;18(4):316-34 for dentin lesions mineral uptake is predominant at the surface and mineral loss at the lesion front 86 .
It must be also pointed out that the dental substrates have usually to be polished before the beginning of the experiment in order to produce more uniform and homogeneous surfaces that can be more accurately standardized, resulting in abraded surfaces. This procedure is essential for some response variables such as surface hardness analysis. The removal of the outermost fluoride-rich enamel layer will render a faster demineralization of the subsurface during the subsequent pH-cycles 5,96 .

Characteristics of Artificial Caries Lesions that May Affect De-and Remineralization in ph-Cycling Models
In some studies, artificial caries lesions are initially produced by immersion of the substrates in buffered lactate or acetate gels 110 or solutions, undersaturated in respect to apatite, with a pH ranging between 4.4 and 5.0, for a time ranging between 16 h and 28 days (Figures 3, 4, 5 and 6). These distinct protocols will lead to different types of lesions formed (surface softened lesions, also known as erosion-like lesions, or subsurface lesions, also called caries-like lesions) (Figure 7). The distinct integrated mineral loss (∆Z) and depth at baseline [54][55][56] in these lesions can have a profound impact on the subsequent de-and remineralization rates thus affecting the performance of the tested products.
It is required that the demineralizing procedures induce caries-like (subsurface lesion with a lessdemineralized surface layer) rather than erosionlike lesions. Many factors are important for the preservation of the surface layer, such as the presence of calcium and phosphate 19 and fluoride 99 in the solution, its pH 97 and the time after an

pH-cycling
Human enamel CSH x TMR [Ten Cate, et al. 92 (1985)] The NaF dentifrice was found to be extremely effective in reducing the progression of caries in enamel  Human enamel R e f l e c t e d l i g h t microscopy, CSH, F/ Ca content by probe ( s a m p l e s ) a n d F a n a l y s i s i n d e -r e solutions NaF dentifrice and mouthrinse lead to a higher uptake of F into the lesion compared to MFP dentifrice, but the mineral content profile did not differ among the groups Human enamel SMH and F uptake ( m i c r o d r i l l b i o p s y t e c h n i q u e a n d F electrode) AmF and MFP only dentifrices were less effective in enamel remineralization than NaF only and NaF+MFP formulations. The inclusion of human saliva as product diluents is a critically important aspect to consider for any in vitro study and most importantly when testing either AmF or MFP containing formulations.   Human enamel PLM (lesion depth) The addition of ACaPO4 to a fluoride dentifrice resulted in a trend toward further reductions in lesion depth following in vitro lesion formation and progression over those obtained with a fluoride dentifrice.
Dentifrices were removed, enamel rinsed for 3 min with deionized water and placed in artificial saliva (20 mM NaHCO 3 , 3 mM NaH 2 PO 4 , 1 mM CaCl 2 , pH 7.0), rinsed with deinized water for 3 min. Dentifrice containing both F and sanguinaria was more effective than dentifrice containing F alone on remineralization of enamel lesion and on the pH of de solution. NaF dentifrices were more effective than MFP dentifrices. H u m a n e n a m e l (4x4x3 mm) Visual examination by 5 examiners scoring the presence and severity of caries-like lesions according to a scale ranked 0 to 3 The association of restorative materials and F dentifrice yielded higher cariostatic effect, except for the conventional glass ionomer cement, whose cariostatic effect was not influenced by the type of dentifrice Human enamel F a n a l y s i s ( d er e s o l u t i o n s ) a n d quantitative PLM and CSH (samples) All treatment reduced the demineralization progress in enamel. However, the laser irradiation did not improve the effect of F.  High-R lesions give better discrimination among the treatments under study and seem to be more appropriate to compare the efficiency of remineralizing systems, such as fluoridated dentifrices. Low-R lesions are more appropriate when physiological mineral distribution is required. Modified from Lynch, et al. 54 (2007) initial demineralization 98 , as the saturation might be reached with time, depending on the volume and viscosity of the demineralization solution relative to the area of enamel exposed to it. These factors interact with each other, making difficult the establishment of their ideal individual characteristics in a pH-cycling model. The formation of the surface layer might be also affected by agitation, whereas a higher agitation increases the risk of surface dissolution (Figure 7). It is important to consider these factors because the thickness of the surface layer may have influence on subsequent de-remineralization 54 . Additionally, porosity and depth of a lesion can also play an important role in mineral diffusion 54,88 . It has been recently shown that lesions with increasing ∆Z at baseline have a marked decrease in further mineral loss and a concomitant increase in further mineral gain. The decrease in demineralization of lesions with higher ∆Z at baseline may be partially a result of decreased intrinsic solubility through modified chemical composition such as loss of carbonate and magnesium. On the other hand, the tendency towards mineral gain might be due to the fact that larger, more porous lesions might be more easily remineralized than smaller and less porous lesions 83 . This may explain the tendency toward net remineralization with increasing ∆Z at baseline in pH-cycling regimes 55 . Furthermore, shallow lesions are more prone to demineralization than deeper ones because in deeper lesions the dissolved mineral from the deeper portions might undergo reprecipitation during outward diffusion 61,78 . On the other hand, the remineralization rate is lower in deeper lesions due to the longer distance for ionic diffusion before mineral deposition can occur 54,61 .
In addition to the initial mineral loss of the artificial caries lesion, its mineral distribution is also very important. Low-R (R=∆Z/depth) lesions are more appropriate when physiological mineral distribution is required, while high-R lesions give better discrimination among the treatments under study and seem to be more appropriate to compare the efficiency of remineralizing systems 54 , such as fluoridated dentifrices (Figure 8). Thus, the comparison of the results from studies in which lesions with different characteristics at baseline were employed must be done with caution. Furthermore, fluoride dose-response studies should be carried out with lesions of various degrees of severity before conclusions on optimal fluoride efficacy are drawn 88 .

Response Variables in ph-Cycling Models to Evaluate Fluoridated Dentifrices
Many response variables can be employed in pHcycling models to evaluate the efficacy of fluoride dentifrices. Some of them (colorimetric methods and atomic absorption spectrometry-AAS) evaluate the ions (mainly calcium and phosphate) released into the de-and remineralizing solutions. Also the calcium fluoride-like material and fluorapatite formed onto the dental substrates as a consequence of the treatments can be removed by alkali or acid biopsies and fluoride can be analyzed using an ionspecific electrode. From these biopsies, the amounts of calcium and/or phosphate can be also evaluated by the methodologies described above.
Regarding the analysis of the samples, depthrelated properties of artificial lesions can be described quantitatively by mineral content and hardness profiles 56 and qualitatively by polarized light microscopy-PLM 39 (more frequently) and scanning electron microscopy-SeM (less frequently) 114 .
Transverse microradiography (TMR) can be regarded as the "gold standard" for the evaluation of mineral distribution in Cariology research. This technique provides a quantitative measurement of the amount of mineral, lesion depth and surface layer thickness 31, 48 .
More recently, microcomputed tomography (Micro-CT) has been used to study teeth. Carious lesions 23 , quantification of mineral distribution in fissure enamel 24 and enamel de-and remineralization 21 have already been studied by this method. It shows promise as a non-destructive method of validation for the presence and depth of tooth de-remineralization 21 . Precise measurements of attenuation coefficients and greater sensitivity to changes in mineral with time and position are provided by this technique. These benefits allow mineral content measurements from intact enamel to extensive demineralization, including a longitudinal tracking of lesion development. Besides, it allows complementary analyses of fluoride, calcium and phosphorus present in the enamel.
Hardness reflects the mechanical resilience of the substrate to the penetration of an indenter. Surface hardness employed with a reduced load (25-50 g) presents a good sensitivity to evaluate early changes (both de and remineralization) in the outermost layer of enamel and to predict the outcome of an anti-caries treatment 116 . It is important to highlight that when surface hardness is intended to be used as response variable in root caries models, the length of the pH-cycling must be shortened (from 10 to 3 days), as well as the length of the demineralization period (from 6 to 1 h) in order to enable the surface hardness of the created lesion to be assessed 36 . Cross-sectional hardness (CSH) can be regarded as an indirect method for evaluation of the mineral distribution because the technique, in fact, evaluates the resilience of the dental substrate to the penetration of an indenter under a given load. Despite different equations have been proposed and used to indirectly derive the mineral volume from the hardness data 31,48 , the correlation between hardness and mineral volume is different depending on the deepness of the lesion 21,56,87 . Additionally, the size of the indentation in demineralized tissues only allows the measurement of cross-sectional hardness at distances of at least 20 µm between two indentations, which might result in inaccuracy when the integrated mineral loss is calculated 21 .
Another limitation of hardness measurement is that the size of the indentation highly depends on the organic and water contents of the tissue. This fact has a especial impact on dentin that seems to present high variation of hardness values depending pH-cycling models for in vitro evaluation of the efficacy of fluoridated dentifrices for caries control: strengths and limitations 2010;18(4):316-34 on the degree of hydration, which, in turn, might compromise the analytical results 7 .
Recently, different methodologies to produce artificial carious enamel lesions (2 gels, 2 buffered solutions and a pH-cycling protocol) were tested using TMR and cross-sectional hardness as response variables. One interesting result of this study was that both formulas to convert hardness to mineral volume 31,48 presented overall high correlation between them and low correlation with TMR data, showing that the conversion of the crosssectional hardness to mineral volume seems to be inadequate. Thus, the data should be expressed as hardness numbers. The results also indicate that the conversion of hardness to mineral volume should not be used, since the formulas and the TMR data showed different results when they were used to compare the five methodologies at each depth. This finding gives more support to the fact that the results are dependent on the protocol used for creating artificial lesions 56 .

ADA Profile Applications of Dentifrices in ph-Cycling Models
Regardless the type of model employed, it must meet the suggested ADA guidelines associated with topical evaluation of dentifrices and determination of efficacy in products 1,2,17,73,74 . The model must preserve two important properties that relate it to the caries process and to the investigator performing the experiment: validity and reliability. The validity of a model can be defined as the degree of success with which the model actually provides information about the phenomenon or process it is being used to study, i.e., the pH-cycling protocol should be able to simulate as closely as possible the clinical situation.
Reliability is related to the manner by which an investigator obtains measurements in an experiment. The reliability of a measurement technique assesses the degree to which similar values would tend to be obtained if repeated measurements were made on the same test sample, under nearly identical conditions 73 . Furthermore, a pH-cycling model must show dose-response effect differentiating dentifrices containing 0, 250 and 1,000 or 1,100 ppm F. It is not mandatory that the models are able to differentiate the anti-caries effect of a low-F dentifrice containing 500-550 ppm F from the conventional 1,000-1,100 ppm F. However, it is recommended to include a 500 ppm F treatment group to obtain a "mini dose-response" 74 .

Controls
A working group report on laboratory models for caries 91 recommended that for tests of fluoridated dentifrices in the traditional concentration range (0-1,100 ppm F), experimental groups treated with controls of 0, 250 and 1,000 or 1,100 ppm F (a clinically proven "gold standard") are required, since clinical data are available on fluoride efficacy in this concentration range. The purpose of the 250 ppm F dentifrice would be to serve as an intermediate "dose-response" control that should generally produce results that are 10 to 20% better than the placebo, but not as effective as the 1,000 ppm F "gold standard". The 250 ppm F dentifrice for tests can be made especially by the manufacturer or by dilution of the 1,000 ppm F dentifrice, and this should then be tested for bioavailability. For studies with products in other concentration ranges, other controls should be included, including the concentration range tested. Treatment should be done with slurries of 1 in 3 (or 1 in 4) weight/weight dilutions of the toothpastes in water or saliva 91 .

Statistical Considerations
A working group report on laboratory models for caries 91 agreed that the PCK (Proskin-Chilton-Kingman) 74 test, originally designed for intra-oral studies 73 , may also be an appropriate statistical test for in vitro pH-cycling models to evaluate products for "equivalence". By definition, a test product is considered equivalent to a control product if its effect is between 90% and 110% of that of the control; that is, if the ratio of true mean effectiveness scores (test over control) is between 0.9 and 1.1. This range of values is the "range of equivalence" 73 .
To establish the equivalence of a test product to a control, the guidelines specify two methods. The first involves either a confidence interval or, alternatively, the use of two one-sided hypothesis tests. The second method is the "power rule". Details on how to conduct these tests were described by Proskin 73 (1992).

ph-Cycling Protocols to Evaluate the Anti-Caries Efficacy of Fluoride Dentifrices
Since the classical study by ten Cate and Duijster 87 (1982), who used a pH-cycling model to show that fluoride (100 µmol/L) present during the remineralization phases causes lesion arrestment, several pH-cycling protocols have been proposed and employed to evaluate the efficacy of fluoride dentifrices. These are summarized in Figures 3,  4, 5 and 6 according to the focus of the studies: dose-response or pH-response of fluoridated dentifrices, comparison of different F compounds in dentifrices, the impact of new active principles on the effect of fluoridated dentifrices and the effect of fluoridated dentifrices associated to other treatments, respectively. As it can be seen, the composition and volume of the de-remineralizing solutions tested varies substantially in the different protocols. Some studies show the volume of the solution by area of the sample. This is important information that should be standardized in all papers. Also the length of the treatments spans a wide range (mainly 7-15 days) and many response variables can be used to assess the result of the treatments (mainly chemical analysis of solutions and physical analysis of the samples).
One of the most often used pH-cycling protocols is the one described by Featherstone, et al. 29 (1986) for human enamel, which was modified from the one proposed by ten Cate and Duijsters 87 (1982). The model is of particular interest because it simulates in vivo high caries risk condition (lesions formed around orthodontic banding following 1 month in vivo) 67 and simultaneously measures the net result of the inhibition of demineralization and the enhancement of remineralization. In this model, the dynamic cycles of de-and remineralization are simulated by sequentially immersing enamel specimens in acidic (demineralizing) and supersaturated (remineralizing) buffer solutions. Dentifrice use is simulated by immersing specimens in slurries during the de-and remineralization stages. Topical efficacy is subsequently evaluated in terms of the ability of a test product to limit caries progression as a result of enhanced remineralization and/or diminished demineralization. The demineralization stage (6 h) uses an acid buffer containing 2 mM Ca (Ca(NO 3 ) 2 ), 2 mM PO 4 (KH 2 PO 4 ) and 75 mM acetate at pH 4.3. The remineralization solution (17 h) contains calcium and phosphate at a known degree of saturation (1.5 mM Ca and 0.9 mM PO 4 ) to mimic the remineralizing properties of saliva, 130-150 mM KCl (to provide background ionic strength) and 100 mM TRIS or 20 mM cacodylate buffer at pH 7.0. This solution approximates the mineral ion composition and supersaturation of saliva as originally reported by ten Cate and Duijsters 87 (1982). Some authors (Figures 3-6) changed the exposure time in de-(3 h, 6 h or 17 h/day) and remineralizing (6 h or 17 h/day) solutions or the concentrations of the ions, according to the focus of the study (de or remineralization). When the focus is more on remineralization, the samples stay less time in the demineralizing solution, and this solution is prepared with lower concentration of acid and ions and a higher pH. On the other hand, the time in the remineralizing solution is higher, but the concentration of ions and the pH remain unchanged (Figures 3-6).
Another common pH-cycling model for bovine enamel is recommended by ten Cate 84 (1993). In this case, the demineralizing solution contains 1.5 mM Ca (CaCl 2 ), 0.9 mM PO 4 (KH 2 PO 4 ), 0.050 M acetate at pH range of 4.6-5.0. The remineralization solution contains calcium and phosphate at a known degree of saturation (1.5 mM Ca and 0.9 mM PO 4 ) to mimic the remineralizing properties of saliva, 130 mM KCl (to provide background ionic strength) and 20 mM HePeS or cacodylate buffer at pH 7.0. The cycles, in this case, are more frequent (6x 0.5 h in De/day and 6x 2.5 h in Re/day). Additionally, the addition of fluoride (0.03-0.06 ppm) into both de-and remineralizing solutions 3,11,75,86,103 has been proposed. For primary teeth, it is recommended to add higher fluoride concentrations in the de-and remineralizing solutions (0.25 ppm F) 94 .
Usually, the samples stay in remineralizing solutions not only between the demineralizing challenges, but also overnight, on the weekends and sometimes all day in the last days. In some protocols the de-remineralizing solutions are changed daily, while in others they are not. This change can be made manually or by custom-made robots 84,88 . Another important point it is that in some papers, the pH cycles are performed for 3 days without the F dentifrice (slurry) treatment 86 to allow baseline values of calcium uptake and loss to be determined. Then, the treatment is performed either before or after the demineralization challenge 93 , 1 to 3 times per day, for 1 to 5 min, under agitation, during 7 to 14 days.
While pH-cycling models using lactic or acetic acids are the most common approaches for testing fluoride dentifrices, the use of biotic models has been proposed, since microbial activity-dependent pH-cycling has been shown to be of benefit in testing dentifrices containing NaF and plant extracts, such as sanguinaria, considering that these plant extracts could affect the activity of microorganisms more than does NaF 40 . However, these models are of much more complex execution, which restricts their use.
pH-cycling models have been shown to be appropriate to show dose-response of NaF dentifrices (Figure 3), both in primary and permanent enamel 3,11,69,75,86,[93][94][95]101,107 and permanent dentin 25,86,93 . In a clinical study, dentifrice usage was found to be effective both in preventing enamel and root dentin caries, with 41% and 67% reductions, respectively, in one-year caries increment data 44 . This is consistent with data from a pH-cycling study showing that fluoride given by means of a dentifrice treatment has a significantly more pronounced effect on dentin than on enamel 86 . Additionally, in the pH-cycling model proposed by Dunipace, et al. 25 (1994) dentin demineralization was reduced by 65% when a 1,100 ppm F (NaF) dentifrice slurry was used, which is almost identical to the result obtained in the clinical trial 44 . However, constantly present low fluoride levels (3 µM in de-and remineralizing solutions) are inadequate to shift the de-remineralization balance sufficiently for dentin, as occurs with enamel. More fluoride is needed for remineralization of dentin than for enamel 38 . It has been speculated that the high concentration fluoride pH-cycling models for in vitro evaluation of the efficacy of fluoridated dentifrices for caries control: strengths and limitations 2010;18(4):316-34 "pulses" that occur after treatment with dentifrices might facilitate secondary nucleation, increasing the internal surface area of dentin for crystallization.
While clinical trials show a beneficial effect of 5,000 ppm F over 1,100 ppm F dentifrices to arrest root carious lesions 9,53 , this was not tested in pHcycling studies. Such studies could help to clarify the mechanism of action of high-fluoride dentifrices on root caries arrestment. Additionally, the effect of fluoride is most pronounced during demineralization than during remineralization for both enamel and dentin 86 .
Also appropriate conclusions about pH-response of NaF dentifrices 3, 11 can be drawn from pHcycling studies (Figure 3). Low-fluoride (500 ppm) acidic (pH 4.5 or 5.5) NaF dentifrices have been shown in pH-cycling studies to be as effective as 1,100 ppm F neutral NaF dentifrices. This was confirmed in clinical studies showing that a 550 ppm F pH 4.5 dentifrice led to similar plaque fluoride concentrations as the 1,100 ppm F pH 7.0 dentifrice 12 and that both dentifrices led to similar caries increments in a 20-month clinical trial with 4-5-year-old children (unpublished date).
One aspect that should be considered in studies involving testing of MFP or amine fluoride (AmF)based dentifrice formulations is the solution used to prepare the dentifrice slurry (Table 2). In these cases, it is important to use natural saliva to make the dilution 14 . For MFP-based formulations, this approach is necessary because salivary enzymes assist in the hydrolysis of the covalently bound MFP to release fluoride ions. It is important that the model is conducted at 37°C because it has been shown that when NaMFP slurries were prepared with fresh human saliva at 21°C, only minimal amounts of the total fluoride (less than 10%) were available as ionic fluoride 25 . Since the enzymatic system is efficient in the in vivo condition, no differences in the anti-caries efficacy between dentifrices formulated with NaF or MFP occur in the clinical situation, as revealed by recent meta-analyses 16,59 . The variable simulation of conditions necessary for MFP hydrolytic activity probably explains the large range of effects seen in in vitro comparisons of NaF and MFP 6,20,25,35,40,42,43,49,62,85,101,107-109,111-113 . It has recently been shown that the minor inhibitory effect of a NaMFP formulation (1,000 ppm F) on lesion formation of dental enamel was a result of the low concentration of free fluoride ion (only 30 ppm) 101 . AmF, in particular, has a very low pH when diluted with water (4.96) rather than saliva (6.37) 14 . When in vitro studies use water instead of saliva as the product diluents, results for AmF are generally more favorable 65,101 . This effect is generally considered to be an artifact of study design rather than product effectiveness when compared to protocols that use natural saliva for this purpose 14 .
In the last decades there has been a proliferation of dentifrices directed toward specific needs of the population 13 . Such designer dentifrices include those directed against tartar, gingivitis, enamel and root caries, root sensitivity, halitosis, and tobacco stains, as well as those with extra-whitening abilities, and those considered to be "natural" dentifrices and dentifrices for children. Despite the various types of toothpastes, fluoride has been maintained in over 95 percent of the dentifrice formulations 39 . pH-cycling studies have been employed to evaluate if the addition of different active principles would interfere with the anti-caries action of fluoride ( Figure 5). Overall, the addition of active principles with different purposes such as pyrophosphate (anticalculus) 30,71 , blue covarine 45 , carbamide peroxide 105 and sodium hexametaphosphate 72 (whitening), sanguinaria (antiplaque) 40 , ionexchange resins 102 , triclosan (antibacterial) combined with PVM/MA 39,76 or zinc citrate 84 have not jeopardized the caries-preventive properties of the fluoridated dentifrices in pH-cycling studies. Variations in model sensitivity can be observed in in vitro assessments of the activity of anticalculus dentifrices 107 , where some protocols show significant inhibition of remineralization with the addition of tartar control inhibitors to fluoride dentifrices, while others show no negative effects with the addition of these inhibitors 30,89,93,107,115 . However, clinical 51,52,82 and in situ 63 studies with tartar control dentifrices confirm that mineralization inhibitors do not appear to affect caries protection of dentifrices, in-line with data reported from some pH-cycling studies. For whitening dentifrices, there is only scanty information on their anti-caries efficacy and there is still a need for further evaluation of both different types of compounds and lesions in pH-cycling and in situ studies. On the other hand, the addition of bioavailable amorphous calcium and phosphate in a NaF dentifrice seems to cause a trend toward further reduction in lesion depth over fluoridated dentifrice in a pH-cycling model simulating caries formation and progression 39 .
pH-cycling models have also been employed to verify the performance of the association between fluoridated dentifrices and other measures for caries prevention such as CO 2 laser irradiation 81 , F varnishes 57 , F solutions 64 or caries treatment such as fluoride-releasing or not dental materials 22,36,77 ( Figure 6). The association between fluoridated dentifrices and other caries-preventive measures, such as CO 2 laser irradiation 81 or fluoride varnishes was not able to increase the cariostatic action of the F dentifrices in pH-cycling protocols. This is in agreement with a recent meta-analysis showing that the combination of fluoride dentifrice with other topical fluoride treatments (mouthrinses, gels, varnishes) for preventing dental caries in children and adolescents had only a mild additive effect (around 10%) over dentifrice alone 58 , indicating that pH-cycling models might be appropriated for this kind of evaluation.
More recently, attention has been devoted to the development of pH-cycling models that would be appropriate to test the efficacy of fluoridated dentifrices on de/remineralization of primary teeth. It has been investigated if the in vitro 10-day pHcycling model used for permanent teeth 43,87 could be used to evaluate de/remineralization effects of child formula toothpastes on the enamel of primary teeth 95 . It was observed that by day 8 all lesions in the sections were eroded and/or had progressed into dentin. This may have been due to the fact that the enamel of primary teeth has lower enamel thickness and mineral content and higher organic content when compared with permanent teeth. Due to the rapid formation of enamel in primary teeth, it may have more imperfections in the hydroxyapatite crystals than permanent enamel. These variations in structure are known to influence caries susceptibility, acid etching characteristics 114 and give lower initial hardness values for primary teeth 8 . Thus, if this pH-cycling model is intended to be used for primary teeth, a reduction from 10 to 7 days in length is recommended. However, shortening of the period of pH-cycling might produce results that inadequately represent the natural process of de-and remineralization. The factors that influence the length of the pH-cycling are the pH and the fluoride concentration of the de-and remineralizing solutions 34 . The de-and remineralizing solutions used in the study by Thaveesangpanich, et al. 95 (2005) did not contain additional fluoride. In the absence of fluoride, even under conditions that are considered to favor remineralization, further demineralization has been shown to take place 34 . Thus, in a subsequent study, it was tested if the addition of 0.25 ppm F in the de-and remineralizing solutions of the 10-day pH cycling model would lead to similar rates of lesion progression when compared to 7-day pH-cycling models where no fluoride was added to de-and remineralizing solutions. The authors observed that the two models led to similar results regarding lesion progression. Thus, a 10-day pH-cycling model similar to that used for permanent teeth 43 can be used for primary teeth provided the remineralizing and demineralizing solutions contain 0.25 ppm F 94 .

Future Perspectives in ph-Cycling Protocols
Research should be focused to fill the gap between in vitro models and the in vivo situation. Thus, in vitro models should be improved regarding their predictive value. Currently, there is a limited number of studies that use solutions that simulate plaque fluid conditions 27, 54 and future studies should focus on this. It would be interesting to design models where the solutions mimic plaque fluid ionic concentration and pH in individuals with low and high caries risk, after fasting and exposure to sucrose, in order to model various caries risk situations. Additionally, the models could include the addition of organic salivary components, a simulation of dental plaque, temperature, volume effects and brushing conditions. Ideally, all these conditions should be included in automated models.
Regarding root caries, it is important to develop models that more closely resemble the clinical progression and reversal of caries in dentin, taking into account not only the mineral content, but also its organic matrix. These models could be used to study the influence of the addition of MMPs inhibitors 33,46 or collagen cross-linkers 104 to fluoridated dentifrices on their anti-caries potential in dentin.
It would also be very useful trying to validate pH-cycling models against in situ challenges with sucrose in the absence or presence of fluoride in different concentrations. If comparable results are obtained, then pH-cycling models can be used instead of in situ protocols that are more timedemanding and difficult to be conducted.

CONCLUSIONS
Critical features of pH-cycling models to evaluate the efficacy of fluoridated dentifrices on caries control include the ability to detect known results established by clinical trials (ADA specifications), to demonstrate dose-related responses in the fluoride content of the dentifrices, and to provide repeatability and reproducibility between tests. In order to accomplish these features satisfactorily, it is mandatory to take into account the type of substrate and baseline artificial lesion, as well as the adequate response variables and statistical approaches to be used. If these aspects are adequately contemplated, the currently available pH-cycling models are appropriate to detect doseresponse and pH-response of fluoride dentifrices, to evaluate the impact of new active principles on the effect of fluoridated dentifrices, as well as their association with other anti-caries treatments. However, further studies should be done in order to make pH-cycling models as close as possible to in vivo conditions.