Excellent reviews to guide the choice of dental substrates for in vitro and in situ studies have been presented by Mellberg⁶⁰ (1992) and Ogaard and Rolla⁶⁸ (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 teeth¹¹⁴. 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 rate¹⁰. 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 tubules⁷⁹.

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 dentifrices⁶⁰. 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 model⁶⁰.

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 odontogenesis⁹⁰. 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 tubules³². 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 situation⁸⁰.

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 matrix¹⁰⁰ (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 models⁴⁷, 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 collagenases¹⁰⁰. 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% NaN₃, 0.9% NaCl solution, at 4ºC)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 enamel⁴¹; (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 enamel³⁸; (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 for dentin lesions mineral uptake is predominant at the surface and mineral loss at the lesion front⁸⁶.

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.

In some studies, artificial caries lesions are initially produced by immersion of the substrates in buffered lactate or acetate gels¹¹⁰ 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^54-56 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 phosphate¹⁹ and fluoride⁹⁹ in the solution, its pH⁹⁷ and the time after an initial demineralization⁹⁸, 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-remineralization54.

Additionally, porosity and depth of a lesion can characteristics in a pH-cycling model. The formation also play an important role in mineral diffusion^54,88. It of the surface layer might be also affected by 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 lesions⁸³. This may explain the tendency toward net remineralization with increasing ∆Z at baseline in pH-cycling regimes⁵⁵. 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 systems⁵⁴, 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 drawn⁸⁸.

Many response variables can be employed in pH cycling 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 profiles⁵⁶ and qualitatively by polarized light microscopy-PLM³⁹ (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 lesions²³, quantification of mineral distribution in fissure enamel²⁴ and enamel de-and remineralization²¹ 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-remineralization²¹. 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 treatment¹¹⁶. 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 assessed³⁶. 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 calculated²¹.

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 on the degree of hydration, which, in turn, might compromise the analytical results⁷.

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 lesions⁵⁶.

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 conditions⁷³. 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.

A working group report on laboratory models for caries⁹¹ 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 saliva⁹¹.

A working group report on laboratory models for caries⁹¹ agreed that the PCK (Proskin-ChiltonKingman)⁷⁴ test, originally designed for intra-oral studies⁷³, 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 Proskin⁷³ (1992).

Since the classical study by ten Cate and Duijster⁸⁷ (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 Duijsters⁸⁷ (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(NO₃)₂), 2 mM PO₄(KH₂PO₄) 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 PO₄) 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 Duijsters⁸⁷ (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 Cate⁸⁴ (1993). In this case, the demineralizing solution contains 1.5 mM Ca (CaCl₂), 0.9 mM PO₄ (KH₂PO₄), 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 PO₄) 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) treatment⁸⁶ to allow baseline values of calcium uptake and loss to be determined. Then, the treatment is performed either before or after the demineralization challenge⁹³, 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 NaF⁴⁰. 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 ^{3,11,69,75,86,93-95,101,107} 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 data⁴⁴. 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 enamel⁸⁶. 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 trial⁴⁴. 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 enamel³⁸. It has been speculated that the high concentration fluoride "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 dentin⁸⁶.

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 dentifrice¹² 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 dilution¹⁴. 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 fluoride²⁵. 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 purpose¹⁴. In the last decades there has been a proliferation of dentifrices directed toward specific needs of the population¹³. 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 formulations³⁹. 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 covarine⁴⁵, carbamide peroxide¹⁰⁵ and sodium hexametaphosphate⁷² (whitening), sanguinaria (antiplaque)⁴⁰, ionexchange resins¹⁰², triclosan (antibacterial) combined with PVM/MA^39,76 or zinc citrate⁸⁴ 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 dentifrices¹⁰⁷, 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 situ⁶³ 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 progression³⁹.

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 CO₂ laser irradiation⁸¹, F varnishes⁵⁷, F solutions⁶⁴ 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 CO₂ laser irradiation⁸¹ 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 alone⁵⁸, 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 teeth⁹⁵. 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 characteristics¹¹⁴ and give lower initial hardness values for primary teeth⁸. 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 solutions³⁴. 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 place³⁴. 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 teeth⁴³ can be used for primary teeth provided the remineralizing and demineralizing solutions contain 0.25 ppm F⁹⁴.

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-linkers¹⁰⁴ 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.