Inter-method reliability for determining total and soluble fluorides in child low-fluoride formula dentifrices

Dental caries results from an imbalance between demineralization and remineralization of tooth hard tissues. Fluoride inhibits demineralization (via fluorapatite formation) and enhances remineralization, and continuous low-level fluoride exposure from fluoridated dentifrices helps prevent caries. Despite fluoride’s benefits, hundreds of millions of children still experience caries in primary teeth globally. Assessing both total fluoride (TF) and total soluble fluoride (TSF) in dentifrices is important because the difference (insoluble or inactive fluoride) limits bioavailability. Prior studies reported that several low-fluoride children’s dentifrices had TSF much lower than TF, indicating substantial insoluble fluoride, whereas higher-fluoride dentifrices (≥1000 ppm) showed TF similar to TSF. Evidence indicates dentifrices with >1000 ppm fluoride more effectively reduce caries than non-fluoridated or low-fluoride (<500 ppm) products, and a dose-response for caries prevention exists. Given prior findings, low-fluoride child dentifrices (400–1000 ppm F) might contain TF and TSF lower than manufacturers’ claims, potentially diminishing caries-preventive efficacy. This study therefore evaluated whether three analytical methods provide reliable and consistent TF/TSF determinations in child dentifrices, testing the null hypothesis that IMR does not differ among DM, MDM, and TAD.

Child dentifrices commonly use sodium fluoride (NaF), sodium monofluorophosphate (NaMFP), and amine fluoride (Olaflur), along with abrasives (e.g., silica, dicalcium phosphate dihydrate, calcium carbonate). Chemical incompatibility between fluoride sources and abrasive salts can form insoluble fluoride, reducing bioavailability and dentifrice efficacy. A reliable analytical method to rapidly detect insoluble fluoride is needed. Regulatory agencies have long recommended the Taves diffusion assay (TAD), which separates fluoride by diffusion and measures with a fluoride ion-selective electrode (F-ISE). Although considered a gold standard, TAD is time-consuming and requires specialized diffusion dishes. Alternatives include direct acid-hydrolysis (DM), acid digestion–gas chromatography, and acid digestion–diffusion; among these, DM is least time-consuming and requires basic equipment, but it is unsuitable for all fluoride sources (e.g., some profluoride compounds). ISO 19448:2018 recommends the standard addition technique for samples containing bound fluoride or potential interferents. DM can be adapted with standard additions (MDM) to address its limitations. However, before this study, no research had compared MDM’s reliability against DM or TAD for fluoride analysis.

Study design and reporting followed GRRAS. Inter-method agreement was defined as the degree to which methods measure identical fluoride concentrations across dentifrices. Inter-method reliability (IMR) was defined as the ability of methods to differentiate between dentifrices based on estimated fluoride concentrations. Fluoride measurement setup: Fluoride concentrations were measured using an F-ISE (Thermo Fisher Scientific) connected to a benchtop potentiometer (Orion 2700). For each experiment, internal standards at 0.1, 1, 10, 100, and 1000 µg/g F were prepared. Calibration used linear regression of mV vs known fluoride (R2 > 0.99), and calibration stability was checked before, during, and after sample runs. Samples/standards were stirred at 250 rpm; the electrode was rinsed and blot-dried between measurements. Samples (child dentifrices): Five commercially available child dentifrices were tested: Group I (Colgate Kids Anticavity, Minions; 600 ppm F, NaF), Group II (Darlie Jolly Junior; 600 ppm F, NaMFP), Group III (Elmex Kinder Zahnpasta; 500 ppm F, amine fluoride), Group IV (Lion Kodomo; 500 ppm F, NaF with 5% xylitol), Group V (Oral-B Kids; 500 ppm F, NaF). TF was defined as total fluoride measurable by current methods; TSF (potentially available fluoride) as the fraction of TF soluble in water or acid. Direct acid-hydrolysis method (DM): About 100 mg dentifrice was diluted 1:100 in deionized water (DIW), vortexed 60 s to homogenize. For TF, 0.25 mL suspension was acid-hydrolyzed with 0.25 mL 2.0 mol/L HCl for 1 h at 45 °C, neutralized with 0.5 mL 1.0 mol/L NaOH, then buffered with 1 mL TISAB II before F-ISE analysis. For TSF, the 1:100 suspension was centrifuged (5000×g, 10 min); 0.25 mL supernatant underwent the same acid/neutralization steps and TISAB II addition as TF. Calibration standards were prepared using the same reagents as samples. Modified direct acid-hydrolysis with standard addition (MDM): Sample preparation for TF/TSF followed DM, but quantification used standard additions per ISO 19448:2018. A series of test aliquots was prepared by mixing sample and DIW at 4:1, spiked with fluoride standards (1, 10, 100, 1000 µg/g). After adding equal volume of TISAB II, F-ISE readings were converted to concentrations using the calibration curve. For each sample, added fluoride (x) vs measured concentration (y) was linearly regressed (R2 > 0.99), and sample fluoride was computed as |x-intercept| = b/m (y = mx + b), adjusted for dilution. Modified Taves acid–HMDS diffusion (TAD): A 1:3 slurry (10 g toothpaste in 30 mL DIW) was vortexed 60 s. For TSF, slurries were centrifuged (5000×g, 2 min) to obtain supernatant. Conway diffusion dishes were sealed (Vaseline), with 4 mL 1.0 mol/L HClO4 saturated with 2.5% HMDS and test solution in the middle compartment, and 0.5 mL 1.0 mol/L KOH in the inner compartment. After adding 0.5 mL test solution to the acid compartment, dishes were sealed and tilt-mixed overnight (~18 h) at 60 rpm at room temperature. Trapped fluoride in KOH was neutralized with 1.0 mol/L HCl, buffered with 1 mL TISAB II, and measured by F-ISE. Calibration standards underwent the same diffusion to account for <100% diffusion efficiency. Statistics: All experiments were in triplicate using different tubes. Data (µg/g) were analyzed in SPSS v25. One-way ANOVA with Tukey’s HSD examined method effects on TF and TSF. Bland–Altman plots with one-sample t-tests assessed between-method agreement; proportional bias was tested with linear regression, with log transformation when needed. IMR was assessed using two-way mixed-effects ICCs for single and average measures, for consistency and absolute agreement. Derived ICCs were compared using Feldt’s test (α = 0.05). Three-way ANOVA tested effects of dentifrice (group), method, and fluoride type (TF/TSF), and their interactions, on fluoride estimates.

• Across most groups, fluoride concentrations estimated by all three methods were lower than label claims, except Group V (all methods exceeded label); for Group IV, DM estimates were similar to label.
• Total fluoride (TF): In Groups I and II (600 ppm), TAD yielded significantly higher TF than other methods (p < 0.05). In Group IV, TAD yielded significantly lower TF than other methods (p < 0.05). In Group III, TAD and DM gave higher TF than MDM (p < 0.05). In Group V, TAD and MDM gave higher TF than DM (p < 0.05).
• Total soluble fluoride (TSF): For all groups except Group V, TAD gave significantly lower TSF than DM and MDM (p < 0.05); DM gave the highest TSF (except Group V). In Group V, TSF by TAD > DM > MDM (p < 0.05).
• Between-method agreement (Bland–Altman): • TF mean differences (µg/g F): DM–MDM 15.04 (95% CI 9.12 to 20.96, p < 0.001); DM–TAD 1.82 (−5.56 to 9.19, p = 0.622); MDM–TAD −13.22 (−19.59 to −6.86, p < 0.001). • TSF: DM–MDM 25.92 (20.46 to 31.38, p < 0.001); DM–TAD 58.60 (48.06 to 69.15, p < 0.001); MDM–TAD 32.68 (25.33 to 40.04, p < 0.001). • Combined TF+TSF: DM–MDM 20.48 (16.37 to 24.59, p < 0.001); DM–TAD 30.21 (21.52 to 38.90, p < 0.001); MDM–TAD 9.73 (2.94 to 16.52, p < 0.001). • Proportional bias was detected between DM and TAD for TF (p < 0.001).
• Inter-method reliability (ICC): All ICCs were significant (p < 0.001). For TF, MDM–TAD showed the highest reliability (single-measure consistency 0.89; absolute 0.85; average-measure consistency 0.94; absolute 0.92). For TSF, DM–MDM had the highest reliability (single-measure consistency 0.96; absolute 0.88; average-measure consistency 0.98; absolute 0.94). DM–TAD showed the lowest reliability for TSF, with absolute agreement ICCs < 0.80 at some outputs (e.g., single-measure absolute 0.61; average-measure absolute 0.75), indicating only substantial reliability. Combined TF+TSF followed similar patterns: highest ICCs for DM–MDM and MDM–TAD; lowest for DM–TAD.
• Feldt’s test comparing ICCs: For TSF, DM–MDM ICCs were significantly higher than DM–TAD across measures and agreement types (p < 0.05). For combined TF+TSF, DM–MDM > DM–TAD (p < 0.05), and MDM–TAD > DM–TAD for absolute agreement (p < 0.05). Overall, MDM showed higher reliability relative to TAD than DM did.
• Factor effects (three-way ANOVA): Group, method, fluoride type, and all interactions (group×method, group×fluoride type, method×fluoride type, group×method×fluoride type) significantly affected fluoride estimates (p < 0.001). Method-specific group rankings showed MDM and TAD discerned similar differences among dentifrices, whereas DM’s pattern was distinct. For example, mean estimates (µg/g F) showed: DM Group I > II > IV > V > III; MDM and TAD Group I > II = V > IV > III.

The study tested whether three analytical methods (DM, MDM per ISO 19448:2018, and TAD) provide equivalent and reliable TF/TSF determinations in low-fluoride child dentifrices. Findings rejected the null hypothesis: methods did not agree to produce identical measurements, and reliability differed by method pairing. Despite calibrated F-ISE performance, between-method agreement was generally lacking (consistent with ANOVA results), and proportional bias was observed between DM and TAD for TF. Exact agreement is unrealistic given differing sample preparations and internal standards per method and run. Importantly, IMR (via ICC) quantifies consistency across methods rather than validity; using TAD as a comparator did not imply a validity assessment. MDM demonstrated consistently higher reliability with TAD than DM did, for TF, TSF, and combined outcomes, across single/average measures and consistency/absolute agreement models. For TSF and combined outcomes, some DM–TAD absolute agreement ICCs fell below 0.80 (substantial, not almost perfect), whereas MDM–TAD mostly exceeded 0.85–0.90. DM and MDM correlated very closely for TSF, likely because MDM is a modification of DM and TSF preparation includes centrifugation that reduces matrix interferences; however, for TF, the standard addition in MDM better handled bound fluoride and interferents, improving reliability relative to DM. Presence of amine fluoride in one dentifrice likely contributed to lower DM–TAD reliability due to source–method incompatibility. The three-way ANOVA supported that MDM and TAD similarly differentiated dentifrices, aligning with Feldt’s test showing significantly higher ICCs for MDM–TAD vs DM–TAD in several comparisons. Practically, MDM can serve as a faster, less resource-intensive alternative to TAD for TF/TSF determination, without relying on TAD’s diffusion efficiency assumption (~80%). Standard additions in MDM place measurements in the optimal electrode response range. However, TAD and MDM both need additional reagents/equipment compared to DM, and DM remains limited for toothpastes with unknown matrices or profluoride compounds. The frequent finding that measured TF was below label (except Group V) highlights potential formulation or manufacturing influences on fluoride availability and reinforces the need for reliable analytical verification in children’s dentifrices.

Under the study conditions, the ISO 19448:2018 modified direct acid-hydrolysis with standard-addition method (MDM) is a reliable alternative to the gold-standard TAD and to DM for determining total and total soluble fluorides in low-fluoride child dentifrices. MDM showed higher inter-method reliability with TAD than DM did, and it can rapidly and reliably detect low fluoride concentrations. Future work should evaluate inter- and intra-laboratory reproducibility and validity of MDM across a broader range of formulations and fluoride concentrations, including products with different fluoride sources and abrasive systems.

• The study assessed inter-method reliability and agreement, not method validity relative to an absolute standard.
• Exact between-method agreement is unlikely due to differing sample preparation steps, internal standards, and calibration curves, introducing inherent variability.
• DM has known limitations with certain fluoride sources (e.g., profluoride compounds, amine fluoride) and unknown matrices, potentially reducing reliability relative to TAD.
• One dentifrice contained amine fluoride, which may have disproportionately affected DM–TAD reliability.
• The inter- and intra-laboratory reproducibility of MDM has not been established; cross-laboratory validation is needed.
• Matrix constituents and manufacturing processes (e.g., in Group IV) were unknown, limiting interpretation of discrepancies with labeled fluoride.