## 2 Results  
The average values of the varnish (the quantity of varnish in mg) used ranged from 7.9 \(\pm\) 0.2645 mg to 8.2 \(\pm\) 0.1527 mg, which corresponded to the average fluoride content in the range from 0.1249 \(\pm\) 0.0055 mg for MI Varnish, 0.1512 \(\pm\) 0.0027 mg for Duraphat and 0.1640 \(\pm\) 0.0065 mg for Embrace Varnish. Figure 1 graphically represents the cumulative release of fluoride for the three varnishes in three different pH (4, 5 and 7) environments, expressed in ppm. Within 168 h of the experiment, regardless of the pH of the environment, the highest amount of fluoride was released by MI Varnish, and the lowest level was released by Embrace Varnish. The cumulative release of fluoride for MI Varnish was 11.52 ppm F\({}^{-}\) at pH = 4, 9.297 ppm F\({}^{-}\) at pH = 5 and 6.470 ppm F\({}^{-}\) at pH = 7. Duraphat achieved 9.753 ppm F\({}^{-}\), 7.513 ppm F\({}^{-}\) and 9.276 ppm F\({}^{-}\), respectively; Embrace Varnish achieved 6.826 ppm F\({}^{-}\), 5.724 ppm F\({}^{-}\) and 4.821 ppm F\({}^{-}\), respectively. In most research groups, significantly higher values were obtained in acidic environments (pH = 4 and 5) as compared with the neutral environment. For MI Varnish, the release of fluoride in the environment with various acidities was different after the first hour; for Duraphat, after 2 h; and for Embrace Varnish, after 24 h. For all three varnishes tested, the highest increases in fluoride release were recorded during the first two hours of observation, with both MI Varnish and Embrace Varnish releasing, respectively, more than 50% and 60% of the total 168 h fluoride release during the first 2 h after application, and more than 90% and 85% after 24 h. Duraphat, on the other hand, during the same time, showed a slower release rate at an average level of 36% after 2 and 68% after 24 h. Based on the results of the variance analysis and post hoc tests, the cumulative release of fluoride from the three tested varnishes differed significantly in each hour of observation and at each acidity of the environment (_p_ < 0.001) (Table 1). For pH = 7 at 168 h, a significant difference occurred only between Embrace Varnish and MI Varnish (4.82 vs. 6.47 mg; \(p\) = 0.012). In the investigated groups, fluoride was released throughout the experiment, with the rate of release decreasing over time for all tested products, with a view to the differences between the first-generation (Duraphat) and second-generation (Embrace Varnish and MI Varnish). The hourly drop in fluoride release from three types of varnish in different pH environments is shown in Figure 2. The analysis uses mathematical models of fluoride release. Due to the non-linear nature of the obtained fluoride release rate scatterplots as a function of time, the results of the measurements were approximated by the exponential function. For empirical data obtained for each of the three types of varnish and three levels of pH, the following types of exponential models were matched:  
\[y=b_{0}\,\times\,\exp(b_{1}\,\times\,x)\]  
where \(y\) = F (ppm/h)--hourly fluoride release and \(x\) = time (h)--fluoride release duration. The parameters of the _b\({}_{0}\)_ and _b\({}_{1}\)_ models were estimated using the quasi-Newton method.