## 4 Discussion
The SEM analysis was confirmed by statistical analysis, where both toothpastes, the fluoride and the non-fluoride, had the ability to restore the surfaces of G3 and G4 to a level of roughness statistically similar to the non-acidified G1. Instead, after the second acid attack in the G6 sample, there was a statistical similarity between its roughness and that of the G2 sample, and a statistical difference between its roughness and that of G1 sample,which demonstrated the inability of the non-fluoride toothpaste to protect the enamel from a second acid attack. SEM analysis corroborated the numerical results, as in the G6 images, a rougher surface could be appreciated, as well as the presence of furrows, comparable with the ones found in G2 images. These findings are in accordance with recent literature, which embraces the hypothesis that a dose-dependent effect exists between toothpaste fluoride concentration and the percentage of demineralization due to an acid oral environment [22; 26]. Moreover, the G7 sample, treated with fluoride toothpaste and subjected to the second acidification cycle, shows a statistical difference compared to the G2 sample and a statistical similarity with the G1 sample. This result, when compared with the lack of statistical difference between the G2 and G6 samples, defines a better efficacy by the fluoride toothpaste in preventing enamel erosion when teeth are subjected to a second acid attack. Looking at the literature, other studies reported results comparable to our findings: all the surfaces previously treated with a fluoridated toothpaste proved to be more resistant to enamel stress, such as tooth wear and erosion. In addition to these findings, [PERSON] et al., 2011, found that the synergy between xylitol and fluoride significantly reduced enamel erosion. In this study, in fact, 10% xylitol- and fluoride-enriched toothpastes proved to have a wider remineralizing action on the enamel surface compared to placebo or common toothpastes filled with xylitol or fluoride [22]. Our results are also analogous to and confirmed by the study of [PERSON] et al., 2018, in which 112 teeth without caries were demineralized and then treated with toothpastes containing different amounts of fluoride. The results obtained showed a tendency for microhardness (used in this study to measure in vitro remineralization) to increase after treatment with toothpaste containing a higher fluoride amount. Instead, the greatest decrease in micro-hardness was found in the enamel surfaces treated with non-fluoride toothpaste [27]. These results agree with the lack of statistical difference between the surface roughness of the G2 and G6 samples and with the presence of a statistical difference between the G2 and G7 samples found in our study. The Dunnet test showed a significant statistical difference between the G1 and G8 samples. Although it initially seemed that the fluoride varnish did not provide sufficient protection of the enamel against acid attack, the G5 and G8 samples were statistically similar, which means that after the second acid attack, the roughness remained unchanged. This indicates that the G5 and G8 samples treated with fluoride varnish did not undergo variations in roughness. Therefore, this result highlights the ineffectiveness of the second acid attack. Following the instructions regarding the method of application of the fluoride varnish, an excess was created on the surfaces of the samples (as can be seen from the images taken by the SEM scanning microscope) (Figure 2). These data are interpreted as measurements of the roughness of the fluoride varnish and not of the enamel surfaces of the samples. In support of the results we obtained, [PERSON] et al., 2009, evaluated the effect of a cola-based drink on the surface of human enamel treated with fluoride varnish. The authors concluded that the fluoride varnish was able to inhibit erosive enamel loss [28].