Are there already clinical studies available?

Yes, many publications confirm the efficacy. In addition to laboratory studies (in vitro), these include studies with test specimens under oral cavity conditions (in situ) as well as clinical studies on patients (in vivo) in particular. Literature

e.g.:
Harks, I. et al. Impact of the daily use of a microcrystal hydroxyapatite dentifrice on de novo plaque formation and clinical/microbiological parameters of periodontal health. A randomized trial. PloS one 11, e0160142 (2016).

Lelli, M. et al. Remineralization and repair of enamel surface by biomimetic Zn-carbonate hydroxyapatite containing toothpaste: a comparative in vivo study. Front. Physiol. 5, 333 (2014).

Orsini, G. et al. A double-blind randomized-controlled trial comparing the desensitizing efficacy of a new dentifrice containing carbonate/hydroxyapatite nanocrystals and a sodium fluoride/potassium nitrate dentifrice. J. Clin. Periodontol. 37, 510-517 (2010).

Kani, K. et al. Effect of apatite-containing dentifrices on dental caries in school children. J. Dent. Health 19, 104-109 (1989).

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