An analytical framework for nanohydroxyapatite evaluation by ICP-OES and quantification of hydroxyapatite-equivalent Ca and P in toothpaste formulations through multivariate optimization

Nano-hydroxyapatite (nHA) is widely incorporated into toothpaste as a biomimetic agent for preventive oral care, yet robust quantitative methods for determining its content in finished formulations remain limited. In this study, nHA was first characterized structurally and morphologically to establish a reference material. X-ray diffraction (XRD) confirmed high crystallinity consistent with pure hydroxyapatite. High-resolution transmission electron microscopy (HRTEM) revealed rod-shaped nanoparticles with an average size of 22.36 nm and an aspect ratio of 2.25. Fourier transform infrared spectroscopy (FTIR) further verified characteristic phosphate vibrational bands at 1023.25, 562.26, and 600.84 cm⁻¹. Following characterization, nHA was incorporated into a toothpaste formulation, and an analytical strategy was developed to quantify hydroxyapatite-equivalent content based on stoichiometric determination of calcium (Ca) and phosphorus (P) using inductively coupled plasma optical emission spectroscopy (ICP-OES). A 2³ factorial design was employed to optimize key instrumental parameters-nebulization gas flow rate, applied power, and plasma flow rate. Exploratory statistical tools, including ANOVA, Pareto charts and residual analyses, identified nebulization gas flow rate as the most influential factor. The optimized method was validated for linearity, sensitivity, accuracy, precision, robustness and matrix interference. Calibration curves for both standard and matrix-matched solutions showed excellent linearity (R² > 0.999). Limits of quantification were 25.16 µg L⁻¹ for Ca and 12.24 µg L⁻¹ for P. Spike recoveries ranged from 95% to 110%, confirming method accuracy. Because ICP-OES measures total elemental Ca and P after digestion, the method quantifies hydroxyapatite-equivalent content and does not distinguish nHA from other Ca/P-containing ingredients. Nonetheless, application to commercial toothpaste samples yielded results consistent with label claims, demonstrating the method's suitability for quality control of hydroxyapatite-containing formulations.