Enamel Fluoride Profile Construction from Biopsy Data

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Abstract
In fitting enamel biopsy data to a curve that describes the F [fluoride] profile in a subset of individuals subjected to a given treatment regimen, an implicit approximation is made that all individuals of a subset have the same F profile. This work assumes that the F profiles for the individuals can be best described by a single polynomial functional form. The coefficients of the polynomial can be calculated for each individual from multilayered biopsy data. The F content at a normalized depth can then be calculated for each individual and be used to compute the mean F content of the subset. The objective was to compare statistically the suitability of 21 polynomial functions in fitting multilayered biopsy data. A function, log F = [a0 + a1 log X + a2(log X)2 + a3(log X)3] + log[a1 + 2a2log X + 3a3(log X)2 + 1], where F and X are enamel F content and depth, respectively, was found to describe the F gradients with a mean standard deviation from regression below the level of analytical errors expected in biopsy data. The profiles are used both to interpolate and extrapolate the F contents of the specimens at standardized depths. This procedure should increase the precision and decrease of cost of clinical F biopsy studies.