Daniel L. Leonard

Statistical estimation of resin composite polymerization sufficiency using microhardness

With respect to determining sub-surface resin polymerization sufficiency, this study compared a traditional method of applying linear regression to bottom- to top-surface Knoop hardness ratios to an alternative method based on nonlinear regression. Inverse linear regression on ratios was used to estimate the exposure duration required for 80% bottom-surface hardness with respect to the top, in six light-by-material groups. Alternatively, a one-phase, two-parameter, exponential association of the form Y=Y(max)(1-e(-kt)) (where Y(max) is maximum hardness, k is a rate constant, and t is exposure duration), was used to model hardness. Inverse nonlinear regression estimated, for each condition, the exposure duration required for the bottom surface to achieve 80% of corresponding condition (light and material) top-surface Y(max). Mathematically, analysis of ratios was demonstrated to yield potentially less precise and biased estimates. Nonlinear regression yielded better statistical fit and provided easily accessible tests for differences in k across light-system groups. Another recently proposed nonlinear model for polymerization, Y=Y(max)kt(n)/(1+kt(n)), was also considered. While this new model has substantially greater phenomenological and mechanistic justification, we found that the model-fitting process was more sensitive to initial parameter values and sometimes yielded untenable results when applied to our data. However, we believe that these problems would not occur if sample points are well distributed across a wide range of exposure durations, and that the model, Y=Y(max)kt(n)/(1+kt(n)), should be considered for such data sets.