@article{chen05c,
  author = {Yin-Chu Chen and Jack L. Ferracane and Scott A. Prahl},
  title = {A pilot study of a simple photon migration model for predicting depth of cure in dental composite},
  journal = {Dental Materials},
  volume = {21},
  pages = {1075-1086},
  year = {2005},
  abstract = {\textit{Objectives:} The purpose of this study was to build a photo migration model to calculate the radiant exposure (irradiance $\cdot$ time) in dental composite and to relate the radiant exposure with extent of cure using polymer kinetics models. \\[3mm] \textit{Methods:} A composite (Z100) cylinder (21\,mm diameter by 15\,mm deep) was cured with tungsten--halogen lamp emitting 600\,mW/cm$^2$, 1\,mm above the composite for 60 seconds. For each of the 2$\times$1\,mm grids along the longitudinal cross section (diameter versus depth), the degree of conversion (DC) and hardness (KHN) were measured to construct the curing extent distribution. The inverse adding--doubling method was used to characterize the optical properties of the composite for the Monte Carlo model simulating the photon propagation within the composite cylinder. The calculated radiant exposure ($H$) distribution along the cross section was related to the curing extent $DC/DC_{max}$ distribution and fitted with two polymer curing kinetics models, the exponential model $DC = DC_{max} [1-\exp((\ln 0.5) H/H^{50\%}_{dc})]$ and Racz's model $DC = DC_{max}/[1+(H/H^{50\%}_{dc})^{-2} ]$, where $H^{50\%}_{dc}$ is a fitting parameter representing the threshold for the 50\% of the maximum curing level. \\[3mm] \textit{Results:} The absorption and scattering coefficients of uncured composite were higher than that of cured composite at wavelength between 420 to 520\,nm. A roughly hemi-sphere distribution of radiant exposure in the Monte Carlo simulation result was comparable with the curing profiles determined by both DC and KHN. The relationship between $DC$ (or $KHN$) and $H$ agreed with the Racz model ($r^2=0.95$) and the exponential model ($r^2=0.93$). The $H^{50\%}_{dc}$ was 1.5$\pm$0.1, equal for the two models ($p<0.05$). The estimated radiant exposure threshold for the 80\% of the maximum curing level was between 3.8 and 8.8\,J/cm$^2$. The simulation results verify that the radiant exposure extends to a greater depth and width for composite with lower absorption and scattering coefficients.},
}