A pilot study of a simple photon migration model for predicting depth of cure in dental composite

The purpose of this study was to build a photo migration model to calculate the radiant exposure (irradiance×time) in dental composite and to relate the radiant exposure with extent of cure using polymer kinetics models. A composite (Z100, Shade A2) cylinder (21 mm diameter by 15 mm deep) was cured with a tungsten-halogen lamp emitting 600 mW/cm², 1 mm above the composite for 60 s. For each of the 2×1 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=DCmax[1-exp((ln0.5)H/Hdc50%)] and Racz's model DC=DCmax/[1+(H/Hdc50%)- 2], where Hdc50% is a fitting parameter representing the threshold for 50% of the maximum curing level. The absorption and scattering coefficients of uncured composite were higher than that of cured composite at wavelengths between 420 and 520 nm. A roughly hemi-spheric 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 (r²=0.95) and the exponential model (r²=0.93). The Hdc50% was 1.5(0.1), equal for the two models (P<0.05). The estimated radiant exposure threshold for 80% of the maximum curing level was between 3.8 and 8.8 J/cm². The simulation results verify that the radiant exposure extends to a greater depth and width for composite with lower absorption and scattering coefficients. Given the optical properties and the geometry of the composite, and the spectrum and the geometry of the light source, the Monte Carlo simulation can accurately describe the radiant exposure distribution in a composite material to predict the extent of cure.