Theoretical analysis of coupled diffuse-photon-density and thermal-wave field depth profiles photothermally generated in layered turbid dental structures

A coupled diffuse-photon-density and thermal-wave model is developed for theoretical analysis of the photothermal field in demineralized teeth. Intact and demineralized layers of enamel, as well as dentin, are described as a layered one-dimensional system. The solution of the radiative transport equation in the limit of diffuse-photon-density field is considered as a source term in the thermal-wave field equation. The influence of optical parameters (absorption and scattering coefficients) and thermal parameters (thermal diffusivity and conductivity) of each layer on the diffuse-photon-density and thermal-wave depth profiles is analyzed using computer simulations, allowing the verification of accuracy and validity of the developed theory. The proposed model and simulations are intended for identifying the parameters most affecting the diffuse-photon-density and thermal-wave fields in turbid media, which leads to optimization of the fitting process of thermal and optical properties of teeth from experimental data obtained by frequency-domain photothermal radiometry.