Diffusion Modelling of Picosecond Laser Pulse Propagation in Turbid Media

Abstract

The increasing use of visible and near infrared light in therapeutic and diagnostic techniques has created a need to model its propagation in tissue. One of the fundamental objectives of such a model is the noninvasive evaluation of the optical properties of tissue. The focus of this thesis was the development of the diffusion approximation in the semi-infinite, slab, cylindrical and spherical geometries. This development required the derivation of approximate boundary conditions which included the zero, extrapolated and partial current boundary conditions. Calculations of the fluence and its related quantities arising from the extrapolated boundary condition were found to be in excellent agreement with the results of the more rigorous partial current boundary condition. A preliminary evaluation of the validity of diffusion theory was performed by comparing its predictions to exact analytical calculations of the fluence in an infinite medium as well as Monte Carlo simulations of the reflectance and transmittance in 1-dimensional planar geometries. In all cases the agreement at late times was excellent. A practical test of the diffusion model was accomplished with the analysis of the reflectance data from a phantom of known optical properties in both the semi-infinite and slab geometries. The model performed well at low concentrations of added absorber, but a considerable discrepancy was found at the highest concentration. A systematic examination of the accuracy of the diffusion model as a function of the fundamental parameters is required to resolve this inconsistency. Approximate expressions describing the equivalent information in the frequency domain were also developed for a semi-infinite medium. These expressions were then used to analyze the phase and modulation obtained from phantoms of known optical properties. Once again reasonable results were obtained at low concentrations of added absorber while a significant discrepancy arose at the highest concentration. The resolution of these discrepancies requires further investigation.