Hybrid Diffusion Approximation Based On P₃ Approximation And Experimental Research

With the development of biomedical optical technology, the determination of optical parameters of biological tissue is becoming one of the most important basic research, and the diffusion reflectance technique which can be used in noninvasive measurement has received a great deal of attention recently. The basic principle of the technique is based on the theory model of the relationship between the reflectance and the optical coefficients of biological media, and an inversion algorithm is used to reconstruct the optical properties of the tissue from the obtained reflectance data. The diffusion approximation (DA) is a successful theory for solving the radiative transport equation. However, the DA model gives accurate solutions for reflectance for source-detector separations larger than several transport mean free paths and high albedo. With the rapid development of the applications of the visible and/or infrared spectral in the optical diagnosis and optical therapy, there is a significant need for methods that accurately quantify optical properties of tissue at smaller source-detector separations in highly absorbing and scattering media. The P3 approximation model can describe the radiance in highly absorbing media or close to sources more accurately than does DA due to consider the two-order and third-order moments of the phase function, but the model have a quite complex mathematical expression. Based on the two models, a modified diffusion approximation model that can be used for highly absorbing media is investigated. This model is called the hybrid diffusion approximation (HDA) in this paper. The problem about the propagation of light for the low reduced albedo close to source in terms of the HDA model have been studied with theoretical, simulated and experimental methods, the main work as following:Firstly, the spheric harmonic function is derived from the Boltzmann's transport equation, and both the equation set of the P3 approximation and its Green's function are derived. The relationship between P1 approximation and DA are demonstrated, and a complete solution of P3 approximation with the extrapolated boundary conditions and collimated beam approximation is obtained. The influence of the reduced albedo a 'on P3 approximation diffuse reflection is studied, and the results are compared with those of the DA and Monte Carlo simulation. The application range of P3 approximation is presented.Secondly, A modified diffusion approximation model that can be used for highly absorbing media is investigated. This model is called the hybrid diffusion approximation in this paper, because the diffusion coefficient D of the standard diffusion approximation is substituted by the diffusion coefficient Da sym of P3 approximation. The analytic solution ( )RH ybridρof the hybrid diffusion approximation for reflectance in two-source approximation and steady-state case with extrapolated boundary is obtained;The effects of source approximation on R Hybrid(ρ) are investigated, and one important fact is validated: two-source approximation in highly absorbing media to describe the optical properties of biological tissue is necessary; Monte Carlo Simulating study of recovering optical parameters from reflectant data with the use of this model are done, the results show that the errors of recoveringμa andμs' are smaller than 15% for the reduced albedo a ' =0.77~0.5 at source-detector separation within several transport mean free path.Thirdly, the sensitivity of the absorption coefficient, the reduced scattering coefficient and the high-order parameters (γandδ) of the scattering phase function based on HAD spatially resolved diffuse reflectance is studied and the analytical expressions of these sensitivities are derived. By comparison with those of Monte Carlo simulation, the results show that the sensitivity of the absorption coefficient increases approximately linearly with the source-detector separationsρand has a slope proportional to 1 .4(μs ' /μa)1/4; the optimum probe spacingρopt at which a variable reduced scattering coefficient has the leaste effect on the measurment of optical absorption in the turbid media are obtained. The study to the sensitivity of the higher-order parameters show that the higher-order parameters have few influences on the HDA diffuse reflectance. The result of the HDA are consistent with that of Monte Carlo simulation if the Henyey-Greenstein (HG) phase function is used for the anisotropy factor g =0.6~0.99.Fourthly, the influences of the second-order and third-order parameters of biological tissue on spatially resolved diffuse reflectance are studied with Monte Carlo simulation. The reflectance R (ρ)is dependent on high-order moments of the tissues for a short source-detector separation. The results show that the effective region of the second-order parameterγis about 5 l t'(transport mean free path), the curve of the reflectance R (ρ) rises withγincreasing in the region of 0 .7l t ' <ρ<2lt'. The effects of the third-order parameterδon the reflectance R (ρ) are studied, and the effective region is about 2 l t'. For the first time, we find that the curves of the reflectance R (ρ) decreases with an increase ofδat a short source detector separation of approximately 0.7-2 transport mean free paths, and show that the effect ofγon R (ρ) appears irregular because that the effect ofγis counteracted by the effect ofδwhen a condition ofΔδ<<Δγis not satisfied. These results are important and useful to reconstruct optical properties of tissue from experimental data of diffuse reflectance close to the source.Finally, a tentative experimental research of the spatial-resolved diffuse reflectance close to source is done. The tissue phantom that the optical properties are given is measured, and the measurement results are comparing with those of the HDA model and Monte Carlo simulation. The study shows that the experimental result is agreement with that of Monte Carlo simulation in highly scattering and low absorbing media.The global variation trend of the experimental result is consistent with those of the HDA model and Monte Carlo simulation in highly absorbing and scattering media.This work is important and useful for developing the technology of diffuse reflection spectral measurement and the theory of radiance measurement.