Radiance modelling using the P3 approximation

Abstract

Light dosimetry is an essential component of effective photodynamic therapy (PDT) of tumours. Present PDT light dosimetry techniques rely on fluence-based models and measurements. However, in a previous paper by Barajas et al, radiance-based light dosimetry was explored as an alternative approach. Although successful in demonstrating the use of Monte Carlo (MC) simulations of radiance in tissue optical characterization, the MC proved time consuming and impractical for clinical applications. It was proposed that an analytical solution to the transport equation for radiance would be desirable as this would facilitate and increase the speed of tissue characterization. It has been found that the P3 approximation is one such potential solution. Radiance and fluence expressions based on the P3 approximation were used to optically characterize an Intralipid-based tissue phantom of varying concentration of scatterer (Intralipid) and absorber (methylene blue) using a plane wave illuminated, semi-infinite medium geometry. The results obtained compare favourably with the Grosjean approximation of fluence (a modified diffusion theory) using the same optical parameters (mu(a), mu(s), g). The results illustrate that radiance-based light dosimetry is a viable alternative approach to tissue characterization and dosimetry. It is potentially useful for clinical applications because of the limited number of invasive measurements needed and the speed at which the tissue can be characterized.

Advance in Photosensitizers and Light Delivery for Photodynamic Therapy

“…It is hard to accomplish a complete glandular ablation with PDT; therefore, transurethral light delivery (circular in distribution) is not suitable for prostate cancer treatment. Monte Carlo simulations are useful in tissue optical characterization and PDT modeling; however, this method is time-consuming and impractical for clinical application 140. Jankun et al141 developed a computer-aided light delivery method that can calculate the volume of ablated tissue and predict the outcome on a three-dimensional virtual model of the prostate.…”

Radiative transport in the delta-P1 approximation for semi-infinite turbid media

“…7-10 Efforts have been undertaken by several groups to develop models for tissue reflectance that implement higher-order P N and ␦-P N approximations in both infinite and semi-infinite geometries. [11][12][13][14][15][16][17][18][19][20][21][22] The effort most relevant to the prediction of spatially resolved diffuse reflectance from a semi-infinite turbid medium is that of Hull and Foster who developed the P 3 approximation for this case. 17 Their implementation provides for the accurate recovery a and s Ј from spatially resolved reflectance measurements made at small s-d separations for ͑ s Ј/ a ͒ ജ 1.…”

Applications of delta-P1 and delta-P3 approximations to optical tomography in small imaging volumes

“…Hull [28], Dickey [30][31], and Faris [32] have studied 3-D P3 approximation. Transferring P3 approximation to delta-P3 approximation is straightforward by following the rules given by Star.…”

“…However, both methods are computation intensive. To provide a computation effective method with moderate accuracy, several improved diffusion models have been proposed, including approximations in the P 3 , P N , delta-P1, and delta-P3 [21][22][23][24][25][26][27][28][29][30][31][32]. It has been shown that delta-P1 and delta-P3 approximations can accurately predict diffuse reflectance when source-detector separation is as short as one fifth of one transport mean free path and delta-P3 is expected even higher accuracy [23,27,28].…”