<title>Determination of tissue optical properties from spatially resolved relative diffuse reflectance</title>

Abstract

Noninvasive determination of μ_s' and μ_a is essential for clinical applications in medical diagnostics and therapeutics. Spatially resolved diffuse reflectance method is more advantageous than other techniques because of its simplicity and low-cost. The methods for solving the nonlinear inverse problem of estimates of μ_s' and μ_a from spatially resolved diffuse reflectance R_d(r) can be classified into the algorithms based on absolute or relative reflectance measurements in nature. Since absolute reflectance measurements are technically more difficult to perform than the relative one, study on the methods based on the relative reflectance has a more important meaning for real applications. Considering that there were several normalizations of R_d(r), in this paper we discussed the varieties of prediction rms errors of μ_s' and μ_a extracted from relative reflectance data of different normalization forms including R_d(r)/R_d(r)_max, r²(R_d(r)/R_d(r)_max), 1n(R_d(r)/R_d(r)_max) and 1n(r²(R_d(r)/R_d(r)max)). Additionally, we compared the accuracies of μ_s' and μ_a determined from absolute reflectance data R_d(r) and 1n(R_d(r)) with that from relative reflectance data to study the loss of accuracy due to normalization. Rather than the traditional neural network methods, we used a new method -- PCA-NN trained with diffuse reflectance data from Monte Carlo simulations to derive μ_s' and μ_a. All the PCA-NNs were trained and tested on the space with μ_s' between 0.1 and 2.0 mm^-1 and μ_a between 0.01 and 0.1 mm^-1. The test results indicate that the rms errors in μ_s' and μ_a are 0.72% and 2.57% for R_d(r), 0.28% and 0.55% for 1n(R_d(r), 2.98% and 5.44% for R_d(r)/R_d(r)_max, 2.22% and 3.21% for 1n(R_d(r)/R_d(r)_max), 6.52% and 20.7% for r²(R_d(r)/R_d(r)_max), and 2.22% and 3.21% for 1n(r²(R_d(r)/R_d(r)_max)), suggesting that the normalization form 1n(R_d(r)/R_d(r)_max) would be the first choice for the estimates of μ_s' and μ_a from relative reflectance data by PCA-NN. Although the loss of accuracy due to normalization is considerable, the preliminary results provide a guideline for relative reflectance measurements.