Gauss and Eisenstein Sums of Order Twelve

The Monte Carlo-based inverse model of diffuse reflectance described in part I of this pair of companion papers was applied to the diffuse reflectance spectra of a set of 17 malignant and 24 normal-benign ex vivo human breast tissue samples. This model allows extraction of physically meaningful tissue parameters, which include the concentration of absorbers and the size and density of scatterers present in tissue. It was assumed that intrinsic absorption could be attributed to oxygenated and deoxygenated hemoglobin and beta-carotene, that scattering could be modeled by spheres of a uniform size distribution, and that the refractive indices of the spheres and the surrounding medium are known. The tissue diffuse reflectance spectra were evaluated over a wavelength range of 400-600 nm. The extracted parameters that showed the statistically most significant differences between malignant and nonmalignant breast tissues were hemoglobin saturation and the mean reduced scattering coefficient. Malignant tissues showed decreased hemoglobin saturation and an increased mean reduced scattering coefficient compared with nonmalignant tissues. A support vector machine classification algorithm was then used to classify a sample as malignant or nonmalignant based on these two extracted parameters and produced a cross-validated sensitivity and specificity of 82% and 92%, respectively.