δ-SPN approximation for numerical modeling of directional sources and scattering.

We propose the δ-SPN approximation for the frequency domain coupled radiative transfer equations modeling fluorescence with collimated incident beams and present its numerical implementation using the finite element method. The performance of the proposed model is investigated with respect to Monte Carlo simulations and the standard SPN approximation over sub-centimeter domains for various optical properties. We find that the δ-SPN approximation is more accurate than the SPN in the near-source region, and provides improved estimates of phase and partial currents, at both excitation and emission wavelengths, over a wider range of optical properties. The accuracy of the δ-SPN model improves with increase in approximation order for normally incident beams.

Second-order adjoint sensitivities for fluorescence optical tomography based on the SPN approximation.

Use of second-order sensitivity information has been shown in the literature to yield faster convergence, better noise tolerance, and localization besides enhanced post-reconstruction analysis capabilities. In this paper, we derive adjoint-based second-order derivatives for SPN-approximation-modeled fluorescence optical tomography. We modify the regularizing Levenberg-Marquardt method to use second-order sensitivity information through a predictor-corrector framework. Reconstruction studies presented for the fluorophore absorption coefficient in low as well as high scattering tissue-mimicking phantoms in both ideal and differential fluorophore-uptake settings show consistently superior noise tolerance and contrast recovery with the second-order scheme as compared to its first-order counterpart.

Effective Screening and Classification of Cervical Precancer Biopsy Imagery.

Microscope images of biopsy samples of cervical precancers conventionally discriminated by histopathology, the current "gold standard" for cancer detection, showed that their correlation properties are segregated into different classes. The correlation domains clearly indicate increasing cellular clustering in different grades of precancer compared with their normal counterparts. This trend indicates the probability of pixel distribution of the corresponding tissue images. Because the cell density is not uniform in the higher grades, the skewness (asymmetry of a distribution), kurtosis (sharpness of a distribution), entropy (randomness), and standard deviation are affected. A combination of these parameters effectively improves the diagnosis and quantitatively classifies the normal and all the three grades of precancerous cervical tissue sections significantly. Thus, the statistical analysis of microscope images is a promising approach for early stage tumor detection and quantitative classification of precancerous grades; this can effectively supplement the qualitative analysis by the pathologist.

Fully Nonlinear ${SP}_{3}$ Approximation Based Fluorescence Optical Tomography.

In fluorescence optical tomography, many works in the literature focus on the linear reconstruction problem to obtain the fluorescent yield or the linearized reconstruction problem to obtain the absorption coefficient. The nonlinear reconstruction problem, to reconstruct the fluorophore absorption coefficient, is of interest in imaging studies as it presents the possibility of better reconstructions owing to a more appropriate model. Accurate and computationally efficient forward models are also critical in the reconstruction process. The approximation to the radiative transfer equation (RTE) is gaining importance for tomographic reconstructions owing to its computational advantages over the full RTE while being more accurate and applicable than the commonly used diffusion approximation. This paper presents Gauss-Newton-based fully nonlinear reconstruction for the approximated fluorescence optical tomography problem with respect to shape as well as the conventional finite-element method-based representations. The contribution of this paper is the Frechet derivative calculations for this problem and demonstration of reconstructions in both representations. For the shape reconstructions, radial-basis-function represented level-set-based shape representations are used. We present reconstructions for tumor-mimicking test objects in scattering and absorption dominant settings, respectively, for moderately noisy data sets in order to demonstrate the viability of the formulation. Comparisons are presented between the nonlinear and linearized reconstruction schemes in an element wise setting to illustrate the benefits of using the former especially for absorption dominant media.