Optical tomography using the time-independent equation of radiative transfer — Part 1: forward model

Abstract

The presented study consists of two parts. The overall goal is to introduce and experimentally test a novel optical tomographic imaging algorithm that is based on the equation of radiative transfer. Using the equation of radiative transfer rather than the diffusion equation permits the consideration of highly scattering media that contain void-like regions that have very low absorption and scattering coefficients. In part I we concentrate on the detailed description and evaluation of a numerical forward model that accurately describes photon propagation in such media. In part II we focus on the inclusion of this forward model into a model-based iterative image reconstruction (MOBIIR) scheme. Using the MOBIIR scheme one can determine the spatial distribution of optical properties inside highly scattering media from measurements acquired on the surface of the medium. The mathematical and numerical background for the reconstruction algorithm, especially the adjoint differentiation scheme for the gradient calculation, will be presented. The code is tested with experimental data from tissue-phantoms that contain water-filled, void-like regions. The forward model to be described in part I is based on an upwind-difference discrete-ordinate formulation of the time-independent equation of radiative transfer. The upwind-difference representation has the advantage that it provides a convenient mathematical framework for calculating the derivative of the fluence with respect to the optical parameters using an adjoint differentiation technique, to be described in part II. The performance of the forward model is tested with experimental data obtained from homogeneous tissue-phantoms and from phantoms that contain void-like regions. We find good agreement between experimental measurements and theoretical predictions of the measurements.