Coupled Forward-Adjoint Monte Carlo Simulations of Radiative Transport for the Study of Optical Probe Design in Heterogeneous Tissues

• Published in: SIAM journal on applied mathematics Vol. 68; no. 1; pp. 253 - 270
• Main Authors: Hayakawa, Carole K., Spanier, Jerome, Venugopalan, Vasan
• Format: Journal Article
• Language: English
• Published: Philadelphia Society for Industrial and Applied Mathematics 01.01.2007
• Subjects: Adjoints; Boundary conditions; Estimation methods; Interrogations; Inverse problems; Investigations; Lasers; Light; Monte Carlo methods; Monte Carlo simulation; Optical properties; Optics; Photons; Probability; Sensors; Trajectories
• ISSN: 0036-1399; 1095-712X
• DOI: 10.1137/060653111

We introduce a novel Monte Carlo method for the analysis of optical probe design that couples a forward and an adjoint simulation to produce spatial-angular maps of the detected light field within the tissue under investigation. Our technique utilizes a generalized reciprocity theory for radiative transport and is often more efficient than using either forward or adjoint simulations alone. For a given probe configuration, the technique produces rigorous, transport-based estimates of the joint probability that photons will both visit any specified target subvolume and be detected. This approach enables the entire tissue region to be subdivided into a collection of target subvolumes to provide a phase-space map of joint probabilities. Such maps are generated efficiently using only one forward and one adjoint simulation for a given probe configuration. These maps are used to identify those probe configurations that best interrogate targeted subvolumes. Inverse solutions in a layered tissue model serve to illustrate and reinforce our analysis.