light/tissue interactions, Monte Carlo methods, transport and diffusion theory
My research at BLI involves analyzing mathematical models of light/tissue interactions, particularly in the transport regime, and developing computational strategies for implementing them. The ongoing study of efficient Monte Carlo solutions of both direct and adjoint radiative transport equations figures prominently in this work. We have developed 1. efficient perturbation/differential Monte Carlo tools for solving many direct problems simultaneously, and estimating sensitivity coefficients, using only a single set of random walks; 2. a tool for computing and displaying rigorous (transport) tissue interrogation maps from which detailed interactions of light fields with tissue volumes can be both quantitatively and qualitatively assessed; 3. adaptive Monte Carlo algorithms whose estimates converge geometrically rather than at the much slower rate governed by the central limit theorem of probability.
Spanier, J., “Monte Carlo Methods”, chapter in Nuclear Computational Science: A Century in Review, A Century Anew, (Y. Azmy and E .Sartori, eds.), Springer 2010.
R. Kong and J. Spanier, “Geometric Convergence of Adaptive Monte Carlo Algorithms for Radiative Transport Problems Based on Importance Sampling” Nucl. Sci. Eng.168 195-225 July, 2011.
M. Martinelli, A. Gardner, D. Cuccia, C. Hayakawa, J. Spanier and V. Venugopalan, “Analysis of single Monte Carlo methods for prediction of reflectance from turbid media”, Optics Express 19(20), 19627-19642, (2011).
C.K. Hayakawa, R. Kong and J. Spanier, “Spatial/Angular Contributon Maps for Improved Adaptive Monte Carlo Algorithms”, Monte Carlo and Quasi-Monte Carlo Methods,Springer-Verlag, 419-434, (2012).
R. Kong, and J. Spanier, "Transport-Constrained Extensions of Collision and Track Length Estimators for Solutions of Radiative Transport Problems." J. Comp. Physics 242, 628-695 (2013).
J. Nguyen, C. Hayakawa, J. Mourant, and J. Spanier, "Perturbation Monte Carlo methods for tissue structure alterations," Biomed. Opt. Express 4, 1946-1963 (2013).