Abstract-An efficient algorithm for solving the transient radiative transfer equation for laser pulse propagation in biological tissue is presented. A Laguerre expansion is used to represent the time dependency of the incident short pulse. The Runge-KuttaFehlberg method is used to solve the intensity. The discrete ordinates method is used to discretize with respect to azimuthal and zenith angles. This method offers the advantages of representing the intensity with a high accuracy using only a few Laguerre polynomials, and straightforward extension to inhomogeneous media. Also, this formulation can be easily extended for solving the 2-D and 3-D transient radiative transfer equations.

Abstract-Light scattering from small spherical particles has applications in a vast number of disciplines including astrophysics, meteorology optics and particle sizing. Mie theory provides an exact analytical characterization of plane wave scattering from spherical dielectric objects. There exist many variants of the Mie theory where fundamental assumptions of the theory has been relaxed to make generalizations. Notable such extensions are generalized Mie theory where plane waves are replaced by optical beams, scattering from lossy particles, scattering from layered particles or shells and scattering of partially coherent (non-classical) light. However, no work has yet been reported in the literature on modifications required to account for scattering when the particle or the source is in motion relative to each other. This is an important problem where many applications can be found in disciplines involving moving particle size characterization. In this paper we propose a novel approach, using special relativity, to address this problem by extending the standard Mie theory for scattering by a particle in motion with a constant speed, which may be very low, moderate or comparable to the speed of light. The proposed Received 29 October 2010, Accepted 13 January 2011, Scheduled 24 January 2011. 350Handapangoda, Premaratne, and Pathirana technique involves transforming the scattering problem to a reference frame co-moving with the particle, then applying the Mie theory in that frame and transforming the scattered field back to the reference frame of the observer.

A novel algorithm for mapping the photon transport equation (PTE) to Maxwell's equations is presented. Owing to its accuracy, wave propagation through biological tissue is modeled using the PTE. The mapping of the PTE to Maxwell's equations is required to model wave propagation through foreign structures implanted in biological tissue for sensing and characterization of tissue properties. The PTE solves for only the magnitude of the intensity but Maxwell's equations require the phase information as well. However, it is possible to construct the phase information approximately by solving the transport of intensity equation (TIE) using the full multigrid algorithm.

Fluorescence has become a widely used technique for applications in noninvasive diagnostic tissue spectroscopy. The standard model used for characterizing fluorescence photon transport in biological tissue is based on the diffusion approximation. On the premise that the total energy of excitation and fluorescent photon flows must be conserved, we derive the widely used diffusion equations in fluorescence spectroscopy and show that there must be an additional term to account for the transport of fluorescent photons. The significance of this additional term in modeling fluorescence spectroscopy in biological tissue is assessed.

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