Photon diffusion in a homogeneous medium bounded externally or internally by an infinitely long circular cylindrical applicator I Steady-state theory (original) (raw)
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Journal of the Optical Society of America, 2011
This is Part II of the work that examines photon diffusion in a homogenous medium enclosed by a concave circular cylindrical applicator or enclosing a convex circular cylindrical applicator. Part I of this work [J. Opt. Soc. Am. A 27, 648 (2010)] analytically examined the steady-state photon diffusion between a source and a detector for two specific cases: (1) the detector is placed only azimuthally with respect to the source, and (2) the detector is placed only longitudinally with respect to the source, in the infinitely long concave and convex applicator geometries. For the first case, it was predicted that the decay rate of photon fluence would become smaller in the concave geometry and greater in the convex geometry than that in the semi-infinite geometry for the same source-detector distance. For the second case, it was projected that the decay rate of photon fluence would be greater in the concave geometry and smaller in the convex geometry than that in the semi-infinite geometry for the same source-detector distance. This Part II of the work quantitatively examines these predictions from Part I through several approaches, including (a) the finite-element method, (b) the Monte Carlo simulation, and (c) experimental measurement. Despite that the quantitative examinations have to be conducted for finite cylinder applicators with large length-to-radius ratio to approximate the infinite-length condition modeled in Part I, the results obtained by these quantitative methods for two concave and three convex applicator dimensions validated the qualitative trend predicted by Part I and verified the quantitative accuracy of the analytic treatment of Part I in the diffusion regime of the measurement, at a given set of absorption and reduced scattering coefficients of the medium.
Journal of the Optical Society of America, 2014
Part VI analytically examines time-domain (TD) photon diffusion in a homogeneous medium enclosed by a "concave" circular cylindrical applicator or enclosing a "convex" circular cylindrical applicator, both geometries being infinite in the longitudinal dimension. The aim is to assess characteristics of TD photon diffusion, in response to a spatially and temporally impulsive source, versus the line-of-sight source-detector distance along the azimuthal or longitudinal direction on the concave or convex medium-applicator interface. By comparing to their counterparts evaluated along a straight line on a semi-infinite medium-applicator interface versus the same source-detector distance, the following patterns are indicated: (1) the peak photon fluence rate is always reached sooner in concave and later in convex geometry; (2) the peak photon fluence rate decreases slower along the azimuthal and faster along the longitudinal direction on the concave interface, and conversely on the convex interface; (3) the total photon fluence decreases slower along the azimuthal and faster along the longitudinal direction on the concave interface, and conversely on the convex interface; (4) the ratio between the peak photon fluence rate and the total fluence is always greater in concave geometry and smaller in convex geometry. The total fluence is equivalent to the steady-state photon fluence analyzed in Part I [J. Opt. Soc. Am. A 27, 648 (2010)]. The patterns of peak fluence rate, time to reaching peak fluence rate, and the ratio of these two, correspond to those of AC amplitude, phase, and modulation depth of frequency-domain results demonstrated in Part IV [
Journal of the Optical Society of America, 2012
This is Part III of the work that examines photon diffusion in a scattering-dominant medium enclosed by a "concave" circular cylindrical applicator or enclosing a "convex" circular cylindrical applicator. In Part II of this work Zhang et al. [J. Opt. Soc. Am. A 28, 66 (2011)] predicted that, on the tissue-applicator interface of either "concave" or "convex" geometry, there exists a unique set of spiral paths, along which the steady-state photon fluence rate decays at a rate equal to that along a straight line on a planar semi-infinite interface, for the same line-of-sight source-detector distance. This phenomenon of steady-state photon diffusion is referred to as "straight-lineresembling-spiral paths" (abbreviated as "spiral paths"). This Part III study develops analytic approaches to the spiral paths associated with geometry of a large radial dimension and presents spiral paths found numerically for geometry of a small radial dimension. This Part III study also examines whether the spiral paths associated with a homogeneous medium are a good approximation for the medium containing heterogeneity. The heterogeneity is limited to an anomaly that is aligned azimuthally with the spiral paths and has either positive or negative contrast of the absorption or scattering coefficient over the background medium. For a weak-contrast anomaly the perturbation by it to the photon fluence rate along the spiral paths is found by applying a well-established perturbation analysis in cylindrical coordinates. For a strong-contrast anomaly the change by it to the photon fluence rate along the spiral paths is computed using the finite-element method. For the investigated heterogeneous-medium cases the photon fluence rate along the homogeneous-medium associated spiral paths is macroscopically indistinguishable from, and microscopically close to, that along a straight line on a planar semi-infinite interface.
arXiv (Cornell University), 2005
Does the diffusion coefficient of a photon depend on time ttt or the probability of absorption kkk? To find an answer to the question, photon transport in a medium of infinite extent is analyzed using the method of moments. It is pointed out that if DDD is defined so as to make it depend on ttt or kkk, it will also depend on the experimental conditions; that the parameter kkk which enters the stationary diffusion equation is in general different from that entering the transient version; and that a hitherto unused non-Markovian partial differential equation may be used for treating photon transport.