Zhang Anqi, Xu Guan, Daluwatte Chathuri, Yao Gang, Bunting Charles F, Pogue Brian W, Piao Daqing
School of Electrical and Computer Engineering, Oklahoma State University, Stillwater, Oklahoma 74078-5032, USA.
J Opt Soc Am A Opt Image Sci Vis. 2011 Feb 1;28(2):66-75. doi: 10.1364/JOSAA.28.000066.
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.
本文是研究光子在由凹圆柱面施加器包围的均匀介质中或包围凸圆柱面施加器的均匀介质中扩散的工作的第二部分。该工作的第一部分[《美国光学学会志A》27, 648 (2010)]分析研究了两种特定情况下源与探测器之间的稳态光子扩散：(1)探测器仅相对于源沿方位角放置，以及(2)探测器仅相对于源沿纵向放置，在无限长的凹面和凸面施加器几何结构中。对于第一种情况，预测在相同源 - 探测器距离下，凹面几何结构中光子注量的衰减率将比半无限几何结构中的小，而凸面几何结构中的将比半无限几何结构中的大。对于第二种情况，预计在相同源 - 探测器距离下，凹面几何结构中光子注量的衰减率将比半无限几何结构中的大，而凸面几何结构中的将比半无限几何结构中的小。本文的第二部分通过几种方法对第一部分的这些预测进行了定量研究，包括(a)有限元法、(b)蒙特卡罗模拟和(c)实验测量。尽管必须针对具有大长径比的有限圆柱施加器进行定量研究，以近似第一部分中建模的无限长条件，但通过这些定量方法针对两个凹面和三个凸面施加器尺寸获得的结果验证了第一部分预测的定性趋势，并在给定的介质吸收和约化散射系数集下，验证了测量扩散区域中第一部分解析处理的定量准确性。
