Photon diffusion in a homogeneous medium bounded externally or internally by an infinitely long circular cylindrical applicator IV Frequency-domain analysis

Abstract

Part IV examines frequency-domain 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 by analogical and finite-element methods the changes of AC amplitude, modulation depth, and phase with respect to the line-of-sight source-detector distance for a source and a detector located along the azimuthal or longitudinal direction on the concave or convex medium-applicator interface. By comparing to their counterparts along a straight line on a semi-infinite medium-applicator interface, for the same line-of-sight source-detector distance, it is found that: (1) the decay-rate of AC photon fluence is smaller along the azimuthal direction and greater along the longitudinal direction on the concave interface, (2) the decay-rate of AC photon fluence is greater along the azimuthal direction and smaller along the longitudinal direction on the convex interface, (3) the modulation depth along both azimuthal and longitudinal directions decays more slowly on the concave interface and faster on the convex interface, and (4) the phase along both azimuthal and longitudinal directions increases more slowly on the concave interface and faster on the convex interface.

On the geometry dependence of differential pathlength factor for near-infrared spectroscopy. I. Steady-state with homogeneous medium

“…The expressions of the photon fluence rate as given in the set of Eqs. (23), (24), and (26), which are resulted from the approximations of their respective general solutions, do show a quasidoubling effect of the spherical geometry when compared to the azimuthal direction of the infinite-length cylinder geometry. Such doubling effect of the spherical geometry compared to the azimuthal direction of the cylinder geometry with respect to the semi-infinite geometry is observable in Fig.…”

“…In our recent approach to a new routine of solutions of DE for an infinite-length cylinder domain as demonstrated in a series of work applicable to CW, 25 frequency domain 26 and time domain, 27 the solutions for DE were presented using a pair of the modified Bessel functions of the first and the second kinds. The basic form of the DE solution for the unbounded homogeneous medium geometry shown in Refs.…”

Challenges of Zinc-Specific Transrectal Fluorescence Tomography to Detect Prostate Cancer

“…Based on a novel analytical approach to photon diffusion in the convex" geometry and "concave" geometry [18,19], we gained new insights to how trans-rectal DOT/FDOT measurements are different from DOT/FDOT measurements in other geometries. By comparing the photon fluence with respect to the line-of-sight source-detector distance in the concave, semi-infinite, and convex geometries, respectively, the effects of the medium-applicator interfacing curvature and the dimension of the curvature to the diffuse photon measurements are better understood [20,21,22]. The tissue is at the concave side of the circular cylindrical tissue-applicator interface, so the equivalent isotropic source of the physical source that illuminates into the medium is located closer to the center axis than the physical source is.…”

“…A is a coefficient determined by the change of the refractive indices across the interface. Similarly, we have for the first time developed the cylindrical coordinate solutions of steady-state photon diffusion in the convex geometry, between a detector r  and a physical source r   on the physical boundary as [18,22]…”

“…On a convex interface with large radius, Eq. (3.conV) indicates   2 ln d conV  reducing versus d as[21,22]…”