Photon diffusion in a homogeneous medium bounded externally or internally by an infinitely long circular cylindrical applicator V Steady-state fluorescence

Abstract

As Part V in our series, this paper examines steady-state fluorescence photon diffusion in a homogenous medium that contains a homogenous distribution of fluorophores, and is enclosed by a "concave" circular cylindrical applicator or is enclosing a "convex" circular cylindrical applicator, both geometries being infinite in the longitudinal dimension. The aim is to predict by analytics and examine with the finite-element method the changing characteristics of the fluorescence-wavelength photon-fluence rate and the ratio (sometimes called the Born ratio) of it versus the excitation-wavelength photon-fluence rate, with respect to the source-detector distance. The analysis is performed for a source and a detector located on the medium-applicator interface and aligned either azimuthally or longitudinally in both concave and convex geometries. When compared to its steady-state counterparts on a semi-infinite medium-applicator interface with the same line-of-sight source-detector distance, the fluorescence-wavelength photon-fluence rate reduces faster along the longitudinal direction and slower along the azimuthal direction in the concave geometry, and conversely in the convex geometry. However, the Born ratio increases slower in both azimuthal and longitudinal directions in the concave geometry and faster in both directions in the convex geometry, respectively, when compared to that in the semi-infinite geometry.

An experimental and numerical modelling investigation of the optical properties of Intralipid using deep Raman spectroscopy

“…This result is similar to what would be expected from an analytical process to solve for diffuse fluorescence with two coupled diffusion processes giving the bi-phasic outcome. 38 The scattering coefficients that we have determined here differ from the values found in other studies, except the value at the concentration of 1% as discussed earlier. There are limited studies, which do not always overlap (see Hohmann et al 39 for an example), and did not return the experimental behaviour we have observed.…”

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

“…The unified analytical treatment of photon diffusion in both "concave" and "convex" geometries, in comparison to "semi-infinite" geometry to which the "concave" and "convex" geometries approach as the radius becomes infinite, has been demonstrated for continuous-wave (CW) [25], frequency-domain (FD) [26], and CW fluorescence [27] measurements. This particular study extends the analytical methodology introduced in [25][26][27] to modeling time-domain (TD) photon diffusion in the specific "concave" and "convex" geometries. The objective is to examine the effect of the "concave" or "convex" shape of the medium-applicator interface and the dimension (radius) of the interface on TD photon diffusion.…”

A geometric-sensitivity-difference method improves object depth-localization for continuous-wave fluorescence diffuse optical tomography: An in silico study in an axial outward-imaging geometry

“…The spatial dependence of the sensitivity of FDOT is also specific to the applicator-medium geometry. Among the applicator-medium geometries that have been investigated for the potential of clinical application of FDOT, an axial outward-imaging geometry [16,17] for endo-rectal or endoscopic imaging is subjected to arguably much stronger variation of the sensitivity of surface measurement with respect to the imaging depth [18], when compared with the geometries involving a curved interface that encloses the medium [12] or a planar interface [15]. For example, the spatial sensitivity of a circular array with optodes evenly distributed along the circumference [11][12][13] is nearly azimuthally uniform; and the spatial sensitivity of a near-planar array with orderly distributed surface optodes or remote source-detector positions [14] changes insignificantly over the lateral dimension of the array.…”