Light propagation from fluorescent probes in biological tissues by coupled time-dependent parabolic simplified spherical harmonics equations

Abstract

We introduce a system of coupled time-dependent parabolic simplified spherical harmonic equations to model the propagation of both excitation and fluorescence light in biological tissues. We resort to a finite element approach to obtain the time-dependent profile of the excitation and the fluorescence light fields in the medium. We present results for cases involving two geometries in three-dimensions: a homogeneous cylinder with an embedded fluorescent inclusion and a realistically-shaped rodent with an embedded inclusion alike an organ filled with a fluorescent probe. For the cylindrical geometry, we show the differences in the time-dependent fluorescence response for a point-like, a spherical, and a spherically Gaussian distributed fluorescent inclusion. From our results, we conclude that the model is able to describe the time-dependent excitation and fluorescent light transfer in small geometries with high absorption coefficients and in nondiffusive domains, as may be found in small animal diffuse optical tomography (DOT) and fluorescence DOT imaging.

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

“…Yet analytical treatment is of fundamental interest in revealing the effect of a particular geometry on fluorescence photon diffusion. Examples of the analytical modeling of fluorescence photon diffusion for infinite and semi-infinite geometries can be found in [14][15][16], and for concave geometry in [17];…”

Diffuse optical tomographic imaging of biological media by time-dependent parabolic SPN equations: a two-dimensional study

“…33,34 Numerical solutions for complex media were also found for simulating light propagation from external sources and fluorescent probes. [29][30][31][32][35][36][37] These results led to the development of SP N model-based image reconstruction algorithms for solving inverse problems in intrinsic, bioluminescence, and fluorescence DOT imaging. [38][39][40][41] However, as far as we know, no image reconstruction method or algorithms based on a time-dependent SP N model was ever attempted.…”

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

“…The spatial-temporal distributions of photon density in a diffusing medium in response to impulse stimulation carry the information of isotropic scattering and absorption of the medium. Time-resolved measurement of photon diffusion has enabled probing of highly scattering biological tissues, including brain [1,2], breast [3,4], forearm [5], other thick tissues or media [6,7], and characterization of fluorescent emissions [8][9][10][11]. In terms of where the optical applicator is placed for measuring the diffusing medium, three idealized interfacing geometries can be inferred: (a) a semi-infinite boundary separating a plain diffusing medium from a void nondiffusing medium; (b) a "concave" geometry wherein a plain diffusing cylinder is embedded in a void nondiffusing medium, as imaging forearm closely resembles; (c) a "convex" geometry wherein a void nondiffusing cylinder is within a diffusing medium, as transrectal imaging of prostate essentially is.…”