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.
Highlights
Fluorescence biomedical imaging techniques offer the possibility to differentiate diseased from normal tissues, pursue the progression of a disease in vivo at a molecular level and monitor possible treatments via fluorescent probes [1,2,3,4,5,6]
We perform numerical experiments in which we compute the time-dependent transfer of excitation and fluorescence light in tissue-like media for two cases of practical interest: (1) a homogeneous cylinder with an embedded fluorescent inclusion which is often used in validation experiments, and (2) a rodent-shaped homogenous body with an organ filled with a fluorescent agent which is of interest in small animal molecular imaging
We introduced an finite element method (FEM) approach for the spatial dependence combined with an finite difference method (FDM) scheme for the temporal dependence of the fields
Summary
Fluorescence biomedical imaging techniques offer the possibility to differentiate diseased from normal tissues, pursue the progression of a disease in vivo at a molecular level and monitor possible treatments via fluorescent probes [1,2,3,4,5,6]. The subject of this paper is the modeling of the time-dependent response of fluorescent agents in biological tissues and the ensuing timedomain propagation of light therein Towards this end, we develop, for the first time, a set of equations (a model) along with a complete numerical scheme for modeling the propagation of excitation and fluorescence light in the time domain in complex 3D geometries based on the simplified spherical harmonics approximation (SPN). Our objective is to be able to compute efficiently (i.e. reduce computation time) and accurately (i.e. near to RTE) both the time and spatial dependencies of the excitation and fluorescence light fields inside an absorbing and scattering medium with complex geometry using the SPN method coupled with the finite element method This will be demonstrated through numerical results for complex geometries with exogenous fluorescent probes (our approach naturally applies to other types of fluorescence sources, such as fluorescent proteins, or endogenous fluorophores).
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