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Improving the accuracy of a solid spherical source radius and depth estimation using the diffusion equation in fluorescence reflectance mode


Hejazi, M; Stuker, F; Vats, D; Rudin, M (2010). Improving the accuracy of a solid spherical source radius and depth estimation using the diffusion equation in fluorescence reflectance mode. BioMedical Engineering OnLine, 9:28.

Abstract

BACKGROUND: Non-invasive planar fluorescence reflectance imaging (FRI) is used for accessing physiological and molecular processes in biological tissue. This method is efficiently used to detect superficial fluorescent inclusions. FRI is based on recording the spatial radiance distribution (SRD) at the surface of a sample. SRD provides information for measuring structural parameters of a fluorescent source (such as radius and depth). The aim of this article is to estimate the depth and radius of the source distribution from SRD, measured at the sample surface. For this reason, a theoretical expression for the SRD at the surface of a turbid sample arising from a spherical light source embedded in the sample, was derived using a steady-state solution of the diffusion equation with an appropriate boundary condition.

METHODS: The SRD was approximated by solving the diffusion equation in an infinite homogeneous medium with solid spherical sources in cylindrical geometry. Theoretical predications were verified by experiments with fluorescent sources of radius 2-6 mm embedded at depths of 2-4 mm in a tissue-like phantom.

RESULTS: The experimental data were compared with the theoretical values which shows that the root mean square (RMS) error in depth measurement for nominal depth values d = 2, 2.5, 3, 3.5, 4 mm amounted to 17%, 5%, 2%, 1% and 5% respectively. Therefore, the average error in depth estimation was < or = 4% for depths larger than the photon mean free path.

CONCLUSIONS: An algorithm is proposed that allows estimation of the location and radius of a spherical source in a homogeneous tissue-like phantom by accounting for anisotropic light scattering effect using FRI modality. Surface SRD measurement enabled accurate estimates of fluorescent depth and radius in FRI modality, and can be used as an element of a more general tomography reconstruction algorithm.

BACKGROUND: Non-invasive planar fluorescence reflectance imaging (FRI) is used for accessing physiological and molecular processes in biological tissue. This method is efficiently used to detect superficial fluorescent inclusions. FRI is based on recording the spatial radiance distribution (SRD) at the surface of a sample. SRD provides information for measuring structural parameters of a fluorescent source (such as radius and depth). The aim of this article is to estimate the depth and radius of the source distribution from SRD, measured at the sample surface. For this reason, a theoretical expression for the SRD at the surface of a turbid sample arising from a spherical light source embedded in the sample, was derived using a steady-state solution of the diffusion equation with an appropriate boundary condition.

METHODS: The SRD was approximated by solving the diffusion equation in an infinite homogeneous medium with solid spherical sources in cylindrical geometry. Theoretical predications were verified by experiments with fluorescent sources of radius 2-6 mm embedded at depths of 2-4 mm in a tissue-like phantom.

RESULTS: The experimental data were compared with the theoretical values which shows that the root mean square (RMS) error in depth measurement for nominal depth values d = 2, 2.5, 3, 3.5, 4 mm amounted to 17%, 5%, 2%, 1% and 5% respectively. Therefore, the average error in depth estimation was < or = 4% for depths larger than the photon mean free path.

CONCLUSIONS: An algorithm is proposed that allows estimation of the location and radius of a spherical source in a homogeneous tissue-like phantom by accounting for anisotropic light scattering effect using FRI modality. Surface SRD measurement enabled accurate estimates of fluorescent depth and radius in FRI modality, and can be used as an element of a more general tomography reconstruction algorithm.

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2 citations in Web of Science®
3 citations in Scopus®
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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:04 Faculty of Medicine > Institute of Pharmacology and Toxicology
04 Faculty of Medicine > Institute of Biomedical Engineering
Dewey Decimal Classification:570 Life sciences; biology
170 Ethics
610 Medicine & health
Language:English
Date:2010
Deposited On:30 Jan 2011 20:46
Last Modified:05 Apr 2016 14:38
Publisher:BioMed Central
ISSN:1475-925X
Publisher DOI:https://doi.org/10.1186/1475-925X-9-28
PubMed ID:20565901
Permanent URL: https://doi.org/10.5167/uzh-43225

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