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Formulation of photon diffusion from spherical bioluminescent sources in an infinite homogeneous medium

Cong, Wenxiang and Wang, Lihong V. and Wang, Ge (2004) Formulation of photon diffusion from spherical bioluminescent sources in an infinite homogeneous medium. BioMedical Engineering OnLine, 3 . Art. No. 12. ISSN 1475-925X. PMCID PMC421737. doi:10.1186/1475-925x-3-12. https://resolver.caltech.edu/CaltechAUTHORS:20190304-125703035

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Abstract

Background: The bioluminescent enzyme firefly luciferase (Luc) or variants of green fluorescent protein (GFP) in transformed cells can be effectively used to reveal molecular and cellular features of neoplasia in vivo. Tumor cell growth and regression in response to various therapies can be evaluated by using bioluminescent imaging. In bioluminescent imaging, light propagates in highly scattering tissue, and the diffusion approximation is sufficiently accurate to predict the imaging signal around the biological tissue. The numerical solutions to the diffusion equation take large amounts of computational time, and the studies for its analytic solutions have attracted more attention in biomedical engineering applications. Methods: Biological tissue is a turbid medium that both scatters and absorbs photons. An accurate model for the propagation of photons through tissue can be adopted from transport theory, and its diffusion approximation is applied to predict the imaging signal around the biological tissue. The solution to the diffusion equation is formulated by the convolution between its Green's function and source term. The formulation of photon diffusion from spherical bioluminescent sources in an infinite homogeneous medium can be obtained to accelerate the forward simulation of bioluminescent phenomena. Results: The closed form solutions have been derived for the time-dependent diffusion equation and the steady-state diffusion equation with solid and hollow spherical sources in a homogeneous medium, respectively. Meanwhile, the relationship between solutions with a solid sphere source and ones with a surface sphere source is obtained. Conclusion: We have formulated solutions for the diffusion equation with solid and hollow spherical sources in an infinite homogeneous medium. These solutions have been verified by Monte Carlo simulation for use in biomedical optical imaging studies. The closed form solution is highly accurate and more computationally efficient in biomedical engineering applications. By using our analytic solutions for spherical sources, we can better predict bioluminescent signals and better understand both the potential for, and the limitations of, bioluminescent tomography in an idealized case. The formulas are particularly valuable for furthering the development of bioluminescent tomography.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1186/1475-925x-3-12DOIArticle
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC421737/PubMed CentralArticle
ORCID:
AuthorORCID
Wang, Lihong V.0000-0001-9783-4383
Additional Information:© Cong et al; licensee BioMed Central Ltd. 2004. This article is published under license to BioMed Central Ltd. This is an Open Access article: verbatim copying and redistribution of this article are permitted in all media for any purpose, provided this notice is preserved along with the article's original URL. Received: 15 October 2003. Accepted: 04 May 2004. Published: 04 May 2004. This work was supported in part by the NIH grant R21/R33 EB001685.
Funders:
Funding AgencyGrant Number
NIHR21/R33 EB001685
Subject Keywords:Diffusion equation; Green's function; analytical solution; Monte Carlo simulation; bioluminescent imaging
PubMed Central ID:PMC421737
DOI:10.1186/1475-925x-3-12
Record Number:CaltechAUTHORS:20190304-125703035
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20190304-125703035
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:93438
Collection:CaltechAUTHORS
Deposited By: George Porter
Deposited On:04 Mar 2019 21:44
Last Modified:16 Nov 2021 16:57

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