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

BioMedical Engineering OnLine

Wenxiang Cong¹  Lihong V Wang²  Ge Wang¹ 

[1] CT/Micro-CT Laboratory University of Iowa Iowa City, Iowa 52242, USA

[2] Optical Imaging Laboratory Department of Biomedical Engineering Texas A&M University College Station, Texas 77843-3120, USA

关键词: bioluminescent imaging;    Monte Carlo simulation;    analytical solution;    Green's function;    Diffusion equation;   

Others  :  798878
DOI  :  10.1186/1475-925X-3-12

 received in 2003-10-15, accepted in 2004-05-04,  发布年份 2004

【 摘 要 】

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.

【 授权许可】

   
2004 Cong et al; licensee 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.

【 图 表 】

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