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

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.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.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.Light propagation in scattering media has attracted attention in many areas of physics, biology, medicine, and engineering. This process can be described by the radiative transfer equation [1], which is a complex integrodifferential equation. Under strong scattering conditions, the radiative transfer equation can be reduced to the diffusion equation, but this still does not permit exact solutions in most