Photon diffusion equation

Photon diffusion equation is a second order partial differential equation describing the time behavior of photon fluence rate distribution in a low-absorption high-scattering medium.

Its mathematical form is as follows. $\nabla (D(r)\cdot \nabla )\Phi ({\vec {r}},t)-v\mu _{a}({\vec {r}})\Phi ({\vec {r}},t)+vS({\vec {r}},t)={\frac {\partial \Phi ({\vec {r}},t)}{\partial t}}$ where $\Phi$ is photon fluence rate (W/cm²), $\mu _{a}$ is absorption coefficient (cm⁻¹), $D$ is diffusion constant, $v$ is the speed of light in the medium (m/s), and $S$ is an isotropic source term (W/cm³).

Its main difference with diffusion equation in physics is that photon diffusion equation has an absorption term in it.

Application

Medical Imaging

diffuse optical tomography

External links

• Diffuse Optics Lab at University of Pennsylvania, Philadelphia, USA