Photon diffusion equation

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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 $Φ$ is photon fluence rate (W/cm²), $μ a$ 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).