A fresh look at the validity of diffusion equations for modelling phosphorescence imaging of biological tissue

Phosphorescence lifetime imaging has become a widely used technique for tomographic oxygen imaging. The conventional model used to characterize photon transport in phosphorescence imaging is two coupled diffusion equations. On the premise that the total energy of excitation and phosphorescence photon flows must be conserved, we derive the diffusion equations in phosphorescence imaging and show that there must be an additional term to account for the transport of phosphorescent photons. This additional term accounts for the transport of phosphorescence photon energy density due to its gradients. The significance of this term in modelling phosphorescence in biological tissue is assessed.