Mathematical model for time-resolved and frequency-domain fluorescence spectroscopy in biological tissues

In general it is not possible to write an analytic expression for the fluorescence signal generated by a fluorophore distributed in a scattering medium such as tissue. However, by assuming that the scattering properties of the tissue are the same at the excitation and emission wavelengths, we have derived a simple relation between the fluorescence and the scatter signals. Along with diffusion theory, this was used to write expressions for the fluorescence signal detected at the tissue surface in both the time and the frequency domains. Experiments using the fluorophore aluminum chlorosulfonated phthalocyanine in tissue-simulating materials confirmed the accuracy of the model. Applications to in vivo spectroscopy are discussed.