Analytic expression of fluorescence ratio detection correlates with depth in multi-spectral sub-surface imaging.

Here we derived analytical solutions to diffuse light transport in biological tissue based on spectral deformation of diffused near-infrared measurements. These solutions provide a closed-form mathematical expression which predicts that the depth of a fluorescent molecule distribution is linearly related to the logarithm of the ratio of fluorescence at two different wavelengths. The slope and intercept values of the equation depend on the intrinsic values of absorption and reduced scattering of tissue. This linear behavior occurs if the following two conditions are satisfied: the depth is beyond a few millimeters and the tissue is relatively homogeneous. We present experimental measurements acquired with a broad-beam non-contact multi-spectral fluorescence imaging system using a hemoglobin-containing diffusive phantom. Preliminary results confirm that a significant correlation exists between the predicted depth of a distribution of protoporphyrin IX molecules and the measured ratio of fluorescence at two different wavelengths. These results suggest that depth assessment of fluorescence contrast can be achieved in fluorescence-guided surgery to allow improved intra-operative delineation of tumor margins.