Mathematical description of photobleaching in vivo describing the influence of tissue optics on measured fluorescence signals

The observed decrease in the fluorescence signal during photodynamic therapy (PDT) may contain dosimetric information as this photobleaching provides direct information on the photodynamic processes occurring in the tissue. A correct interpretation of the photobleaching signal, however, is crucial for its use in dosimetry. In this study the influence of scattering and absorption phenomena in tissue on the emitted fluorescence signal are described mathematically. Analytical solutions of the resulting expression show a difference from the single-decaying-exponential function generally used for describing photobleaching signals. The solutions are a function of the fluence rate at the inner side of tissue boundary psi(0*), the photobleaching dose constant beta, the incident irradiation power I0 and time. The accuracy of the results was investigated by comparison of the analytic solutions with numerical calculations using fluence rate profiles and escape functions obtained by Monte Carlo (MC) simulations. Good resemblance is observed when the value for psi(0*) calculated by the MC simulations is used in the analytical solutions. Experimental results in this study indicate the photobleaching dose constant of ALA-induced PpIX to be 33 +/- 3 J cm-2. Determination of beta for different types of photosensitizer and the development of an accurate method to determine psi(0*) can make monitoring of photobleaching during PDT valuable for dosimetr