Practical identifiability of photophysical parameters in photodynamic therapy

Photodynamic therapy (PDT) is an alternative treatment for cancer that involves the administration of a photosensitizing agent, which will be activated by light at a specific wavelength. In order to compare different photosensitisers for their cytotoxic activity, photophysical parameters provide good indicators. These parameters are generally estimated one by one from in vitro dedicated experiments, but they cannot always predict the in vivo cytotoxic action. So far, the estimation of photophysical parameters from in vivo data sets has never been regarded as a system identification problem. This paper deals with the practical identifiability of photophysical parameters. Practical identifiability deals with the uniqueness of the model parameters estimates, given the experimental data. The practical identifiability approach and its application to the photoreaction model of PDT are developed in this paper. It is shown that that the photophysical parameters involved in the kinetic model of photoreactions are identifiable in a practical framework with only one measurement - the intracellular photosensitizer concentration, and a wide square pulse as irradiation signal.