System identification of photosensitiser uptake kinetics in photodynamic therapy

This study draws the interest of system identification to the experimental modelling of in vitro uptake kinetics of photosensitising agents (PS) into cancer cells. The proposed identification methodology must be usable and valid for every PS. Therefore, three PSs characterized by opposing chemical and biological properties have been selected: (1) PC: a second generation photosensitising agent conjugated via   a spacer to a VEGF receptor-specific heptapeptide, (2) Ce6: Chlorin e6, and (3) TPP: TetraPhenylPorphyrin. Experiments have been carried out with two rates (2% and 9%) of foetal bovin serum in the culture medium and one cancer cell line U87U87 a human malignant glioma. Difficulties of such an application are triple: (i) lack of data, (ii) low signal-to-noise ratio and (iii) ‘poor’ stimulus signals. The proposed identification methodology deals with the design of experiments, the selection of a model structure, the estimation of the model parameters and the estimation of the parameter uncertainties. The photosensitiser uptake phenomenon is described by a first-order transfer function. Estimates of the time constant and the static gain provide quantitative information about the uptake rate and yield of the PS. The parameter uncertainty is described by confidence regions in parameters space. This representation is presented as an efficient way to discriminate the uptake characteristics of different photosensitisers. This representation also emphasizes the effects of some biological factors, such as the serum rate, on the uptake yield.