Parabolic quantitative structure-activity relationships and photodynamic therapy: Application of a three-compartment model with clearance to the in vivo quantitative structure-activity relationships of a congeneric series ofpyropheophorbide derivatives used as photosensitizers for photodynamic therapy

An open three-compartment pharmacokinetic model was applied to the in vivo quantitative structural activity relationship (QSAR) data of a homologous s eries of pyropheophorbide photosensitizers for photodynamic therapy (PDT), The physical model was a lipid compartment sandwiched between two identical aqueous compartments. The first compartment was assumed to clear irreversi bly at a rate K-0. The measured octanol-water partition coefficients, P-i ( where i is the number of carbons in the alkyl chain) and the clearance rate K-0 determined the clearance kinetics of the drugs. Solving the coupled di fferential equations of the three-compartment model produced clearance kine tics for each of the sensitizers in each of the compartments. The third com partment was found to contain the target of PDT, This series of compounds i s quite lipophilic, Therefore these drugs are found mainly in the second co mpartment, The drug level in the third compartment represents a small fract ion of the tissue level and is thus not accessible to direct measurement by extraction. The second compartment of the model accurately predicted the c learance from the serum of mice of the hexyl ether of pyropheophorbide a, o ne member of this series of compounds. The diffusion and clearance rate con stants were those found by fitting the pharmacokinetics of the third compar tment to the QSAR data. This result validated the magnitude and mechanistic significance of the rate constants used to model the QSAR data. The PDT re sponse to dose theory was applied to the kinetic behavior of the target com partment drug concentration. This produced a pharmacokinetic-based function connecting PDT response to dose as a function of time postinjection, This mechanistic dose-response function was fitted to published, single time poi nt QSAR data for the pheophorbides, As a result, the PDT target threshold d ose together with the predicted QSAR as a function of time postinjection wa s found.