Quantitative model calculation of the time-dependent protoporphyrin IX concentration in normal human epidermis after delivery of ALA by passive topical application or lontophoresis.

We present a mathematical layer model to quantitatively calculate the diffusion of 5-aminolevulinic acid (ALA) in the skin in vivo, its uptake into the cells and its conversion to protoporphyrin IX (PpIX) and subsequently to heme. The model is a modification and extension of a recently presented three-compartment model. The diffusion of ALA in the skin (epidermis, dermis) is described by the time-dependent diffusion equation, and the sink in this equation accounts for ALA uptake in the cells. As boundary conditions, we use the ALA flux across the human stratum corneum (SC) in vitro during passive or iontophoretic ALA delivery as measured in vitro. Besides the diffusion equation, the model includes three additional equations, similar in form to those of the three-compartment model but with a different interpretation. Our additional equations are supposed to describe, respectively, the conversion of ALA in the cytoplasm to some intermediate compound in the mitochondria and the conversion of the latter to PpIX and of PpIX to heme. The first conversion is a process of the Michaelis-Menten type, the other two are first-order rate processes. When fitted to the published data of PpIX fluorescence from normal human skin following iontophoresis of ALA, the model yields the tissue concentration of PpIX as a function of time after ALA application. The computed concentrations are in good agreement with the published phototoxic concentrations of PpIX in the tissues obtained from extraction. The model parameters obtained from the fit are subsequently used to compute the PpIX concentration in normal human skin after 4 h topical application of 10, 20 and 40% ALA. This again yields the PpIX concentrations in tissue, in good agreement with the published values. The saturation of the PpIX concentration as a function of applied ALA concentration is calculated and agrees with clinical observations on the effectiveness of photodynamic therapy. Photobleaching is simulated, with subsequent resynthesis of PpIX in qualitative agreement with experiment. Finally, the model predicts that only 2.5-3.5% of the ALA entering the skin after passing the SC is converted to PpIX. The layered model is a considerable simplification of real skin, but its successful qualitative and quantitative reproduction of experimental data may encourage further studies to test and refine the model to improve our understanding of the kinetics of ALA and the synthesis of PpIX in the skin.