A mathematical evaluation of dose-dependent PpIX fluorescence kinetics in vivo

The in vivo pharmacokinetics of protoporphyrin IX (PpIX) after administration of 5-aminolevulinic acid (ALA) cannot be described accurately by mathematical models using first-order rate processes. We have replaced first-order reaction rates by dose-dependent (Michaelis-Menten [MM]) reaction rates in a mathematical compartment model. Different combinations of first-order and dose-dependent reaction rates were evaluated to see which one would improve the goodness-of-fit to experimentally determined in vivo PpIX fluorescence kinetics as a function of concentration. The mathematical models that were evaluated are all based on a three-compartment model for drug distribution, conversion to PpIX and subsequent conversion to heme. Implementation of dose-dependent reaction rates improved the goodness-of-fit and enabled interpolation to other drug doses. For most data sets the time constant for delivery to the target cells turned out to be dose dependent. For all data sets the use of MM rates for the conversion of ALA to PpIX yielded better fits. The clearance of PpIX turned out to be a first-order process for all doses and types of administration. Fluorescence curves measured on a specific tissue type but obtained in different studies with different measurement techniques could be described with a single set of parameters.