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

The in vivo pharmacokinetics of protoporphyrin IX (PpIX) after administrati on of 5-aminolevulinic acid (ALA) cannot be described accurately by mathema tical 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 an d dose-dependent reaction rates were evaluated to see which one would impro ve the goodness-of-fit to experimentally determined in vivo PpIX fluorescen ce kinetics as a function of concentration. The mathematical models that we re evaluated are all based on a three-compartment model for drug distributi on, conversion to PpIX and subsequent conversion to heme. Implementation of dose-dependent reaction rates improved the goodness-of-fit and enabled int erpolation to other drug doses. For most data sets the time constant for de livery to the target cells turned out to be dose dependent. For all data se ts the use of MM rates for the conversion of ALA to PpIX yielded better fit s. The clearance of PpIX turned out to be a first-order process for all dos es and types of administration. Fluorescence curves measured on a specific tissue type but obtained in different studies with different measurement te chniques could be described with a single set of parameters.