A Mathematical Evaluation of Dose-dependent PpIX Fluorescence Kinetics In Vivo¶

Abstract

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.

Quantitative Model Calculation of the Time-dependent Protoporphyrin IX Concentration in Normal Human Epidermis After Delivery of ALA by Passive Topical Application or Iontophoresis¶

“…Diffusion of ALA. As an ad hoc assumption, Aalders et al (1) assumed that the ALA concentration in the tissue (skin, rat liver, rat small intestine) decays exponentially in time or according to the M-M equation. This may not be the most suitable form for ALA in the skin after iontophoretic or passive topical ALA application.…”

“…Recently, Aalders et al (1) devised a three-compartment model for the time-dependent clearance of 5-aminolevulinic acid (ALA) in tissue and for its conversion to protoporphyrin IX (PpIX) and subsequently to heme. The model was fitted to the data of ALA-induced PpIX fluorescence in human skin, mouse skin and rat liver and small intestine after topical or systemic ALA administration.…”

“…M-M equations account for saturation effects, which are observed in the PpIX fluorescence as a function of topical or systemic ALA dose. In the model of Aalders et al (1) the ALA concentrations and the PpIX concentrations in tissue are known, except for a single constant factor. Consequently, only time constants could be obtained from the fits and only the ratio of the M-M parameters for each compartment.…”

“…We wanted to use these data in an attempt to quantitatively calculate the transport of ALA in the skin and the subsequent synthesis of PpIX and its conversion to heme. We have modified the model of Aalders et al (1) by using the time-dependent diffusion equation for the propagation of ALA in the skin. Equations similar to those of Aalders et al were used to describe the cellular processes leading to the formation of heme.…”

Decreasing Systemic Toxicity Via Transdermal Delivery of Anticancer Drugs

“…Unfortunately, treatment with 5-ALA is also associated with liver damage. A high dose of 5-ALA brings a potential risk of phototoxic liver damage during exposure to high intensity operating room lights for several hours [29]. Also, Bechara et al demonstrated that 5-ALA produced reactive oxygen species during metal-catalyzed aerobic oxidation, and subsequently caused an iron-catalyzed calcium-dependent oxidative damage to the inner membrane of rat liver mitochondria [30].…”