Reduced models of drug delivery in the presence of fast protein binding

Abstract

Drug dosage determination and potential drug interference when multiple medical compounds must be administered simultaneous is an important long-standing problem both in practical pharmacokinetics and in theoretical drug design modeling. Very simple, and mostly linear, models are currently used to describe drug distribution in a body, drug function, and drug elimination. Many of the processes involved in drug delivery occur on vastly different time scales. This fact and, in particular, the presence of fast forward and reverse drug binding to blood proteins, is used in this paper to produce the reduced models describing time dependent drug dynamics during intravenous drug delivery, i.e., when the drug is administered directly in patient's vein via catheter. In addition, the questions on whether the drug dosage must be adjusted in the presence of protein binding compared to the case of drugs which do not bind, as well as what happens when two administered drugs participate in competing protein binding reactions are addressed. The singularly perturbed models derived under natural assumptions are analyzed using the boundary function method approach.

Keywords

• boundary function method
• small parameter
• singular perturbations
• drug-protein binding
• pharmacokinetics
• competing reactions