Application of Distributed Delay Differential Equations to Modeling Drug Absorption Delays
Wojciech Krzyzanski, PhD
Professor, University at Buffalo, Department of Pharmaceutical Sciences
Dr. Krzyzanski received a PhD in applied mathematics and an MA in pharmacology from the University at Buffalo. He is currently a Professor in the Department of Pharmaceutical Sciences at this university. His research interests include computational pharmacometrics, PKPD systems with delays, and modeling drug effects on cell populations. He has published over 120 articles in peer-reviewed journals and contributed three chapters. He serves as an associate editor for the Journal of Pharmacokinetics and Pharmacodynamics. He is a Fellow of the International Society of Pharmacometrics.
Extravascular drug administration involves a cascade of processes before drug molecules reach the systemic circulation. The lag time between administration and entry to the circulation is called the absorption delay. Existing PK models describe the absorption using input rates that feed into the central compartment representing circulating blood. The input rate consists of absorption delay model of discrete or continuous distribution of lag times followed by an absorption compartment that transfers drug molecules to the central compartment at first order-rate. The lag time distribution may be described by a compartment model (transit compartments) or an explicit function (Dirac, gamma, Weibull).
The objective of this presentation is to demonstrate how to implement the absorption PK models with distributed lag times using distributed delay differential equations (DDDEs). We will show how to apply available DDDE solvers in NONMEM 7.6 (ICON Plc) and Phoenix 8.6 (Certara Inc) to assess differences in performance between standard and DDDE models using simulated data.