Time Delays in Drug Administration: Effect, Transit, Tricks and Oscillations∗

Time delays naturally occur in the administration of drugs, either to mimic normal physiological processes, like the pulsatile release of hormones, or to properly take into account physiological mechanisms (such as distribution to target tissue) which do not occur on a time scale short enough to be considered instantaneous. A number of avenues have been taken to represent these lags mathematically, some more direct than others. We present different approaches employed in pharmacokinetic-pharmacodynamic (PKPD) modeling, in a simple model for the regulation of the glucose-insulin system, and also in the design of pulsatile release mechanism where oscillations are driven by the finite relaxation of a hydrogel membrane. We also illustrate the explicit use of delay-differential equations in a PKPD model for a chemotherapeutic intervention.