A Two Compartment, One Drug Model with Decaying Exponential Forcing
by Mike Martin

This page generates output plots for a two compartment, one drug delivery model with decaying exponential forcing

Consider a single medication on the time interval from [0, tfinal]. The drug is administered orally and absorbed first in the gastrointestinal (GI) tract and that is the first compartment. Let x(t) denote the concentration of the drug at time t in the GI tract; further, let that drug have a half-life of τx in the GI tract. The drug moves from the GI tract to the bloodstream, the second compartment, and is eventually expelled or broken down. Let y(t) denote the concentration of the drug at time t and τy be the half-life of the drug in the bloodstream. x(0)=0 and y(0)=0 are the initial conditions for the drug in the respective compartments. We assume there are none of the drug in the compartments to start with and, therefore, the initial conditions are all zero. The dosing function, f(t), is periodic on the interval from [0, Dinterval]. On this page we assume the dosing function is decaying exponentially on a dosing interval of length Dinterval. The decaying exponentially starts at a value of Fo and decay parameter of α. In a dosing interval, however, the dosing is "turned on" only on a subinterval, [0, Dadmin], and is otherwise zero (or "turned off").

Graphs are generated for the dynamics of this two compartment, one drug model. The first graph shows the dosing function on a dosing interval, [0, Dinterval]. The second graph shows the dosing function on the entire time interval, [0, tfinal]. The next graph shows the concentrations of the drug in the GI tract (x(t), plotted in blue) and in the bloodstream (y(t), plotted in red).

Enter in the values of the non-negative parameters tfinal, Dinterval, Dadmin, τx, τy, Fo, and α, then press the "Evaluate" button.

tfinal =  

Dinterval =  

Dadmin =  

τx =  

τy =  

Fo =  

α =  

References:

Spitznagel, E, Two Compartment Pharmacokinetic Models, CODEE Newsletter, Fall 1992, p. 2-4.

Macheras, P, A Iliadis, Modeling in Biopharmaceutics, Pharmacokinetics, and Pharmacodynamics. Springer, New York, NY, 2006.