C. Plasma data
1. Scheme or diagram
The one compartment pharmacokinetic model can be represented schematically as:-
Diagram IV-2, Scheme for a One Compartment Model, Intravenous Bolus Administration
2. Differential equation
Going back to the slope calculations, if we measure the slope over small intervals we are calculating the tangent to the line. We can now say that the rate of elimination is the differential of the concentration with respect to time as 
t - - - > 0 then Cp/t - - - > dCp/dt which gives:-
Equation IV-2. Rate of Change of Drug Concentration - First Order, IV Bolus
Equation IV-2 is a differential equation for the one-compartment model after IV bolus administration. With the calculus term dCp/dt we are going from the gross or large time interval term
Cp/t to the continuously varying dCp/dt term.
3. Elimination rate constant, kel
We should now distinguish between the elimination rate and the elimination rate constant. The rate (tangent or slope, dCp/dt) changes as the concentration changes, however, for a linear model the rate constant (kel) is constant, it does not change.
This page was last modified: 12 February 2001
Copyright 2001 David W.A. Bourne