One compartment with constant elimination rate of a drug, a first order process, and instantaneous injection of drug dose.

Description

 A one compartment model with intravenous (i.v.) injection is the simplest description 
 of a drug time course through the body. It assumes that the concentration of the 
 drug within the blood stream is representative of that throughout the body and 
 that drug concentration within the tissue is instantaneously in equilibrium with 
 blood concentration. With an i.v. injection the concentration at time t.min is
 equal to the amount injected into the vein.

 A compartment model has a volume and a concentration of a substance. Here the volume 
 is equal to the dose (total quantity of drug) injected divided by the measured 
 concentration in the blood stream. The change in the quantity of drug in the 
 compartment is described by mass balance equations.

 The apparent volume of distribution is designated as V, the concentration as C, and the amount of 
 material or drug as Q. The change in concentration, dQ/dt is governed by sources 
 (which add material to Q) and sinks which subtract material from Q. A source will 
 be a positive quantity. A sink will be a negative quantity. The change in
 Q can be written as:

        dQ/dt = d(V*C)/dt = C*dV/dt+V*dC/dt. 

 Assuming V is constant,

        dQ/dt = V*dC/dt.

 The ODE equation describing the first order decay process is given as:

 V*dC/dt = -Clearance*C, where Clearance is the amount of drug removed from the 
 compartment. This equation is usually rewritten as:

 dC/dt = -(Kelim)*C, after dividing both sides by the volume, where
                     Kelim (Elimination rate const) = Clearance/V

 The term on the right hand side is a sink term. It is negative and removes 
 material from the compartment.

 A note on V, the apparent volume of distribution: This is not a physiological volume but
 rather a ratio that measures the extent of drug distribution within a compartment. If the 
 compartment represented blood volume and the drug distributed only in the plasma and not 
 the red blood cells (RBCs), then the volume of distribution for the drug would be less than the 
 volume of distribution of another drug that distributed into the RBCs as well as plasma. 
 The volume of distribution is drug dependent.

Equations

The equations for this model may be viewed by running the JSim model applet and clicking on the Source tab at the bottom left of JSim's Run Time graphical user interface. The equations are written in JSim's Mathematical Modeling Language (MML). See the Introduction to MML and the MML Reference Manual. Additional documentation for MML can be found by using the search option at the Physiome home page.