Case Studies and Project Ideas: Pharmacokinetics - Chronic Oral Dosing

Simple Pharmacokinetic Three-Compartment model

Source:

Model design and case study design by Robert R. Gotwals, Jr.

Goal:

To learn about basic pharmacokinetics through the building and use of a simple compartment model for drug absorption and disposition.

Key concepts and terminology:

Half-life:

The period of time required for the concentration or amount of drug in the body to be reduced to exactly one-half of a given concentration or amount. Symbolized as "t1/2".

Volume of distribution:

The volume, in an organism, throughout which a drug appears to have been distributed; the volume into which a drug appears to have been dissolved after administration to an organism. Symbolized by Vd, measured in liters (L). Calculated by amount of drug in the body / concentration in the plasma.

Absorption rate constant:

Typically referred to as "ka", the rate at which an orally-dosed drug enters the bloodstream.

Elimination:

The removal of a drug from the blood stream, usually through the urine.

Elimination rate constant:

Typically referred to as "ke", the rate at which an orally-dosed drug is removed from the bloodstream.

Threshold dosage:

A dose of drug just sufficient to produce a pre-selected effect. Frequently, and improperly, restricted to the dose just sufficient to produce a minimal detectable effect.

Plasma concentration:

The amount of drug in the plasma divided by the volume of distribution. Concentrations are typically the parameter of most interest to pharmacologists

Background Reading:

The simplest type of model used in the study of pharmacokinetics is the compartment model. In this model, we are concerned with following the progression of a drug as it enters the intestines (stomach), is absorbed into the blood (plasma), and eventually ends up in the urine. As such, we look at the amount of drug in three "compartments":

Drug in the intestine

Drug in the plasma

Drug in the urine The purpose of this model is to look at the effect of how a change in the amount of drug (the dose) and the dosing interval affects the amount of drug in the three compartments. We will want to try to stabilize the plasma concentration over a period of about eight days.

Building the Model:

In this model we are interested in the concentrations of drug in three-compartments, as described above. The algorithm for this particular model is outlined below. Using these algorithms and these initial values, your task is to build this model and then use it to investigate a number of scenarios, described in the section below.

Initial values:

Initial drug in the intestine = 0 mg/L

Initial drug in the plasma = 0 mg/L

Inital drug in the urine = 0 mg/L

Absorption rate constant (ka) = 1 /hour

Volume of distribution (Vd) = 70 L

Simulation time = 192 hours in 15 minute intervals (dt = 0.25 hour)

Using the Model:

Once you have completed your model, you should try a number of scenarios. What is the difference in changing the dosage and the dosing intervals? What settings might you use to reach a "threshold" dosage of 5.0 mg/L?

Algorithm Set for the Model:

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