Introduction to Veterinary Pharmacokinetics: Home Administration Distribution Elimination Modeling Models Glossary

## Pharmacokinetic Models

### Physiologic models

Attempt to describe the actual events which control drug absorption, distribution, and elimination

• Derived from measurements of drug concentrations in specific fluids (bile, portal and hepatic veins, tissue fluids, urine, etc.).
• Deal with an organ, a tissue or an organ system
• Combined to describe functions and processes

### Mathematic models

Attempt to accurately predict the time course of drug concentrations in one (usually blood or plasma) or two (urine as well) body fluids.  Predictions are generally made for tissues which can be sampled from intact patients.

"Pharmacokinetics" on package inserts represent these kinds of model.

• Modeling begins with a single dose experiment:
• A dose of drug is administered, samples are taken at timed intervals after dosing, samples are analyzed for drug concentrations.
• Drug concentrations are then plotted and analyzed mathematically to determine the drug's clearance, the rate constant of elimination, half-life, and the volume of distribution of the drug.

### Michaelis-Menten kinetics

All pharmacokinetics are biochemical or physiological processes. For the most part, these processes obey Michaelis-Menten kinetics. At low amounts of substrate, capacity (for aborption, elimination, etc.) greatly exceeds concentration. Changing the concentration changes the rate (pharmacokinetics depend on one thing so are first order). At very high amounts of substrate, capacity reaches a maximum. Changing the concentration has no effect on rate (pharmacokinetics no longer depend on concentration - zero order). In between, the pharmacokinetics change as the dose changes (pharmacokinetics are mixed order or dose dependent).

#### First Order (The pharmacokinetics of MOST drugs is first order at therapeutic doses.)

• A fraction the dose of drug is absorbed per unit time
• A fraction of the amount of drug in the body is eliminated per unit time.
• Half-life will be the same at all doses.
• Repeated dosing will produce a steady-state.

#### Zero order (special dose forms, high concentrations of some drugs)

• A constant amount of drug is absorbed per unit time (or)
• Drug is constantly released from some dose forms (patches, some oral drugs) to produce continuous therapy.
• A constant amount of drug is eliminated per unit time
• There is no elimination half-life (or the half-life changes constantly)
• Drug will accumulate with no maximum so long as zero order elimination rate is exceeded by administration rate.

#### Dose Dependent Behavior

For most drugs (99%), it is logical to assume that the relationship between the dose we give and the concentration(s) that the dose produces in the body are linear. (We double the dose, the concentrations double, the effects double). The PHARMACOKINETICS of these drugs are said to be dose-independent.

Occassionally, drug dosing behave differently:

• If the pharmacokinetics of ABSORPTION change when we increase the dose (the absorption rate decreases as the dose increases -- as would be the case for the "ball" of drug described earlier in these notes under "routes of administration"), the drug is said to exhibit dose-dependent absorption. Doubling the dose produces less than a doubling of tissue concentrations and effects.
• If the pharmacokinetics of ELIMINATION change when we increase the dose (clearance and the elimination rate constant decrease as the dose increases), the drug is said to exhibit dose-dependent elimination . Doubling the dose produces MORE than a doubling of tissue concentrations and effects.
Michaelis-Menten saturation curve showing how the rate of a process changes with the concentration of substrate.

This curve is labeled to show three pharmacokinetic states (dependencies). First order at low doses (typical for drug therapy), zero order at high doses (ethanol behaves this way at "effective" doses), and mixed order in between.