One-Compartment IV Bolus Concentration

What is this formula?

The one-compartment IV bolus concentration equation describes how drug concentration decreases over time after an instantaneous intravenous bolus injection.

The model assumes that the drug distributes instantly throughout a single, well-mixed compartment and is eliminated according to first-order kinetics.

This is one of the most fundamental equations in pharmacokinetics.

When to use it

Use this formula when a drug is administered as a rapid intravenous bolus and can be reasonably described by a one-compartment model with first-order elimination.

It is widely used in pharmacokinetic analysis, therapeutic drug monitoring, dose design, and pharmacology education.

Example

A drug is administered intravenously. The initial concentration is 20 mg/L and the elimination rate constant is 0.15 h⁻¹.

Determine the concentration after 6 hours.

Data:

C0 = 20 mg/L

k = 0.15 h⁻¹

t = 6 h

Formula:

C = C0·e^(-kt)

Substitution:

C = 20·e^(-0.15×6)

C = 20·e^(-0.9)

C = 20×0.4066

Result:

C = 8.13 mg/L

Applications

- Intravenous drug pharmacokinetics

- Therapeutic drug monitoring

- Dose regimen design

- Pharmacokinetic simulations

- Drug development studies

Note

This model assumes instantaneous distribution throughout the body and first-order elimination. Many drugs exhibit distribution phases that require two-compartment or multicompartment models for greater accuracy. The one-compartment model is most appropriate when distribution is rapid relative to elimination.