last updated 06-06-2023

#### Effect of Clearance and Volume of Distribution on Half-life

The question arises how the volume of distribution (Vd), clearance (CL) and half-life are related. This figure illustrates two processes with a similar clearance mechanism (capable of clearing the same amount of volume of distribution per time). It is clear that it takes longer to remove all drug from the larger container.

However, what if the volume of distribution of both processes is similar, but the clearance mechanism of the lower container is much more efficient (i.e. clears more drug)? The lower container will be cleared much faster. Half-life is therefore dependent upon both clearance and volume of distribution.

More specifically, the half-life is defined as:

t½ = 0.693 × (Vd / Cl)

It can also defined with the elimination rate constant in the equation:

t½ = 0.693 / kel

Furthermore, this allows us to calculate the clearance when the following equation is used:

CL = kel · Vd

1

MDMA is a well-known party drug (ecstasy). The half-life time of MDMA is 7 hours. A patient is seen in the Emergency Room in a comatose state. After a laboratory test the plasma concentration of MDMA is 0.6 mg/L. After how many hours is the plasma concentration of MDMA reduced to 0.15 μg/L? (Assume linear kinetics).

2

A patient with TIAs and hypertension is treated with enalapril (ACE-inhibitor) in an oral daily dose of 10 mg. The patient forgets to take his medication. The half-life (t½) of enalapril is 11 hours and this drug is eliminated at a fixed fraction per unit time. What percentage of the original amount of enalapril is left after 2 days?

3

A patient (56 kg) with an infection is treated with gentamicin intravenously in a dosing regimen of 4 mg/kg every 24 h. Gentamicin has a volume of distribution of 0.3L/kg and a half-life of 3 hours.

Because of the narrow therapeutic window and serious side effects of gentamicin, plasma concentrations are monitored carefully. After the first loading dose the plasma concentration of gentamicin in this patient was 16 mg/L. What plasma concentration of gentamicin do you expect after 24h, just before the next dose is administrated?