last updated 29-05-2023

#### Elimination rate constant

##### Elimination rate constant

In most drug elimination systems, elimination is a fixed percentage over time. Therefore the change in plasma concentration per time (dC/dt) is directly proportional to the plasma concentration C. This is sometimes called either concentration dependent or first order kinetics. The proportionality constant kel is called the elimination rate constant. If this differential equation is integrated the following formula is obtained, allowing us to calculate the concentration of a drug at any time.

Ct = Co × e -k(t)

Often clinicians simplify things by determining the half-life of a drug instead of k. This is possible because the relationship between plasma concentration and time is exponential. If one places drug concentrations on a log-scale, a straight line with slope -k is obtained as seen in the graph below. This gives us the following relationship kel = 0,693 / t½.

See here how half-life (and Vd, dose interval and dose size) influence the concentration over time.

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?