The elimination rate constant K is a value used in pharmacokinetics to describe the rate at which a drug is removed from the system.
It is often abbreviated K or Ke. It is equivalent to the fraction of a substance that is removed per unit time measured at any particular instant and has units of T−1. This can be expressed mathematically with the differential equation
where
The solution of this differential equation is useful in calculating the concentration after the administration of a single dose of drug via IV bolus injection:
Derivation
In first-order (linear) kinetics, the plasma concentration of a drug at a given time t
where:
Therefore, the amount of drug present in the body at time t
where Vd is the apparent volume of distribution
Then, the amount eliminated from the body after time t
Then, the rate of elimination at time t is given by the derivative of this function with respect to t;
And since