Elimination rate constant

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
 * $$C_{t+dt} = C_t - C_t \cdot K \cdot dt$$,

where $$C_t$$ is the blood plasma concentration of drug in the system at a given point in time $$t$$, $$dt$$ is an infinitely small change in time, and $$C_{t+dt}$$ is the concentration of drug in the system after the infinitely small change in time.

The solution of this differential equation is useful in calculating the concentration after the administration of a single dose of drug:


 * $$C_t = C_{0}\cdot e^{-Kt} \,$$


 * Ct is concentration after time t
 * C0 is the initial concentration (t=0)
 * K is the elimination rate constant