#### 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 k 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 second graph. This gives us the following relationship k = 0,693 / t½.

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