How Does Drug Concentration Decline Over Time? - First-order Kinetics
For most drugs, the process of drug elimination, whether by metabolism or excretion, is a high capacity process that does not become limited or saturated, even at high doses beyond the normal therapeutic range. Within this range, the rate of elimination is proportional to the amount of drug in the body (i.e. the higher the drug concentration the faster the rate of elimination). This is a logical consequence of the 'law of mass action' because higher molecular concentrations will drive faster metabolic reactions or support higher renal filtration. This results in so-called first-order kinetics where a constant fraction of the drug remaining in the body is eliminated in a given time, described mathematically by the equation:
Rate of elimination = �dA/dt = �kA
where A is the amount of drug in the body and k is the elimination rate constant. Given that once drug distribution has occurred, the amount of drug remaining in the body is proportional to the plasma concentration of the drug, the following equation also applies:Rate of elimination = �dC/dt = �kC
Integrating this equation yields:C = C0.e-kt
This equation indicates that the decline in concentration over time is exponential and determined by the elimination rate constant (Fig 3). The importance of this relationship to prescribers is that it means the effect of increasing doses on plasma concentration is predictable (Fig 4) - a doubled dose leads to doubled concentration at all time points.
