Pharmacokinetics
Pharmacokinetics describes how the amount or concentration of a drug changes in the body through absorption, distribution and elimination.
One-compartment model
For an amount \(A(t)\) eliminated at a first-order rate \(k\),
\[\frac{dA}{dt}=-kA,\qquad A(t)=A_0e^{-kt}.\]If the apparent volume of distribution is \(V\), concentration is \(C=A/V\).
Half-life
\[t_{1/2}=\frac{\ln2}{k}.\]More detailed models use several compartments and explicit absorption or infusion terms.
Key idea. Pharmacokinetic models describe what the body does to a drug by tracking its movement and removal through time.