
Empirical pharmacokinetics 23
Box 2.1 Direct derivation of the convolution equation
We will here do a derivation of equation 2.12 from first principles, in order
to highlight the underlying assumptions. Concentrations are assumed to be
given in mg/L.
Assume that we give a unit bolus dose at time s, the plasma concentration
at time t>sis given by G(t, s). The mathematical linearity of the system
then implies that if the dose instead is D mg, the plasma concentration at
time t is DG(t, s). Consider a small interval (s, s +Δs), during which there is
approximately a(s)Δs mg of drug absorbed. Its contribution to C(t)isthen
given by G(t, s)a(s)Δs, and the