plasma concentration will fall, usually in an exponential curve, because the
biological situation is now the same as if a dose of the drug had been given at
that time by intravenous IV bolus injection (section 8.4.1).
The rate of change of the plasma concentration during intravenous infusion
may be described by the relationship:
rate of change of plasma concentration ¼rate of infusion rate of elimination (8:15)Since the rate of infusion is normally maintained at a constant value, infusion
will usually follow zero order kinetics (Equation (8.4) ). Therefore, assuming
that elimination processes exhibit first order kinetics, it follows that:
dCp=dt¼k 0 kelCp (8:16)
wherek 0 is the rate constant for the infusion. Initially the rate of infusion is
greater than the rate of elimination, but at the the steady state the rate of
elimination is equal to the rate of infusion and so the plasma concentration
does not change.
Consequently, dCp=dt¼0 andkelCp¼k 0 (8:17)
but at the steady stateCss¼Cp (8:18)
and soCss¼
k 0
kel
(8:19)
substituting forkelfrom Equation (8.9) in Equation (8.19) gives:
Css¼
k 0 Vd
ClT
¼
k 0
ClT
(8:20)
wherek 0 is the amount of drug infused per unit time. Equations (8.19) and (8.20)
can be used to calculate the rate of infusion required to achieve a specific steady
state plasma concentration. These equations are independent of time and so an
increase in the rate of infusion and a subsequent increase in the value ofk 0
will not result in a reduction of the time taken to reach a specific value ofCss.
It will simply increase the value ofCss, as the rate of elimination and hencekel
will remain constant. Consequently, too high a rate of infusion could increase
the steady state plasma concentration of the drug to a value above the top limit
of the therapeutic window for the drug, which in turn would increase the
chances of a toxic response from the patient.
The time (t) taken to reach a specific value ofCpin the initial part of the
infusion before the plasma concentration reaches the steady state concentration
170 PHARMACOKINETICS