wherek 0 is the zero rate constant for the absorption process. However, it should
be realised that some drug absorption and elimination processes do not exhibit
zero or first order kinetics, and so these processes cannot always be so easily
quantified.
8.5.2 The calculation oftmaxandCmax
The calculation oftmaxandCmaxfor a drug normally starts from the relevant
equation for the change in plasma concentration of the drug with time derived
from Equation (8.29). For example, for drugs that exhibit first order absorption
and elimination kinetics, Equation (8.30) (see section 8.5.1) shows how Cp
changes with time. Differentiation of Equation (8.30) gives:
dCp
dt
¼
FD 0
Vd
kab
(kabkel)
(kele
keltþkabe
kabt)(8:32)
but attmaxdCp/dt¼ 0 and so:
FD 0
Vd
kab
(kabkel)
(kele
keltmaxþkabe
kabtmax)¼0(8:33)
simplifying : kele
keltmaxþkabe
kabtmax¼0(8:34)
and : kabe
kabtmax¼kele
keltmax(8:35)
taking logs to base e : lnkabkabtmax¼lnkelkeltmax (8:36)
and so : tmax¼
lnkellnkab
kelkab
(8:37)
Once tmax has been calculatedCmaxcan be found by substitution of the
appropriate values ofF,Vd,D 0 ,kabandkelfor the drug in Equation (8.30).
SinceFandVdare constantsCmaxis proportional to the dose administered: the
larger the dose the greaterCmax.
8.5.3 Repeated oral doses
In order that a drug is therapeutically effective its plasma concentration must be
maintained within its therapeutic window for a long enough period of time to
176 PHARMACOKINETICS