A-Textbook-of-Clinical-Pharmacology-and-Therapeutics-5th-edition

14 PHARMACOKINETICS
this way (e.g. penicillin to treat a mild infection), but a steady
state concentration greater than some threshold value is often
needed to produce a consistent effect throughout the dose
interval. Figure 3.3b shows the plasma concentration–time
curve when a bolus is administered repeatedly at an interval
less than t 1/2 . The mean concentration rises toward a plateau,
as if the drug were being administered by constant-rate infusion.
That is, after one half-life the mean concentration is 50%
of the plateau (steady-state) concentration, after two half-lives
it is 75%, after three half-lives it is 87.5%, and after four
half-lives it is 93.75%. However, unlike the constant-rate infusion
situation, the actual plasma concentration at any time
swings above or below the mean level. Increasing the dosing
frequency smoothes out the peaks and troughs between doses,
while decreasing the frequency has the opposite effect. If the
peaks are too high, toxicity may result, while if the troughs are
too low there may be a loss of efficacy. If a drug is administered
once every half-life, the peak plasma concentration (C max )
will be double the trough concentration (C min ). In practice, this
amount of variation is tolerable in many therapeutic situations,
so a dosing interval approximately equal to the half-life
is often acceptable.
Knowing the half-life alerts the prescriber to the likely
time-course over which a drug will accumulate to steady
state. Drug clearance, especially renal clearance, declines with
age (see Chapter 11). A further pitfall is that several drugs
have active metabolites that are eliminated more slowly than
the parent drug. This is the case with several of the benzodiazepines
(Chapter 18), which have active metabolites with
half-lives of many days. Consequently, adverse effects (e.g. confusion)
may appear only when the steady state is approached
after several weeks of treatment. Such delayed effects may
incorrectly be ascribed to cognitive decline associated with
ageing, but resolve when the drug is stopped.
Knowing the half-life helps a prescriber to decide whether
or not to initiate treatment with a loading dose. Consider
digoxin (half-life approximately 40 hours). This is usually
prescribed once daily, resulting in a less than two-fold variation
in maximum and minimum plasma concentrations, and
reaching 90% of the mean steady-state concentration in
approximately one week (i.e. four half-lives). In many clinical
situations, such a time-course is acceptable. In more urgent
situations a more rapid response can be achieved by using a
loading dose. The loading dose (LD) can be estimated by multiplying
the desired concentration by the volume of distribution
(LD C p V d ).
DEVIATIONS FROM THE
ONE-COMPARTMENT MODEL WITH
FIRST-ORDER ELIMINATION
TWO-COMPARTMENT MODEL
[Drug] in plasma
Following an intravenous bolus a biphasic decline in plasma
concentration is often observed (Figure 3.4), rather than a simple
exponential decline. The two-compartment model (Figure
3.5) is appropriate in this situation. This treats the body as a
smaller central plus a larger peripheral compartment. Again,
these compartments have no precise anatomical meaning,
although the central compartment is assumed to consist of
60
(a)
[Drug] in plasma
Plasma concentration (log scale)
50
40
30
20
Mainly distribution
some elimination
Mainly elimination
some distribution
(kinetic homogeneity attained)
10 0 1 2 3 4 5 6 7 8 9 10
(b)
Time
Figure 3.3: Repeated bolus dose injections (at arrows) at (a)
intervals much greater than t 1/2 and (b) intervals less than t 1/2 .
Time, t
Figure 3.4: Two-compartment model. Plasma concentration–time
curve (semi-logarithmic) following a bolus dose of a drug that fits
a two-compartment model.