A Textbook of Clinical Pharmacology and Therapeutics

this way (e.g. penicillinto 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 t1/2. The mean concentration rises toward a plateau,
as if the drug were being administered by constant-rate infu-
sion. 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 infu-
sion 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 adminis-
tered once every half-life, the peak plasma concentration (Cmax)
will be double the trough concentration (Cmin). In practice, this
amount of variation is tolerable in many therapeutic situa-
tions, 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 benzodi-

azepines (Chapter 18), which have active metabolites with

half-lives of many days. Consequently, adverse effects (e.g. con-

fusion) 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 varia-

tion 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 mul-

tiplying the desired concentration by the volume of distribu-

tion (LDCpVd).

DEVIATIONS FROM THE

ONE-COMPARTMENT MODEL WITH

FIRST-ORDER ELIMINATION

TWO-COMPARTMENT MODEL

Following an intravenous bolus a biphasic decline in plasma

concentration is often observed (Figure 3.4), rather than a sim-

ple 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

14 PHARMACOKINETICS

[Drug] in plasma

(a)

[Drug] in plasma

Time

(b)

Figure 3.3:Repeated bolus dose injections (at arrows) at (a)
intervals much greater than t1/2and (b) intervals less than t1/2.

60

50

40

30

20

10

012345678910

Plasma concentration (log scale)

Time,t

Mainly distribution

 some elimination

Mainly elimination

 some distribution

(kinetic homogeneity attained)

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.