and
C¼C 0 ekelt (8:2)
whereC 0 is the plasma concentration of the drug in the body at a timet¼ 0,
that is, the concentration immediately following bolus injection,Cis the plasma
concentration of the drug in the body at a timet,tis the lapsed time between the
administration and the measurement andkelis the rate constant for the irrevers-
ible elimination of the drug.
The plasma concentrationCof a drug in the system is related to the total
amount of the drug in the systemDby the relationship:
C¼D=Vd (8:3)
whereVdis the apparent volume of distribution. The value ofVdis a measure of
the total volume of the body perfused by the drug. It is an apparent volume
because it is the volume of plasma that isequivalentto the total volume of the
body readily perfused by the drug. It is not the volume of the tissue and the
circulatory system actually perfused by the drug. This means that the values of
Vdfor a drug can be considerably higher than the volume of the blood in the
circulatory system which is usually about 5 litres for a 70 kg person. Values of
Vdare usually recorded in terms of litres per kilogram (Table 8.1), which gives a
value of 0.071 (litres kg
1) for a 70 kg person. A value of less than 0.071 forVd
indicates that the drug is probably distributed mainly within the circulatory
system, whilst values greater than 0.071 indicate that the drug is distributed in
both the circulatory system and specific tissues.
The value ofVdmay be calculated by substituting the values for the doseD 0
administered andC 0 , the plasma concentration at timet¼ 0, in equation (8.3).
However, it is not possible to accurately measure the concentration of the drug in
the system at the timet¼0 because of the time taken to administer a drug and for
it to achieve a homogeneous distribution throughout the system. Consequently, a
theoretical value ofC 0 obtained by extrapolation of a plot of drug plasma
concentrationCpagainst time (Figure 8.5) is normally used to calculateVd.
Table 8.1 The values ofVdandt1/2for some common drugs (various sources)Drug Vd(litres kg
1
) t1/2(hours) Drug Vd(litres kg 1
) t1/2(hours)Aspirin 0.1–0.2 0.28 Ibuprofen 0.14 2
Ampicillin 0.3 1–2 Propranolol 3.9 2–6
Cimetidine 2.1 1–3 Morphine 3.0–5.0 2–3
Chlorpromazine 20 15–30 Warfarin 0.15 42
Diazepam 1.0 48
164 PHARMACOKINETICS