Volume of distribution
The apparent volume of distribution (Vd) is the amount of drug in the body (Ap) divided by the plasma concentration (Cp) after distribution equilibrium has been established:
It can be difficult to determine Vd experimentally because elimination will typically start before distribution equilibrium is reached. An estimate of Vd can be obtained by calculating the concentration before elimination has occurred by extrapolating the concentration versus time curve for intravenous doses to time zero (C0) and dividing this value into the dose delivered.
If oral doses are used the dose must be adjusted for the bioavailability (F):
Drugs that are taken up into body fat or bind to cellular structures have a higher Vd and it is not uncommon for volumes of distribution to be over 1.0 L/kg. Morphine has a Vd of 3–5 L/kg. A range of 0.5 to 5 L/kg is seen for most of the amfetamines and many of the benzodiazepines. The highly lipid-soluble THC has a volume of distribution of about 10 L/kg. Drugs with high octanol–buffer partition coefficients, such as psychotropic drugs, generally have high volumes of distribution. Octanol–water coefficients for specific drugs are available (e.g. Clarke’s Analysis of Drugs and Poisons, 3rd edition, 2004, Vol. II monographs). The drug concentration in body fluids other than plasma may be used, e.g. whole blood, but different values for Vd are obtained for each; hence it is important to note which fluid is being used. The value of the volume of distribution is determined mainly by the physiological processes of perfusion and protein binding, but it seldom has a true physiological meaning. For example, the volume of distribution of highly protein-bound furosemide (syn. frusemide), is of the order of 15 L, and that of ethanol is about 35 L; however, the value for digoxin, which is extensively distributed and bound in extravascular tissues, is of the order of 450 L.
After distribution equilibrium has been established, knowledge of the volume of distribution allows the amount of drug in the body (D) to be estimated from a single measured blood concentration (C):
D=Vd x C (2.4)
If the time elapsed since drug administration (t) is known, together with some pharmacokinetic data for the drug, then it should be possible to estimate the original dose (D0) of the drug. Thus, for a drug given by intravenous injection:
D0=VdCekel t (2.5)
where kel is the elimination rate constant (see later). However, if the drug is given orally, a much more complex relationship applies. It is necessary to know the bioavailability (F), and the absorption rate constant (ka). Then the dose is given by the expression:
If a drug were distributed instantaneously throughout the body, then the volume of distribution would be constant at all times and the decrease in plasma concentration could be attributed solely to elimination of the drug. However, in practice there are time-dependent changes in tissue concentration, which include absorption and distribution. In a drug overdose, nonlinear pharmacokinetics may occur, that is the plasma concentration does not increase in proportion to the dose since one or more of the pharmacokinetic processes reaches saturation. Hence, calculation of dose from the volume of distribution can be substantially wrong and misleading. The recommendation is to use the volume of distribution only when an overdose has not been taken and there is a reasonable chance of equilibrium.
