NURS 735 - APPLIED TOXICOLOGY

Module 2 Concepts: Volume of Distribution
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The proportionality constant that relates concentration, C to amount, X is the volume, V:

V = X / C

If you dissolve 40 mg of X in an unknown volume and end up with a concentration of 20 mg/L, the volume will be:

V = 40 mg / 20 mg.L-1 = 2 L

Now consider that you have a two compartment closed model such as the one illustrated in Fig. 1 with total volume of 2 L (A = B = 1 L). This time, however, you have water in A and octanol in B and have no access to compartment B. Drug X has a octanol/water partition coefficient (Po/w) of 3, i.e., it is 3-fold more soluble in octanol than it is in water. Dissolve 40 mg of X in A and wait for equilibrium. Now if you estimate concentration in the accessible compartment (A) you will notice that:

CA = 10 mg/L,

and the apparent volume of A + B:

V = 40 mg / 10 mg.L-1 = 4 L.

It is apparent that the calculated volume of 4 L represents an overestimation of true volume of 2 L and is based on the assumption that the system is a homogenous one i.e., both compartments have the same solvent. This situation is very similar to that of humans: drugs are injected intravenously to humans, the concentration in plasma is measured, and the volume is estimated by dividing the dose by the plasma concentration attained immediately after injection (before any elimination takes place):

Vd = Dose / Co

where Vd is called volume of distribution and Co is the concentration at time zero.

It is obvious that Vd has no physiological meaning. Nevertheless, it is a very useful pharmacokinetic parameter. It is defined as the hypothetical volume of plasma (analogous to the solvent in compartment A) in which the drug is dissolved. Vd is an indicative of the extent of distribution of a drug. The larger the Vd, the greater is the extent of the distribution. Recall the above example in which a Vd of 4 L was estimated while the real volume was only 2 L. This indicates that the drug has escaped from compartment A (analogous to human plasma) to the deeper compartment B (analogous to human fat, muscle, etc.). Hence the drug has a broad extent of distribution. The cardiac drug digoxin, for example, has a Vd of approximately 400 L in humans due to its extensive affinity for binding to human muscle.

Now let us consider a drug with an opposite Po/w than the one discussed above: drug Y with Po/w of 0.33. If you dissolve 40 mg of Y in the above beaker and estimate C in A you will get:

CA = 30 mg/L and,

Vd = 40 mg / 30 mg.L-1 = 1.33 L.

This is an underestimation of V as the true A+B volume is 2 L. A small Vd indicates that the drug is more confined to the accessible compartment (i.e., A in the above example and plasma in humans). While there is no limit to how large a Vd can be, it cannot be smaller than the volume of A or plasma in man. To conceptualize this, assume two drugs one in each extreme: X with Po/w of 3/0 and Y with Po/w of 0/3. Vd of X will approach infinity and that of Y approaches the volume of A i.e., 1 L.

Table I depicts the relationship between Vd and the extent of distribution. The values represented there can be used to approximate the extent of a drug distribution.

Table 1. Relationship Between the Extent of Distribution and Vd in a 70 kg normal person

(The numbers are only rough approximation)

 Vd, L % Body Weight Extent of Distribution 5 7 Only in plasma 5-20 7-28 In extracellular fluids 20-40 28-6 In total body fluids. >40 >56 In deep tissues; bound to peripheral tissues

The extent of distribution of drugs are controlled by two main physicochemical properties: protein binding and partition coefficient.

Protein Binding

Proteins are large molecules capable of attracting and binding smaller molecules. Plasma proteins circulate in the body while other proteins are somewhat stationary. Drugs may bind to both the circulating and the stationary proteins with different consequences: a highly plasma protein bound drug (e.g., ibuprofen and similar drugs) will have a small Vd while a drug with high tissue protein binding (digoxin) will have a large Vd. A given drug, however, may have similar extent of binding to proteins in both sites. In plasma, acidic drugs tend to bind mainly to albumin while basic compounds have greater affinity towards alpha acid glycoproteins.

Due to the limitation in both the number and the type of binding sites 1) binding may be saturable and, 2) drugs may compete with one another for binding to the same site.

Partition Coefficient

Unbound drugs (or unbound fraction of drugs) distribute into the body depending upon their affinity towards tissues relative to that towards the vascular space. For example a drug with high Po/w accumulates in fat tissues with a greater extent than does a very water soluble drug with poor Po/w.

As Vd can be influenced by the body size and fat content, it is sometimes necessary to normalize this parameter for the body weight:

Coefficient of Distribution (CD) = Vd / Body Weight