# Chapter 4: Pharmacokinetics

Pharmacokinetics is the mathematical description of the rate and extent of uptake, distribution, and elimination of drugs in the body.

Volume of distribution (*V _{D}*) is a calculation of the apparent volume in which a drug is dissolved.

This definition assumes that the drug is evenly distributed and that metabolism or elimination has not taken place. In reality, it does not correspond to any real volume:

This equation is very easy to remember. Suppose you take 1000 mg of sugar and dissolve it into a beaker of water. After it has dissolved, you take a sample of water (let’s say, 10 mL) and determine the concentration of sugar in that sample (for example, 1 mg/mL). From this finding you can calculate the volume of water in which the sugar was dissolved, as follows:

Thus,

In this case the volume was 1000 mL or 1 L. If you keep the units straight, the equation does not need to be memorized.

Try another one. Suppose 500 mg of “Newdrug” is administered to a medical student. The plasma concentration is 0.01 mg/mL. What is the volume of distribution?*

The volume of distribution is rather large. Your selected medical student is not, however, a huge water balloon. The only explanation is that the drug is hiding at some place in the body where it is not recorded by the measurement of plasma concentration. The drug could be lipid soluble and stored in fat, or it could be bound to plasma proteins. As this example shows, the volume of distribution is a hypothetical volume and not a real volume.

The volume of distribution gives a rough accounting of where a drug goes in the body, especially if you have a feel for the various body fluid compartments and their sizes (Figure 4–1). In addition, it can be used to calculate the dose of a drug needed to achieve a desired plasma concentration.

^{*}

Answer: 50,000 mL or 50 L.

The order of a reaction refers to the way in which the concentration of drug or reactant influences the rate of a chemical reaction. For most drugs, we need only consider first-order and zero-order.

Most drugs disappear from plasma by processes that are concentration-dependent, which results in first-order kinetics. With first-order elimination, a constant percentage of the drug is lost per unit time. An elimination rate constant can be described.

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