Volume of Distribution

The volume of distribution is a hypothetical volume of fluid into which a drug is dispersed. Although the volume of distribution has no physiologic or physical basis, it is sometimes useful to compare the distribution of a drug with the volumes of the water compartments in the body 

(Figure  Relative size of various distribution volumes within a 70-kg individual.)

 A. Water compartments in the body

Once a drug enters the body, from whatever route of administration, it has the potential to distribute into any one of three functionally distinct compartments of body water or to become sequestered in a cellular site.

 1. Plasma compartment:

If a drug has a very large molecular weight or binds extensively to plasma proteins, it is too large to move out through the endothelial slit junctions of the capillaries and, thus, is effectively trapped within the plasma (vascular) compartment. As a consequence, the drug distributes in a volume (the plasma) that is about six percent of the body weight or, in a 70-kg individual, about 4 L of body fluid. Heparin  shows this type of distribution. 

 2. Extracellular fluid:

If a drug has a low molecular weight but is hydrophilic, it can move through the endothelial slit junctions of the capillaries into the interstitial fluid. However, hydrophilic drugs cannot move across the lipid membranes of cells to enter the water phase inside the cell. Therefore, these drugs distribute into a volume that is the sum of the plasma water and the interstitial fluid, which together constitute the extracellular fluid. This is about twenty percent of the body weight, or about 14 L in a 70-kg individual. Aminoglycoside antibiotics  show this type of distribution. 

3. Total body water: 

If a drug has a low molecular weight and is hydrophobic, not only can it move into the interstitium through the slit junctions, but it can also move through the cell membranes into the intracellular fluid. The drug, therefore, distributes into a volume of about sixty percent of body weight, or about 42 L in a 70-kg individual. Ethanol exhibits this apparent volume of distribution .

 4. Other sites:

 In pregnancy, the fetus may take up drugs and thus increase the volume of distribution. Drugs that are extremely lipid-soluble, such as thiopental , may also have unusually high volumes of distribution.

 B. Apparent volume of distribution 

A drug rarely associates exclusively with only one of the water compartments of the body. Instead, the vast majority of drugs distribute into several compartments, often avidly binding cellular components for example, lipids (abundant in adipocytes and cell membranes), proteins (abundant in plasma and within cells), or nucleic acids (abundant in the nuclei of cells). Therefore, the volume into which drugs distribute is called the apparent volume of distribution, or Vd. Another useful way to think of this constant is as the partition coefficient of a drug between the plasma and the rest of the body. 

1. Determination of Vd 

a. Distribution of drug in the absence of elimination: The apparent volume into which a drug distributes, Vd, is determined by injection of a standard dose of drug, which is initially contained entirely in the vascular system. The agent may then move from the plasma into the interstitium and into cells, causing the plasma concentration to decrease with time. Assume for simplicity that the drug is not eliminated from the body; the drug then achieves a uniform concentration that is sustained with time

)Figure  Drug concentrations in serum after a single injection of drug at time = 0. Assume that the drug
distributes but is not eliminated.)

 The concentration within the vascular compartment is the total amount of drug administered, divided by the volume into which it distributes, Vd:

 where C = the plasma concentration of the drug and D = the total amount of drug in the body. For example, if 25 mg of a drug (D = 25 mg) are administered and the plasma concentration is 1 mg/L, then Vd = 25 mg/1 mg/L = 25 L

b. Distribution of drug when elimination is present:
In reality, drugs are eliminated from the body, and a plot of plasma concentration versus time shows two phases. The initial decrease in plasma concentration is due to a rapid distribution phase in which the drug is transferred from the plasma into the interstitium and the intracellular water. This is followed by a slower elimination phase during which the drug leaves the plasma compartment and is lost from the body for example, by renal or biliary excretion or by hepatic biotransformation

(Figure  Drug concentrations in serum after a single injection of drug at time = 0. Assume that the drug
distributes and is subsequently eliminated.)

The rate at which the drug is eliminated is usually proportional to the concentration of drug, C; that is, the rate for most drugs is first-order and shows a linear relationship with time if lnC (where lnC is the natural log of C, rather than C) is plotted versus time 

(Figure  Drug concentrations in serum after a single injection of drug at time = 0. Data are plotted on a log scale. )

This is because the elimination processes are not saturated. Figure 1.11 Drug concentrations in serum after a single injection of drug at time = 0. Assume that the drug distributes and is subsequently eliminated. c. Calculation of drug concentration if distribution is instantaneous: Assume that the elimination process began at the time of injection and continued throughout the distribution phase. Then, the concentration of drug in the plasma, C, can be extrapolated back to time zero (the time of injection) to determine C0, which is the concentration of drug that would have been achieved if the distribution phase had occurred instantly. For example, if 10 mg of drug are injected into a patient and the plasma concentration is extrapolated to time zero, the concentration is C0 = 1 mg/L , and then Vd = 10 mg/1 mg/L = 10 L. d. Uneven drug distribution between compartments: The apparent volume of distribution assumes that the drug distributes uniformly, in a single compartment. However, most drugs distribute unevenly, in several compartments, and the volume of distribution does not describe a real, physical volume, but rather, reflects the ratio of drug in the extraplasmic spaces relative to the plasma space. Nonetheless, Vd is useful because it can be used to calculate the amount of drug needed to achieve a desired plasma concentration. For example, assume the arrhythmia of a cardiac patient is not well controlled due to inadequate plasma levels of digitalis. Suppose the concentration of the drug in the plasma is C1 and the desired level of digitalis (known from clinical studies) is a higher concentration, C2. The clinician needs to know how much additional drug should be administered to bring the circulating level of the drug from C1 to C2

2. Effect of a large Vd on the half-life of a drug

A large V  has an important influence on the half-life of a drug, because drug elimination depends on the amount of drug delivered to the liver or kidney (or other organs where metabolism occurs) per unit of time. Delivery of drug to the d organs of elimination depends not only on blood flow, but also on the fraction of the drug in the plasma. If the V  for a drug is large, most of the drug is in the extraplasmic space and is unavailable to the excretory organs. Therefore, any factor that increases the volume of distribution can lead to an increase in the half-life and extend the duration of action of the drug. 

 [Note: An exceptionally large V  indicates considerable sequestration of the drug in some organ or

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