Transcript
0:00Half-life
Lesson 5.4 of our excretion module: clearance, volume and half-life. Elimination is the irreversible loss of a drug from the body by metabolism and excretion. Metabolism is the chemical change of the drug by enzymes, and excretion is its removal, mainly in urine and bile. Plasma is the liquid part of the blood. Half-life is the time for the plasma concentration to fall by half. The rate of elimination is the amount of drug that the body removes per unit of time. For many drugs, the rate is proportional to the amount of drug in the body. The rate divided by the amount is the elimination rate constant, k. The body thus removes the same fraction of the drug in each hour. After one half-life, the plasma concentration is 50 percent of its first value. After two half-lives, it is 25 percent, and after five half-lives, it is about 3 percent.
1:14Clearance and volume set k
Two quantities set k. Clearance, CL, is the rate of elimination divided by the plasma concentration. It is the volume of plasma from which the body removes all of the drug per unit of time. Distribution is the reversible movement of drug between the blood and the tissues. The volume of distribution, Vd, is the amount of drug in the body divided by the plasma concentration. It can be larger than the volume of the body, because drug bound in the tissues lowers the plasma concentration. The rate is CL times the concentration, and the amount is Vd times the concentration. The concentration cancels, so k equals CL divided by Vd. With CL in liters per hour and Vd in liters, k has units of 1 per hour.
2:18The half-life equation
Half-life equals the natural logarithm of 2, which is 0.693, divided by k. It therefore equals 0.693 times the volume of distribution divided by the clearance. Half-life thus depends on two quantities: it falls with the clearance and rises with the volume of distribution.
2:45Effect of clearance
The first is clearance. Clearance depends on the blood flow to the liver and the kidneys and on their enzymes. It also depends on their transport proteins, proteins in the cell membrane that move the drug into or out of the cell. Clearance also depends on the fraction of drug in plasma that is free of plasma proteins, such as albumin, that bind drug in the blood. At the same volume, a higher clearance removes a larger fraction of the drug per hour, and the half-life is shorter.
3:25Effect of volume
The second is the volume of distribution. The liver and the kidneys remove drug only from the blood that flows through them. With a large volume, most of the drug is in the tissues, so the same clearance removes a small fraction of the drug per hour. The half-life is then long. The volume depends on binding to plasma proteins and to tissues. In drug design, chemists change the half-life mainly through clearance, and to a lesser extent through volume.
4:04Midazolam and diazepam
Midazolam and diazepam show the effect of clearance. In young men, midazolam had a volume of distribution of 1.3 liters per kilogram and a half-life of 2.1 hours. Its clearance was 7.8 milliliters per minute per kilogram. In people of normal weight, diazepam had a similar volume, about 1.2 liters per kilogram. Midazolam clearance was nearly 20 times the diazepam clearance, and the diazepam half-life was 32 hours.
4:44Diazepam in obesity
Diazepam in obesity shows the effect of volume. Diazepam is lipophilic, or fat-soluble, and lipophilic drugs distribute well into adipose tissue, or body fat. At normal weight, its volume of distribution was 70 liters and its half-life was 32 hours. In obesity, the volume was 228 liters and the half-life was 82 hours. Clearance was similar: 1.56 liters per hour at normal weight and 1.92 in obesity. For the group with obesity, 0.693 times 228 liters, divided by 1.92 liters per hour, gives 82 hours.
5:38Steady state
The longer half-life delays steady state, the condition in which the dose rate equals the rate of elimination. For a given dose rate, clearance sets the average concentration at steady state. In one study, both groups took 2 milligrams each night for 30 nights. They took the same dose, although the mean weights were 60 kilograms at normal weight and 92 in obesity. Diazepam reached half of its steady-state concentration after 3.1 days at normal weight and after 7.8 days in obesity. These times are longer than the single-dose half-lives in both groups. The ratio between the groups, about 2.5, agrees with the ratio of the half-lives. The mean steady-state concentrations were similar, 67 nanograms per milliliter at normal weight and 68 in obesity, because the clearance was similar. The authors concluded that patients with obesity may reach the full effect of diazepam much later.
6:51Summary
In summary, half-life equals 0.693 times the volume of distribution divided by the clearance. Midazolam has a short half-life because of its high clearance. In obesity, diazepam had a long half-life because of its large volume. For a given dose rate, clearance sets the average concentration at steady state, and half-life sets the time to reach it. In drug design, chemists change half-life mainly through clearance. This concludes lesson 5.4 on clearance, volume and half-life.
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