# Figure

Quantal dose-response curves based on all-or-none responses. A. Relationship between the dose of phĂ©nobarbital and the protection of groups of rats against convulsions. B. Relationship between the dose of phenobarbital and the drug's lethal effects in groups of rats. ED50, effective dose, 50%; LD50, lethal dose, 50%.

were not; this indicates that the rats differ in their sensitivity to phenobarbital.

The quantal dose-response curve is actually a cumulative plot of the normal frequency distribution curve. The frequency distribution curve, in this case relating the minimum protective dose to the frequency with which it occurs in the population, generally is bell shaped. If one graphs the cumulative frequency versus dose, one obtains the sigmoid-shaped curve of Figure 2.2A. The sigmoid shape is a characteristic of most dose-response curves when the dose is plotted on a geometric, or log, scale.

Therapeutic Index

### Effective Dose

The quantal dose-response curve represents estimates of the frequency with which each dose elicits the desired response in the population. In addition to this information, it also would be useful to have some way to express the average sensitivity of the entire population to phenobarbital. This is done through the calculation of an ED50 (effective dose, 50%; i.e., the dose that would protect 50% of the animals). This value can be obtained from the dose-response curve in Figure 2.2A, as shown by the broken lines. The ED50 for phenobarbital in this population is approximately 4mg/kg.

### Lethal Dose

Another important characteristic of a drug's activity is its toxic effect. Obviously, the ultimate toxic effect is death. A curve similar to that already discussed can be constructed by plotting percent of animals killed by phenobarbital against dose (Fig. 2.25). From this curve, one can calculate the LD50 (lethal dose, 50%). Since the degree of safety associated with drug administration depends on an adequate separation between doses producing a therapeutic effect (e.g., ED50) and doses producing toxic effects (e.g., LD50), one can use a comparison of these two doses to estimate drug safety. Thus, one estimate of a drug's margin of safety is the ratio LD50/ED50; this is the therapeutic index. The therapeutic index for phenobarbital used as an anticonvulsant is approximately 40/4, or 10.

As a general rule, a drug should have a high therapeutic index; however, some important therapeutic agents have low indices. For example, although the therapeutic index of the cardiac glycosides is only about 2 for the treatment and control of cardiac failure, these drugs are important for many cases of cardiac failure. Therefore, in spite of a low margin of safety, they are often used for this condition. The identification of a low margin of safety, however, dictates particular caution in its use; the appropriate dose for each individual must be determined separately.

It has been suggested that a more realistic estimate of drug safety would include a comparison of the lowest dose that produces toxicity (e.g., LD1) and the highest dose that produces a maximal therapeutic response (e.g., ED99). A ratio less than unity would indicate that a dose effective in 99% of the population will be lethal in more than 1% of the individuals taking that dose. Figure 2.2 indicates that Phenobarbital's ratio LD1/ED99 is approximately 2.

### Protective Index

The margin of safety is only one of several criteria to be used in determining a drug's clinical merit. Clearly, the therapeutic index is a very rough measure of safety and generally represents only the starting point in determining whether a drug is safe enough for human use. Usually, undesirable side effects occur in doses lower than the lethal doses. For example, phenobarbital induces drowsiness and an associated temporary neurological impairment. Since anticonvulsant drugs are intended to allow people with epilepsy to live normal seizure-free lives, sedation is unacceptable. Thus, an important measure of safety for an anticonvulsant would be the ratio ED50 (neurological impairment)/ED50 (seizure protection). This ratio is called a protective index. The protective index for phenobarbital is approximately 3. It is easy to see that data derived from dose-response curves can be used in a variety of ways to compare the clinical usefulness of drugs. For instance, a drug with a protective index of 1 is useless as an anti-convulsant, since the dose that protects against convulsion causes an unacceptable degree of drowsiness. A drug with a protective index of 5 would be a more promising anticonvulsant than one with an index of 2.

More common than the quantal dose-response relationship is the situation in which a single animal (or patient) gives graded responses to graded doses; that is, as the dose is increased, the response increases. With graded responses, one can obtain a complete dose-response curve in a single animal. A good example is the effect of the drug levarterenol (l-norepinephrine) on heart rate.

Results of experiments with levarterenol in guinea pigs are shown in Figure 2.3. The data are typical of what one might obtain from constructing complete dose-response curves in each of five different guinea pigs (a-e). In animal a, a small increase in heart rate occurs at a dose of 0.001 ^g/ kg body weight. As the dose is increased, the response increases until at 1 ^g/kg, the maximum increase of 80 beats per minute occurs. Further increases in dose do not produce greater responses. At the other extreme, in guinea pig e, doses below 0.3 ^g/kg have no effect at all, and the maximum response occurs only at about 100 ^g/kg.

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### Responses

• marko
What is the main resean for"bellshaped"nature of quantal dose response curve?
2 years ago