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Since an entire dose-response relationship is determined from one animal, the curve cannot tell us about the degree of biological variation inherent in a population of such animals. Rather, variability is reflected by a family of dose-response curves, such as those given in Figure 2.3. The ED50 in this type of dose-response curve is the dose that produced 50% of the maximum response in one animal. In guinea pig e, the maximum response is an increase in heart rate of 80 beats per minute. Thus, 50% of the maximum is 40 beats per minute. From Figure 2.3, it can be seen that the dose causing this effect in guinea pig e is about 3 ^g/kg. The average sensitivity of all of the animals to levarterenol can be estimated by combining the separate dose-response curves into a mean (average) dose-response curve and then calculating the mean ED50. An estimate of the variation within the population can be indicated by calculating a statistical parameter, such as a confidence interval.

It is also possible to construct quantal dose-response curves for drugs that produce graded responses. To do so, one chooses a quantum of effect, for example, an increase in heart rate of 20 to 30 beats per minute above the control, or resting, rate. Doses of the drug are then plotted against the frequency with which each dose produces this amount of effect. The resulting graph has the same characteristics as the graph for the anticonvulsant activity of phenobarbital.

The doses in Figures 2.2 and 2.3 are on not an arithmetic but a logarithmic, or geometric, scale (i.e., the doses are displayed as multiples). This is more apparent in Figure 2.3 because of the greater range of doses. There are many reasons for the common practice of using geometric scales, some of which will become apparent later in this book. One important reason is that in most instances significant increases in response generally occur only when doses are increased in multiples. For example, in Figure 2.3, curve e, if one increased the dose from 10 to 11 or 12 ^g/kg, the change in response would hardly be measurable. However, if one increased it 3 times or 10 times (i.e., to 30 or 100 ^g/kg), one could easily discern increased responses.

The concept of the therapeutic index as a measure of the margin of safety has already been discussed. In the ratio LD50/ED50, the ED50 can be obtained from either quantal (Fig. 2.2A) or graded (Fig. 2.3) dose-response curves. In the latter case, it must be a mean ED50, that is, the average ED50 obtained from several individuals.