Quantal concentration-effect curve

Data on the association of drug levels with efficacy and toxicity must be interpreted in the context of the pharmacodynamic variabihty in the population (e.g., genetics, age, disease, and other drugs). The variability in pharmacodynamic response in the population may be analyzed by constructing a quantal concentration-effect curve (Figure 5-4A). 

FIGURE 5—4 Frequency distribution curves and quantal concentration-effect and dose-effect curves. A. Frequency distribution curves. An experiment was performed on 100 subjects, and the effective plasma concentration that produced a quantal response was determined for each individual. The number of subjects who required each dose is plotted, giving a log-normal frequency distribution (colored bars). The gray bars demonstrate that the normal frequency distribution, when summated, yields the cumulative frequency distribution—a sigmoidal curve that is a quantal concentration-effect curve. B. Quantal dose-effect curves. Animals were injected with varying doses of sedative-hypnotic, and the responses were determined and plotted. The calculation of the therapeutic index, the ratio of the to the ED q, is an indication of how selective a drug is in producing its desired effects relative to its toxicity. (See text for additional explanation.)... 

Fig. 15. Relationship between the alfentanil plasma concentrations and the probability of needing naloxone to restore adequate spontaneous ventilation. The diagram at the upper part shows the alfentanil plasma concentrations of the patients who required naloxone (upward deflection) or did not require naloxone (downward deflection). The plasma concentration-effect curve for this clinical endpoint (lower part) was defined from the quantal data shown in the upper diagram using logistic regression. Bars indicate SE of C5o%. (From Ausems ME, Hug CC, Stanski DR, Burm AGE. Plasma concentrations of alfentanil required to supplement nitrous oxide anaesthesia for general surgery. Anaesthesiology 1986 65 362-73, reproduced by permission.)...

It is possible to use a preliminary dilution step of 1 100 when the pT-scale relies, for instance, on a < 20% effect endpoint measurement (e.g., determination of IC < 20 in non quantal tests with algae and bacteria). In this case, the pT-value should be calculated from the concentration-effect curve. The pT-value is determined by using the first sample concentration that generates an effect below 20%. If, for example, the concentration incurring a 19% effect is equated with a dilution factor of 1 3200, the pT-value is calculated with equation 5 as demonstrated below. The modulus for transforming decadic logarithms into binary ones, 1 / logio 2 , yields equation 6. For the 1 100 diluted wastewater example above, the pT-value can then be calculated with the help of equation 8. 

Inhaled (volatile) anesthetics are delivered to the lungs in gas mixtures in which concentrations and flow rates are easy to measure and control. However, dose-response characteristics of volatile anesthetics are difficult to quantify. Although achievement of an anesthetic state depends on the concentration of the anesthetic in the brain (ie, at the effect site), concentrations in the brain tissue are obviously impossible to measure under clinical conditions. Furthermore, neither the lower nor the upper ends of the graded dose-response curve defining the effect on the central nervous system can be ethically determined because at very low gas concentrations awareness of pain may occur. Moreover, at high concentrations there is a high risk of severe cardiovascular and respiratory depression. Nevertheless, a useful estimate of anesthetic potency can be obtained using quantal dose-response principles for both the inhaled and intravenous anesthetics. 

Dose Rate The chemical s dose delivered per unit lime or the radiation dose delivered per unit time. Dose-Response Curves Demtnstrate the relation between dose and the proportion of individuals responding with a quantal effect (q.v.). In general, dose-response curves are S-shaped (increasing), and they have upper and lower asymptotes, usually but not always 1(X) and 0%. D Response Relationship The systematic relationship between the dose (or effective concentration) of a drug or xenobiotic and the magnitude (or intensity) of the response it elicits. 

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