Concentration-response relationships

This is usually described as the Hill equation (see also Appendix 1.2C [Section 1.2.4.3]). Here, H is again the Hill coefficient, and y and vm l, are, respectively, the observed response and the maximum response to a large concentration of the agonist, A. [A]50 is the concentration of A at which y is half maximal. Because it is a constant for a given concentration-response relationship, it is sometimes denoted by K. While this is algebraically neater (and was the symbol used by Hill), it should be remembered that K in this context does not necessarily correspond to an equilibrium constant. Employing [A]50 rather than K in Eq. (1.6) helps to remind us that the relationship between... 

FIGURE 1.2 (Upper) Concentration-response relationship for the action of acetylcholine in causing contraction of the frog rectus abdominis muscle. The curve has been drawn using Eq. (1.4). (Lower) Hill plots for the action of acetylcholine on frog ventricle (curve I) and rectus abdominis (curve II). (From Clark, A. J., J. Physiol., 61, 530-547, 1926.)... 

FIGURE 1.5 Comparison of the log concentration-response relationships for P-adrenoceptor-mediated actions on six tissues of a full and a partial agonist (isoprenaline [closed circles] and prenalterol [open circles], respectively). The ordinate shows the response as a fraction of the maximal response to isoprenaline. (From Kenakin, T. P. and Beek, D., J. Pharmacol. Exp. Ther., 213, 406-413, 1980.)... 

FIGURE 1.16 The predicted effect of three concentrations of a reversible competitive antagonist, B, on the log concentration-response relationship for an agonist. The calculation of the concentration ratio (r3) for the highest concentration of antagonist, [B]3, is illustrated. 

AEGL-1 (Nondisabling) NR NR NR NR Not recommended due to inadequate data concentration-response relationships suggest little margin between exposures causing minor effects and those resulting in serious toxicity. 

AEGL-1 values for dimethylhydrazine are not recommended because of inadequate data to develop health-based criteria and because the concentration-response relationship for dimethylhydrazine indicated that a very narrow margin exists between exposures producing no toxic response and those resulting in significant toxicity. 

The adjusted exposure value estimated to be the threshold level of AEGL-2 effects (12 ppm for 15 min) was then scaled to AEGL time frames using the Cn xt=k relationship (ten Berge et al. 1986). For relatively brief exposures (i.e., <4 h), the data for dimethylhydrazine implied a linear concentration-response relationship (C1 t=k), which was used for AEGL derivations. LC50 data on... 

Animal to Human Dosimetric Adjustment None applied, insufficient data Time Scaling Cn t=k, where n=l and k=180 ppm-min LC50 data were available for 5-, 15-, 30-, 60-, and 240-min exposures in rats and 5-, 15-, and 60-min in dogs. Exposure-response data indicated a near linear concentration-response relationship (n=0.84 for rats n=0.80 for dogs). For time-scaling, a linear relationship was assumed and a value where n= 1 was selected. 

Coureaud, G., Langlois, D., Sicard, G. and Schaal, B. (2004) Newborn rabbit reactivity to the mammary pheromone Concentration-response relationship. Chem. Senses 29, 341-350. 

Doses selected for safety pharmacology studies are typically based on the criteria established in the ICH S7A guidance.25 Doses should exceed those projected for clinical efficacy and at the upper limit be bound by (1) adverse pharmacodynamic effects in the safety pharmacology study (2) moderately adverse effects in other non-clinical studies that follow a similar route and duration of dosing or (3) limit of solubility/toxicity. In the absence of adverse effects, the maximum administrable dose can be used. If nonreusable animals enter the study, then the maximum tolerated dose may be appropriate. Most importantly, the doses/concentrations should establish the dose/concentration-response relationship of the adverse effect. 

Non-linear concentration/response relationships are as common in pesticide residue analysis as in analytical chemistry in general. Although linear approximations have traditionally been helpful the complexity of physical phenomena is a prime reason that the limits of usefulness of such an approximation are frequently exceeded. In fact, it should be regarded the rule rather than the exception that calibration problems cannot be handled satisfactorily by linear relationships particularly as the dynamic range of analytical methods is fully exploited. This is true of principles as diverse as atomic absorption spectrometry (U. X-ray fluorescence spectrometry ( ), radio-immunoassays (3), electron capture detection (4) and many more. 

The first and subsequent studies of a NME in humans should aim to obtain dose-concentration-response relationships for desired and undesired effects. These objectives may be summarised as follows ... 

Knowledge of the concentration-response relationship and the nature of the pharmacodynamic responses and toxicity in animals are the... 

In turn, whether significant pharmacokinetic differences arising from the pol)nnorphisms translate into relevant alterations in pharmaco-d)mamics (and clinical efficacy) depends on the operating region of the concentration-response relationship, therapeutic index and utility, and whether kinetic variability is outweighed by variability in receptor sensitivity or number, or in the turnover of the natural receptor ligand. 

Neuroleptic and antidepressant drugs interact with a number of different receptors in the brain, which may partly explain their PK-PD relationships. Figure 9 shows the bell shaped concentration-response relationship for the antidepressant drug nortriptyline. 

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