R

where Rmax is the maximal response achieved by a drug with all receptors occupied, q is a proportionality constant, and C is the concentration of drug. Mishima showed that Eq. (6) predicted the miosis of carbachol and pilocarpine on the sphincter muscle of the cat (see Fig. 12) (3).

Based on maximum and minimum pupil diameters of 8.5 and 1 mm, respectively, it can be shown that for a miotic response,

Concentration (mol/L)

Figure 12 Dose-response relationship from carbachol (*) and pilocarpine (O) in isolated human sphincter muscle strip. (Replotted from Ref. 3.)

Concentration (mol/L)

Figure 12 Dose-response relationship from carbachol (*) and pilocarpine (O) in isolated human sphincter muscle strip. (Replotted from Ref. 3.)

and for a mydriasis response,

where D0 is the pupil diameter before drug application and D is the pupil diameter following drug administration (9). Figure 13 shows a log-linear plot of the response versus time, from which is derived the following equation:

where RL is the intercept value of R/, t0 if the lag time after instillation when response is observed, and A and B are apparent elimination and absorption rate constants (9).

Chien and Schoenwald investigated aqueous humor concentration of phenylephrine and the corresponding mydriatic response in rabbit eyes following topical ocular administration of phenylephrine or a prodrug of phenylephrine (114). Ocular bioavailability of 10% prodrug was eightfold higher than that of the 10% HCl salt. However, mydriatic activity only improved fourfold, demonstrating that the mydriatic response did not accurately reflect drug distribution to the iris. The observed clockwise hysteresis in the response versus concentration plot was suggestive of pharmacological tolerance. An Emax model with a Michaelis-Menten relationship between

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