Figure 2.2 Log flux-pH profiles at dosing concentrations: (a) ketoprofen (acid, pKa 3.98), dose 75 mg; (b) verapamil (base, pKa 9.07), dose 180 mg; (c) piroxicam (ampholyte, pKa 5.07, 2.33), dose 20 mg. The permeability and the concentration of the uncharged species are denoted P0 and C0, respectively. [Avdeef, A., Curr. Topics Med. Chem., 1, 277-351 (2001). Reproduced with permission from Bentham Science Publishers, Ltd.]

which case it is equal to the solubility. Since the uncharged molecular species is the permeant, Eq. (2.4) may be restated as where P0 and C0 are the intrinsic permeability and concentration of the uncharged species, respectively. The intrinsic permeability does not depend on pH, but its cofactor in the flux equation C0 does. The concentration of the uncharged species is always equal to or less than the intrinsic solubility of the specie, S0, which never depends on pH. Note that for the uncharged species, Eq. (2.3) takes on the form where Kp = Cm(0)/CD0; also, Kp = Cm (h)/CA0; CD0 and CA0 are the aqueous solution concentrations of the uncharged species in the donor and acceptor sides, respectively.

In solutions saturated (i.e., excess solid present) at some pH, the plot of log C0 versus pH for an ionizable molecule is extraordinarily simple in form; it is a combination of straight segments, joined at points of discontinuity indicating the boundary between the saturated state and the state of complete dissolution. The pH of these junction points is dependent on the dose used in the calculation, and the maximum value of log C0 is always equal to log S0 in a saturated solution. [26] Figure 2.2 illustrates this idea using ketoprofen as an example of an acid, verapamil as a base, and piroxicam as an ampholyte. In the three cases, the assumed concentrations in the calculation were set to the respective doses [26]. For an acid, log C0 (dashed curve in Fig. 2.2a) is a horizontal line (log C0 = log S0) in the saturated solution (at low pH), and decreases with a slope of —1 in the pH domain where the solute is dissolved completely. For a base (Fig. 2.2b) the plot of log C0 versus pH is also a horizontal line at high pH in a saturated solution and is a line with a slope of +1 for pH values less than the pH of the onset of precipitation.

We have called the plot of log C0 versus pH the "flux factor'' profile, with the idea that such a plot when combined with intrinsic permeability, can be the basis of an in vitro classification scheme to predict passive oral absorption as a function of pH. This will be discussed later.

Figures 2.1 and 2.2 represent the basic model that will be used to discuss the literature related to the measurement of the physicochemical parameters and the interpretation of their role in the oral absorption process [19,20,23,45-61].

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