## R

Note that Eqs. (7.20) and (7.21) are nearly identical to Eqs. (7.12) and (7.13); the differences are the 1 — R term (to reflect membrane retention) and the lag time offset, tLAG (the time needed to saturate the membrane with solute). These differences warrant the new equations to be denoted with the subscript e.

When using the 96-well microtiter plate format, typical metrics are VA = 200400 mL, VD = 200-400 mL, A = 0.3 cm2, VM = 4-6 mL, h (filter thickness) = 125 mm, 70% porosity (e), t (permeation time) = 3-15 h, tLAG = 0-60 min. As noted

Permeation Time (hrs)

Figure 7.15 Kinetics of transport across a filter-immobilized artificial membrane: (a) desipramine and (b) dihydromethysticin concentrations in acceptor well. [Reprinted from Avdeef, A., in van de Waterbeemd, H.; Lennernas, H.; Artursson, P. (Eds.). Drug Bioavailability. Estimation of Solubility, Permeability, Absorption and Bioavailability. Wiley-VCH: Weinheim, 2003 (in press), with permission from Wiley-VCH Verlag GmbH.]

Figure 7.15 Kinetics of transport across a filter-immobilized artificial membrane: (a) desipramine and (b) dihydromethysticin concentrations in acceptor well. [Reprinted from Avdeef, A., in van de Waterbeemd, H.; Lennernas, H.; Artursson, P. (Eds.). Drug Bioavailability. Estimation of Solubility, Permeability, Absorption and Bioavailability. Wiley-VCH: Weinheim, 2003 (in press), with permission from Wiley-VCH Verlag GmbH.]

above, the time constant for the kinetic process is defined as teq = [(VAVD)/ (VA + VD)]/(APe). For membranes made with 2% DOPC in dodecane, metoprolol at pH 7.4, has teq = 4.8 x 10 5 s or 134 h for the donor concentration to decay to 1/e (37%) from the final equilibrium value. For diltiazem, the time constant is 5.3 h. However, for membranes made with 20% soy lecithin in dodecane, under sink conditions created by an anionic surfactant in the acceptor wells, the metoprolol and diltiazem time constants decrease to 3.2 and 2.6 h, respectively, since the permeability coefficients increase in the soy-based membrane under artificially imposed sink conditions (as discussed in a later section).

Figure 7.15 shows the appearance curves of desipramine and dihydromethysticin [556] in the acceptor wells as a function of time. Because some of the material is lost to the membrane, the curves level off asymptotically at acceptor concentration fractions considerably less the 0.5 value expected in the thin-membrane model (Fig. 7.14). The solid curve for desipramine in Fig. 7.15a is a least-squares fit of the data points to Eq. (7.21), with the parameters: Pe 24 x 10~6 cm/s, R 0.13, and tLag 11 min. The solid curve for dihydromethisticin in Fig. 7.15b is described by the parameters: Pe 32 x 10~6 cm/s, R 0.42, and tLAG 35 min.

Ketoprofen, a weak-acid drug, with a pKa 4.12 (25°C, 0.01 M ionic strength), was selected to illustrate Eqs. (7.20) and (7.21) in a series of simulation calculations, as shown in Fig. 7.16. The membrane-buffer apparent partition coefficients Kd(pH) were calculated at various pH values, using the measured constants from

Iso-pH PAMPA: Ketoprofen if IT^ ph

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