## Info

Source: Based on data in Ref. 558.

"Po = intrinsic permeability, SD = estimated standard deviation. bPu = unstirred water permeability. cData range actually used in the regression analysis. ''Number of Pe measurements.

eGOF = goodness of fit in the weighted nonlinear regression analysis.

^Carbamazepine, caffeine, and antipyrine are neutral molecules. Their effective permeabilities were corrected for the unstirred water layer using the average unstirred water layer permeability of 1.6 x 10~5 cm/s, determined by the other molecules.

Source: Based on data in Ref. 558.

"Po = intrinsic permeability, SD = estimated standard deviation. bPu = unstirred water permeability. cData range actually used in the regression analysis. ''Number of Pe measurements.

eGOF = goodness of fit in the weighted nonlinear regression analysis.

^Carbamazepine, caffeine, and antipyrine are neutral molecules. Their effective permeabilities were corrected for the unstirred water layer using the average unstirred water layer permeability of 1.6 x 10~5 cm/s, determined by the other molecules.

Similar analysis can be applied to side-by-side diffusion cell systems, where stirring is effected by bubbling an O2/CO2 gas mixture. For a bubbling rate of 40 mL gas/min, each UWL was estimated to be 282 mm [515].

7.7.6.4 Determination of UWL Permeabilities from Transport across Lipid-Free Microfilters

An infrequently used method (in pharmaceutical research) for determining the UWL permeability involves measuring transport of molecules across a high-porosity microfilter that is not coated by a lipid. The molecules are able to diffuse freely in the water channels of the microfilter. The filter barrier prevents convective mixing between the donor and acceptor sides, and an UWL forms on each sides of the microfilter. Camenisch et al. [546] measured the effective permeabilities of a series of drug molecules in 96-well microtiter plate-filterplate (Millipore GVHP mixed cellulose ester, 0.22 mm pore) ''sandwich'' where the filters were not coated by a lipid. The permeabilities were nearly the same for all the molecules, as shown in Fig. 7.8a. Our analysis of their data, Fig. 7.8b, indicates haq = 460 mm (sandwich stirred at 150 rpm). We have been able to confirm similar results in our laboratory with different microfilters, using the lipid-free method.

7.7.6.5 Estimation of UWL Thickness from pH Measurements Near the Membrane Surface

Antonenko and Bulychev [84] measured local pH changes near BLM surfaces using a variably positioned 10 mm antimony-tip pH microelectrode. Shifts in pH near the membrane surface were induced by the addition of (NH4)2SO4. As the neutral NH3 permeated, the surface on the donor side of the BLM accumulated excess H+ and the surface on the acceptor side of the membrane was depleted of H+ as the permeated NH3 reacted with water. These effects took place in the UWL. From measurement of the pH profile as a function of distance from the membrane surface, it was possible to estimate haq as 290 mm in the stirred solution.

### 7.7.6.6 Prediction of Aqueous Diffusivities Daq

The method preferred in our laboratory for determining the UWL permeability is based on the pH dependence of effective permeabilities of ionizable molecules [Eq. (7.52)]. Nonionizable molecules cannot be directly analyzed this way. However, an approximate method may be devised, based on the assumption that the UWL depends on the aqueous diffusivity of the molecule, and furthermore, that the diffusivity depends on the molecular weight of the molecule. The thickness of the unstirred water layer can be determined from ionizable molecules, and applied to nonionizable substances, using the (symmetric) relationship Pu = Daq/ 2haq. Fortunately, empirical methods for estimating values of Daq exist. From the Stokes-Einstein equation, applied to spherical molecules, diffusivity is expected to depend on the inverse square root of the molecular weight. A plot of log Daq versus log MW should be linear, with a slope of —0.5. Figure 7.37 shows such a log-log plot for 55 molecules, with measured diffusivities taken from several log D = -4.14 -0.417 log MW 0 r2 = 0.791, s=0.18, n=55

ganciclovir log D = -4.14 -0.417 log MW 0 r2 = 0.791, s=0.18, n=55

ganciclovir

Figure 7.37 Log aqueous diffusivities versus log molecular weights.

sources [40,553,594]. Molecular weights spanned from -100 to 500,000 Da. The linear regression equation from the analysis is log D.

with r2 = 0.79, s = 0.2, n = 55. The slope is close to the theoretically expected value of —0.5.

The Pu values in Table 7.15 can be combined with Eq. (7.59) to determine approximate haq. The plot of log Pu versus log MW for 11 molecules is shown in Fig. 7.38. The solid line in the plot was determined from the equation (based on Pu = Daq/h)

where h is the sum UWL thickness. The best-fit value of h was determined by regression to be 4.5 mm. Thus each UWL thickness is —2300 mm. Note that this represents approximately the thickness of the water layer in the unagitated micro-titer plate sandwich configuration of the pION system. The two highest deviation points in Fig. 7.38 correspond to metoprolol and salicylic acid. These deviations are due mainly to the weak UV spectra of these molecules in the acceptor wells in the PAMPA iso-pH assay.

7.7.6.7 Intrinsic Permeability-log Kp Octanol-Water Relationship

Once the 2% DOPC/dodecane permeability data have been corrected for pH and UWL effects, the resulting intrinsic permeabilities P0 should be linearly related

Unstirred Water Layer vs log MW -- Iso-pH Mapping 2%DOPC

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