Permeability effective

X (p in Q cm) as in Table 30.1 /= frequency of the system in Hz p = effective permeability of the medium in which the field exists (aluminium in the present case), and will depend upon the electric field induced in the enclosure... 

In PAMPA, the effective permeability coefficient, Pe, is related to the membrane and ABL permeability coefficients, P and Pabl. respectively, as... 

Hydraulic fracturing is a technique to stimulate the productivity of a well. A hydraulic fracture is a superimposed structure that remains undisturbed outside the fracture. Thus the effective permeability of a reservoir remains unchanged by this process. The increased productivity results from increased wellbore radius, because in the course of hydraulic fracturing, a large contact surface between the well and the reservoir is created. 

Using liposomes made from phospholipids as models of membrane barriers, Chakrabarti and Deamer [417] characterized the permeabilities of several amino acids and simple ions. Phosphate, sodium and potassium ions displayed effective permeabilities 0.1-1.0 x 10 12 cm/s. Hydrophilic amino acids permeated membranes with coefficients 5.1-5.7 x 10 12 cm/s. More lipophilic amino acids indicated values of 250 -10 x 10-12 cm/s. The investigators proposed that the extremely low permeability rates observed for the polar molecules must be controlled by bilayer fluctuations and transient defects, rather than normal partitioning behavior and Born energy barriers. More recently, similar magnitude values of permeabilities were measured for a series of enkephalin peptides [418]. 

The effective permeability of ionizable molecules depends on pH, and the shapes of the permeability-pH profiles can be theoretically predicted when the pKa of the molecule is known, the pH partition hypothesis are valid, and the resistance of... 

When membrane retention of the solute needs to be considered, one can derive the appropriate permeability equations along the lines described in the preceding section Eqs. (7.1)—(7.3) apply (with P designated as the effective permeability, Pe). However, the mass balance would need to include the membrane compartment, in addition to the donor and acceptor compartments. At time t, the sample distributes (mol amounts) between three compartments ... 

Given this relationship between CA(t) and Co(t), where retention is factored in, we can proceed to convert Eq. (7.3) into Eq. (7.5), where a is the same as before, and b now needs to be multiplied by the partition-related factor, 1 — R. The so-modified ordinary differential, Eq. (7.5), is solved by standard methods, using integration limits from xLAG to t (not 0 to t), and the desired effective permeability derived as... 

A more general analysis requires the use of two effective permeability coefficients, one for each pH, each of which would be valid in the respective iso-pH conditions. Since fewer limiting assumptions are made, the more general method may be more suitable for high-throughput applications. We continue to derive the appropriate new model. 

In the introductory discussion in Chapter 2, it was indicated that the effective permeability Pe linearly depends on the apparent membrane-water partition... 

Four neutral lipid models were explored at pH 7.4 (1) 2% wt/vol DOPC in dode-cane, (2) olive oil, (3) octanol, and (4) dodecane. Table 7.5 lists the effective permeabilities Pe, standard deviations (SDs), and membrane retentions of the 32 probe molecules (Table 7.4). The units of Pe and SD are 10 6 cm/s. Retentions are expressed as mole percentages. Figure 7.22a is a plot of log Pe versus log Kd (octanol-water apparent partition coefficients, pH 7.4) for filters loaded with 2% wt/vol DOPC in dodecane (model 1.0, hlled-circle symbols) and with phospholipid-free dodecane (model 4.0, open-circle symbols). The dashed line in the plot was calculated assuming a UWL permeability (see Section 7.7.6) Pu, 16 x 10-6 cm/s (a typical value in an unstirred 96-well microtiter plate assay), and Pe of 0.8 x 10-6 cm/s... 

Tables 7.12-7.14 list the pH 7.4 permeability and retention values of the probe series of drug substances, grouped as bases, acids, and neutral molecules. Figures 7.31a-c are graphs of the effective permeabilities with and without sink as a function of increasing soy content, beginning with 2% DOPC for a benchmark. Figures 7.32a-c are plots of the corresponding membrane retentions.

The UWL permeability is nearly the same for drugs of comparable size, and is characterized by the water diffusivity (Daq) of the drug divided by twice the thickness of the layer (ftaq), Pu = Aiq / (2 h.Aq), in a symmetric permeation cell [40], The unstirred water layer permeability can be determined experimentally in a number of ways based on pH dependency of effective permeability [25,509,535-538], stirring rate dependence [511-514,552,578], and transport across lipid-free microfilters [25,546],... 

As can be seen from the second line of Eq. (7.52), a plot of l/Pe versus 1/[H+] is expected to be linear (for a weak acid), with the intercept 1/PU + 1/P0 and the slope KJP0. When the pKa of the molecule is known, then both P0 and Pu can be determined. If Pu can be independently determined, then, in principle, the ionization constant may be determined from the pH dependence of the effective permeability. 

Figure 7.34 Permeability-pH profiles of ketoprofen (a) log-log plot solid curve represents effective permeability, and the dashed curve is the membrane permeability, calculated by Eq. (7.53). The latter curve levels off at the intrinsic permeability, Pq. The effective curve levels off to approximately the unstirred water layer permeability, Pu. (b) Direct plot the inset curve for the fraction neutral substance levels of at 100% (scale not shown). [Avdeef, A., Curr. Topics Med. Chem., 1, 277-351 (2001). Reproduced with permission from Bentham Science Publishers, Ltd.]...

TABLE 7.15 Intrinsic Permeabilities and Unstirred Water Layer Permeabilities Determined from Iso-pH Dependence of Effective Permeabilities 2% DOPC in Dodecane... 

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 pm 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 / aq = 460 pm (sandwich stirred at 150 rpm). We have been able to confirm similar results in our laboratory with different microfilters, using the lipid-free method. 

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/ 2/iaq. 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... 

The above iso-pH measurements are based on the 2% DOPC/dodecane system (model 1.0 over pH 3-10 range). Another membrane model was also explored by us. Table 7.16 lists iso-pH effective permeability measurements using the soy lecithin (20% wt/vol in dodecane) membrane PAMPA (models 17.1, 24.1, and 25.1) The negative membrane charge, the multicomponent phospholipid mixture, and the acceptor sink condition (Table 7.1) result in different intrinsic permeabilities for the probe molecules. Figure 7.40 shows the relationship between the 2% DOPC and the 20% soy iso-pH PAMPA systems for ketoprofen. Since the intrinsic permeability of ketoprofen in the soy lecithin membrane is about 20 times greater than in DOPC membrane, the flat diffusion-limited transport region of the log Pe... 

Carbamazepine, antipyrine, terbutaline, and hydrochlorothiazide were treated as neutral molecules. Their effective permeabilities were corrected for the unstirred water layer using estimated unstirred water layer permeabilities, determined by the other molecules of similar lipophilicities and size. 

It is difficult to prove that quaternary ammonium compounds can cross lipid bilayers using cell uptake experiments, since several mechanisms may be operative, and separating contributions from each may be very difficult [1]. It may be an advantage to use PAMPA to investigate transport properties of permanently ionized molecules. Of all the molecules whose permeabilities were measured under iso-pH conditions in 2% DOPC/dodecane, verapamil, propranolol, and especially quinine seem to partially violate the pH partition hypothesis, as shown in Figs. 7.47a-c. In Fig. 7.47c, the solid line with slope of +1 indicates the expected effective permeability if the pH partition hypothesis were strictly adhered to. As can be seen at pH 4... 

Figures 7.57a-c show the acceptor, donor, and reference spectra of 48 pM propranolol at the end of 15 h PAMPA assay using 20% wt/vol soy lecithin in dode-cane. The sum of the donor (3 pM) and the acceptor (<1 pM) well concentrations indicates that 45 pM is lost to the membrane. In the absence of sink-creating surfactant, only a trace of propranolol reached the acceptor wells at the end of 15 h, with 94% of the compound trapped in the membrane, compared to 19% in the 2% wt/vol DOPC case (Table 7.5). The effective permeability in 20% soy dropped to 1.8 x 10 6cm/s, compared to the DOPC value of 10.2 x 10 6cm/s.

In terms of the effective permeability or the total resistance, we have... 

J = flux, mass/sec A = cross-sectional area, cm2 Pe = effective permeability coefficient, cm/sec CD, Cr = concentrations in the donor and receiver, respectively... 

The effective permeability coefficient is composed of the permeability coefficients for the various transport barriers in series—the ABLs, the cell monolayer, and the filter support ... 

The permeability coefficients, PD and PR, are influenced by hydrodynamics. Depending upon the geometric symmetry or asymmetry of stirring in the donor and receiver chambers, their values may be equal or unequal. To analyze these situations, let us define PAm, as the effective permeability coefficient of the ABLs therefore, the geometric average of the mass transfer resistance of the ABLs is... 

Figure 17 depicts the rapid flux of sucrose across the filter into the receiver. Upon treatment of the data with Eq. (7), the effective permeability coefficient (Pe) is found to be 2.29 X 10 4 cm/sec, which takes into account the filter and the ABLs on both sides of the filter hence,... 

As described in Section II, the effective permeability coefficient is expressed as... 

The slow and linear fluxes of hydrocortisone and dexamethasone under various hydrodynamic conditions are quantified in terms of effective permeability coefficients, P by Eq. (9), i.e.,... 

The summary of Pe values for the steroids as a function of stirring rates is found in Table 11 and their correlations with log PC (n-octanol-water) in Figure 20. The transport kinetics of the relatively hydrophilic hydrocortisone and dexa-methasone are controlled by passive diffusion across the cell monolayer. On the other hand, the Pe values of testosterone and progesterone are highly dependent on stirring rate. The results for testosterone are used to obtain the relationships between the effective permeability coefficients of the ABL on the donor and receiver sides and the stirring rate, using the linear expression (see Eq. (69)]... 

Figure 21 Linearized double reciprocal plot of the effective permeability coefficients and corresponding stirring rates to determine the power dependency of the stirring rate and mass transfer resistances for the aqueous boundary layers and the Caco-2 cell monolayer in the Transwell system. 

Table 12 Effective Permeability Coefficients and Thicknesses of the Aqueous Boundary Layer of the Caco-2 Cell Monolayer/ Transwell System as a Function of Stirring by Planar Rotating Shaker3...

To begin, we reintroduce the familiar effective permeability coefficient Pe to put Pparaceii in context with other permeability coefficients ... 

Figure 24 shows a schematic diagram of the pathways the various species of a permeant (e.g., weak base) take during their passage across the cell monolayer-filter support system. From a general point of view, the effective permeability coefficient may be expressed in the form... 

Figure 26 Correlation of the effective permeability coefficients of (3-blockers determined at pH 6.5 (O) and 7.4 ( ) with stirring rates and log partition coefficients (n-octanol/buffer at pH 6.5 and 7.4). APL, alprenolol ATL, atenolol PDL, pindolol PPL, propranolol.

The effective permeability coefficient of the diester, as viewed from the donor side, can be found by treating the data with Eq. (113) hence,... 

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