Permeation times

Perhaps the simplest Fick s law permeation model consists of two aqueous compartments, separated by a very thin, pore-free, oily membrane, where the unstirred water layer may be disregarded and the solute is assumed to be negligibly retained in the membrane. At the start (t = 0 s), the sample of concentration CD 0), in mol/cm3 units, is placed into the donor compartment, containing a volume (Vo, in cm3 units) of a buffer solution. The membrane (area A, in cm2 units) separates the donor compartment from the acceptor compartment. The acceptor compartment also contains a volume of buffer (VA, in cm3 units). After a permeation time, t (in seconds), the experiment is stopped. The concentrations in the acceptor and donor compartments, CA(t) and C (t), respectively, are determined. 

We define this permeability as apparent, to emphasize that there are important but hidden assumptions made in its derivation. This equation is popularly (if not nearly exclusively) used in culture cell in vitro models, such as Caco-2. The sink condition is maintained by periodically moving a detachable donor well to successive acceptor wells over time. At the end of the total permeation time f, the mass of solute is determined in each of the acceptor wells, and the mole sum mA (t) is used in Eq. (7.10). Another variant of this analysis is based on evaluating the slope in the early part of the appearance curve (e.g., solid curves in Fig. 7.14) ... 

The combination of increased Pe and decreased %R allowed the permeation time to be lowered to 4 h, in comparison to the originally specified time of 15 h [547,550], a considerable improvement for high-throughput applications. The quality of the measurements of the low-permeability molecules did not substantially improve with sink conditions or the reduced assay times. 

The PG models 9.1 and 10.1 show similar trends as indicated by PA, but the effects are somewhat muted. The increase in PG from 0.6% to 1.1% causes the permeabilities of weak bases to decrease and membrane retentions to increase, with many bases showing R > 60%. Many molecules were not detected in the acceptor compartments by UV spectrophotometry after 4 h permeation times (Table 7.7). These properties of the PG system make it less attractive for high-throughput applications than the other two-component models. 

With 35 mM SLS in the acceptor compartment (Fig. 3.4b), the amount of propranolol reaching the acceptor wells is dramatically increased, with the concomitant decrease in membrane retention from 94% to 41%. Furthermore, the effective permeability rises to 25.1 x 10-6 cm s 1 (a more than ten-fold increase), presumably due to the desorption effect of the SLS creating an effective sink condition. Only 3 h permeation time was used in this case (Fig. 3.4b). With such a sink at work, one can lower the permeation time to less than 2 h and still obtain very useful UV spectra, and this represents a major benefit for high-throughput requirements. 

PAMPA can quickly provide information about passive-transport permeability that is not complicated by other mechanisms (e.g., active transport, paracel-lular transport, and metabolism) [103], The procedure is used increasingly in pharmaceutical research in major pharmaceutical companies as well as in CROs [13, 137, 175, 179, 165, 119, 70], However, it should be stated that PAMPA to date comprises numerous methods applied in various laboratories using different membrane constituents, sink conditions, permeation times, etc., which makes interlaboratory comparison extremely difficult. Therefore, standardization and validation methods of this technique should be introduced. 

Figure 29 Temperature dependence of the permeability of p-nitrophenol for A-ProOMe grafted films. The permeability (P) was calculated from the equation, P = KVjAC, where k, V, A, and C are the slope of the permeation-time curve, the volume of the receiver chamber, the surface area of the membrane, and the concentration of p-nitropenol in the donor chamber, respectively.

Li et al. [107] also reported the change in residual radical concentration vs oxygen permeation time for a homopolymerization of EGDMA. At 110°C, the radical concentration decreased by approximately 12.5% in 90 min. While at 180 °C, the radical concentration dropped nearly 62.5% over the same time period. While these reactions occurred over a relatively short time period, the temperatures were quite high and certainly one would expect significantly reduced rates at lower temperatures below the glass transition temperature of... 

Most experimental determinations of Dt, D2 reported to date 13 15 16 23 26,55,56) have been obtained by the method described above but sorption kinetics 16,17,27) and permeation time lag measurements 29,57 58> have also been employed for this purpose. 

These parameters are in many ways analogous to permeation time lags but the relevant expressions for the case of S(X), DT(X) are considerably more complicated (even in the case of the First njoment which is the simplest)171> than the corresponding time lag formulae 4). Accordingly, moments represent a less efficient way of making use of the information contained in transient diffusion data than the methods discussed above. In spite of these limitations, further study of moments should prove worthwhile. 

The permeation-time behavior of a cracked and embrittled membrane differs in another fundamental way from membranes that do not suffer such cracking, i.e., when the H2 in voids is not high enough in pressure to cause spreading. In the case of the... 

In the second case D can be calculated from the permeation time lag by means of the equation ... 

On the other hand, PAMPA is a purely artificial method and PAMPA membranes do not reassemble real lipid bilayer structures as barriers for permeation but much thicker barriers. The thickness and material of the supporting PVDF filters also influences artificially the permeation of compounds depending on the lipophilicity of the compounds more than the thin polycarbonate filter does in CACo2 experiments. Also the best choice of membrane constituents for PAMPA experiments is still under investigation and it seems that it will depend a lot on the goal of the PAMPA experiment which membrane is used (e.g. blood brain barrier permeation or intestinal absorption). One has to take into account that PAMPA today is a summary term on a lot of different methods applied in different laboratories using different membrane constituents, sink conditions, permeation times etc., which makes inter laboratory comparison difficult. 

The more conventional method for studying the energetics of diffusion in membranes is to perform permeation experiments as a function of equilibrium temperature. Figure 13 illustrates the eflEect of temperature on the apparent diflEusion coeflScient calculated from the water vapor permeation time lag established by steady-state permeation with a 75 to 0% RH gradient across the membrane. The principles of the time lag permeation method are adequately discussed elsewhere (58). The lower curve corresponds to a sample which was not mechanically supported and was observed to deform into a hemispherical shape. This deformation is the combined result of a small pressure diflEerence across the membrane and a decrease in modulus of stratum corneum as the temperature is increased. The upper curve corresponds to a supported sample. Previous to the experiment, both samples had identical thermal histories. Stresses accompanying deformation of the unsupported cor-... 

Schmidt number temperamre (K) permeation time (h) cleaning time (h) ultrafiltration... 

Nafarelin PG, azone glyceryl mono-oleate EtOH P-cyclodextrin Dermatomed human and monkey skin In vitro 80 h permeation time [28]... 

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