Mean permeability coefficient

Permeability coefficients for phenol in isolated skin patches from nude mice have been determined (Behl et al. 1983). The permeability coefficient increased as the concentration of the applied aqueous phenol solution increased doubling the concentration from 20 to 40 g/L resulted in a 12-fold increase in mean permeability coefficient (0.007-0.085 cm/hour). The value obtained for the permeability coefficient when 60 g/L was applied to the skin patch (0.169 cm/hour) was similar to that obtained for skin patches in which the stratum comeum had been removed. It was concluded that phenol concentrations exceeding 20 g/L may destroy a diffusion barrier normally provided by the intact stratum comeum, permitting increased percutaneous absorption. 

It can be shown that the mean permeability coefficient P is a product of a mean diffusion coefficient, D, and a function 5 related to the solubility of the penetrant gas in the polymer [1-9] ... 

C. With Eq. (61), the permeability coefficient of the filter, PF, is 6.75 X 10 4 cm/sec, which is several times larger than Pe = 2.29 X 1(T4 cm/sec. This means that the mass transfer resistance of the ABLs must be appreciable ... 

Thus, the fraction of dose absorbed is exponentially related to the absorption number. Equation (10) shows that the absorption number (and therefore the membrane permeability) is a fundamental parameter while other parameters such as the partition coefficient and pKa are useful guides but not fundamental parameters. For highly soluble drugs with linear absorption kinetics, dose and dissolution have no effect on the fraction of dose absorbed. In the case of drugs that are absorbed by a carrier-mediated process, a mean permeability should be used [30],... 

Figure 2. Permeability coefficient as a function of the mean oxygen pressure.

In Figure 2 we presented the permeability coefficient K of oxygen as a function of the mean gas pressure experimentally obtained for a sample of porous material from acetylene black modified with 35% PTFE. The experimental linear dependence is obtained. The intercept with the abscissa corresponds to the Knudsen term DiK. The value obtained is 2,89.1 O 2 cm2/s. The slope of the straight line is small, so that the ratio K,/ Dik at mean gas pressure 1 atm. is small ( 0.1) which means that the gas flow is predominantly achieved by Knudsen diffusion and the viscous flow is quite negligible. At normal conditions (1 atm, 25°C) the mean free path of the air molecules (X a 100 nm) is greater than the mean pore radii in the hydrophobic material (r 20 nm), so that the condition (X r) for the Knudsen-diffusion mechanism of gas transport is fulfilled. 

The above-mentioned inverse selectivity/permeability relationship of polymers has been summarized by Robeson by means of log-log plots of the overall selectivity versus the permeability coefficient, where A is considered to be the more rapidly permeating gas. These plots were made for a variety of binary gas mixtures from the list He, H2, O2, N2, C02, and CH4, and for a large number of rubbery and glassy polymer membranes. Such representations, shown in Fig. 8 and Fig. 9 are often referred to as upper bound plots (Robeson, 1991). The upper bound lines clearly show the inverse selectivity/permeability relationship of polymer membranes. While these plots were prepared in 1991, only small advances have been made to push the upper bound higher since that time. 

Two compounds had to be excluded from the data set. They were outliers (1.3 log units deviation) as also found in the analysis by Abraham et al. [26], It must also be remembered when considering the derived equations that log BB is a complex parameter that encompasses brain partitioning and permeability and may also depend on other processes such as metabolism, active transport, and so forth. Thus, the standard deviations of these determinations may fall within the range of the mean values. The authors could demonstrate that the derived equation could also estimate log BB outside of the training data set. Therefore, the value of the above correlation with the solvation free energy lies in its power to rank compounds for their ability to cross the blood-brain barrier before synthesis. Interestingly, it was also shown by Lombardo et al. [71] that the calculated AG°W correlated well with the determined permeability coefficient, PC, using endothelial cell monolayers from bovine brain mi-... 

We can now consider some typical nutrient solutes like amino acids and phosphate. Such molecules are ionized, which means that they would not readily cross the permeability barrier of a lipid bilayer. Permeability coefficients of liposome membranes to phosphate and amino acids have been determined [46] and were found to be in the range of 10 11 -10 12 cm/s, similar to ionic solutes such as sodium and chloride ions. From these figures one can estimate that if a primitive microorganism depended on passive transport of phosphate across a lipid bilayer composed of a typical phospholipid, it would require several years to accumulate phosphate sufficient to double its DNA content or pass through one cell cycle. In contrast, a modern bacterial cell can reproduce in as short a time as 20 min. 

One obtains the permeability coefficient with the help of Eq. (9-1) using the slope of the asymptote in Fig. 9-1, which means steady state permeation has been reached ... 

Most of the permeability coefficients for small solutes crossing the plasma membrane range from 10-10 to 10-6 m s-1. Hence, a cell wall generally has a higher permeability coefficient than does a membrane, which means that the cell wall is usually more permeable for small solutes than is the plasma membrane. For comparison, let us consider a permeability coefficient appropriate for an unstirred liquid layer adjacent to a cell wall or membrane. Specifically, Dj for a small solute may be 1 x 10-9 m2 s-1 in water, Kj is 1 in the aqueous solution, and let us assume that Ax is 30 pm for the unstirred... 

Figure 16. Coefficient ot variation for the five grids in Figure 14. The statistically significant drop for 0CR0P4 reflects properties being measured entirely within one bed. Inter-septile range shows the same effect although the mean permeability did not vary greatly. (Reproduced from Ref. 5 )...

When the diffusion process is not ideal, the diffusion coefficient calculated from Equation 6 for a stationary state process is the mean diffusion coefficient corresponding to a particular concentration difference. Methods of determining the true diffusion coefficient pertaining to a particular concentration were reported by Crank (9). The permeability coefficient calculated from Equation 4 is also a mean value corresponding to a particular vapor pressure difference if the diffusion process is not ideal. 

Normalized permeability coefficient = Papplalcohop/Papp (methanol). Mean value from three rabbits at pH 6.0 and 37°C. 

One method which is known under the name of permeametry [131] or Poiseuille-Knudsen method [124] is based on the law of gas permeability in a porous media in the two flow regimes molecular flow (Knudsen) and laminar or viscous flow (Poiseuille). According to Darcy s law, the gas flux through a membrane with a thickness / can be written as / = KAP/l, where K is the permeability coefficient and AP (AP = Pi - P2) the pressure difference across the membrane. If the membrane pore diameter is comparable to the mean free path of the permeating gas, K can be expressed as a stun of a viscous and a non-vis-cous term... 

Physiologic model-physiologically based pharmacokinetic model (PB/PK) A physiologically based model for Gl transit and absorption in humans is presented. The model can be used to study the dependency of the fraction dose absorbed (Fabs) of both neutral and ionizable compounds on the two main physico-chemical input parameters [the intestinal permeability coefficient (Pint) and the solubility in the intestinal fluids (Sint)] as well as the physiological parameters, such as the gastric emptying time and the intestinal transit time. For permeability-limited compounds, the model produces the established sigmoidal dependence between Fabs and Pnt. In case of solubility-limited absorption, the model enables calculation of the critical mass-solubility ratio, which defines the onset of nonlinearity in the response of fraction absorbed to dose. In addition, an analytical equation to calculate the intestinal permeability coefficient based on the compound s membrane affinity and MW was used successfully in combination with the PB-PK model to predict the human fraction dose absorbed of compounds with permeability-limited absorption. Cross-validation demonstrated a root-mean-square prediction error of 7% for passively absorbed compounds. 

Tracer Molecular weight (Da) Molecular radius (nm) Permeability coefficient (x 10 6 cm/sec) (mean SD)... 

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