Model permeability rate-limited

Fig. 17.5 Schematic representation of a physiological based model. Left figure shows the physiological structure, upper right figure shows a model for a perfusion rate limited tissue, and lower right figure shows a model for a permeability rate-limited tissue. Q denotes the blood flow, CL the excretion rate, KP the tissuerplasma distribution coefficient, and PS the permeability surface area coefficient.

The simple assumptions that constitute blood-flow-limited PBPK models often are inadequate for characterizing the pharmacokinetics of macromolecules. Instead, a membrane- or permeability-rate-limited model is more common, where it is assumed that mass transfer across the cell membrane is rate-limiting. For these models, organ compartments are subdivided into at least two well-stirred spaces representing vascular Cry) and extravascular (Ct,ev) compartments. Such a system might be described by the following equations for a noneliminating tissue ... 

Permeability-pH profiles, log Pe - pH curves in arhficial membrane models (log Pjpp - pH in cehular models), generally have sigmoidal shape, similar to that of log Dod - pH cf. Fig. 3.1). However, one feature is unique to permeabihty profiles the upper horizontal part of the sigmoidal curves may be verhcally depressed, due to the drug transport resistance arising from the aqueous boundary layer (ABL) adjacent to the two sides of the membrane barrier. Hence, the true membrane contribution to transport may be obscured when water is the rate-limiting resistance to transport. This is especially true if sparingly soluble molecules are considered and if the solutions on either or both sides of the membrane barrier are poorly stirred (often a problem with 96-well microhter plate formats). 

Lipophilicity is intuitively felt to be a key parameter in predicting and interpreting permeability and thus the number of types of lipophilicity systems under study has grown enormously over the years to increase the chances of finding good mimics of biomembrane models. However, the relationship between lipophilicity descriptors and the membrane permeation process is not clear. Membrane permeation is due to two main components the partition rate constant between the lipid leaflet and the aqueous environment and the flip-flop rate constant between the two lipid leaflets in the bilayer [13]. Since the flip-flop is supposed to be rate limiting in the permeation process, permeation is determined by the partition coefficient between the lipid and the aqueous phase (which can easily be determined by log D) and the flip-flop rate constant, which may or may not depend on lipophilicity and if it does so depend, on which lipophilicity scale should it be based ... 

The physiologically based model developed by Willman et al. [53, 54], for the prediction of both rat and human Fibs, was shown to be predictive for the human situation if passively transported compounds were studied. In their study, they used a semiempirical formula for the prediction of human permeability trained with a set of 119 passively transported drugs that did not show solubility or dissolution rate-limited absorption. 

For carrier-mediated transport of L-lactic acid across human carcinoma cell line, it was found that increasing agitation rate resulted in a larger fractal dimension accompanied by a decrease in the substrate permeability rate. The classical Michaelis-Menten model is known to be only valid for a limited range of glucose concentrations. An alternative model was proposed including convective and non-linear diffusive mechanisms corresponding to the first and second (fractal power function) terms in Eq. (30). 

Since the solubility of various gases in ILs varies widely, they may be uniquely suited for use as solvents for gas separations [97]. Since they are non-volatile, they cannot evaporate to cause contamination of the gas stream. This is important when selective solvents are used in conventional absorbers, or when they are used in supported liquid membranes. For conventional absorbers, the ability to separate one gas from another depends entirely on the relative solubilities (ratio of Henry s law constants) of the gases. In addition, ILs are particularly promising for supported liquid membranes because they have the potential to be incredibly stable. Supported liquid membranes that incorporate conventional liquids eventually deteriorate because the liquid slowly evaporates. Moreover, this finite evaporation rate limits how thin one can make the membrane. This means that the net flux through the membrane is decreased. These problems could be eliminated with a non-volatile liquid. In the absence of facilitated transport (e.g., complexation of CO2 with amines to form carbamates), the permeability of gases through supported liquid membranes depends on both their solubility and diffusivity. The flux of one gas relative to the other can be estimated using a simplified solution-diffusion model ... 

The absorption of class III drugs is limited by their permeability over the intestinal wall. Thus, as this process is not at all modeled by the classical in vitro dissolution test, no IVIVC should be expected. When drug dissolution becomes slower than gastric emptying, a reduction in the extent of bioavailability will be found in slower dissolution rates as the time when the drug is available for permeation over the gut wall in the small intestine will then be reduced. Thus, the same type of relationship can be expected between bioavailability and in vitro dissolution, as shown in Fig. 21.12 for a class I drug. 

This limited amount of kinetic evidence suggests that the kinetic models developed for reactivity in aqueous micelles are directly applicable to reactions in vesicles, and that the rate enchancements have similar origins. There is uncertainty as to the appropriate volume element of reaction, especially if the vesicular wall is sufficiently permeable for reaction to occur on both the inner and outer surfaces, because these surfaces will have different radii of curvature and one will be concave and the other convex. Thus binding, exchange and rate constants may be different at the two surfaces. 

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