Permeability limited distribution

Important limitations of the PBPK approach are realized for class 3 and 4 compounds with significant active distribution/absorption processes, where biliary elimination is a major component of the elimination process or where the assumptions of flow-limited distribution and well mixed compartments are not valid and permeability-limited distribution is apparent. These drawbacks could be addressed by the addition of permeability barriers for some tissues and by the incorporation of a more complex liver model which addresses active uptake into the liver, active efflux into the bile, biliary elimination and enterohepatic recirculation. However, this improvement to current methodologies requires the availability of the appropriate input data for quantification of the various processes involved as well as validation of the corresponding in vitro to in vivo scaling approaches. 

Distribution of proteins to tissues is controlled by the permeability (porosity) of the vasculatures and thereby influenced by the molecular size of the protein. A protein of greater than 150kDa ( 50nm) in size will have limited distribution and may be restricted to blood volume. Infrequently a large protein has amino acid recognition sequences that allow passage across epithelial cells lining the vasculatures by transcy-tosis, a process that allows directional transport of protein into and out of a cell. 

Figure 7.9 A. Illustrates the differences in perfusion rate on the proposed distribution and redistribution of thiopental. (Redrawn from http //www.cvm.okstate.edu/Courses/vmed5412/LECT006.htm) B. Drug equilibration in the cerebrospinal fluid with plasma water for various drugs in the dog (redrawn from Figure 5-11 in Rowland and Tozer, 2006, and Brodie et al., 1960. Plasma drug concentration was kept constant throughout the study. Thiopental displays perfusion limited distribution whereas the distribution of salicylic acid is permeability rate limited.

Specific barriers may serve to limit dmg distribution. The placental barrier is of obvious importance to dmg action in the fetus. Dmg transfers across the placenta primarily by Hpid solubiHty. Hence, this barrier is not particularly restrictive. Similarly, the Hpid solubiHty of a dmg is a primary deterrninant in access to the brain and cerebrospinal fluid. Generally, hydrophilic or charged dmgs can also penetrate to these latter areas, but the result is slow and incomplete. The blood brain barrier is composed of cells having tight junctions which are much less permeable to solutes than are the endotheHal cells of other tissues. 

The lack of a method to determine the spatial distributions of permeability has severely limited our ability to understand and mathematically describe complex processes within permeable media. Even the degree of variation of intrinsic permeability that might be encountered in naturally occurring permeable media is unknown. Samples with permeability variations will exhibit spatial variations in fluid velocity. Such variations may significantly affect associated physical phenomena, such as biological activity, dispersion and colloidal transport. Spatial variations in the porosity and permeability, if not taken into account, can adversely affect the determination of any associated properties, including multiphase flow functions [16]. 

One of the key parameters for correlating molecular structure and chemical properties with bioavailability has been transcorneal flux or, alternatively, the corneal permeability coefficient. The epithelium has been modeled as a lipid barrier (possibly with a limited number of aqueous pores that, for this physical model, serve as the equivalent of the extracellular space in a more physiological description) and the stroma as an aqueous barrier (Fig. 11). The endothelium is very thin and porous compared with the epithelium [189] and often has been ignored in the analysis, although mathematically it can be included as part of the lipid barrier. Diffusion through bilayer membranes of various structures has been modeled for some time [202] and adapted to ophthalmic applications more recently [203,204]. For a series of molecules of similar size, it was shown that the permeability increases with octa-nol/water distribution (or partition) coefficient until a plateau is reached. Modeling of this type of data has led to the earlier statement that drugs need to be both... 

The determination of the evolution of the permeability of these rocks during acidizing is necessary when attempting to predict the evolution of the skin (Equation 2). Previous studies (6) have tried to model the shift of the pore size distribution due to acid attack. Then, permeability profiles were computed by integrating the contributions to the overall flow of each of the rock pores, all over the considered volume of rock. The main limitation of this method lies in the disregarding of the spatial correlation between rock pores. 

Also, it seems that most of these properties are interdependent. For example, deaeration and permeability (Mainwaring and Reed, 1987) and perhaps the bulk density ratio (Jones and Mills, 1989) seem to provide an adequate mechanism to detect changes in material performance due to different particle size distribution, density and/or shape. However, possibly the greatest disadvantage or limitation of these empirical techniques is the need to standardize the experimental apparatus and techniques. For exam-... 

Recovery of DNAPL is a very slow process that is alfected by those factors encountered with LNAPL (i.e., relative permeability, viscosity, residual hydrocarbon pool distribution, site-specific factors, etc ). Dissolution of a DNAPL pool is dependent upon the vertical dispersivity, groundwater velocity, solubility, and pool dimension. Dispersivities for chamolid solvent are estimated for a medium to coarse sand under laboratory conditions on the order of 1(L3 to 1(H m. Thus, limited dispersion at typical groundwater velocities is anticipated to be slow and may take up to decades... 

As a result, these membranes suffer two deficiencies low flux rate due to the low porosity (i.e., limited permeability) and high fouling rate due to the asymmetric pore-size distribution having small pores on the surface [113]. 

The overall gain of the multiphase mixture model approach above is that the two-phase flow is still considered, but the simulations have only to solve pseudo-one-phase equations. Problems can arise if the equations are not averaged correctly. Also, the pseudo-one-phase treatment may not allow for pore-size distribution and mixed wettability effects to be considered. Furthermore, the multiphase mixture model predicts much lower saturations than those of Natarajan and Nguyen - and Weber and Newman even though the limiting current densities are comparable. However, without good experimental data on relative permeabilities and the like, one cannot say which approach is more valid. 

---