Permeability coefficient modeling

Physiologically Based Phamiacokinetic (PBPK) Model—Comprised of a series of compartments representing organs or tissue groups with realistic weights and blood flows. These models require a variety of physiological information tissue volumes, blood flow rates to tissues, cardiac output, alveolar ventilation rates and, possibly membrane permeabilities. The models also utilize biochemical information such as air/blood partition coefficients, and metabolic parameters. PBPK models are also called biologically based tissue dosimetry models. 

Mathai and Singh have estimated the permeability coefficient P, using the formula P = kD where k is the partition coefficient and D is the diffusivity. They have used both parallel and series models to calculate P. The experimental values are always greater than measured values. The poor agreement between the experimental and calculated values is attributed to the polar-polar interaction between the epoxy group and nitrile group. 

While the model helps us understand the chemical structure dependencies of skin permeability, it isn t all that useful for calculating permeability coefficients because of the many iffy assumptions it contains. A different tack has to be taken to gain a sense of the limits, especially the upper limit, of cutaneous drug delivery. There is no lower limit. Even proteins penetrate intact skin to some extent. Some idea of the upper... 

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... 

Using regression analysis on a data set of about 50 different molecules, it was found that a. = —4.4,8 = —0.5, Df = 12 cm2/s, and =2.5x 10 5 cm2/s [192], A graphic representation of the effect of relative molecular mass (Mr) and distribution coefficient on corneal permeability is shown in Fig. 13. One observes a rapid reduction in permeability coefficient with decreasing P and increasing Mr. The addition of pores to the model, a mathematical construct, is necessary to account for permeability of polar molecules, such as mannitol and cromolyn. These would also be required for correlating effects of compounds, such as benzalkonium chloride, which may compromise the... 

The rough brush stroke agreement between model and experiment is illustrated by the results shown in Fig. 14, for which the correspondences of theoretical with experimental permeability coefficients for the compounds listed in Table 2, (3-adrenegic blockers studied by Lee et al. [207,208] and Schoenwald and Huang [191], are plotted. The calculated values utilized the physical model with pores [205]. Characteristic of... 

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. 

The initial conditions are CD = CD(0) at t = 0 and CR = 0 at t = 0. Efforts to obtain analytical solutions are tedious and unnecessary. By applying the change in concentrations (or mass) in the donor and receiver solutions with time to the Laplace transforms of Eqs. (140) and (141), the inverse of the simultaneous transformed equations can be numerically calculated with appropriate software for best estimates of a, (3, and y. It is implicit here that P Pap, Pbh and Ke are functions of protein binding. Upon application of the transmonolayer flux model to the PNU-78,517 data in Figure 32, the effective permeability coefficients from the disappearance and appearance kinetics points of view are in good quantitative agreement with the permeability coefficients determined from independent studies involving uptake kinetics by MDCK cell monolayers cultured on a flat dish... 

Instead of using the oral bioavailability of a drug, one can attempt to correlate PM values with permeability coefficients generated from in situ perfused intestinal preparations. Here, one eliminates the complexities of liver metabolism, clearance, and formulation variables. Recently, this type of in vitro-in situ correlation has been conducted using the model peptides (described previously in Section V.B.2). The permeabilities of these model peptides were determined using a perfused rat intestinal preparation which involved cannulation of the mesenteric vein (Kim et al., 1993). With this preparation, it was possible to measure both the disappearance of the peptides from the intestinal perfusate and the appearance of the peptides in the mesenteric vein. Thus, clearance values (CLapp) could be calculated for each peptide. Knowing the effective surface area of the perfused rat ileum, the CLapp values could be converted to permeability coefficients (P). When the permeability coefficients of the model peptides were plotted as a function of the lipophilicity of the peptides, as measured by partition coefficients in octanol-water, a poor correlation (r2 = 0.02) was observed. A better correlation was observed between the permeabilities of these peptides and the number of potential hydrogen bonds the peptide can make with water (r2 = 0.56,... 

Figure 18 Relationship between permeability coefficients for various model drugs in a series of hydrated benzyl ester membranes of various degrees of esterification (100%, 75%, 50%) and reciprocal hydration. (Reprinted with permission from Ref. 58.)... 

Only a subset of the parameter values in the O Flaherfy model require inputs from the user to simulate blood and tissue lead concentrations. Lead-related parameters for which values can be entered into the model include fractional absorption from the gastrointestinal tract partition coefficients for lead in nonbone tissues and in the surface region of bone maximum capacity and half-saturation concentration for capacity-limited binding in the erythrocyte elimination clearance fractional clearance of lead from plasma into forming bone and the restricted permeability coefficients for lead diffusion within bone, from plasma into bone, and from bone into plasma (O Flaherty 1991a). 

Fig. 4.1. Relationship between the absorbed vivo perfusion of the human jejunum (B) (data fraction (FA) of structurally diverse sets of compiled from publications by Lennernas orally administered drugs and permeability laboratory [63, 115]). Sigmoidal relationships coefficients obtained in Caco-2 cell monolayers were obtained between FA and the (A) (data compiled from publications by permeability coefficients in both models.

In our own studies to establish an in-house correlation between Caco-2 permeability and extent of drug absorption in humans, a set of 25 model drugs was used (Table 5.1). The importance of concentration and pH conditions were investigated and transport was studied both in apical to basolateral (absorptive) and basolateral to apical (secretory) directions. The apparent permeability coefficients were determined at concentrations of 10, 50, and 500 pM, and at two different settings of apical/basolateral pH values 6.5/7.4 and 7.4/7.4. The marker compounds represented a good diversity in molecular structure and transport properties and covered a range of low (<20%), moderate (20-80%) and high (>80%) extent of absorption in humans (Tab. 5.1). 

From an industrial perspective, quantitative knowledge of the existence of different transporters within the cellular system used in screening procedures is of major importance as it can influence both the predictive value of the permeability coefficients and interpretation of the results. In addition, information on species differences or similarities or discrepancies between cell culture models and animals now provide an important basis for the scaling of data during the early phases of drug discovery for animals or humans [48]. 

It was postulated that the aqueous pores are available to all molecular species, both ionic and non-ionic, while the lipoidal pathway is accessible only to un-ionised species. In addition, Ho and co-workers introduced the concept of the aqueous boundary layer (ABL) [9, 10], The ABL is considered a stagnant water layer adjacent to the apical membrane surface that is created by incomplete mixing of luminal contents near the intestinal cell surface. The influence of drug structure on permeability in these domains will be different for example ABL permeability (Paq) is inversely related to solute size, whereas membrane permeability (Pm) is dependent on both size and charge. Using this model, the apparent permeability coefficient (Papp) through the biomembrane may therefore be expressed as a function of the resistance of the ABL and... 

Keywords Skin permeability Percutaneous absorption Skin penetration Mathematical model Quantitative structure-activity relationships Permeability coefficient Human skin... 

For some compounds in the Wilschut database more than one permeability coefficient was gathered from literature. In some cases, the differences in kp were greater than one log unit underlining the interlaboratory variations of such measurements. For the development of a new QSPR model one may now either choose one representative data point for each molecule or combine the multiple data points in a reasonable way. In some cases authors even employed all the available data for a single compound. Apart from the permeability data, the data on the partition coefficient and even on the molecular weight may vary from one report to another. Differences in the partition coefficient are easily explained Some collections list experimentally determined values which depend on the experimental procedure employed... 

The first QSPR models for skin tried to establish linear relationships between the descriptors and the permeability coefficient. In many cases validation of these models using, for example, external data sets was not performed. Authors of more recent models took advantage of the progress in statistical methods and used nonlinear relationships between descriptors and predicted permeability and often tried to assess their predictive quality using some validation method. 

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