Equilibrium dialysis, partitioning coefficient

Equilibrium dialysis is used in a number of examples to analyse the ratio of lipid-bound to free analyte. Kramer et al. (1998) described the use of equilibrium dialysis by separating the liposome suspension and the water phase by a semi-permeable membrane. The analyte is dissolved in the water compartment of the system and diffuses into the liposome compartment. If equilibrium is reached, the remaining concentration of the analyte in the water compartment is determined by means of a quantification method (mainly HPLC or LCMS, fluorescence techniques) and the partition coefficient is calculated. Kramer et al. (1997) used a radio tracer substance as analyte to quantify the compound in both compartments using liquid scintillation counting. 

Physicochemical parameters. Partition coefficients are the most common type of physicochemical parameter in a PBPK model. Values for these quantities can be measured through experimental means (e.g., equilibrating tissue homogenates in a vial with an atmosphere containing the test chemical [9,10], or from ultrafiltration/equilibrium dialysis studies for nonvolatile chemicals), or through the use of quantitative structure activity/property relationships (QSA(P)Rs) [11],... 

Once the structure of the PBPK model is formulated, the next step is specifying the model parameters. These can be classified into a chemical-independent set of parameters (such as physiological characteristics, tissue volumes, and blood flow rates) and a chemical-specific set (such as blood/tissue partition coefficients, and metabolic biotransformation parameters). Values for the chemical-independent parameters are usually obtained from the scientific literature and databases of physiological parameters. Specification of chemical-specific parameter values is generally more challenging. Values for one or more chemical-specific parameters may also be available in the literature and databases of biochemical and metabolic data. Values for parameters that are not expected to have substantial interspecies differences (e.g., tissue/blood partition coefficients) can be imputed based on parameter values in animals. Parameter values can also be estimated by conducting in vitro experiments with human tissue. Partitioning of a chemical between tissues can be obtained by vial equilibration or equilibrium dialysis studies, and metabolic parameters can be estimated from in vitro metabolic systems such as microsomal and isolated hepatocyte syterns. Parameters not available from the aforementioned sources can be estimated directly from in vivo data, as discussed in Section 43.4.5. 

Biochemical parameters such as tissue/blood partition coefficients can be obtained from in vitro experiments with vial equilibration (18) or equilibrium dialysis techniques (19). A less expensive process involves exploiting the similarities in physical characteristics of similar tissues in animals and humans and using in vitro animal data (20). Other, even more cost-effective techniques include extrapolation from experimentally determined octanol/water partition coefficients (21), or in sUico parameter estimation via techniques based on structure-property relationships (22, 23). 

Lin et al. derived an equation for blood flow-limited compartment partition coefficients based on in vitro equilibrium dialysis binding smdies of a diluted tissue homogenate. Assuming Langmuir-type drug-protein binding, and equality of unbound plasma and tissue drug concentration, the partition coefficient, R, is... 

Cuprophan membranes made from regenerated cellulose are frequently used in hemodialysis. Model this membrane as one consisting of cylindrical capillaries of radius 18 A. Determine the separation factors of the dialysis membrane for two solutes, urea and vitamin B12. The characteristic radii of urea and vitamin B12 are 2.8 A and 8.5 A, respectively. The diffusion coefficients of urea and vitamin B12 at infinite dilution in isotonic saline at 37 °C are 1.81 x 10 and 0.38 x 10" cm /s, respectively. Compare the result for the given pore size estimate with that obtained from the data of Colton et al (1971), namely 16 (based on effective diffusion coefficients without any consideration of equilibrium partition coefficients in their Figure 6). (Ans. 23.5.)... 

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