Institute of Fundamental Technological Research

The main interest of pharmacokinetics is the study of the fate of drugs in the living organism. This work proposes the system of the conservation laws that describes time-dependent concentrations of a drug, after a single intravenous administration. Compared with others, the proposed model considers both free and protein-bound drug concentrations at the same time. Plasma protein binding captured in the model enters the nonlinearity arising from the Guldberg-Waage law. According to our best knowledge, the analytical solution for our system does not exist. Our model allows the calculation of the free and bound-drug protein concentrations at any time point and at any dose after single intravenous bolus dose administration. In order to compare the empirical with simulated data, a numerical approach has been proposed. On the basis of published experimental data the model validation has been carried out. The goodness of fit was satisfactory (R2 = 0.99) and the experimental and simulated AUC (area under the curve) values, as the measure of the bioavailability of drug, were similar (150 M/hxh−1). The preliminary assessment of the model credibility was positive and encouraged further studies.

Evolution equations, non-linear model, drug protein binding

It is commonly accepted that the existence of entropy imposes restrictions on the constutive functions in the Navier-Stokes-Fourier equations. In the paper: S. Piekarski, „On the Navier-Stokes equation for water” (Archives of Acoustics, 31, 2, 265-271, 2006) it has been shown that if the energy per unit mass is a function of the temperature T only, then the pressure p is an arbitrary function of the density ρ multiplied by the temperature T. Now the general form of the relations between the energy density and the pressure is given (both quantities are understood as functions of the mass density and the temperature). These relations can be approximated in different ways and different approximations suggest different classifications of dense fluids (some of them are similar to the virial expansions).

Gibbs identity, thermodynamics