A whole-body physiologically based pharmacokinetic model incorporating dispersion concepts: short and long time characteristics.

In whole-body physiologically based pharmacokinetic (PBPK) models, each tissue or organ is frequently portrayed as a single well-mixed compartment with distribution, perfusion rate limited. However, single-pass profiles from isolated organ studies are more adequately described by models which display an intermediate degree of mixing. One such model is the dispersion model, which successfully describes the outflow profiles from the liver and the perfused hindlimb of many compounds, under a variety of conditions. A salient parameter of this model is the dispersion number, a dimensionless term, which characterizes the relative axial spreading of compound on transit through the organ. We have developed a whole-body PBPK model wherein the distribution of drug on transit through each organ is described by the dispersion model with closed boundary conditions incorporated. The model equations were numerically solved using finite differencing methods, in particular, the method of lines. An integrating routine suitable for solving stiff sets of equations was used. Physiological parameters, blood flows, and tissue volumes, were taken from the literature, as were the tissue dispersion numbers, which characterize the mixing properties of each tissue; where none could be found, the value was set as that for liver. On solution, tissue, venous and arterial blood concentration-time profiles are generated. The profiles exhibited both short and long time characteristics. Oscillations were observed in the venous and arterial profiles over the first 10 min of simulation for the rat. On scale-up to human, the effects were seen over a 30 min period. Longer time effects of tissue distribution involve buildup of drug in the large tissues of distribution: skeletal muscle, skin, and adipose. The extent of distribution in the large tissues was somewhat dependent on the magnitude of the dispersion number, the lower the dispersion number, the greater the extent of distribution after an intravenous bolus dose. The model has a distinct advantage over the well-stirred organ whole-body PBPK model in its ability to describe both short and long time characteristics.