From piecewise to full physiologic pharmacokinetic modeling: applied to thiopental disposition in the rat

Physiologically based pharmacokinetic modeling procedures employ anatomical tissue weight, blood flow, and steady tissue/blood partition data, often obtained from different sources, to construct a system of differential equations that predict blood and tissue concentrations. Because the system of equations and the number of variables optimized is considerable, physiologic modeling frequently remains a simulation activity where fits to the data are adjusted by eye rather than with a computer-driven optimization algorithm. We propose a new approach to physiological modeling in which we characterize drug disposition in each tissue separately using constrained numerical deconvolution. This technique takes advantage of the fact that the drug concentration time course, CT(t), in a given tissue can be described as the convolution of an input function with the unit disposition function (UDFT) of the drug in the tissue, (i.e., CT(t) = (Ca(t)QT)*UDFT(t) where Ca(t) is the arterial concentration, Q tau is the tissue blood flow and * is the convolution operator). The obtained tissue until disposition function (UDF) for each tissue describes the theoretical disposition of a unit amount of drug infected into the tissue in the absence of recirculation. From the UDF, a parametric model for the intratissue disposition of each tissue can be postulated. Using as input the product of arterial concentration and blood flow, this submodel is fit separately utilizing standard nonlinear regression programs. In a separate step, the entire body is characterized by reassembly of the individuals submodels. Unlike classical physiologic modeling the fit for a given tissue is not dependent on the estimates obtained for other tissues in the model. Additionally, because this method permits examination of individual UDFs, appropriate submodel selection is driven by relevant information. This paper reports our experience with a piecewise modeling approach for thiopental disposition in the rat.