398
van Rossum and de Bie
Response to Commentary J. M . van R o s s u m 1 a n d J. E. G. M . de B i e 1
Received March 20, 1989--Final April 11, 1989
The commentary of Michael Weiss certainly emphasizes some of the points we attempted to make. Some of his remarks, however, require a correction. Pharmacokinetics is dominated by a point attractor so that measurements of only a single variable provides a reasonable insight into the behavior of the system. In addition, for most drugs linearity holds. Consequently pharmacokinetics is rather simple. Our approach is based on linear systems dynamics as generally applied in control system engineering. Essential is a realistic description of the subsystems according to common knowledge of circulation physiology (blood flows, transit times, distributions, and extraction ratios). Since the animal body consists of the pulmonary circulation and the systemic circulation, recirculation is very important for overall drug transport. As reference points for input and output we have taken the vena cava as the entrance of the pulmonary circulation and the aorta as the entrance of the systemic circulation (see Fig. 1). The overall transport function, being a density function of residence times, depends on the choice of the reference points in the circulation. In the majority of drug applications (oral, skin, im, etc.) drug transport converges to the vena cava, so that the vena cava seems to be the logical input reference site. Likewise blood sampling is done in the arm vein, which directly relates to the aorta. The aorta therefore seems the logical reference output point. If other reference points in the circulation are taken, slightly different system equations evolve. Since the blood circulation converges at the vena cava and the aorta, only these sites are considered, leading to four possibilities, each with a different system equation. These possibilities are given in the Fig. 2 with their corresponding systems equation. The first possibility is our own choice and the fourth is the reverse in which the aorta is the input site and the vena cava the output site. As the transport function is slightly different in the four cases, so is the M R T or mean time of that transport function. How the M R T ' s depend on the mean transit times of the circulation is given in Table I.
~Department of Pharmacology,Universityof Nijmegen Nijmegen, The Netherlands.
Response to Commentary
399
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In the experimental situation one deals with an application site (gastrointestinal tract, etc.) and an observation site (peripheral vein) so that the mean time as calculated from the concentration curve also includes the mean time o f the dosage input, the mean absorption time, and the mean observation time. For these and other reasons we have assigned T A U C / A U C = M C T as the mean time as calculated from the measured concentration curve at some observation site. The M C T equals M R T only when the input is given as a Dirac-delta pulse at the assigned input site (vena cava), while the output is measured at the output site (aorta). The basic system parameters are the MTT, the CO, and the extraction ratio. The other parameters are in fact derived parameters. The volume of
Table I. Dependence of M R T s on Mean Transit Times of the Circulation Input V. cava V. cave proximal
Output
MR T ~
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TH+MTT. (1-E)/E MTT- ( 1 - E ) / E
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~TH and TH are the mean transit times of the pulmonary and systemic circulation, M T T = TH + TF and E is the extraction ratio.
400
van Rossum and de Bie
distribution is by definition: Vss = C O x M T T . Since open-loop studies are not possible, only an approximation of Vss can be obtained from overall measurements of the blood concentration at some observation site. Finally, we fully agree with Michael Weiss that the compartment approach in pharmacokinetics should give way to pragmatic studies based on systems dynamics of the circulation.
