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Retention and Excretion Kinetics of Chemical Agents

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Abstract

The sections in this article are:

1 Metabolic Models and Compartmental Analysis
1.1 Exponential Models
1.2 Reliability of Concepts Underlying Compartmental Analysis
1.3 Simplification of Exponential Models
1.4 Power Function Model
2 Kinetic Solutions for Various Patterns of Exposure
2.1 Single Instantaneous Exposure
2.2 Continuous Exposure
2.3 Interrupted Exposure Cycles
2.4 Accumulation of Chemicals
Figure 1. Figure 1.

Typical curves of elimination rate after single exposure to a chemical. I, one‐compartment model; II, metabolic model; III, two‐compartment open model. Ordinate, common logarithm (base 10) of concentration; abscissa, time after the dose.

From Piotrowski
Figure 2. Figure 2.

Basic kinetic models (see Fig. ). I, one‐compartment model; II, metabolic model; III, two‐compartment open model. A, rapid‐exchange compartment; B, slow‐exchange compartment; E, substance or metabolite in the excreta; M, metabolite in the body; k, and k5, coefficients of elimination.

From Piotrowski
Figure 3. Figure 3.

Kinetic models obtained by introducing parallel metabolic processes. A, rapid‐exchange compartment; B, slow‐exchange compartment; M, metabolite in the body; k1 and k5, coefficients of elimination.

From Piotrowski
Figure 4. Figure 4.

Tri‐term exponential function: excretion rate of 210Pb in rat urine and feces, expressed in fraction of dose per day. Ordinate (V), excretion rate; abscissa (t), time in days.

From Bolanowska and Piotrowski
Figure 5. Figure 5.

Excretion rate of lead in rats presented in log‐log scale. Ordinate (V), excretion rate in fraction of dose per day; abscissa (t), time in days. Curve I, statistical calculation from experimental data on excretion (Equation ); curve II, derivation of a modified retention function (Equation ).

From Bolanowska and Piotrowski
Figure 6. Figure 6.

Schematic presentation of continuous exposure (one‐compartment model), q, Constant rate of absorption; S, substance contained in the body; SE, substance excreted.

Figure 7. Figure 7.

Excretion rate of excess phenol as a function of time of exposure, expressed as a fraction of absorption rate of phenol. Mean values ± standard deviations. Dotted line, theoretical curve for k = 0.2 h−1.

From Piotrowski
Figure 8. Figure 8.

The principle of graphic summation assuming regular weekly periods free from exposure.

From Piotrowski
Figure 9. Figure 9.

Example of a moderate accumulation: daily excretion of p‐nitrophenol in subsequent days of experimental exposure, with a Sunday break. Ordinate (un/u1), excretion expressed in relation to that of first day of exposure; abscissa, time in days; solid line, theoretical curve obtained from kinetic calculations; dotted line, mean experimental data.

From Piotrowski
Figure 10. Figure 10.

Accumulation of lead in bones of rats after daily exposure to 210Pb, with Sunday breaks. Ordinate (R), units (daily dose) retained in whole skeleton; abscissa (t), time of observation in days; curve I, mean experimental data; curve II, theoretical curve calculated from kinetic data.

From Bolanowska and Piotrowski


Figure 1.

Typical curves of elimination rate after single exposure to a chemical. I, one‐compartment model; II, metabolic model; III, two‐compartment open model. Ordinate, common logarithm (base 10) of concentration; abscissa, time after the dose.

From Piotrowski


Figure 2.

Basic kinetic models (see Fig. ). I, one‐compartment model; II, metabolic model; III, two‐compartment open model. A, rapid‐exchange compartment; B, slow‐exchange compartment; E, substance or metabolite in the excreta; M, metabolite in the body; k, and k5, coefficients of elimination.

From Piotrowski


Figure 3.

Kinetic models obtained by introducing parallel metabolic processes. A, rapid‐exchange compartment; B, slow‐exchange compartment; M, metabolite in the body; k1 and k5, coefficients of elimination.

From Piotrowski


Figure 4.

Tri‐term exponential function: excretion rate of 210Pb in rat urine and feces, expressed in fraction of dose per day. Ordinate (V), excretion rate; abscissa (t), time in days.

From Bolanowska and Piotrowski


Figure 5.

Excretion rate of lead in rats presented in log‐log scale. Ordinate (V), excretion rate in fraction of dose per day; abscissa (t), time in days. Curve I, statistical calculation from experimental data on excretion (Equation ); curve II, derivation of a modified retention function (Equation ).

From Bolanowska and Piotrowski


Figure 6.

Schematic presentation of continuous exposure (one‐compartment model), q, Constant rate of absorption; S, substance contained in the body; SE, substance excreted.



Figure 7.

Excretion rate of excess phenol as a function of time of exposure, expressed as a fraction of absorption rate of phenol. Mean values ± standard deviations. Dotted line, theoretical curve for k = 0.2 h−1.

From Piotrowski


Figure 8.

The principle of graphic summation assuming regular weekly periods free from exposure.

From Piotrowski


Figure 9.

Example of a moderate accumulation: daily excretion of p‐nitrophenol in subsequent days of experimental exposure, with a Sunday break. Ordinate (un/u1), excretion expressed in relation to that of first day of exposure; abscissa, time in days; solid line, theoretical curve obtained from kinetic calculations; dotted line, mean experimental data.

From Piotrowski


Figure 10.

Accumulation of lead in bones of rats after daily exposure to 210Pb, with Sunday breaks. Ordinate (R), units (daily dose) retained in whole skeleton; abscissa (t), time of observation in days; curve I, mean experimental data; curve II, theoretical curve calculated from kinetic data.

From Bolanowska and Piotrowski
References
 1. Atkins, G. L. Multicompartment Models for Biological Systems. New York: Barnes & Noble (Methuen), 1969.
 2. Bolanowska, W., and J. Piotrowski. Kinetyka rozmieszczania i wydalania olowiu Pb‐210 u szczurów (II) [The kinetics of distribution and excretion of lead 210Pb in the rat (II)]. Med. Pracy 19: 133, 142, 1968.
 3. Bolanowska, W., and J. Piotrowski. Kinetyka rozmieszczania i wydalania olowiu (Pb‐210) u szczurów (III) [The kinetics of distribution and excretion of lead 210Pb in the rat (III)]. Med. Pracy 20: 494–503, 1969.
 4. Dutkiewicz, T., I. Balcerska, and B. Dutkiewicz. Dynamika rozmieszczania selenu w narzαdach i tkankach po podaniu dozylnym i dotchawiczym Na2SeO3 [Body distribution of selenium after intravenous and intratracheal administration of sodium selenite]. Bromatol. Chem. Toksykol. 4: 185–191, 1971.
 5. Golubev, A. A., E. I. Lublina, N. A. Tolokoncev, and W. A. Filov. Kolitshestvennaja Toksikologija [Quantitative Toxicology]. Leningrad; Meditsina, 1973, p. 89–158.
 6. Horiuchi, K. Lead in the environment and its effect on man in Japan. Osaka City Med. J. 16: 1–28, 1970.
 7. Piotrowski, J. The Application of Metabolic and Excretion kinetics to Problems of Industrial Toxicology. Washington, D. C.; U. S. Govt. Printing Office, 1971.
 8. Piotrowski, J. K. Evaluation of exposure to phenol: absorption of phenol vapour in the lungs and through the skin and excretion of phenol in urine. Brit. J. Ind. Med. 28: 172–178, 1971.
 9. Piscator, M., and B. Lind. Cadmium, zinc, copper and lead in human renal cortex, Arch. Environ. Health 24: 426–431, 1972.
 10. Reuning, R. H., R. A. Sams, and R. E. Rotari. Role of pharmacokinetics in drug dosage adjustment. J. Clin. Pharmacol. 13: 127–141, 1973.
 11. Sanders, S. M., Jr. Power functions relating excretion to body burden. Health Phys. 2: 295–307, 1960.
 12. Solomon, A. K. The kinetics of biological processes: special problems connected with the use of tracers. Advan. Biol. Med. Phys. 3: 65–80, 1953.

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How to Cite

Jerzy K. Piotrowski. Retention and Excretion Kinetics of Chemical Agents. Compr Physiol 2011, Supplement 26: Handbook of Physiology, Reactions to Environmental Agents: 389-396. First published in print 1977. doi: 10.1002/cphy.cp090124