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Retention and Excretion Kinetics of Chemical Agents

Jerzy K. Piotrowski

10.1002/cphy.cp090124

Source: Supplement 26: Handbook of Physiology, Reactions to Environmental Agents

Originally published: 1977

Published online: January 2011

Full Article on Wiley Online Library



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 7
Figure 2. Figure 2.

Basic kinetic models (see Fig. 1). 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 7
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 7
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 2
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 10); curve II, derivation of a modified retention function (Equation 18).

From Bolanowska and Piotrowski 2
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 8
Figure 8. Figure 8.

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

From Piotrowski 7
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 7
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 3


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 7


Figure 2.

Basic kinetic models (see Fig. 1). 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 7


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 7


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 2


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 10); curve II, derivation of a modified retention function (Equation 18).

From Bolanowska and Piotrowski 2


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 8


Figure 8.

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

From Piotrowski 7


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 7


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 3
References
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Article Title: Retention and Excretion Kinetics of Chemical Agents
 

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