Absorption and Distribution of Toxicants
5.7 TOXICOKINETICS
The explanation of the pharmacokinetics or toxicokinetics involved in absorption, distribution, and elimination processes is a highly specialized branch of toxicology, and is beyond the scope of this chapter. However, our focus here is to introduce a few basic concepts that are related to the several transport rate processes that have been described earlier in this chapter. Toxicokinetics is an extension of pharmaco- kinetics in that these studies are conducted at higher doses than pharmacokinetic studies, and the principles of pharmacokinetics are applied to xenobiotics. In addi- tion, these studies are essential to provide information on the fate of the xenobiotic following exposure by a defi ne route . This information is essential if one is to ade- quately interpret the dose – response relationship in the risk assessment process.
In recent years, these toxicokinetic data from laboratory animals are utilized in physiologically based pharmacokinetic (PBPK) models to help extrapolations to low - dose exposures in humans. The ultimate aim in all of these analyses is to provide an estimate of tissue concentrations at the target site associated with the toxicity.
Immediately on entering the body, a chemical begins changing location, concen- tration, or chemical identity. It may be transported independently by several com- ponents of the circulatory system, absorbed by various tissues, or stored; the chemical may effect an action, be detoxifi ed, or be activated; the parent compound or its metabolite(s) may react with body constituents, be stored, or be eliminated — to name some of the more important actions. Each of these processes may be
TOXICOKINETICS 109
described by rate constants similar to those described earlier in our discussion about fi rst - order rate processes which are associated with toxicant absorption, distribu- tion, and elimination that are occurring simultaneously. Thus, at no time is the situ- ation stable but is constantly changing as indicated in Figure 5.11 .
It should be noted however, that as the toxicant is being absorbed and distributed throughout the body, it is being simultaneously eliminated by various metabolism and/or excretion mechanisms which will be discussed in more detail in future chap- ters. However, one should mention here that an important pharmacokinetic param- eter known as clearance (Cl) can be used to quantitatively assess elimination of a toxicant. Clearance is defi ned as the rate of toxicant excreted relative to its plasma concentration, C p :
Cl=Rate of Toxicant ExcretionCp
The rate of excretion is really the administered dose times the fractional elimina- tion rate constant K el described earlier. Therefore, we can express the above equa- tion in terms of K el and administered dose as well as V d :
Cl=KeliDoseCp =Keli
(
VdiCp)
Cp=KeliVdIn physiological terms, we can also defi ne clearance as the volume of blood cleared of the toxicant by an organ or body per unit time. Therefore, as the
Metabolism to More Toxic Metabolites
Metabolism to Less Toxic Metabolites
Metabolism to Conjugation
Products
Interaction with Macromolecules (Proteins, DNA, RNA, Receptors, etc.)
Exposure
Excretion
Toxic Effects
(Genetic, Carcinogenic, Reproductive, Immunologic, etc.)
Turnover and Repair Distribution
Distribution to Body Absorption at Portals of Entry
Figure 5.11 Sequence of events following exposure of an animal to exogenous chemicals.
110 ABSORPTION AND DISTRIBUTION OF TOXICANTS
equations above indicate, the body clearance of a toxicant is expressed in units of volume per unit time (e.g., liter/hour), and can be derived if we know the V d of the toxicant and fractional rate constant. In many instances, this can only be derived by appropriate pharmacokinetic analysis of a given data set following blood or urine sample collection and appropriate chemical analyses to determine toxicant concen- trations in either of these biological matrices.
Each of the processes discussed thus far, absorption, distribution, and elimina- tion, can be described as a rate process. In general, these are assumed to be fi rst - order processes in which the rate of transfer at any time is proportional to the amount of drug in the body at that time. Recall that the rate of transport ( dC / dt ) is proportional to toxicant concentration ( C ) or stated mathematically:
dC dt=KC
where K is the rate constant (fraction per unit time). Many pharmacokinetic analy- ses of a chemical are based primarily on toxicant concentrations in blood or urine samples. It is often assumed in these analyses that the rate of change of toxicant concentration in blood refl ects quantitatively the change in toxicant concentration throughout the body (fi rst - order principles). Because of the elimination/clearance process which is also assumed to be a fi rst - order rate process, the above rate equa- tion now needs a negative sign. This is really a decaying process that is observed as a decline of toxicant concentration in blood or urine after IV administration. The IV route is preferred in these initial analyses because there is no absorption phase, but only chemical depletion phase. However, one cannot measure infi nitesimal change of C or time, t ; therefore there needs to be integration after rearrangement of the above equation:
−dC C=kdt becomes
∫
−dC C=k dt∫
or expressed as:
C=C e0 −kt
where e is the base of the natural logarithm, and we can remove e by taking the ln of both sides:
lnCt=lnC0−kt.
Please note that K is the slope of the straight line for a semilog plot of toxicant concentration versus time (Figure 5.12 ), and in the above equation, it is the elimina- tion rate constant that is related to half - life of the toxicant described earlier in this chapter. The derived C 0 can now be used to calculate the V d of the toxicant as follows:
Vd=Dose C0.
However, toxicokinetic data for many toxicants do not always provide a straight line when plotted as described above, and more complicated equations with more than one exponential term with rate constants may be necessary to mathematically describe the concentration - time profi le. These numerous rate constants are indica- tive of chemical transport between various compartments in the body and not
TOXICOKINETICS 111
Ka
Kel
(a) (b)
Central
Time lnCp
Slope = −Kel Cp0
Figure 5.12 (a) Semilog plot of plasma concentration ( C p ) versus time. Cpo is the intercept on the y - axis, and K el is the elimination rate constant. (b) Single compartment model with rate constants for absorption, K a and for elimination, K el .
a single central compartment as suggested in the simple equation and semilog plot described above in Figure 5.12 . In some instances, the data may fi t to a bi - exponential concentration - time profi le Figure 5.13 , and the equation to describe this model is:
C=Ae−αt+Be−βt
In other instances, complex profi les may require a three - or multi - exponential concentration - time profi le (Figure 5.14 ), and the equation to describe the former is:
C=Ae−αt+Be−βt+Ce−γt
In the physiological sense, one can divide the body into “ compartments ” that may represent discrete parts of the whole — blood, liver, urine, and so on — or the math- ematical model describing the process may be a composite representing the pooling of parts of tissues involved in distribution and bioactivation. Usually, pharmacoki- netic compartments have no anatomical or physiological identity; they represent all locations within the body that have similar characteristics relative to the transport
(a) (b)
Central (1)
Peripheral (2) Time
lnCp
Cp0
K12 K21 Kel =K10 β=λ2
A2 =B A1 =A
α=λ1
Figure 5.13 (a) Semilog plot of plasma concentration for ( C p ) versus time representative of a two - compartment model. The curve can be broken down into an α or λ 1 distribution phase and β or λ 2 elimination phase. (b) Two - compartment model with transfer rate constants, K 12 and K 21 , and elimination rate constant, K el .
112 ABSORPTION AND DISTRIBUTION OF TOXICANTS
rates of the particular toxicant. Simple fi rst - order kinetics is usually accepted to describe individual rate processes for the toxicant after entry. The resolution of the model necessitates mathematical estimates (as a function of time) concerning the absorption, distribution, biotransformation, and excretion of the toxicant.
Drugs and toxicants with multi - exponential behavior depicted in Figure 5.14 require calculation of the various micro - constants. An alternative method involves using model - independent pharmacokinetic to arrive at relevant parameters. This would not be covered in any detail in this chapter, but very briefl y it involves deter- mination of AUC of the concentration - time profi les, and the emergence of micro- computers in recent years has greatly facilitated this approach.
In conclusion, pharmacokinetics is a study of the time course of absorption, distribution, and elimination of a chemical. We use pharmacokinetics as a tool to analyze plasma concentration time profi les after chemical exposure, and it is the derived rates and other parameters that refl ect the underlying physiological pro- cesses that determine the fate of the chemical. There are numerous software pack- ages available today to accomplish these analyses. The user should, however, be aware of the experimental conditions and time frame over which the data were collected and many of the assumptions embedded in the analyses. For example, many of the transport processes described in this chapter may not obey fi rst - order kinetics and thus may be nonlinear especially at toxicological doses. The reader is advised to consult other text for more detailed descriptions of these nonlinear interactions and data analyses.
BIBLIOGRAPHY AND SUGGESTED READING
Bloom , D. and W. Fawcett . Bloom and Fawcett: A Textbook of Histology . Philadelphia : Saunders , 1975 .
Bronaugh , R. and H. Maibach , eds. Percutaneous Absorption . New York : Marcel Dekker , 1989 .
(a) (b)
Time (h)
K12 K21
K31 K13 Kel= K10
λ1
λ2
λ1
λ2 λ3
0
0 5 10
10 100
20 40 60 80
100 10 1 0.1 0.01
Concentration (μg/mL)
2 1 3
Figure 5.14 (a) Semilog plot of plasma concentration for ( C p ) versus time representative of a three - or multicompartment model. The curve can be broken down into three phases, λ 1 , λ 2 , and λ 3 . (b) Three - compartment model with transfer rate constants, K 12 , K 21 , K 13 , K 31 , and elimination rate constant, K el . As these models can get more complicated; the α , β , and γ nomenclature may get replaced with λ n as indicated in the profi le.
SAMPLE QUESTIONS 113 Gilman , A. G. , T. W. Rall , A. S. Nies , eds. Goodman and Gilman ’ s The Pharmacological Basis
of Therapeutics , 8th ed. Elmsford, NY : Pergamon Press , 1990 .
Grandjean , P. , ed. Skin Penetration: Hazardous Chemicals at Work . Philadelphia : Taylor &
Francis , 1990 .
Ham , A.W. and D. H. Cormack . Histology , 8th ed . Philadelphia : Lippincott , 1979 .
Hodgson , E. and P. E. Levi , eds. Introduction to Biochemical Toxicology , 2nd ed. Norwalk, CT : Appleton & Lange , 1994 , p. 12 .
Krieger , R. , ed. Handbook of Pesticide Toxicology , 2nd ed . San Diego, CA : Academic Press , 2001 .
Maliwal , B. P. and F. E. Guthrie . Interactions of insecticides with human liopproteins . Chem. Biol. Interact. 35 : 177 – 188 , 1981 .
Moran , C. J. and W. H. Walker . The binding of salicylate to human serum . Biochem. Pharmacol.
17 : 153 – 156 , 1968 .
Rowland , M. and T. N. Tozer , eds. Clinical Pharmacokinetics: Concepts and Applications , 3rd ed. Philadelphia : Lea and Febiger , 1995 .
Schottelius , B. A. and D. D. Schottelius . Textbook of Physiology . St. Louis, MO : Mosby , 1973 . Shargel , L. and A. B. C. Yu , eds. Applied Biopharmaceutics and Pharmacokinetics , 4th ed.
Norwalk, CT : Appleton & Lange , 1999 .
Singer , S. J. and G. L. Nicolson . The fl uid mosaic model of the structure of cell membranes . Science 175 : 720 – 731 , 1972 .
Skalsky , H. L. and F. E Guthrie . Affi nities of parathion, DDT, dieldrin, and carbaryl for macromolecules in the blood of the rat and American cockroach and the competitive interaction of steroids . Pest. Biochem. Physiol. 7 : 289 – 296 , 1977 .
SAMPLE QUESTIONS
1. (a) In carrier - mediated transport, chemical transport can reach saturation.
(b) In passive diffusion, energy is usually expended in chemical transport.
(c) In general, a chemical is more readily absorbed across human skin than mouse skin.
(d) The unionized form of a chemical is more readily absorbed than the ionized form.
2. (a) In zero - order transport, the amount moved per unit time is constant.
(b) In fi rst - order transport, the fraction moved is dependent on dose.
(c) A chemical that binds extensively to plasma proteins will most likely have a high V d.
(d) A chemical with high lipid solubility most likely has a high V d .
(e) The half - life of any chemical can be increased by increasing the V d and/or decreasing its clearance.
3. Explain how signifi cant plasma protein binding can infl uence distribution of a toxicant in the body.
4. What are the differences between active and passive transport of toxicants?
5. Defi ne the term partition coeffi cient. How is it related to Fick ’ s law?
CHAPTER 6