Casaret and Dull Tox

7/23/2019 Casaret and Dull Tox

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Toxicokinetics is the quantitative study of the movement of an exogenous chemical from its

entry into the body, through its distribution to organs and tissues via the blood circulation, and to

its final disposition by way of biotransformation and excretion. The basic kinetic concepts for the

absorption, distribution, metabolism, and

excretion of chemicals in the body system initially came from the study of drug actions or

pharmacology; hence, this area of study is traditionally referred to as pharmacokinetics.

Toxicokinetics represents

extension of kinetic principles to the study of toxicology and encompasses applications ranging

from the study of adverse drug effects to investigations on how disposition kinetics of exogenous

chemicals derived from either natural or environmental sources (generally refer to as

xenobiotics) govern their deleterious effects on organisms including humans. The study of

toxicokinetics relies on mathematical description or modeling of the time course of toxicant

disposition in the whole organism. The classic approach to describing the kinetics of drugs

is to represent the body as a system of one or two compartments even though the compartments

do not have exact correspondence to anatomical structures or physiologic processes. These

empirical compartmental models are almost always developed to describe the kinetics of

toxicants in readily accessible body fluids (mainly blood)

or excreta (e.g., urine, stool, and breath). This approach is particularly suited for human studies,

which typically do not afford organ or tissue data. n such applications, extravasculardistribution, which

does not require detail elucidation, can be represented simply by lumped compartments. !n

alternate and newer approach, physiologically based toxicokinetic modeling attempts to portray

the body as an elaborate system of discrete tissue or organ compartments that are interconnected

via the circulatory system. "hysiologically based models are capable of describing a chemical#s

movements in body tissues or regions of toxicological interest. t also allows a priori predictions

of how changes in specific physiological processes affect the disposition kinetics of the toxicant

(e.g., changes in respiratory status on pulmonary absorption and exhalation of a volatile

compound) and the extrapolation of the kinetic model across animal species to humans.

t should be emphasi$ed that there is no inherent contradiction between the classic and

physiologic approaches. The choice of modeling approach depends on the application context,

the available


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data, and the intended utility of the resultant model. %lassic compartmental model, as will be

shown, requires assumptions that limit its application. n comparison, physiologic models can

predict tissue concentrations; however, it requires much more data input and often the values of

the required parameters cannot be estimated accurately

or precisely, which introduces uncertainty in its prediction. &e begin with a description of the

classic approach to toxicokinetic modeling, which offers an introduction to the basic kinetic

concepts for toxicant absorption, distribution, and elimination. This will be followed by a brief

review of the physiologic approach to toxicokinetic modeling that is intended to illustrate the

construction and application of these elaborate models.

CLASSIC TOXICOKINETICS

deally, quantification of xenobiotic concentration at the site oftoxic insult or in'ury would afford

the most direct information on exposureresponse relationship and dynamics of response over

time. erial sampling of relevant biological tissues following dosing can be cost*prohibitive

during in vivo studies in animals and is nearly impossible to perform in human exposure studies.

The most accessible and simplest means of gathering information on

absorption, distribution, metabolism, and elimination of a compound is to examine the time

course of blood or plasma toxicant concentration over time. f one assumes that the concentration

Figure 7-1. Compartmental toxicokinetic models.

ymbols for one*compartment model+ ka is the first*order absorption rate

constant, and kel is the first*order elimination rate constant. ymbols for twocompartment

model+ ka is the first*order absorption rate constant into the

central compartment (), k10 is the first*order elimination rate constant from

the central compartment (), k12 and k21 are the first*order rate constants for

distribution between central () and peripheral (-) compartment.

of a chemical in blood or plasma is in some describable dynamic equilibrium with its

concentrations in tissues, then changes in plasma toxicant concentration should reflect changes in

tissue toxicant concentrations and relatively simple kinetic models can adequately describe the


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behavior of that toxicant in the body system. %lassic toxicokinetic models typically consist of a

central compartment representing blood and tissues that the toxicant has ready access and

equilibration is achieved almost immediately following its introduction, along with one or more

peripheral compartments that represent tissues in slowequilibration with the toxicant in blood

(ig. /*). 0nce introduced into the central compartment, the toxicant distributes between central

and peripheral compartments.

1limination of the toxicant, through biotransformation and2or excretion, is usually assumed to

occur from the central compartment, which should comprise the rapidly perfused visceral organs

capabl of eliminating the toxicant (e.g., kidneys, lungs, and liver). The obvious advantage of

compartmental toxicokinetic models is that they do not require information on tissue physiology

or anatomic structure. These models are useful in predicting the toxicant concentrations in blood

at different doses, in establishing the time course of accumulation of the toxicant, either in its

parent form or as biotransformed products during continuous or episodic exposures, in defining

concentration response (vs. doseresponse) relationships, and in guiding the choice of effective

dose and design of dosing regimen in animal toxicity studies (3owland and To$er, 445).

One-Compartment Model

The most straightforward toxicokinetic assessment entails quantification of the blood or more

commonly plasma concentrations of a toxicant at several time points after a bolus intravenous

(iv) in'ection. 0ften, the data obtained fall on a straight line when they are plotted as the

logarithms of plasma concentrations versus time; the kinetics

of the toxicant is said to conform to a one*compartment model (ig. /*-). 6athematically, this

means that the decline in plasma concentration over time profile follows a simple exponential

pattern as represented by the following mathematical expressions+

C 7 C8 9 e:kel9t (/*)

or its logarithmic transform

ogC 7 ogC8 : kel 9 t

-.


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elimination rate constant with dimensions of reciprocal time (e.g., min: or hr:). The constant

-. or to eliminate 58> of the original body load. @y substituting C/C8 7 8.5 into

1quation (/*), we obtain

the following relationship between T/- and kel+


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T/- 7 8.?444> (exactly 44.->) elimination. Thus, given the elimination

T/- of a toxicant, the length of time it takes for near complete

washout of a toxicant after discontinuation of its exposure

can easily be estimated. !s will be seen in next section, the concept

of T/- is applicable to toxicants that exhibit multi*exponential

kinetics.

&e can infer from the mono*exponential decline of blood or

plasma concentration that the toxicant equilibrates very rapidly between

blood and the various tissues relative to the rate of elimination,

such that extravascular equilibration is achieved nearly instantaneously

and maintained thereafter. Bepiction of the body system

by a one*compartment model does not mean that the concentration

of the toxicant is the same throughout the body, but it does assume

that the changes that occur in the plasma concentration reflect proportional

changes in tissue toxicant concentrations (ig. /*- upper,

right panel). n other words, toxicant concentrations in tissues are

expected to decline with the same elimination rate constant or T/-

as in plasma.

Two-Compartment Model

!fter rapid iv administration of some toxicants, the semi*logarithmic

plot of plasma concentration versus time does not yield a straight line

but a curve that implies more than one dispositional phase (ig. /*-).

n these instances, it takes some time for the toxicant to be taken up

into certain tissue groupings, and to then reach an equilibration with


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the concentration in plasma; hence, a multi*compartmental model

is needed for the description of its kinetics in the body (ig. /*).

The concept of tissue groupings with distinct uptake and equilibration

rates of toxicant becomes apparent when we consider the

factors that govern the uptake of a lipid*soluble, organic toxicant.

Table /*- presents data on the volume and blood perfusion rate of

various organs and tissues in a standard si$e human. rom these

data and assuming reasonable partitioning ratios of a typical lipidsoluble,

organic compound in the various tissue types, we can estimate

the uptake equilibration half*times of the toxicant in each

organ or tissue region during constant, continuous exposure. The results

suggest that the tissues can be grouped into rapid*equilibrating

visceral organs, moderately slow*equilibrating lean body tissues

(mainly skeletal muscle), and very slow*equilibrating body fat; these


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visceral organs. or example, very rapid metabolism or excretion

at the visceral organs would limit distribution into the slow or very

slowtissue groupings. !lso, there are times when equilibration rates

of a toxicant into visceral organs overlaps with lean body tissues,

such that the distribution kinetics of a toxicant into these two tissue

groupings become indistinct with respect to the exponential

decline of plasma concentration, in which case two instead of three

tissue groupings may be observed. The concept of tissue groupings

with respect to uptake or washout kinetics serves to 'ustify the

seemingly simplistic, yet pragmatic, mathematical description of

extravascular distribution by the classic two* or three*compartment

models.

Table

"lasma concentration*time profile of a toxicant that exhibits

multi*compartmental kinetics can be characteri$ed by multiexponential

equations. or example, a two*compartment model can

be represented by the following bi*exponential equation.

C 7A 9 e:9t CB 9 e:9t (/*=)

whereA andB are coefficients in units of toxicant concentration,

and and are the respective exponential constants for the initial

and terminal phases in units of reciprocal time. The initial () phase

is often referred to as the distribution phase, and terminal () phase

as the post*distributional or elimination phase. The lower, middle

panel of ig. /*- shows a graphical resolution of the two exponential

phases from the plasma concentration*time curve. t should be noted

that the constant is the slope of the residual log linear plot and

not the initial slope of the decline in the observed plasma toxicant

concentration; that is, the initial rate of decline in plasma concentration

approximates, but is not exactly equal, the rate constant in


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1quation (/*=).

t should be noted that distribution into and out of the tissues

and elimination of the toxicant are ongoing at all times; that

is, elimination does occur during the DdistributionE phase, and

distribution between compartments is still ongoing during the

DeliminationE phase. !s illustrated in ig. /*


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concentration of gentamicin initially falls very quickly with a halflife

of around - hours; a slow terminal phase does not emerge until

serum concentration has fallen to less than 8> of initial concentration.

The terminal half*life of serum gentamicin is in the range

of = to / days. This protracted terminal half*life reflects the slow

turnover of gentamicin sequestered in the kidneys. n fact, repeated

administration of gentamicin leads to accumulation of gentamicin

in the kidneys, which is a risk factor for its nephrotoxicity. @ecause

of the complication arising from the interplay of distribution and

elimination kinetics, it has been recommended that multiphasic disposition

should be simply described as consisting of early and late or

rapid and slow phases; mechanistic labels of distribution and elimination

should be applied with some caution. astly, the initial phase

may last for only a few minutes or for hours. &hether multiphasic

kinetics becomes apparent depends to some extent on how often

and when the early blood samples are obtained, and on the relative

difference in the exponential rate constants between the early and

later phases. f the early phase of decline in toxicant concentration

is considerably more rapid than the later phase or phases, the timing

of blood sampling becomes critical in the ability to resolving two

or more phases of washout.

ometimes three or even four exponential terms are needed to

fit a curve to the plot of log C versus time. uch compounds are

viewed as displaying characteristics of three* or four*compartment

open models. The principles underlying such models are the same

as those applied to the two*compartment open model, but the mathematics

is more complex and beyond the scope of this chapter.

Apparent Volume o !"#tr"but"on

or a one*compartment model, a toxicant is assumed to equilibrate

between plasma and tissues immediately following its entry into the

systemic circulation. Thus, a consistent relationship should exist


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between plasma concentration and the amount of toxicant in each

tissue and, by extension, to the entire amount in the body or body

burden. The apparent volume of distribution (Vd) is defined as the

proportionality constant that relates the total amount of the toxicant

in the body to its concentration in plasma, and typically has units

of liters or liters per kilogram of body weight (3owland and To$er,

445). Vd is the apparent fluid space into which an amount of toxicant

is distributed in the body to result in a given plasma concentration.

!s an illustration, envision the body as a tank containing an unknown

volume () of well mixed water. f a known amount (mg) of dye

is placed into the water, the volume of that water can be calculated

indirectly by determining the dye concentration (mg2) that resulted

after the dye has equilibrated in the tank; that is, by dividing the

amount of dye added to the tank by the resultant concentration of

the dye inwater. !nalogously, the apparent volume of distribution of

a toxicant in the body is determined after iv bolus administration, and

is mathematically defined as the quotient of the amount of chemical

in the body and its plasma concentration. Vd is calculated as

Vd 7Doseiv

9AUCG

8

(/*5)

whereDoseiv is the intravenous dose or known amount of chemical

in body at time $ero; is the elimination rate constant; andAUCG

8

is the area under the toxicant concentration versus time curve from

time $ero to infinity.AUCG

8 is estimated by numerical methods, the


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most common one being the trape$oidal rule (Hibaldi and "errier,

4A-). The product, 9AUCG

8 , in unit of concentration, is the theoretical

concentration of toxicant in plasma if dynamic equilibration

were achievable immediately after introduction of the toxicant into

the systemic circulation. or a one*compartment model, immediate

equilibration of the toxicant between plasma and tissues after an

acute exposure does hold true, in which case Vd can be calculated

by a simpler and more intuitive equation

Vd 7Doseiv

C8

(/*?)

where C8 is the concentration of toxicant in plasma at time $ero.

C8 is determined by extrapolating the plasma disappearance curve

after iv in'ection to the $ero time point (ig. /*-).

or the more complex multi*compartmental models, Vd is calculated

according to 1quation (/*5) that involves the computation

of area under the toxicant concentration*time curve. 6oreover, the

concept of an overall apparent volume of distribution is strictly applicable

to the terminal exponential phase when equilibration of the

toxicant between plasma and all tissue sites are attained. This has

led some investigators to refer to the apparent volumes of distribution

calculated by 1quation (/*5) as V (for a two*compartment

model) or V$ (for a general multi*compartmental model); the subscript

designation refers to the terminal exponential phase (Hibaldi

and "errier, 4A-). t should also be noted that when 1quation (/*?)

is applied to the situation of a multi*compartmental model, the resultant

volume is the apparent volume of the central compartment,

often times referred to as Vc. @y definition, Vc is the proportionality

constant that relates the total amount of the toxicant in the central

compartment to its concentration in plasma. t has limited utility;


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for example, it can be used to calculate an iv dose of the toxicant to

target an initial plasma concentration.

Vd is appropriately called the apparent volume of distribution

because it does not correspond to any real anatomical volumes. The

magnitude of the Vd term is toxicant*specific and represents the extent

of distribution of toxicant out of plasma and into extravascular

sites (Table /* 2kg). The

mechanisms of tissue sequestration include partitioning of a toxicant

into tissue fat, high affinity binding to tissue proteins, trapping

in speciali$ed organelles (e.g., pJ trapping of amine compounds in

acidic lyso$omes), and concentrative uptake by active transporters.

n fact, the equation below is an alternate form of 1quation (/*/),

which features the interplay of binding to plasma and tissue proteins


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in determining the partitioning of a toxicant in that only free

or unbound drug can freely diffuse across membrane and cellular

barriers.

Vd 7 Vp C

I

fup

fut,i

9 Vt,i (/*A)

wherefup is the unbound fraction of toxicant in plasma (Table /*


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removal of a toxicant from the body. @y definition, clearance has the

units of flow (e.g., m2min or 2hr). n the classic compartmental

context, clearance is portrayed as the apparent volume containing

the toxicant that is cleared per unit of time. !fter intravenous bolus

administration, total body clearance (Cl) is calculated by

Cl 7Doseiv

AUCG

8

(/*8)

%learance can also be calculated if the volume of distribution and

elimination rate constants are known; that is, Cl 7 Vd 9 kel for a

one*compartment model and Cl 7 Vd 9 for a two*compartment

model. t should be noted that the relationship is a mathematical

derivation and does not imply that clearance is dependent upon the

distribution volume (see later section for further commenting). !

clearance of 88 m2min can be visuali$ed as having a 88 m

of blood or plasma completely cleared of toxicant in each minute

during circulation.

The biological significance of total body clearance is better

appreciated when it is recogni$ed that it is the sum of clearances by

individual eliminating organs (i.e., organ clearances)+

Cl 7 Clr C Clh C Clp CK K K (/*)

where Clr depicts renal, Clh hepatic, and Clp pulmonary clearance.

1ach organ clearance is in turn determined by blood perfusion flow

through the organ and the fraction of toxicant in the arterial inflow

that is irreversibly removed, i.e., the extraction fraction (Ei).Larious

organ clearance models have been developed to provide quantitative

description of clearance that is related to blood perfusion flow

(Qi), free fraction in blood (fub), and intrinsic clearance (Clint,i)

(&ilkinson, 4A/). or example, for hepatic clearance (Clh), if the

delivery of the toxicant to its intracellular site of removal is ratelimited


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by liver blood flow (Qh) and the toxicant is assumed to have

equal, ready access to all the hepatocytes within the liver (i.e., the

so*called well*stirred model)+

Clh 7 Qh 9Eh 7 Qh 9fub 9 Clint,h

fub 9 Clint,h C Qh

(/*-)

where Clint,h is the hepatic intrinsic clearance that embodies a combination

of factors that determines the access of the toxicant to the

en$ymatic sites (e.g., plasma protein binding and sinusoidal membrane

transport) and the biochemical efficiency of the metaboli$ing

en$ymes (e.g., Vmax

K6

for an en$yme obeying 6ichaelis kinetics).

1quation (/*-) dictates that hepatic clearance of a toxicant from

the blood is bounded by either liver blood flow or intrinsic clearance

(i.e.,fub 9 Clint,h). Mote that whenfub 9 Clint,h is very much

higher than Qh,Eh approaches unity (i.e., near complete extraction

during each passage of toxicant through the hepatic sinusoid

or high extraction) and Clh approaches Qh. "ut in another way,

hepatic clearance cannot exceed the hepatic blood flow rate even

if the maximum rate of metabolism in the liver is more rapid than

the rate of hepatic blood flow, because the rate of overall hepatic

clearance is limited by the delivery of the toxicant to the metabolic

en$ymes in the liver via the blood. !t the other extreme, when

fub 9 Clint,h is very much lower than Qh,Eh becomes quite small

(i.e., low extraction) and Clh nearly equalsfub 9 Clint,h n this instance,

the intrinsic clearance is relatively inefficient; hence, alteration

in liver blood flow would have little, if any, influence on liver

clearance of the toxicant. Thus, the concept of clearance is grounded

in the physiological and biochemical mechanisms of an eliminating

organ.


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4elat"on#."p o El"m"nat"on 3al-L"e

to Clearan*e and Volume

1limination half*life (T/-) is probably the most easily understood

pharmacokinetic concept and is an important parameter as it determines

the persistence of a toxicant following discontinuation of

exposure. !s will be seen in a later section, elimination half*life also

governs the rate of accumulation of a toxciant in the body during

continuous or repetitive exposure. 1limination half*life is dependent

upon both volume of distribution and clearance. T/- can be

calculated from Vd and Cl+

T/- 7 8.?4< 9 Vd

Cl

(/*


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8 after intravenous and extravascular dosing. @ecause

intravenous dosing assures full (88>) delivery of the dose into

the systemic circulation, the !N% ratio should equal the fraction

of extravascular dose absorbed and reaches the systemic circulation

in its intact form, and is called !oa"a!la!l!t# ($). n acute toxicokinetic

studies, bioavailability can be determined by using different

iv and non*iv doses according to the following equation, provided

that the toxicant does not display dose*dependent or saturable

kinetics.

$ 7

I

AUCnon*iv

Dosenon*iv

II

AUCiv

Doseiv

(/*=)

whereAUCnon*iv,AUCiv,Dosenon*iv, andDoseiv are the respective

area under the plasma concentration versus time curves and doses for

non*iv and iv administration. @ioavailabilities for various chemicals

range in value between 8 and . %omplete availability of chemical to

the systematic circulation is demonstrated by$ 7 . &hen$ < ,

less than 88> of the dose is able to reach the systemic circulation.

@ecause the concept of bioavailability is 'udged by how much of

the dose reaches the systemic circulation, it is often referred to as

systemic availability. ystemic availability is determined by how

well a toxicant is absorbed from its site of application and any

intervening processes that could remove or inactivate the toxicant

between its point of entry and the systemic circulation. pecifically,

systemic availability of an orally administered toxicant is governed


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by its absorption at the gastrointestinal barrier, metabolism within

the intestinal mucosa, and metabolism and biliary excretion during

its first transit through the liver. 6etabolic inactivation and excretion

of the toxicant at the intestinal mucosa and the liver prior to its

entry into the systemic circulation is called pre*systemic extraction

or first*pass effect. The following equation accounts for the action

of absorption and sequential first*pass extraction at the intestinal

mucosa and the liver as determinants of the bioavailability of a

toxicant taken orally+

$ 7fg 9 ( :Em) 9 ( :Eh) (/*5)

wherefg is the fraction of the applied dose that is released and

absorbed across the mucosal barrier along the entire length of the gut,

Em is the extent of loss due to metabolism within the gastrointestinal

mucosa, andEh is the loss due to metabolism or biliary excretion

during first*pass through the liver. Mote thatEh in this equation is

same as the hepatic extractionEh defined in 1quation (/*-), which

refers to hepatic extraction of a toxicant during recirculation. This

means that poor oral bioavailability of a chemical can be attributed to

multiple factors. The chemical may be absorbed to a limited extent

because of lowaqueous solubility preventing its effective dissolution

in the gastrointestinal fluid or poor permeability across the brushborder

membrane of the intestinal mucosa. 1xtensive degradation by

metabolic en$ymes residing at the intestinal mucosa and the liver

may also hinder entry of the chemical in its intact form into the

systemic circulation.

The rate of absorption of a toxicant via an extravascular route

of entry is another critical determinant of outcome, particularly in

acute exposure situations. !s shown in ig. /*5, slowing the absorption

rate of a toxicant, while maintaining the same extent of

absorption or bioavailability, leads to a delay in time to peak plasma

concentration (Tp) and a decrease in the maximum concentration


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(Cmax) (compare case - to case ). The converse is true; accelerating

absorption shortens Tp and increases Cmax. The dependence

of Tp and Cmax on absorption rate has obvious implication in the

speed of onset and maximum toxic effects following exposure to a

chemical. %ase < in ig. /*5 illustrates the peculiar situation when

the absorption rate is so much slower than the elimination rate (e.g.,

ka I kel for a one*compartment model). The terminal rate of decline

in plasma concentration reflects the absorption rate constant,

instead of the elimination rate constant; that is, the washout of toxicant

is rate*limited by slow absorption until the applied dose is

completely absorbed or removed, beyond which time the toxicant

remaining in the body will be cleared according the elimination

rate*constant. This means that continual absorption of a chemical

can affect the persistence of toxic effect following an acute

exposure, and that it is important to institute decontamination procedure

quickly after overdose or accidental exposure to a toxicant.

This is especially a consideration in occupational exposure via dermal

absorption following skin contact with permeable industrial

chemicals.

Metabol"te K"net"*#

The toxicity of a chemical is in some cases attributed to its biotransformation

product(s). Jence, the formation and subsequent

disposition kinetics of a toxic metabolite is of considerable interest.

!s expected, the plasma concentration of a metabolite rises as

the parent drug is transformed into the metabolite. 0nce formed,

the metabolite is sub'ect to further metabolism to a nontoxic byproduct

or undergoes excretion via the kidneys or bile; hence at

some point in time, the plasma metabolite concentration peaks and

falls thereafter. igure /*? illustrates the plasma concentration time

course of a primary metabolite in relation to its parent compound

under contrasting scenarios. The left panel shows the case when


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the elimination rate constant of the metabolite is much greater than


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first*order toxicokinetics are independent of dose. &hen plasma protein

binding or elimination mechanisms are saturated with increasing dose, pharmacokinetic

parameter estimates become dose*dependent. Vd may increase,

for example, when protein binding is saturated, allowing more free toxicant

to distribute into extravascular sites. %onversely, Vd may decrease with

increasing dose if tissue protein binding saturates. Then, chemical may redistribute

more freely back into plasma. &hen chemical concentrations exceed

the capacity for biotransformation by metabolic en$ymes, overall clearance

of the chemical decreases. These changes may or may not have effects on

T1/2 depending upon the magnitude and direction of changes in both Vd and

Cl.

the overall elimination rate constant of the parent compound (i.e.,

km I kp). The terminal decline of the metabolite parallels that of

the parent compound; the metabolite is cleared as quickly as it is

formed or its washout is rate*limited by conversion from the parent

compound. The right panel shows the opposite case when the elimination

rate constant of the metabolite is much lower than the overall

elimination rate constant of the parent compound (i.e., km I kp).

The slower terminal decline of the metabolite compared to the parent

compound simply reflects a longer elimination half*life of the

metabolite. t should also be noted that theAUCG

8 of the metabolite

relative to the parent compound is dependent on the partial clearance

of the parent drug to the metabolite and clearance of the derived

metabolite. ! biologically active metabolite assumes toxicological

significance when it is the ma'or metabolic product and is cleared

much less efficiently than the parent compound.

Saturat"on To/"*o5"net"*#

!s already mentioned, the distribution and elimination of most

chemicals occurs by first*order processes. Nnder first*order elimination

kinetics, the elimination rate constant, apparent volume of


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distribution, clearance and half*life are expected not to change with

increasing or decreasing dose (i.e., dose independent). !s a result, a

semi*logarithmic display of plasma concentration versus time over

a range of doses shows a set of parallel plots. urthermore, plasma

concentration at a given time or theAUCG

8 is strictly proportional

to dose; for example, a twofold change in dose results in an exact

twofold change in plasma concentration orAUCG

8 . Jowever,

for some toxicants, as the dose of a toxicant increases, its volume

of distribution and2or clearance may change, as shown in ig. /*/.

This is generally referred to as non*linear or dose*dependent kinetics.

@iotransformation, active transport processes, and protein binding

have finite capacities and can be saturated. or instance, most

metabolic en$ymes operate in accordance to 6ichaelis6enten kinetics

(Hibaldi and "errier, 4A-). !s the dose is escalated and

concentration of a toxicant at the site of metabolism approaches or

exceeds theK6 (substrate concentration at one*half Vmax, the maximum

metabolic capacity), the increase in rate of metabolism becomes

less than proportional to the dose and eventually approaches a

maximum at exceedingly high doses. The transition from first*order

to saturation kinetics is important in toxicology because it can lead

to prolonged persistence of a compound in the body after an acute

exposure and excessive accumulation during repeated exposures.

ome of the salient characteristics of nonlinear kinetics include the

following+ () the decline in the levels of the chemical in the body is

not exponential; (-)AUCG

8 is not proportional to the dose; (


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change in response with an increasing dose, starting at the dose at

which saturation effects become evident.

nhaled methanol provides an example of a chemical whose

metabolic clearance changes from first*order kinetics at low level

exposures to $ero*order kinetics at near toxic levels (@urbacher et al.,

-88=). igure /*A shows predicted blood methanol concentrationtime

profiles in female monkeys followed a -*hour controlled exposure

in an inhalation chamber at two levels of methanol vapor,

-88 ppm and =A88 ppm. @lood methanol kinetics at -88 ppm exposure

follows typical first*order kinetics. !t =A88 ppm, methanol

metabolism is fully saturated, such that the initial decline in blood

methanol following the -*hour exposure occurs at a constant rate

(i.e., a fixed decrease in concentration per unit time independent

of blood concentration), rather than a constant fractional rate. !s

a result, a rectilinear plot of blood methanol concentration versus

time yields an initial linear decline, whereas a convex curve is observed

in the semi*logarithmic plot (compare left and right panels

of ig. /*A). n time, methanol metabolism converts to first*order kinetics

when blood methanol concentration falls belowK6 (i.e., the

6ichaelis constant for the dehydrogenase en$yme); at which time,

blood methanol shows an exponential decline in the rectilinear plot

and a linear decline in the semi*logarithmic plot. 6oreover, ig. /*A

shows the greater than proportionate increase (i.e., > fourfold) in

Cmax andAUCG

8 as the methanol vapor concentration is raised from

-88 ppm to =A88 ppm. t should be noted that a constant T/- or

kel does not exist during the saturation regime; it varies depending

upon the saturating methanol dose.

n addition to the complication of dose*dependent kinetics,

there are chemicals whose clearance kinetics changes over time (i.e.,

time*dependent kinetics). ! common cause of time*dependent kinetics


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is auto*induction of xenobiotic metaboli$ing en$ymes; that is,

the substrate is capable of inducing its own metabolism through activation

of gene transcription. The classic example of auto*induction

is with the antiepileptic drug, carbama$epine. Baily administration

of carbama$epine leads to a continual increase in clearance and

shortening in elimination half*life over the first few weeks of therapy

(@ertilsson et al., 4A?).


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concentration is expected during continuous exposure and the time

it takes for a toxicant to reach steady state is governed by its elimination

half*life. t takes one half*life to reach 58>, four half*lives

to reach 4, and seven half*lives to reach 44.-> of steady state.

Time to attainment of steady state is not dependent on the intake rate

of the toxicant. The left panel of ig. /*4 shows the same time to

58> steady state at three different rates of intake; on the other hand,

the steady*state concentration is strictly proportional to the intake

rate. %hange in clearance of a toxicant often leads to a corresponding

change in elimination half*life (see right panel of ig. /*4), in

which case both the time to reach and magnitude of steady*state

concentration are altered. The same steady*state principle applies

to toxicants that exhibit multi*compartmental kinetics; except that,

accumulation occurs in a multi*phasic fashion reflective of the multiple

exponential half*lives for inter*compartmental distribution and

elimination. Typically, the rise in plasma concentration is relatively

rapid at the beginning, being governed by the early (distribution)

half*life, and becomes slower at later times when the terminal (elimination)

half*life takes hold.

The concept of accumulation applies to intermittent exposure

as well. igure /*8 shows a typical occupational exposure scenario

to volatile chemicals at the workplace over the course of a

week. &hether accumulation occurs from day to day and further

from week to week depends on the intervals between exposure and

the elimination half*life of the chemicals involved. or a chemical

with relatively short half*life compared to the interval between

work shifts and the Dexposure holidayE over the weekend, little accumulation

is expected. n contrast, for a chemical with elimination


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-

to -= hours), progressive accumulation is expected over the successive

workdays. &ashout of the chemical may not be complete over

the weekend and result in a significant carry forward of body burden

into the next week. t should also be noted that the overall exposure

as measured by the !N% over the cycle of a week is dependent on

the toxicant clearance.

Con*lu#"on

or many chemicals, blood or plasma chemical concentration versus

time data can be adequately described by a one* or twocompartment,

classic pharmacokinetic model when basic assumptions

are made (e.g., instantaneous mixing within compartments and

first*order kinetics). n some instances, more sophisticated models

with increased numbers of compartments will be needed to describe

blood or plasma toxicokinetic data; for example, if the chemical is

preferentially sequestered and turns over slowly in select tissues.

The parameters of the classic compartmental models are usually

estimated by statistical fitting of data to the model equations using

nonlinear regression methods. ! number of software packages are

available for both data fitting and simulations with classic compartmental

models; examples include&inMonlin ("harsight %orp., "alo

!lto, %!), !!6 (!!6 nstitute, Nniversity of &ashington,

eattle, &!), !B!"T (Nniversity of outhern %alifornia, os

!ngeles, %!), and "O olutions (ummit 3esearch ervices, 6ontrose,


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%0).

+la#ma Con*

Mon Tue 6ed T.ur )r" Sat Sun Mon

T172 8 29 .r#

T172 8 : .r#

Figure 7-10. Simulated accumulation of plasma concentration from occupational

exposure over te c!cle of a "ork "eek compared #et"een t"o

industrial cemicals "it sort and long elimination alf-lives.

hading represents the exposure period during the A*hour workday, 6onday

through riday. ntake of the chemical into the systemic circulation is

assumed to occur at a constant rate during exposure. 1xposure is negligible

over the weekend. or the chemical with the short elimination half*life of

A hours, minimal accumulation occurs from day to day over the work days.

Mear complete washout of the chemical is observed when work resumes on

6onday (see arrow). or the chemical with the long elimination half*life

of -= hours, progressive accumulation is observed over the five work days.

&ashout of the longer half*life chemical over the weekend is incomplete; a

significant residual is carried into the next work week. @ecause of its lower

clearance, the overall !N% of the long half*life chemical over the cycle of a

week is higher by threefold.####################


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are now well within the reach of toxicologists.

The advantages of physiologically based models compared

with classic models are that () these models can describe the time

course of distribution of toxicants to any organ or tissue, (-) they

allow estimation of the effects of changing physiologic parameters

on tissue concentrations, (


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not completely different. @oth contain a liver compartment because

the hepatic metabolism of each chemical is an important element

of its disposition. t is important to reali$e that there is no generic

physiologic model. 6odels are simplifications of reality and should

contain elements believed to represent the essential disposition features

of a chemical.

n view of the fact that physiologic modeling requires more effort

than does classic compartmental modeling, what then accounts

for the popularity of this approach among toxicologistsP The answer

lies in the potential predictive power of physiologic models.

Toxicologists are constantly faced with the issue of extrapolation in

risk assessmentsQfrom laboratory animals to humans, from high to

low doses, from occasional to continuous exposure, and from single

chemicals to mixtures. @ecause the kinetic constants in physiologic

models represent measurable biological or chemical processes, the

resultant physiologic models have the potential for extrapolation

from observed data to predicted scenarios.


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448). The conclusion is that the same model structure is capable of

describing the chemicals# kinetics in two different species. @ecause

the parameters underlying the model structure represent measurable

biological and chemical determinants, the appropriate values

for those parameters can be chosen for each species, forming the basis

for successful interspecies extrapolation. 1ven though the same

model structure is used for both rodents and humans, the simulated

and the observed kinetics of both chemicals differ between rats and

humans. The terminal half*life of both organics is longer in the human

compared with the rat. This longer half*life for humans is due to

the fact that clearance rates for smaller species are faster than those

for larger ones. 1ven though the larger species breathes more air or

pumps more blood per unit of time than does the smaller species,

blood flows and ventilation rates per unit of body mass are greater

for the smaller species. The smaller species has more breaths per

minute or heartbeats per minute than does the larger species, even

though each breath or stroke volume is smaller. The faster flows per

unit mass result in a more efficient delivery of a chemical to organs

responsible for elimination. Thus, a smaller species can eliminate

the chemical faster than a larger one can. @ecause the parameters

in physiologic models represent real, measurable values, such as

blood flows and ventilation rates; the same model structure can resolve

such disparate kinetic behaviors among species.

Compartment#

The basic unit of the physiologic model is the lumped compartment,

which is often depicted as a box in a graphical scheme (ig. /*


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kidney, or a widely distributed tissue type such as fat or skin. %ompartments

usually consist of three individual well*mixed regions, or

sub*compartments, that correspond to specific physiologic spaces

or regions of the organ or tissue. These sub*compartments are+

() the vascular space through which the compartment is perfused

with blood, (-) the interstitial space that forms the matrix for the

cells, and (


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information on organ and tissue volumes across species, @rownet al.

(44/) is a good starting point.

+.#"olo"* "hysiologic parameters encompass a wide variety of

processes in biological systems. The most commonly used physiologic

parameters are blood flows and lung ventilation. The blood

flow rate (Qt in volume per unit time, such as m2min or 2h) to

individual compartments must be known. !dditionally, information

on the total blood flow rate or (ar)!a( o&tp&t (Qc) is necessary. f

inhalation is the route for exposure to the chemical or is a route of

elimination, the alveolar ventilation rate (Qp) also must be known.

@lood flowrates and ventilation rates can be taken from the literature

or can be obtained experimentally.

"arameters for renal excretion and hepatic metabolism are another

subset of physiologic parameters, and are required, if these

processes are important in describing the elimination of a chemical.

or example, glomerular filtration rate and renal tubular transport

parameters are required to describe renal clearance. f a chemical is

knownto be metaboli$ed via a saturable process, both Vmax (the maximum

rate of metabolism) andK6 (the concentration of chemical at

one*half Vmax) for each of the en$ymes involved must be obtained

so that elimination of the chemical by metabolism can be described

in the model. n principle, these parameters can be determined from

in vitro metabolism studies with cultured cells, tissue homogenates,

or cellular fractions containing the metabolic en$ymes (e.g., microsomes

for cytochrome "=58 en$ymes and NB"*HTs), along with appropriate

in vitro*in vivo scaling techniques (watsubo et al., 44/;

6acHregor et al., -88; 6iners et al., -88?). !lthough there have

been examples of remarkable success with quantitative prediction of

in vivo metabolic clearance based on in vitro biochemical data, there

are also notable failures. Nnfortunately, estimation of metabolic parameters

from in vivo studies is also fraught with difficulties, especially


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when multiple metabolic pathways and en$ymes are present.

1stimation of metabolic parameters remains a challenging aspect of

physiologically based toxicokinetic modeling.

T.ermodnam"* Thermodynamic parameters relate the total concentration

of a chemical in a tissue (Ct) to the concentration offree

chemical in that tissue (Cf). Two important assumptions are that

() total and free concentrations are in equilibrium with each other,

and (-) only free chemical can be exchanged between the tissue

sub*compartments (ut$ et al., 4A8). 6ost often, total concentration

is measured experimentally; however, it is the free concentration

that is available for passage across membrane barriers, binding to

proteins, metabolism, or carrier*mediated transport. Larious mathematical

expressions describe the relationship between these two

entities. n the simplest situation, the toxicant is a freely diffusible

water*soluble chemical that does not bind to any molecules. n this

case, free concentration of the chemical is equal to the total concentration

of the chemical in the tissue+ total 7 free, or Ct 7 Cf.

The affinity of many chemicals for tissues of different composition

varies. The extent to which a chemical partitions into a tissue is directly

dependent on the composition of the tissue and independent

of the concentration of the chemical. Thus, the relationship between

free and total concentration becomes one of proportionality+ total 7

free9partition coefficient, or Ct 7 Cf 9Pt. n this case,Pt is called

a tissue partition coefficient, which is most often determined from

tissue distribution studies in animals, ideally at steady*state during

continuous intravenous infusion of the chemical. 1stimation ofPt

based on in vitro binding studies with human or animal tissues or tissue

fractions has proven successful in some cases (in et al., 4A-;

6acHregor et al., -88). Onowledge of the value ofPt permits an

indirect calculation of the free concentration of toxicant in the tissue

or Cf 7 Ct/Pt.


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Table /*= compares the partition coefficients for a number of

toxic volatile organic chemicals. The larger values for the fat2blood

partition coefficients compared with those for other tissues suggests

that these chemicals distribute into fat to a greater extent than they

distribute into other tissues. This has been observed experimentally.

at and fatty tissues, such as bone marrow, contain higher concentrations

of ben$ene than do tissues such as liver and blood. imilarly,

styrene concentrations in fatty tissue are higher than styrene

concentrations in other tissues. t should be noted that lipophilic

organic compounds often can bind to plasma proteins and2or blood

cell constituents, in which case the observed tissue2blood partition

coefficients will be a function of both the tissue and blood partition

coefficient (i.e.,Pt/Pb). Jence, partitioning or binding to blood


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e.g.,m2h) for the chemical and the total barrier surface area (A, in

m-). The permeability coefficient takes into account the diffusivity

of the specific chemical and the thickness of the cell membrane.

C and C- are the respectivefree concentrations of the chemical in

the originating and receiving compartments. Biffusional flux is enhanced

when the barrier thickness is small, the barrier surface area

is large, and a large concentration gradient exists. 6embrane transporters

offer an additional route of entry into cells, and allow more

effective tissue penetration for chemicals that have limited passive

permeability. !lternately, the presence of efflux transporters at epithelial

or endothelial barriers can limit toxicant penetration into critical

organs, even for highly permeable toxicant (e.g., "*glycoprotein

mediated efflux functions as part of the bloodbrain barrier). or

both transporter*mediated influx and efflux processes, the kinetics

is saturable and can be characteri$ed by Tmax (the maximum transport

rate) andKT (the concentration of toxicant at one*half Tmax) for

each of the transporters involved. n principle, kinetic parameters

for passive permeability or carrier*mediated transport can be estimated

from in vitro studies with cultured cell systems. Jowever, the

predictability and applicability of such in vitro approaches for physiologic

modeling has not been systematically evaluated (6acHregor

et al., -88). !t this time, the transport parameters have to be estimated

from in vivo data, which are at times difficult and carry some

degree of uncertainty.

There are two limiting conditions for the uptake of a toxicant

into tissues+ perfusion*limited and diffusion*limited. !n understanding

of the assumptions underlying the limiting conditions

is critical because the assumptions change the way in which the

model equations are written to describe the movement of a toxicant

into and out of the compartment.

+eru#"on-L"m"ted Compartment#


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! perfusion*limited compartment, alternately referred to as blood

flow*limited or simply flow*limited compartment, describes the situation

when permeability across the cellular or membrane barriers

(PA) for a particular toxicant is much greater than the blood flow

rate to the tissue (Qt), i.e.,PAI Qt. n this case, uptake of toxicant

by tissue sub*compartments is limited by the rate at which

the toxicant is presented to the tissue via the arterial inflow, and

not by the rate at which the toxicant penetrates through the vascular

endothelium, which is fairly porous in most tissues, or gains

passage across the cell membranes. !s a result, equilibration of a

toxicant between the blood in the tissue vasculature and the interstitial

sub*compartment is maintained at all times, and the two subcompartments

are usually lumped together as a single extracellular

compartment. !n important exception to this vascular*interstitial

equilibrium relationship is in the brain, where the capillary endothelium

with its tight 'unctions poses a diffusional barrier between

the vascular space and the brain interstitium. urthermore, as indicated

in ig. /* -), cellular permeability generally does not

limit the rate at which a molecule moves across cell membranes.

or these molecules, flux across the cell membrane is fast compared

with the tissue perfusion rate (PAI Qt), and the molecules

rapidly distribute throughout the sub*compartments. n this case,

free toxicant in the intracellular compartment is always in equilibrium

with the extracellular compartment, and these tissue subcompartments

can be lumped as a single compartment. uch a flowlimited

tissue compartment is shown in ig. /*=. 6ovement into

and out of the entire tissue compartment can be described by a single


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equation.

Vt 9 )Ct

)t

7 Qt 9 (Cin : Cout) (/*A)

where Vt is the volume of the tissue compartment, Ct is the toxicant

concentration in the compartment (Vt 9 C equals the amount

of toxicant in the compartment), Vt 9 dCt/dt is the change in the

amount of toxicant in the compartment with time, expressed as mass

per unit of time, Qt is blood flow to the tissue, Cin is the toxicant

concentration entering the compartment, and Cout is the toxicant

Figure 7-1,. Scematic representation of a tissue compartment tat features

#lood flo"limited uptake kinetics.

3apid exchange of toxicant between the extracellular space (l&e) and intracellular

space (l!-t l&e), unhindered by a significant diffusional barrier as

symboli$ed by the dashed line, allows equilibrium to be maintained between

the two sub*compartments at all times. n effect, a single compartment represents

the tissue distribution of the toxicant. t is blood flow, C"n is the

chemical concentration entering the compartment via the arterial inflow, and

Cout is the chemical concentration leaving the c


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1quation (/*A)) equals the difference in the rate of entry via arterial

inflow and the rate of departure via venous outflow (right*hand side

of 1quation (/*A)).

n the perfusion*limited case, the concentration of chemical in

the venous drainage from the tissue is equal to the free concentration

of chemical in the tissue (i.e., Cout 7 Cf) when the chemical is not

bound to blood constituents. !s was noted previously, Cf (or Cout)

can be related to the total concentration of chemical in the tissue

through a simple linear partition coefficient, Cout 7 Cf 7 Ct2Pt. n

this case, the differential equation describing the rate of change in

the amount of a chemical in a tissue becomes

Vt 9 dCt/dt 7 Qt 9 RCin : Ct/PtS (/*4)

n the event the chemical does bind to blood constituents, blood

partitioning coefficient needs to be recogni$ed in the mass balance

equation.

Vt 9 dCt/dt 7 Qt 9 RCin : Ct/(Pt/Pb)S (/*-8)

The physiologic model shown in ig. /*-, which was developed

for volatile organic chemicals such as styrene and ben$ene,

is a good example of a model in which all the compartments are

described as flow*limited. Bistribution of a toxicant in all the compartments

is described by using equations of the type noted above.

n a flow*limited compartment, the assumption is that the concentrations

of a toxicant in all parts of the tissue are in equilibrium. or

this reason, the compartments are generally drawn as simple boxes

(ig. /*-) or boxes with dashed lines that symboli$e the equilibrium

between the intracellular and extracellular sub*compartments

(ig. /*=). !dditionally, with a flow*limited model, estimates of

fluxes between sub*compartments are not required to develop the

mass balance differential equation for the compartment. Hiven the

challenges in measuring flux across the vascular endothelium and

cell membrane, this is a simplifying assumption that significantly


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reduces the number of parameters required in the physiologic model.

!"u#"on-L"m"ted Compartment#

&hen uptake of a toxicant into a compartment is governed by its

diffusion or transport across cell membrane barriers, the model is

said to be diffusion*limited or barrier*limited. Biffusion*limited uptake

or release occurs when the flux, or the transport of a toxicant

across cell membranes, is slow compared with blood flow to the

tissue. n this case, the permeability*area product is small compared

with blood flow, i.e.,P! I Qt . The distribution of large polar

molecules into tissue cells is likely to be limited by the rate at which

the molecules pass through cell membranes. n contrast, entry into

the interstitial space of the tissue through the leaky capillaries of the

vascular space is usually rapid even for large molecules. igure /*5

shows the structure of such a compartment. The toxicant concentrations

in the vascular and interstitial spaces are in equilibrium and

make up the extracellular sub*compartment, where uptake from the

incoming blood is flow*limited. The rate of toxicant uptake across

the cell membrane from the extracellular space into the intracellular

space is limited by membrane permeability, and is thus diffusionlimited.

Two mass balance differential equations are necessary to

Figure 7-1. Scematic representation of a tissue compartment tat features

mem#rane-limited uptake kinetics.

"erfusion of blood into and out of the extracellular compartment is depicted

by thick arrows. Transmembrane transport (flux) from the extracellular to

the intracellular sub*compartment is depicted by thin double arrows. t is

blood flow, C"n is chemical concentration entering the compartment, and

Cout is chemical concentration leaving the compartment.

describe the events in these two sub*compartments+

E'tra(ell&lar Vt 9 dCt/dt 7 Qt 9 (Cin : Cout)

:PAt 9 (Ct/Pt)CPAt 9 (Ct-/Pt-) (/*-)

0ntra(ell&lar Vt- 9 dCt-/dt 7PAt 9 (Ct/Pt)


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:PAt 9 (Ct-/Pt-) (/*--)

Qt is blood flow, and C is the chemical concentration in entering

blood (in), exiting blood (out), tissue extracellular space (t),

or tissue intracellular space (t-). The subscript (t) for thePA term

acknowledges the fact thatPA, reflecting either via passive diffusion

or carrier*mediated processes, can differ between tissues. @oth

equations feature fluxes or transfers across the cell membrane that

are driven by free concentration. Jence, partition coefficients are

needed to convert extracellular and intracellular tissue concentration

to their corresponding free concentration. The physiologic model in

ig. /* is composed of two diffusion*limited compartments each

of which contain two sub*compartmentsQextracellular and intracellular

space, and several perfusion*limited compartments.

Spe*"al">ed Compartment#

Lun The inclusion of a lung compartment in a physiologic model

is an important consideration because inhalation is a common route

of exposure to many volatile toxic chemicals. !dditionally, the lung

compartment serves as an instructive example of the assumptions

and simplifications that can be incorporated into physiologic models

while maintaining the overall ob'ective of describing processes and

compartments in biologically relevant terms. or example, although

lung physiology and anatomy are complex, Jaggard (4-=) developed

a simple approximation that sufficiently describes the uptake

of many volatile chemicals by the lungs.!diagram of this simplified

lung compartment is shown in ig. /*?. The assumptions inherent

in this compartment description are as follows+ () ventilation is continuous,

not cyclic; (-) conducting airways (nasal passages, larynx,

trachea, bronchi, and bronchioles) function as inert tubes, carrying

the vapor to the pulmonary or gas exchange region; (


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from the inspired air appears in the arterial blood (i.e., there is no

hold*up of chemical in the lung tissue and insignificant lung mass);

and (5) vapor in the alveolar air and arterial blood within the lung

compartment are in rapid equilibrium and are related byPb


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merge in the vena cava and heart chambers to form mixed venous

blood. n ig. /*, a blood compartment is created in which the

input is the sum of the toxicant outflow from each compartment

(Qt 9 Cvt). 0utflow from the blood compartment is a product of

the blood concentration in the compartment and the total cardiac

output (Qc 9 Cbl). The mass*balance differential equation for the

blood compartment in ig. /* is as follows+

Vbl 9 dCbl/dt 7 (Qbr 9 Cvbr C Qot 9 Cvot C Qk 9 Cvk C QlCvl)

: Qc 9 Cbl, (/*-/)

where Vbl is the volume of the blood compartment; C is concentration;

Q is blood flow; l, r, ot, k, and l represent the blood, brain,

other tissues, kidney, and liver compartments, respectively; and "r,

"ot, "k, and "l represent the venous blood leaving the organs. Qc is

the total blood flow equal to the sum of the venous blood flows from

each organ.

n contrast, the physiologic model in ig. /*- does not feature

an explicit blood compartment. or simplicity, the blood volumes

of the heart and the ma'or blood vessels that are not within organs

are assumed to be negligible. The venous concentration of a chemical

returning to the lungs is simply the weighted average of the

concentrations in the venous blood emerging from the tissues.

Cv 7 (Ql 9 Cvl 9 Qrp 9 Cvrp C Qpp 9 Cvpp C Qf 9 Cvf)/Qc

(/*-A)

where C is concentration; Q is blood flow; ", l, rp,pp, andf represent

the venous blood entering the lungs, liver, richly perfused,

poorly perfused, and fat tissue compartments, respectively; and "l,

"rp, "pp, and "f represent the venous blood leaving the corresponding

organs. Qc is the total blood flow equal to the sum of the blood

flows exiting each organ.

n the physiologic model in ig. /*-, the blood concentration

entering each tissue compartment is the arterial concentration


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(Cart) that was calculated above for the lung compartment

(1quation (/*-=)). The decision to use one formulation as opposed

to another to describe blood in a physiologic model depends on

the role the blood plays in disposition and the type of application.

f the toxicokinetics after intravenous in'ection is to be simulated

or if binding to or metabolism by blood components is suspected,

a separate compartment for the blood that incorporates these additional

processes is required. ! blood compartment is obviously

needed if the model were developed to explain a set of blood

concentrationtime data for a toxicant. 0n the other hand, if blood

is simply a conduit to the other compartments, as in the case for

inhaled volatile organics shown in ig. /*-, the algebraic solution

is acceptable.

igure /*A shows the application of physiologic modeling in

elucidating the disposition fate of methylmercury and its demethylated

product, inorganic mercury following a single peroral administration

in the growing adult rat (arris et al., 44


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@, %, and B show two prominent features of methylmercurcy disposition+

() methylmercury is rapidly demethylated to inorganic

mercury, which is slowly eliminated from the brain and the kidneys,

two ma'or sites of methylmercury toxicities; and (-) a significant

portion of mercury is sequestered in hair and the ingestion of hair by

the animal contributes to the remarkable persistence of mercury in

the rat. This example illustrates the capability of physiologic models

to deal with the varied and complex disposition kinetics of toxicants

from a wide range of sources under a multitude of experimental and

environmental exposure scenarios.

Con*lu#"on#

The second section provides an introduction to the simpler elements

of physiologic models and the important assumptions that underlie

model structures. or more detailed aspects of physiologic modeling,

the readers can consult several in*depth and well*annotated

reviews on physiologically based toxicokinetic models (%lewell and

!nderson, 44=, 44?; 0#laherty, 44A; Orishnan and !nderson,

-88; Orishnan et al., -88-; !nderson, -88


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models describing biochemical interactions among xenobiotics,

and more biologically realistic descriptions of tissues previously

viewed as simple lumped compartments are 'ust a few of the

more sophisticated applications. inally, physiologically based toxicokinetic

models are beginning to be linked to biologically based

toxicodynamic models to simulate the entire exposure dose

response paradigm that is basic to the science of toxicology.

Documents

Casaret and Dull Tox