Casaret and Dull Tox
Transcript of 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.