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OCR for page 113
Approaches for Using Toxicokinetic
Information in Assessing Risk to
Deployed U.S. Forces
by Karl K. Rothmans
ABSTRACT
If there is no exposure, there is no toxicity. If there is exposure, toxicity might ensue when exposure
exceeds a certain dose or time, a topic discussed under toxicokinetics and toxicodynamics. Analysis of
the fundamental equation of toxicity yields the recognition of three independent time scales. One is the
dynamic time scale, which is an intrinsic property of a given compound (what does a chemical do to an
organism). The second is the kinetic time scale, which is an intrinsic property of a specific organism
(what does an organism do to a chemical). The frequency of exposure denotes the third time scale,
which is independent of dose and of the dynamic and kinetic time scales. Frequency of exposure
depends on the experimental design or nature, but not on the organism or substance. A liminal
condition occurs when the frequency becomes infinite, which corresponds to continuous exposure.
Continuous exposure forces the dynamic and kinetic time scales to become synchronized, thereby
reducing complexity to three variables: dose, elect, and one time scale. Keeping one of those variables
constant allows one to study the other two variables reproducibly under isoe~ective, isodosic, or
isotemporal conditions. However, any departure from continuous exposure will introduce the full
complexity of four independent variables (dose, and the kinetic, dynamic, and frequency time scales)
impacting on the elect (dependent variable) at the same time. The examples discussed in this paper
demonstrate how nature in the form of long half-lives provides liminal conditions when either kinetic or
dynamic half-lives force synchronization of all three time scales.
The original charge for this paper was to conceptualize the role of toxicokinetics in the risk
assessment of deployed forces exposed to chemicals. Most toxicologists familiar with current trends in
toxicology are aware of the tremendous proliferation of publications combining physiologically based
pharmacokinetic (PBPK) models with various dose-response extrapolation models, usually with the
linearized multistage (LMS) model, or more recently with the benchmark (BM) curve-fitting approach.
1Department of Pharmacology, Toxicology and Therapeutics, University of Kansas Medical Center, Kansas City, KS,
66160 and Section of Environmental Toxicology, GSF-Institut fur Toxikologie, Neuherberg, 85758 Germany.
113
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4
STRATEGIES TO PROTECT THE HEALTH OF DEPLOYED U.S. FORCES: WORKSHOP PROCEEDINGS
This author has used both PBPK and classical pharmacokinetics in many experiments. Although both
are conceptually sound, there is one fundamental difference: classical pharmacokinetics uses time as
an explicit function, whereas PBPK deals with time mostly as a variable, to be predicted based on
physiological and physicochemical parameters. Therefore, the concepts of classical pharmacokinetics
were helpful in the development of the initial core of a theory of toxicology, as presented in this
document, whereas the concepts of PBPK were not as useful. This is not to say that combining PBPK
with a theoretically sound biological model will not provide appropriate answers in some instances.
However, as long as PBPK is used in conjunction with biologically implausible models (LMS, BM), it
will lead (not surprisingly) to insignificant improvements. Central to the development of the concepts
presented here was the notion that time is a variable equivalent to dose in toxicology. This idea has
been around among toxicologists for almost exactly 100 years. Nevertheless, claims of exceptions to
this idea as embodied in Haber's Rule prevented the development of time as a variable of toxicity. Even
today toxicologists tend to focus on the so-called "exceptions" when elects are overwhelmingly dose-
but not time dependent. They do not realize that they are studying extreme parts of a spectrum under
liminal conditions (e.g., a highly reversible elect on a short time scale), and they use experimental
models with insufficient time resolution. When time resolution is satisfactory (such as pungency on a
scale of seconds), clear summation elects emerge.
Recognition of the limits of the current risk-assessment paradigm made a paradox clear: none of
the current risk projections include time as a variable even though any and all such risk predictions are
by definition made in time. From this recognition it was concluded that something that is basically
flawed cannot be fixed. Therefore, a new risk-assessment paradigm that includes time as a variable of
toxicity, is being suggested. It is clear that although dose is a simple function (number of molecules),
time is a complex variable, which runs on many different scales, at least three of which are interacting
with dose to provide the complexity that seems to have bewildered generations of toxicologists. The
three time scales are the toxicokinetic and toxicodynamic half-lives and the frequency of exposure.
Thus, there are three liminal conditions:
i. When the toxicokinetic half-life is very long, it keeps the frequency of exposure essentially infinite
(continuous exposure), and the toxicodynamic half-life by definition will be the same as the toxicokinetic
one. Under these liminal conditions, c x t = k for isoe~ective experiments, because there is only dose-
dependence and one time-dependence.
2. When the toxicodynamic half-life is very long, it requires no additional injury to occur to keep
injury constant nor the continuous presence of the noxious agent to result under isoe~ective conditions
in c x t = k, because there is only dose-dependence and one time-dependence.
3. When the toxicokinetic/toxicodynamic half-lives become very short, they will blur the distinction
between the kinetic and dynamic time scales and both will become less important, because in that case
the frequency of exposure dominates the time-dependence. Under liminal (continuous exposure =
infinite frequency) and isoe~ective conditions, this will also lead to c x t = k.
When experiments are conducted under isodosic or isotemporal conditions, then the relationship
will obey the equation c xt = k Prefect. The vast majority of exposure scenarios are of course farfrom
these liminal situations (ideal conditions) and will, therefore, yield c x to = k. There are clear sugges-
tions in this paperfor the type of experiments that need to be done to determine x with exactitude. In the
meantime, practical suggestions are included, which illustrate how to use a decision tree or available
databases to conduct risk assessments for deployment situations that are less arbitrary by using both
dose and time as variables of toxicity.
The decision tree approach uses a top-to-bottom analysis of identifying rate-determining or rate-
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APPROACHES FOR USING TOXICOKINETIC INFORMATION IN ASSESSING RISK
115
limiting steps in the toxic action of a given compound for a specific ewe ct. The advantage of this
approach is its flexibility of determining at what level to contemplate modeling (risk assessment) of
toxicity without having to rely on default assumptions. As recognized by other scientific disciplines,
understanding of complexity is always advanced at three levels of investigations: experimental, compu-
tational, and theoretical. For the most part, toxicologists were and are engaged in experimental and
computational studies with very little, if any, progress having been made in developing a comprehensive
theory of toxicology. The combined theory and decision-tree analysis presented here should allow
rapid progress in improving predictions of toxicity, if experimental design, computational goal, and
theory come into equilibrium in terms of checks and balances. Instead of claiming exceptions, the three
questions to be asked should be:
1. Why do some experimental results deviate from c x t = k (isoe~ective) or c x t = k x Elect
(isodosic, isotemporal)?
2. What kind of computational (modeling) approach, and what level of integration, is needed to
transform c xtX = k or c xtX = k Prefect back to c xt = k or c xt = k Prefect?
3. How does exploration of Questions I and 2 improve the theory of toxicology, specifically the
understanding of k?
It must be recognized that eventually experiments will be conducted under ideal conditions tc x t =
k or c x t = k x Elects. Once it is known how to transform c x to = k or c x to = k x Elect (real-life
situations) back to the ideal conditions, then any projection will also be possible in the opposite
direction. Thus, it can be expected that the vast majority of experiments conducted under less-than-
ideal conditions will then become interpretable by using a related study, which has been conducted
under ideal conditions.
TOXICITY
Introduction
~ ~ ~ . ~ . ~ . . ,
Toxicity (1) is a function of exposure (E) and E is a function of dose (c) and time (t) (T=;ffE(c,t)~.
Toxicity is the manifestation of an interaction between molecules constituting some form of life and
molecules of exogenous chemicals or forms of life affected by physical insults. Consequences of
molecular interactions or physical insults might propagate, through causality chains, all the way to the
organismic level. There are two fundamental ways to view this interaction: (1) what does an organism
do to a chemical, and (2) what does a chemical do to an organism? Dealing with the first question led
to the development of the discipline of pharmacokinetics, which was later incorporated into some
toxicity studies; in that context it would be more appropriately called toxicokinetics (K). The other
question was addressed by the discipline of pharmacology in the form of pharmacodynamic experi-
ments, which again in the context of toxicity, would be more properly termed toxicodynamics (D).
Thus, toxicity (1) might be defined as a function of E, K, and D.
T = f(E,K,D)
A definition of toxicity according to Rozman and Doull (1998) runs as follows "Etoxicity] is the
accumulation of injury over short or long periods of time, which renders an organism incapable of
functioning within the limits of adaptation." This definition implies that toxicity is a function of time
in addition to the dose. The latter was already recognized by Paracelsus 500 years ago. A closer
scrutiny of the earlier definition of toxicity indicates that the relationship between toxicity, dose (c)
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6
STRATEGIES TO PROTECT THE HEALTH OF DEPLOYED U.S. FORCES: WORKSHOP PROCEEDINGS
and time (t) is a complex one because toxicokinetics itself is dose- and time-dependent ILK = f~c,t)] as
is toxicodynamics tD = fee, ted. It is noteworthy that the various time-dependencies seldom run on the
same time scale.
Conceptually, K might also be viewed as a function of the dynamic change between absorption
(Alec) and elimination (El),
K = f(Abs,EI)
because it is the ratio between entry rate (absorption) and exit rate (elimination) that determines the
time course of a compound in an organism. In the simplest case of an iv bolus injection (instanta-
neous absorption), the time course is determined by the rate of elimination alone for a compound
obeying a one-compartment model. Usually absorption is faster than elimination-making processes
related to elimination (distribution, biotransformation, excretion) rate-determining or rate-limiting in
most instances.
By analogy, D might be viewed as a function of the dynamic change between injury (I) and recovery (R),
D =f(I,R)
because it is the ratio of injury to recovery that determines the time course of an adverse effect in an
organism. The simplest case for such an injury would be when an organism would recover from an
acute injury in accordance with a one-compartment toxicodynamic model. Again, processes related to
recovery are usually slower than the rate of injury. Therefore, recovery (adaptation, repair, reversibility)
will more often be rate-determining or rate-limiting.
Most often compounds do not behave in an organism according to a one-compartment model. The
reason for this is that elimination from the systemic circulation itself can be a function of excretion (Ex),
distribution (Dist), and biotransformation (Bio).
El = f(Ex,Dist,Bio)
When any or all of these processes become rate-limiting, two- or multi-compartmental models are
needed.
Again, by analogy to K, recovery (R) in a D model might not be a simple function of, for example,
reversibility (Rv), but could also require repair (Rp). In addition, adaptation (Adp) might also be
occurring.
R = f(Adp,Rp,Rv)
In such instances, two- or multi-compartment toxicodynamic analyses are needed to describe the toxic-
ity of a compound that affects any or all of these processes. Absorption and injury can be thought of as
being analogous manifestations of K and D. Absorption is a function of site (S) and mechanism (M) as
. . .
IS injury.
Abs=f(S,M)
I =f(S,M)
This analysis can be continued all the way to the molecular level. It is clear that any rate-determining or
rate-limiting steps, originating at the level of molecular interactions, will then propagate through causal-
ity chaints) to the levels depicted in Figure 1, which represents a schematic illustration of this concept.
Each of these processes might be dose- and time-dependent, although past experiments often failed
to demonstrate this because they were conducted with preponderant emphasis on one or the other
variable; for example, D was mainly studied as a function of dose and K mainly as a function of time.
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APPROACHES FOR USING TOXICOKINETIC INFORMATION IN ASSESSING RISK
Decision Tree
lAosVAgent Interaction [Toxicity- <~,D,K)]
What does agent do to organism?
D - f (cif)
ARMY''''';
R
ill
Adp Up Rv
dT _ dT dD dK
dE dD dK dE
E- f(C,{}
T Tox~city
D Toxicodynamic processtes)
K Toxicokinetic processtes)
E Exposure
c . ~)ose
{ time
117
What does organism do to agents
Kin f(&~)
Abs
i''1~
El
~ r
D'st B,o Ex
FIGURE 1 Schematic presentation of the decision-tree concept and a mathematical description of toxicity as a
function of exposure, kinetics, and dynamics using the chain expansion.
History
Time has always been an important factor in designing toxicological experiments, yet time as an
explicit variable of toxicity has been afforded very little attention. It is even more interesting that after
Warren (1900) was severely criticized by Ostwald and Dernoscheck (1910) for his analogy of c x t = k
to P x V= k of ideal gases, the entire issue was forgotten. Even though c x t = k kept surfacing
repeatedly (e.g., Flury and Wirth 1934; Druckrey and Kupfmuller 1948; Littlefield et al. 1980; Peto et
al. 1991), an analogy to thermodynamics was not contemplated again, at least not to this author's
knowledge! With the "rediscovery" of the c x t = k concept in still another context (delayed acute oral
toxicity), some reevaluation regarding the role of time in toxicology in a historical context is required.
Ostwald and Dernoscheck's (1910) analogy of toxicity to an adsorption isotherm is problematic,
because adsorption entails processes far from ideal conditions. Much more reasonable is Warren's
(1900) analogy to P x V = k for ideal gases as a comparison to ideal conditions in toxicology. Reducing
the volume of a gas chamber containing a given number of molecules or atoms of an ideal gas will
decrease the time for any given molecules or atoms to collide with the wall of the chamber and will lead
to increased pressure, which is simply an attribute of the increased number of molecules per unit
volume, which is concentration. Thus, c x t = k and P x V= k are compatible with each other if looked
at mechanistically. Of course, Ostwald and Dernoscheck's comparison of toxicity to an adsorption
isotherm is much closer to the real-life situation of toxicology where the most frequent finding is that of
c x to = k
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8
STRATEGIES TO PROTECT THE HEALTH OF DEPLOYED U.S. FORCES: WORKSHOP PROCEEDINGS
These thought experiments and some discussions led to the recognition that toxicologists did every-
thing the opposite of what thermodynamicists did. Instead of starting out with the simplest model (ideal
gas in thermodynamics corresponds to ideal conditions in toxicological experiments) and building into
it step by step the increasing complexity of the real world, toxicologists tried to predict from one
complex situation to another complex situation. In addition, time was largely ignored, although it is one
of two fundamental variables of toxicity (Rozman 1998~. It is unlikely that a better understanding of
biological processes at the molecular level alone will lead to improved risk predictions in toxicology, as
long as the experimental designs of toxicological studies provide the wrong reference points for depar-
ture from ideal to real conditions. For example, the standard inhalation toxicity protocols (6 hid for
5 d/wk) cannot yield c x t = k because after 6 h intoxication, there are up to 18 h of recovery, and on
weekends there are up to 66 h of recovery, at least for compounds of short half-life. This would require
at least two additional functions to correct for departure from steady state. The real-life situation is even
more complex when departures from the ideal condition (steady state) are highly irregular. Neverthe-
less, it is reasonable to expect that risk predictions will be possible for even the most irregular exposure
scenarios once the reference points are established as dose- and time-responses under ideal conditions
(toxicodynamic or toxicokinetic/toxicodynamic steady state) and then departures of increasing com-
plexity are defined.
In 25 years of studying the toxicity of tetrachlorodibenzodioxin (TCDD) and related compounds,
the concept of c x t = k did not emerge in any other experimental context except in the two recent
subchronic and chronic toxicity studies, which were conducted under conditions of toxicokinetic steady
state (Rozman et al. 1996; Viluksela et al. 1997, 1998~. Nevertheless, a general interest in the role of
time in toxicology pervaded the line of thinking presented here for many years (Rozman et al. 1993;
Rozman et al. 1996; Rozman and Doull 1998; Rozman 1998~. Most toxicologists are familiar with
Haber's Rule of inhalation toxicology and its applicability to war gases and some solvents. Much less
reference has been made to Druckrey's work (Druckrey and Kupfmuller 1948, Druckrey et al. 1963,
1964, 1967), which extended the c x t concept to lifetime cancer studies by oral rather than inhalation
exposure. And finally, there is very little cross-referencing of the c x t = k data, which were generated
by entomologists (e.g., Peters and Ganter 1935; Busvine 1938; Bliss 1940) and those established by
toxicologists. History demonstrates that a fundamental relationship in science keeps reappearing in
different contexts, as is the case with c x t = k. During this period many apparent exceptions seem to be
occurring with no satisfactory explanation. Attempts at generalization usually fail until a commonality
is detected among all experiments, as is the case among those that yielded c x t = k. This commonality
is toxicokinetic steady state or irreversibility of an effect, which of course can be interrelated. Anesthe-
sia, like intravenous infusion, leads to rapid and sustained steady state for compounds of short half-life.
Most anesthetics and solvents do have short half-lives and many obey Haber's Rule, except when
measurements are taken while an adaptive process is under way, that is, induction of a protein. Druckrey
and the EDo~-Study used feeding as a route of exposure, which yields a better steady state for com-
pounds of intermediate half-life than, for example, gavage. However, the exponent x in the term of
Druckrey's general formula increases above one rapidly as the half-life of compounds becomes shorter,
because there is intermittent recovery between bouts of feeding. Most of the entomology studies were
related to fumigation, which often but not always resulted in fairly rapid steady state. And finally
1,2,3,4,5,6,7,8-heptachlorodibenzo-p-dioxin (HpCDD), which has a half-life of 314 days (Viluksela et
al. 1997) in female rats yields virtual steady state for a 70-d observation period after any route of
administration but not TCDD with a half-life of 20 d. However, when TCDD's toxicity was studied
under steady-state conditions, its subchronic and chronic toxicity also occurred according to c x t= k
(Rozman et al. 1993~.
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APPROACHES FOR USING TOXICOKINETIC INFORMATION IN ASSESSING RISK
DOSE AND TIME AS VARIABLES OF TOXICITY
Definition of Dose and Time
119
Before analyzing dose and time relationships further, it is useful to come up with clear definitions of
these fundamental variables of toxicity. Due to historical developments, neither dose nor time has been
defined with clarity as variables of both toxicokinetics and toxicodynamics. It is customary to use the
term acute dose and acute effect as if the two were interchangeable. In fact, an acute dose can lead to
chronic effects (Druckrey et al. 1964) and multiple doses can trigger a fulminant episode of toxicity
(Garrettson 1983~. In risk (safety) assessment it is always the total dose delivered that is of concern,
although in therapeutics the daily dose is often referred to simply as the dose. Therefore, a useful
definition of dose in toxicology, would be:
n
Dose = I, Dose Rates
n=1
According to this definition a single acute dose would represent the liminal case when the dose rate
equals the dose. This definition would be valid for any kind of irregularity in the dosing regimens and
is analogous to the definition of dose in radiation biology.
Ever since the dawn of human consciousness, humanity has struggled with the notion of time. It is
not possible to predict what influence the concept of toxicological time will have on our perception of
time. Suffice it to say at this junction, it is not possible to think of toxicty without the implicit presence
of time as a variable, although in toxicological studies, time received only semiquantitative designations
(acute, subacute, subchronic, chronic). In fact, one could view organisms as instruments exquisitely
sensitive to time. Important for toxicology is that the time course of a toxicant in an organism (kinetics)
is very often different than the time course of toxicity (dynamics). Underlying biological processes
(absorption, distribution, elimination, injury, adaptation, recovery) have their own time scales, depend-
ing on the molecular events behind each process (e.g., enzyme induction, receptor regulation either
directly or via gene expression). Thus, in toxicology the dose is a pure variable, but there are many
different processes occurring on different time scales yielding different ~cdt integrals leading to complex
interactions, which can be described as c x to. In spite of this complexity, science can deal with it in a
traditional, analytical fashion. Because only knowledge of rate-limiting steps is required to accurately
describe toxicity, this will often reduce complexity to manageable proportions.
Dose and Time Relationships
Consequences of interactions between a toxic agent and an organism at the molecular level propa-
gate through toxicodynamic or toxicokinetic/toxicodynamic causality chains all the way to the manifes-
tation of toxicity at the organismic level (Figure 1~. If the recovery (adaptation, repair, and reversibility)
half-life of an organism is longer than the half-life of the causative agent in the organism, then toxico-
dynamics become rate-determining (one-compartment model) or rate-limiting (multi-compartment
model). If the toxicokinetic half-life of the compound is longer than the recovery half-life, then
toxicokinetics will be rate-determining (rate-limiting), in which case the toxicokinetic area under the
curve (AUC) will be identical to the toxicodynamic AUC. There are three liminal conditions for c x t = k
that emerge when the causality chain propagates through either toxicodynamic or toxicokinetic/toxico-
dynamic processes:
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120
Toxicodynamics
STRATEGIES TO PROTECT THE HEALTH OF DEPLOYED U.S. FORCES: WORKSHOP PROCEEDINGS
1. In case of no recovery (no reversibility, no repair, no adaptation) linear accumulation of injury
will occur according to a triangular geometry (c x t /2 = k) following repeated doses or according to a
rectangular geometry after a single dose (c x t = k), provided that the c x t lifetime threshold has been
exceeded, which occurs when c threshold. X t lifespan = k.
2. After recovery (reversibility, repair, adaptation) steady state has been reached, injury will occur
according to a rectangular geometry (c x t = k), after exceeding the c x t lifetime threshold.
Toxicokinetics
1. No elimination will lead to linear accumulation of a compound and, as a consequence, to accumu-
lation of injury according to a triangular geometry (c x t/2 = k) after repeated doses or according to
rectangular geometry after a single dose (c x t = k) above the c x t lifetime threshold.
2. After toxicokinetic (and as a consequence toxicodynamic) steady state has been reached, injury
will occur above the c x t lifetime threshold according to a rectangular geometry (c x t = k).
Exposure Frequency
As the toxicokinetic and toxicodynamic half-lives become shorter and shorter, the distinction be-
tween elimination and recovery half-lives becomes less important, because another time-dependence,
that of the frequency of exposure, starts dominating the time-dependence.
1. Compounds having very short toxicokineticltoxicodynamic half-lives will reach steady state
. .. . . . . . . .. . . . . .
rapidly and yield c x t = k upon continuous exposure according to a rectangular geometry, provided that
adaptation and repair are also at steady state.
2. Other types of geometries certainly can be created by elaborate, but regular, dosing regimens.
These scenarios are less likely to play a practical role in toxicology, although they might be of theoreti-
cal interest.
It should be kept in mind that the mathematics of first-order processes, when appropriate, are valid
for bi-molecular reactions (e.g., receptor binding), which result in the propagation of the causality chain
to the level of modeling (Figure 1~. Therefore, 90% of toxicodynamic steady state will not be reached
until 3.32 recovery half-lives have elapsed. Thus, Haber's Rule will be obeyed only if the observation
period is outside of about 4 recovery half-lives or if recovery is a zero order process.
Thus, the various (c x t = k) scenarios represent liminal conditions. The magnitude of the c x t
product is a function of the potency of the compound, of the susceptibility of the organism, and of the
deviation from the ideal conditions and will yield c x tx = k for nonliminal conditions. (Large c x tx
product indicates either low potency, lack of susceptibility, or low exposure frequency.) It must be
recognized that the dose (c) does not have exponential properties, but time (t) does have such properties,
because under nonidea1 conditions toxicity is a function of at least two independent time scales. One
independent time scale is the half-life of the rate-determining step (toxicodynamic or toxicodynamic/
toxicokinetic) of the intoxication (intrinsic property of compound or organism), the other one is the
frequency and duration of exposure. which is independent of both the compound and the organism.
In conclusion, these data and considerations of a significant body of evidence accumulated over the
last 100 years suggest that c x t = k is a fundamental law of toxicology, and possibly of biology in
general, that can be seen only under ideal conditions. If confirmed using other classes of compounds
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APPROACHES FOR USING TOXICOKINETIC INFORMATION IN ASSESSING RISK
12
and the ideal conditions described here, then Paracelsus' famous statement might have to be supple-
mented to read Dosis et tempus fiant (faciant) venenum (Dose and time together make the poison).
Implications for risk assessment are that the margin of exposure (MOE) must be defined in terms of both
dose and time. This can be done by relating the real-life exposure scenario to that of the ideal exposure
condition:
MOE= cxt
cxt
Above the c x t lifetime threshold, this will yield the margin of safety and its reciprocal, the margin of
risk.
Figure 1 might also be viewed as a decision tree to identify critical steps needed for modeling to
predict toxicity. It is important to note that a high degree of irreversibility and toxicokinetic steady state
are rare phenomena in toxicology, although both can be seen any time when the observation period is
much shorter than the recovery or the elimination half-life. In the real-life situation, there are usually at
least two or three rate-limiting steps in toxicokinetics and likely as many in toxicodynamics. It must be
emphasized though, that multiple toxicokinetic compartmental models do not necessarily require mul-
tiple toxicodynamic models, and vice versa. However, if there are three different rate-limiting processes
occurring on different time scales in toxicokinetics and three different rate-limiting processes taking
place on three different time scales in toxicodynamics, such a scenario would represent a formidable
computational task for a theoretical treatise. Therefore, a practical approach would be to conduct
experiments at toxicodynamic steady state (which of course would require a preexisting toxicokinetic
steady state in many instances) as a point of reference clearly defined by c x t = k. Then, experiments
need to be carried out for different compounds with different half-lives to establish model parameters,
which describe departures from toxicokinetic/toxicodynamic steady state of increasing frequency and
irregularity.
In summary, c x t = k represents the most efficient (a kind of worst-case) exposure scenario for
producing an effect, namely continuous exposure until manifestation of an effect. Experimentally, this
condition is often met by continuous inhalation exposure (e.g., Gardner et al. 1977), or daily oral
administration of compounds that have toxicodynamic/toxicokinetic half-lives of a few days or longer
or effects that are essentially irreversible. It must be emphasized that any departure from the worst-case
scenario will result in a change of c x t = k into c x tX= k. Departures are represented by regular or
irregular interruptions of exposure or intermittent recovery from injury. The larger the departure, the
larger will be x, and with that k. It is somewhat counterintuitive, but increasing x and k are equivalent to
decreasing toxicity. This is entirely logical. however. when it is recognized that increasing interruptions
~ ~ _
~ ~ ~ ~ , , ~ ~ ~
,. . . ... .. . . .. . . .... . . . . . . . . ..
ot exposure or Injury Will result In longer and longer periods ot time needed to cause equivalent tOXlClty
to that of continuous exposure, because of increasing intermittent recovery. A liminal condition for
first-order processes will be reached when exposure occurs outside of 6.6 toxicokinetic/toxicodynamic
half-lives, because at that time 99% elimination or recovery will have occurred. Under such conditions
(which are closest to the real-life situation for most compounds), toxicity will be less dose-dependent
and toxicokinetic/toxicodynamic time-dependent, and mainly the frequency of exposure will determine
x. If x is then determined experimentally, for example, for 1, 2, 4, 8, 16, and 32 days for a compound
with a toxicokinetic/toxicodynamic half-life < 3.6 h after continuous versus intermittent exposure under
isoeffective conditions, then plotting the data will allow extrapolation to any exposure scenario outside
of 6.64 half-lives (which corresponds to 1 day). Most dietary constituents fall in this category. For zero-
order processes, 2 half-lives are needed for elimination or recovery. It should be kept in mind that the
half-life of zero-order processes (unlike that of first-order processes) is dependent on concentration.
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STRATEGIES TO PROTECT THE HEALTH OF DEPLOYED U.S. FORCES: WORKSHOP PROCEEDINGS
Analogy to Thermodynamics
In physics, Boyle's Law of ideal gases, gave rise to thermodynamics, and molecular and mechanistic
considerations led to a theory of gas reactions. The former is based on the idea of finding the minimum
number of fundamental variables that can describe the simplest possible dynamic system (P x V= k for
ideal gases). The latter required a great deal of knowledge about the mechanism of chemical reactions,
such as wall reaction and activation energy. Both of these approaches have been attempted in toxicology
with, as yet, limited success, as shown in subsequent discussions in this paper. The reason for the lack of
advance in theoretical toxicology is probably due to the fact that, unlike thermodynamicists, toxicologists
did not start out with defining the simplest possible toxicological conditions with a minimum number of
variables as a point of departure toward more complexity. Coincidentally, experiments were conducted
under such ideal conditions and in every such instance Haber's Rule proved to be applicable (Gardner et al.
1977), even though researchers might have failed to notice it (Sivam et al. 1984~.
The lack of conceptualization of the three variables of toxicity resulted in arbitrary study designs,
which further eroded the predictability from one experiment to another. It is this author' s opinion that
analogous thinking to thermodynamics might help to optimize study design and eventually to build a
theory of toxicology. Thermodynamics, like toxicology, has three fundamental variables (P. V, and T
versus c, t, and W). (W E German for Wirkung]) will be used for effect, because of the many Es
("exposure, elimination, effect, excretion] in English.) Before the development of a comprehensive
theory of thermodynamics, it was clear to scientists that to study an independent and a dependent
variable, a third or other variables had to be kept constant. This has not been done in toxicology,
although most dose-response studies have been conducted at constant time (isotemporal). However, to
study the relationship between time and effect, the dose needs to be kept constant (isodosic). Moreover,
to examine the relationship between dose and time, the effect must be kept constant (isoeffective). The
c x t product will not emerge from the equation of ergodynamics (Figure 2) until after elucidation of the
relationship between specific effect at constant time and specific effect at constant dose. In other words,
more must be learned about k before significant theoretical advance is possible. As mentioned before,
most experiments have been conducted isotemporally in the past (14 d, 90 d, 104 wk), which is
appropriate for dose-response studies. The arbitrary choice of these time points and the inexactitude of
diagnosis (stuff them and count them) led to a great deal of confusion in the 14-day studies, because
different dose responses with different mechanisms were often lumped together. Experiments in toxi-
cology have frequently been conducted under isoeffective conditions, mainly with the endpoint being
100% of an effect (mortality. cancers. However. systematic investigation of c x t = k has not been done.
~ , As, ~ . .
O
for example, at 20 or 80% of an effect. Finally, there have been very few experiments conducted under
isodosic conditions, because this requires that the concentration be kept constant at the site of action.
The only experiment-driven condition when this is often the case is inhalation exposure. Gardner et al.
(1977) have reported such data after continuous exposure of experimental animals to benzene and SO2
when the endpoint in question was measured immediately after termination of exposure (chronaxy,
leukopenia). However, when the endpoint of measurement was not immediately done (streptococcal
infection-related mortality) after cessation of NO2 exposure, the time response started flattening out
(Gardner et al. 1979~. A systematic investigation of these issues has been done recently for HpCDD
after oral administration with as yet only one endpoint of toxicity (delayed acute toxicity), although
preliminary analysis indicates that there are other valid endpoints such as anemia and lung cancer
(Rozman 1999~. These data provide support for the suggestion of Rozman et al. (1996) that the dose-
time-response be viewed as a 3-dimensional surface area similar to, but conceptually distinctly different
from, the model of Hartung (1987) (Figure 3~. Experiments conducted under isoeffective conditions
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APPROACHES FOR USING TOXICOKINETIC INFORMATION IN ASSESSING RISK
ERGOI)YNAMICS
dew—~ dc+6 ~ dt
L~c)~ :~)c
—~ dc~ ~ dip
Lo~cJI ~ ~ )c
dW= 0 isoeffect~ve
owe] dc
i ~ 'c
dt = 0 isotemporal
dc ~ O isodosic
FIGURE 2 Definition of toxicity in
analogy to thermodynamics.
123
/
. '
-
stice /1
/
FIGURE 3 Schematic presentation of the dose-time-
response surface area showing slices for isoeffective
(hyperbolas), isodosic (S-shaped time response), and
isochronic (S-shaped dose response) responses.
(slices parallel to the dose-time plane) correspond to Haber' s Rule of c x t = k represented by hyperbo-
las. Studies carried out under isotemporal conditions (slices parallel to the time-effect plane) yield S-
shaped dose-response curves along which c x t = k x W whereas isodosic investigations (slices parallel
to the dose-effect plane) produce S-shaped time-response curves along which c x t = k x W also. Indeed,
plotting the c x t product against effect (W) for HpCDD for doses causing about 10 to 90% wasting/
hemorrhage, yielded a straight line of high correlation (r2 = 0.96) (Figure 4~. This is the beginning core
of a theory of toxicology, which is analogous to P x V = k for isotherms, and P x V = k x T for isobars
or isochors. Of course, thermodynamicists know that k = n x R (n = number of moles; R = gas constant),
but toxicology is not yet there. What is clear already at this junction is that the dimension of P x V is
energy, whereas the dimension of c x t is energy x time, which is action and is called effect in toxicology
(Figure 5~.
DECISION TREE
A recent series of articles explored how other disciplines deal with complex systems (Goldenfeld
and Kandanoff 1999; Whitesides and Ismagilov 1999; Weng et al. 1999; Koch and Laurent 1999~.
Goldenfeld and Kandanoff (1999) made some important observations, that are relevant for toxicology.
Simple laws of physics give rise to enormous complexity when the number of actors is very large. The
same paradox exists in toxicology in that the c x t concept is very simple, but the "real world" of the
manifestation of toxicity is very complicated. Their other observation is equally relevant; "Use the right
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APPROACHES FOR USING TOXICOKINETIC INFORMATION IN ASSESSING RISK
Risk Assessment for Soman
Single dose, subcutaneous exposure:
c x t = 17~858 uc/kc/min (Sivam et al. 1984)
139
, , ~
17,858 / (24 x 60) = 12.4 uglkglday
This is valid if exposure is continuous and effect entirely irreversible.
Primates are about 10 times more sensitive, because of the lower levels of the nonspecific esterases
(as a detoxification sink) (Anzueto et al. 1986; 1990)
12.4/10= 1.24 uglkglday
Primates are very similar to each other, including humans (Talbot et al. 1988)
The dose response for soman is extremely steep, at most a factor of 2
1.24/2 = 0.62 uglkglday (Acts et al. 1985)
Recovery half-life from soman intoxication is estimated at 12 h (Sterri et al.1980; Lintern et al.1998)
Therefore, if exposure occurs outside of 6.64 recovery half-lives, there will be no accumulation of injury.
If exposure occurs within 6.64 recovery half-lives, there will be accumulation of injury to steady
state after 6.64 half-lives.
As a first approximation, the daily reference dose needs to be divided further by the number of days
exposure occurred.
Oral
1-day deployment exposure limit (DEL) by ingestion: 0.62 uglkglday
14-day DEL by ingestion: 0.04 uglkglday
30-day DEL by ingestion: 0.02 uglkglday
These are probably very conservative estimates because organophosphates have strong hepatic first-
pass effect and these numbers were derived from subcutaneous injection, which is kinetically closer to
inhalation than ingestion. This notion is supported by the similarity of the c x t product after inhalation
and subcutaneous injection.
Inhalation (Acts et al. 1985)
c x t = 520 mg/m3/min at a concentration of 21 mg/m3
t= 24.8 min
Rats (~150 to 200) inhale about 500-600 ml air/min (Druckrey et al. 1967)
According to calculations using metabolic body size and caloric utilization (Kleiber, 1975; Kleiber,
1975), rats of this size should have a breathing rate of 481 ml/min, which is close to Druckrey's
estimate.
Converting inhalation to oral dose:
500 ml/min air inhaled for 24.8 min ~ 12,400 ml ~ 12.41 ~ 0.0124 m3
at 21 mg/m3 ~ 0.2604 mg/rat for a 260 g rat ~ 1.002 mg/kg = 1,002 g/kg
c x t= 24,848 g/kg/min
This is very similar to the subcutaneous c x t (17,858 ,ug/kg/min).
c x t= 520 mg/m3/min
Primates 10 times more sensitive than rats (Anzueto et al. 1990)
c x t= 52 mg/m3 /min
Steep dose response of factor 2
c x t = 26 mg/m3/min (LOEL)
c x t= 433 ugim31h
cxt= 18.0 uglm31day
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140
STRATEGIES TO PROTECT THE HEALTH OF DEPLOYED U.S. FORCES: WORKSHOP PROCEEDINGS
Breathing-rate conversion of rat to human' s ~ 3.7
c x t= 66.6 ,ugim316ay
Because this represents an estimated lowest-observable-effect level (LOEL), risk managers might
divide it by a safety factor of 10 to ascertain that no one will be exposed to near toxic concentrations of soman.
1-day deployment exposure limit (DEL): 7 ,ug/m3
14-day DEL: 0.5 ,ug/m3
30-day DEL: 0.2 ,ug/m3
These values are DELs for continuous exposure. If exposure is intermittent, the following rule will
provide protection: If exposure occurs outside of 6.62 recovery half-lives (3.3 days at a half-life of ~ 12 h) the
1-day DEL will provide protection for all scenarios, because there will be no accumulation of injury.
The 1-day DEL should not be exceeded if exposure occurs for shorter durations (e.g., 1 h or 10 min),
because in 24 h there will be only 75% recovery and injury will proceed to steady state, and after 3.32
half-lives it will be accumulating according to c x t= k.
APPENDIX 2
Strategies for Developing Exposure Guidelines of Deployed Forces
Development of exposure guidelines from existing databases (ACGIH, NIOSH, OSHA):
(1) Identify if compound exerts its rate-determining steppes) by toxicodynamic or toxicokinetic
means (Figure 1~.
(2) Narrow down critical steppes) to injury/absorption or elimination/recovery or further to adapta-
tion/distribution, repair/biotransformation, and reversibility/excretion.
(3) Estimate half-life of critical stepts).
This is a very important step. Failure to identify the proper process and its half-life can lead to
erroneous conclusions. This can be illustrated with a pharmacological example to indicate the univer-
sality of this approach.
Omperazole is a H+ -ion pump inhibitor. The binding half-life to its receptor is 24 h. Its
biological half-life is about 1 h. If the therapeutic dose would be based on the biological half-life of
the compound, the conclusion would be that after 6.64 half-lives (6.64 h) 99% of the drug would be
eliminated. Therefore, a dosing regiment entailing the administration of the drug every 6 h still would
yield a very poor steady state and, with that, moderate to low therapeutic efficacy. Omperazole in fact
is given daily once or every other day in accordance with its pharmacodynamic half-life of 24 h. It
has been reported that it takes 3 days for maximum effect (clinically indistinguishable from 3.32 half-
lives) and 3 to 5 days for cessation of effect, which is clinically also indistinguishable from 3.32
reversibility half-lives. The action of this drug is entirely dominated by D and any opinion, based on
K, would be in error.
(4) Because threshold limit values (TLVs), short-term exposure limits (STELs) and ceilings
(ACGIH), permissible exposure limit (PELs) (OSHA), and recommended exposure levels (RELs) (NIOSH)
represent NOAELs, one could use these values and convert them to any given deployment situation by
considering duration and frequency of exposure along with the half-life of the critical step, which could
be designated as exposure kinetics (see equation in Figure 1~. A twofold critical question is: When are
time-weighted averages (TWAs) and when are peak concentrations important for converting these
standards into standards for various deployment situations?
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APPROACHES FOR USING TOXICOKINETIC INFORMATION IN ASSESSING RISK
Derivation of DEL When Toxicokinetics Is Rate-Determining
Very long toxicokinetic half-lives
141
Compounds having half-lives of years or longer (e.g., mirex, dioxins, cadmium, asbestos) are the
simplest to deal with. (It is amazing that regulatory agencies have been struggling with this for
decades.)
For such compounds, any c x t conversion will be fairly accurate without regard to route and
frequency of exposure. A single high dose exposure will not be much different from exposure to
proportionally smaller daily dose rates. Thus, for these types of compounds, there is little difference
between TWA and peak exposure.
Example: cadmium half-life _ 30 years (in humans)
Inhalation
TLV (ACGIH): 0.01 mg/m3, 8-h TWA for 5 days/week for 45 years at 10 m3/8 h
Total dose: 1,170 mg/70 kg person
16.7 mg/kg
1-day limit by inhalation: 1,170 mg/20 m3 = 58.5 mg/m3 at 20 m3 (air inhaled/24 h)
Similar to radiation, this is a ceiling value for total exposure, which might not be exceeded. Persons
must be protected from further exposure. It is a risk management decision to reduce this number, e.g.,
by dividing it by 10.
1-day deployment exposure limit (DEL) by inhalation: 5.9 mg/m3
14-day DEL by inhalation: 0.4 mg/m3
3-month DEL by inhalation: 0.2 mg/m3
Oral
Conversion of inhalation to oral dose:
20 m3 x 5.9 mg/m3 - 70 kg = 1.69 mg/kg
Absorption of cadmium salts in the GI tract is very limited at 5 to 8% of dose (Goyer 1996), which
provides additional safety.
1-day DEL by ingestion: 1.69 mg/kg
14-day DEL by ingestion: 0.12 mglkglday
3-month DEL by ingestion: 0.06 mglkglday
It is a risk management decision to reduce these numbers to leave room for reserve capacity, although
the safety factor does not have to be large, because of low fractional absorption, which reduces systemic
exposure by nearly a factor of a 100.
Dermal
Dermal penetration of cadmium salts and of highly lipophilic compounds of very long half-life is very
inefficient.
Intermediate toxicokinetic half-lives
For compounds having a half-life 3.6 h or longer, but shorter than months or years, elimination
will not be complete within 24 h after a single dose. This is important, because, as a consequence,
recovery from injury will also not be complete. Recovery from injury by chemicals having inter-
mediate half-lives will be probably as often rate-determining (rate-limiting) as the biological half-
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STRATEGIES TO PROTECT THE HEALTH OF DEPLOYED U.S. FORCES: WORKSHOP PROCEEDINGS
life. Therefore, a discussion of these types of chemicals will be also found in the toxicodynamic
section as well. For such compounds, peak exposures as well as TWA concentrations will be of
consequence. Therefore, particular attention must be paid to the ratio between the biological half-
life and various exposure scenarios when setting DELs for such chemicals. It is worthwhile to
consider that the half-life of 3.6 h represents among this class of compounds the best case scenario,
because the longer the half-life, the higher the accumulation will be by the time a steady state is
reached.
Example: monochloroacetic acid (MCA)
half-life _ 4 h (rats)
The half-life is probably very similar in humans because the mechanism of toxicity is the same and
the rat's LD50 = 75 mg/kg is similar to the human's lethal dose _ 220 mg/kg.
Inhalation
TLV recommendation: 2 mg/m3,8-h TWA for 5 days/week for 45 years at 10 m3/8 h
Total dose: 234,000 mg/70 kg person
3,343 mg/kg
1-day DEL by inhalation: 1 mg/m3 at 20 m3/24 h
14-day DEL by inhalation: 0.07 mg/m3
3-month DEL by inhalation: 0.03 mg/m3
This is the most conservative conversion, assuming continuous exposure. A comparison of the 1-day
total DEL (20 ma) with the total occupational exposure limit (OEL) in 45 years (234,000 ma) indicates
how sensitive these type of compounds are to the frequency of exposure.
After 6.64 half-lives, 99% of steady state will be reached. The half-life of MCA is about 4 h, and
steady-state concentration will be reached after about 1 day. Thereafter, the AUC will increase accord-
ing to c x t (above the lifetime threshold) if exposure is uninterrupted.
However, if exposure is intermittent, say for 1 h every day, then higher levels might be tolerated
without adverse effect, because complete (99%) elimination/recovery will occur between any two
episodes of exposure.
1-hour DEL by inhalation: 16 mg/m3 at 1.25 m3/h air inhaled
Oral
Assuming six (three eating and drinking and three additional drinking) intake episodes per day with
a half-life of 4 h, almost 99% of steady state will be reached after 1 day. Continuous exposure for 14 or
30 days will be occurring with smaller or larger fluctuations between Cmaximum serum contration an] Cminimum
serum concen~cra~cion if eating/drinking are not equally paced, which will not effect the average AUC. There-
fore, safe levels can be calculated for oral exposure according to c x t = k also for this compound.
Conversion of inhalation dose to oral dose:
1 mg/m3 x 20 m3 (air inhaled/ 24 h) = 20 mg/70 kg person = 0.3 mg/kg
The same (cumulative) dose can be ingested safely during 14 or 30 days of deployment according to the
most conservative conversion, which assumes repeated exposures every day.
1-day DEL by ingestion: 0.3 mg/kg
14-day DEL by ingestion: 0.02 mglkglday
30-day DEL by ingestion: 0.01 mglkglday
Again 1-h ingestion (single daily exposure) might be higher since there will be 99% elimination/
recovery within 24 h.
1-hour DEL by ingestion: 7.1 mg/kg if no further exposure occurs on that day.
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APPROACHES FOR USING TOXICOKINETIC INFORMATION IN ASSESSING RISK
143
Dermal
Dermal toxicity of MCA is similar to its oral toxicity as dermal penetration of MCA is extremely
efficient, particularly at higher temperatures. Therefore, the same numbers are recommended for
dermal exposure as for oral exposure.
As the half-life of compounds becomes longer than about 4 h, accumulation to steady state will take
correspondingly longer. Nevertheless, c x t conversions will remain conservative (but not extremely
conservative and not arbitrary) estimations of safe levels of exposure, because the increase of AUC during
the ascending phase of the exposure curve will be smaller than at steady state. With increasing half lives,
deviations from c x t =k will become less dependent on the frequency and duration of exposure.
Very short toxicokinetic half lives
If half-lives are shorter than 3.6 h then more than 99% of the compound will be eliminated within 24
h of exposure. With such compounds, the frequency of exposure will become more and more important
as the half-life decreases further, because of increasing periods of recovery between exposure episodes.
Example: Methylene chloride (MCI)
half-life _ 5 to 40 min (humans), indicating an average of 22.5 min
Inhalation
TLV: 174 mg/m3, 8-h TWA for 5 days/week for 45 years at 10 m3/8 h
For compounds of very short half-life, it is not meaningful to use the c x t conversion unless
exposure is continuous, because of rapid elimination/recovery after cessation of exposure. Rapid
elimination/recovery in turn reduces time-dependence of toxicity. Compounds having very short half-
lives will be mainly concentration-dependent, particularly when considering short time scales such as 1
day, 14 days, or 30 days. In fact, toxicity of such compounds depends primarily on the time scale of
frequency and duration of exposure in addition to the dose (concentration). For these reasons, an GEL
of 25 to 50 parts per million (ppm) (86.8 to 174 mg/m3) was derived for MCI from impaired flicker
fusion reflex data (4-h exposure) in humans (Storm and Rozman 1998~. Although this behavioral effect
is highly reversible, it impairs optimum performance. Therefore, in a deployment situation these values
could be used as ceilings not to be exceeded. Because these values were derived with continuous
exposure, the 1-hour DEL (continuous exposure) could be set based on c x t yielding 100 to 200 ppm
(348 to 696 mg/m3~. However, longer-term intermittent exposures should use the ceiling approach:
1-day DEL by inhalation: 174 mg/m3
14-day DEL by inhalation: 174 mg/m3
30-day DEL by inhalation: 174 mg/m3
1-hour DEL by inhalation: 696 mg/m3
Oral
Because of significant first-pass biotransformation, oral DELs require additional considerations, but
they would be higher than those obtained for inhalation.
Derivation of DEL When Toxicodynamics is Rate-Determining
Compounds having very long recovery half-lives
There are few examples for recovery taking place on a time scale of years or longer. Damage to
neurons (e.g., lead encephalopathy) is the closest example that comes to mind. Because of the enormous
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STRATEGIES TO PROTECT THE HEALTH OF DEPLOYED U.S. FORCES: WORKSHOP PROCEEDINGS
reserve capacity and plasticity of the nervous system, it is difficult to conduct conclusive studies in this
area. Unlike compounds with very long toxicokinetic half-lives (which amounts to continuous expo-
sure), both the frequency and duration and the kinetics of compounds are important when dynamics of
the effects are rate-determining. When the toxicokinetic half-life of a compound is long (lead), a TWA
approach (c x t = k) will be the best way to protect deployed forces, whereas in the case of short half-life
compounds (methanol), the ceiling approach must be applied to prevent the beginning of accumulation
~ · .
at injury.
Example: lead
half-life _ 20 years
Inhalation
TLV: 0.05 mg/m3, 8-fur TWA for 5 days/week for 45 years at 10 m3/8h
Total dose: 5,850 mg
5,850 mg/20 m3= 293 mg/m3
It might be advisable to reduce these numbers by a safety factor of 10.
1-day DEL: 29.3 mg/m3
14-day DEL: 2.1 mg/m3
30-day DEL: 1.0 mg/m3
1-hour DEL should not significantly exceed the TWA, even if exposure remains infrequent.
Oral
Conversion of inhalation to oral dose:
20 m3 x 29.3 mglm3170 kg = 8.4 mglkg
Adults absorb 5 tol5% of ingested lead, which provides enough margin of safety.
1-day DEL: 8.4 mglkg
14-day DEL: 0.6 mglkg/day
30-day DEL: 0.3 mglkg/day
Dermal
Insignificant.
Example: methanol
Inhalation
TLV: 200 ppm = 262.1 mg/m3
It is not appropriate to use a TWA for methanol, because in this case accumulation of injury will
be a function of the frequency of exposure above the threshold. Any exposure above the threshold
will be cumulative. Therefore, to protect deployed forces from such scenarios a ceiling must be
established.
1-day DEL: 262.1 mg/m3
14-day DEL: 262.1 mg/m3
30-day DEL: 262.1 mg/m3
Intermediate toxicodynamic half-lives
Recovery from injury caused by compounds having a toxicodynamic half-life of 3.6 h or longer, but
shorter than years, will be incomplete after 1 day. In the best-case scenario of 3.6 h, recovery will be
99% complete. However, even for such compounds, c x t = k would be running at about 1% residual
damage. This might be of little consequence if exposure is intermittent, but in some instances it might
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APPROACHES FOR USING TOXICOKINETIC INFORMATION IN ASSESSING RISK
145
represent a hazard. A better illustration of this point can be made by using nitrosamines as examples.
Nitrosamines are strong alkylating agents with short toxicokinetic half-lives (Druckrey 1967~. How-
ever, the repair half-life of the DNA abducts is about 20 to 40 days. Consequently, the steady state of
DNA damage will not be reached until about 200 days (on average). Thereafter, damage will accumu-
late according to c x t = k. Just like a single dose of a chemical having very lone toxicokinetic half-lives
O O . O . , O
, ~ . . . . , ~
can cause cancer (Kozman lady), single doses of d~alkyln~trosam~nes can also cause cancer (L,ruckrey
et al. 1964~. If one mole (approximate LD50) of dimethylnitros amine is administered to rats, and
assuming that 0.0001 % of it will end up binding to DNA, this will still yield 6 x 10~7 abducts. With a 30-
day toxicodynamic half-life this will leave a 900-day old rat still with about 6 x 108 abducts. It is very
likely that the traditional distinction between initiators and promoters in carcinogenesis is due to the
respective compounds having toxicokinetic or toxicodynamic processes as rate-determining steps in
their mechanism of action.
Example: dimethyl-or diethyluitrosamine
TLV: This is a compound listed in the TLV booklet without a value.
Dimethylnitrosamine's carcinogenicity was studied by Druckrey et al. (1963) under isoeffective
conditions (100% carcinomas). Different daily dose rates of diethylnitros amine yielded a c x t = k equal
to 73,248 + 5,234 (SE) mglkglday. Druckrey et al. (1967), like everybody else, viewed the daily dose
rate as dose. Therefore, they plotted the daily dose rate versus time to derive a slope, which yielded the
equation C X t2-3 = k. This erroneous view led to the introduction of the notion about the reinforcing
action (200-fold) of low doses. This mistake was due to the fact that their studies were not conducted
under isotemporal conditions. Therefore, some rats received on the average 68 dose rates, whereas
others received up to 840 dose rates. In fact, the difference in terms of cumulative dose was only 15-fold
between the highest and lowest dose, which is comparable to the difference in induction time (12-fold).
Suffice to say that Druckrey et al.'s (1963) data are in fact very consistent with c x t = k, when viewing
the dose as the sum of all dose rates.
Derivation of DELs from the c x t data:
c x t = 73,248 _ 15,700 (SD)
Rat: c x t~ifespan = 73,248 mglkglday
Lifespan of rat: 900 days
c = 73,248/900 = 81.4 mg/kg
This is the minimum dose required to cause cancer in rats after lifetime exposure. If it was chosen
to protect rats from the carcinogenic effects of diethylnitrosamine to the extent of 99.94% (3 SD), then
this dose would be:
c x t = 73,248 _ 15,700 (SD)
73,248 - 47,100 = 26,148/ 900 = 29.1 mg/kg
However, humans do not live 900 days, so let us assume 75 years (27,375 days). Under assumption
of equal sensitivity this would yield a minimum carcinogenic dose in humans of 26,148/ 27,375 _ 1 mglkg
If human in vivo repair of DNA abducts were known, this number could be adjusted quite accurately,
and species differences could be dealt with in a scientific rather than arbitrary fashion.
A small safety factor might be applied by risk managers to move from a LOAEL to a NOAEL. The
number should be small, because individual sensitivity was corrected for based on normal distribution
rather than on arbitrary assumptions.
Inhalation
0.5 mg/kg x 70 kg = 35 mg/kg
35 mg/20 m3= 1.75 mg/20 m3 (air inhaled/ 24 h)
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146
Oral
Dermal
STRATEGIES TO PROTECT THE HEALTH OF DEPLOYED U.S. FORCES: WORKSHOP PROCEEDINGS
1-day DEL: 1.75 mg/m3
14-day DEL: 0.13 mg/m3
30-day DEL: 0.06 mg/m3
1-day DEL: 0.5 mglkg
14-day DEL: 0.04 mglkg/day
30-day DEL: 0.016 mglkg/day
Because it is a small amphophilic molecule, it will be readily absorbed through the skin. If needed,
the oral data apply.
Very short toxicodynamic half-lives
The distinction between toxicokinetic and toxicodynamic half lives becomes fuzzy for compounds of
very short recovery half-lives (<3.6 hi, because for both of them another time scale (frequency of expo-
sure) becomes the dominant time function. A very short recovery half-life implies rapid reversibility, or
repair, or adaptation. Infrequent exposure to such compounds will have the least toxicological conse-
quences, although in the case of air this could become rapidly fatal.
The efficient repair of oxygen-induced DNA repair appears to be a good example for rapid reversibility
(Ames, 1989; Fraga et al. 1990~. It takes continuous exposure to air over a lifetime to result in accumu-
lation of oxidative damage in the form of aging.
Acknowledgement
Even though I am sole author of this paper for technical reasons, Dr. John Doull's intellectual
contribution to the conceptualization of time along with dose as variables of toxicity must be recog-
nized. Although I did much of the thinking and all of the writing, his daily probing of the ideas and his
profound knowledge of toxicology were invaluable in the development of the concepts presented.
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Representative terms from entire chapter:
continuous exposure
