49, 102–109 (1999)
Copyright © 1999 by the Society of Toxicology
TOXICOLOGICAL SCIENCES
Delayed Acute Toxicity of 1,2,3,4,6,7,8-Heptachlorodibenzo-p-Dioxin
(HpCDD), after Oral Administration, Obeys Haber’s
Rule of Inhalation Toxicology
Karl K. Rozman 1
Department of Pharmacology, Toxicology, and Therapeutics, University of Kansas Medical Center, Kansas City, Kansas 66160; and Section of
Environmental Toxicology, GSF-Institut für Toxikologie, Neuherberg, 85758 Germany
Received September 4, 1998; accepted January 8, 1999
Eight different doses (2.5 to 10.0 mg/kg) of 1,2,3,4,6,7,8-heptachlorodibenzo-p-dioxin (HpCDD) were administered acutely to a
total of 272 female Sprague-Dawley rats. The doses ranged from a
NOAEL for wasting/hemorrhage to supralethal doses. Dose-and
time-responses of wasting/hemorrhage, anemia, and cancer were
and are being studied as end points of toxicity. The experiments
will be continued until the last rat dies. There was a very steep
dose- and time-response between the LOAEL for wasting/hemorrhage (2.8 mg/kg) and the third highest dose (4.1 mg/kg) of
HpCDD. The dose-and time-responses were nearly symmetrical,
obeying Haber’s Rule of inhalation toxicology (c 3 t 5 constant)
even beyond 100% mortality. Introduction of a minimum of 25%
body weight loss as a discriminatory criterion to separate wasting
from hemorrhage as the primary cause of death reduced variability from 5.8 to 3.2%. An arithmetic plot of the dose and time data
resulted in a nearly perfect hyperbola. A logarithmic plot of these
data yielded a straight line of similar perfection. Dose-response
data at constant times illustrate the shifting of the dose-response
curve towards a liminal value, which represents the necessary
observation period for this effect. Time-response data at constant
doses demonstrate the shifting of the time-response curve towards
a liminal value, which represents the LOAEL for the dose-response
of this effect. A three-dimensional plot of dose- and time-response
data depicts the surface area on which c 3 t is constant along
hyperbolas, in terms of wasting as the end point of toxicity.
Surviving rats in all groups started developing anemia 126
days after dosing, but no rat died of wasting/hemorrhage after
day 74. Rats surviving anemia began to die of lung cancer as of
day 397 after dosing. Thus, although the experiment has been
completed as far as dose- and time-responses of wasting/hemorrhage are concerned, it will be about another 2 years before
complete dose and time responses will become available for anemia and lung cancer.
Key Words: 1,2,3,4,6,7,8-heptachlorodibenzo-p-dioxin (HpCDD)
toxicity; Haber’s Rule; oral administration; anemia; wasting/
hemorrhage; rat.
The first widely circulated statement about the role of time
in toxicology (inhalation concentration of war gases 3 exposure time 5 constant) is attributed to Haber (1924), although
some awareness of it was present earlier as indicated by the
work of Warren (1900) and Ostwald and Dernoscheck (1910).
Warren (1900) studied the toxicity of sodium chloride in Daphnia magna (Straus). Ostwald and Dernoscheck (1910) also
investigated the toxicity of sodium chloride, both in Daphnia
magna and Gammarus. Flury and co-workers examined the
relationship between toxic effects, dose, and time, stated as
inhalation concentration (c) 3 time (t) 5 constant, for a large
number of gases and vapors, mainly in cats. They confirmed
this relationship for a number of compounds but also found
many exceptions (e.g., Flury and Wirth, 1934). The toxicological endpoints measured were usually anesthesia and death.
Haber’s Rule eventually fell in disfavor to the point that most
recent textbooks of toxicology do not even mention it.
The c 3 t concept emerged again in an entirely different area
of toxicology, namely in cancer research. Druckrey and
Küpfmüller (1948) reported that the latency period of butter
yellow-induced cancer occurred in agreement with the dose 3
time 5 constant concept, i.e., increasing doses resulted in a
decreasing latency period, but the overall product of dose 3
time remained constant. However, Druckrey (1967) also found
many exceptions to this rule and eventually suggested that the
latency period in cancer formations obeys the general rule of
dose 3 time x 5 constant, where x can assume values between
1 and up to about 6. Recent reliance on the linear no-threshold
dose-response assumption, which was introduced in cancer risk
assessment by Crump et al., (1976) effectively ended this line
of research, because it included the underlying assumption that
time was not a variable at low doses. This assumption is in
stark contradiction to the herein-presented c 3 t concept. The
latter implies that there is a dose that will have no effect: during
the natural life span of a given species. This dose, according to
this concept, is a practical threshold dose:
1
Address correspondence to Department of Pharmacology, Toxicology and
Therapeutics, University of Kansas Medical Center, Kansas City, KS 66160 –
7417. Fax: (913) 588-7501. E-mail: [email protected].
102
cthreshold 5
constant
tlifespan
103
HABER’S RULE IS VALID FOR HpCDD TOXICITY
Dose and time dependencies in the form of c 3 t x 5 constant
kept surfacing in other large cancer studies such as the ED 01
(Littlefield et al., 1980) and the BIBRA Study (Peto et al.,
1991). The ED 01 Study was the largest toxicology experiment
ever conducted, examining the carcinogenicity of 2-acetaminofluorene in about 25,000 mice. The Bibra Study used about
4000 rats to investigate the carcinogenicity of nitrosamines. In
a series of papers, Rozman et al., (1993, 1996); Rozman and
Doull (1998) and Rozman (1998) suggested that the relationship c 3 t 5 constant might be generalizable for all of
toxicology, and as such it could be a reflection of a fundamental characteristic of nature. In these experiments, the a priori
hypothesis was tested that the c 3 t 5 constant relationship is
valid for the delayed acute toxicity of a highly lipophilic
chemical of very long half-life, after oral administration. The
rationale for these criteria was that the observation period
had to be much shorter than the half-life of a compound, in
order to provide near steady state conditions after acute oral
dosing. Because it satisfied these criteria, and because a previous study indicated that the development of preneoplastic
foci occurred in female Sprague-Dawley rats according to c 3
t 5 constant in terms of the surface area of ATPase-deficient
foci (Rozman et al., 1996), 1,2,3,4,6,7,8-heptachlorodibenzop-dioxin (HpCDD) was chosen as a prototype compound.
MATERIALS AND METHODS
Chemicals. 1,2,3,4,5,6,7,8-heptachlorodibenzo-p-dioxin (HpCDD), CAS
No. 35822– 46 –9, mw 425.4, purity 98.7%, was obtained from Cambridge
Isotope Laboratories Inc. (Woburn, MA). Analysis by GC/MS at the GSFInstitut für Ökologische Chemie (85758 Neuherberg, Federal Republic of
Germany) revealed that the impurities structurally related to HpCDD were
different isomers of hexachlorodibenzo-p-dioxin (HxCDD) (1,2,4,6,7,9HxCDD 0.020%; 1,2,3,6,7,9-HxCDD, 0.032%; 1,2,3,4,7,8-HxCDD, 0.144%;
1,2,3,6,7,8-HxCDD, 0.079%; 1,2,3,7,8,9-HxCDD, 0.152 %, and 1,2,3,4,6,7HxCDD, 0.021) and octachlorodibenzo-p-dioxin (0.173%). These impurities
accounted for 0.621% of the material. This HpCDD batch did not contain any
detectable amounts of tetrachlorodibenzo-p-dioxin (TCDD) and pentachlorodibenzo-p-dioxin isomers.
Animals. A total of 272 female Sprague-Dawley rats (body weight 270 –
310 g) were obtained from Harlan (Indianapolis, IN). Rats were acclimated to
experimental conditions for one week. During acclimatization and throughout
the experiments their health status and body weight (bw) were monitored. Rats
were kept individually in stainless steel, wire-bottom cages (17.5 3 25.5 3
17.5 cm; Shoreline, Kansas, City, MO). They received Purina 5001 rodent
chow (Ralston Purina, St. Louis, MO) and water ad libitum. The room was
artificially illuminated from 6 A.M. to 6 P.M. and air-conditioned with a
Honeywell Delta Net W1044 computer controller (Honeywell, Minneapolis,
MN) programmed to maintain ambient temperature at 21–22°C and relative
humidity at 40 – 60%.
Dosing. The total dose of HpCDD was dissolved in corn oil and administered by gavage at 4 ml/kg, as 4 dose rates, at 12-h intervals during the first
2 days of the experiments. Lack of sufficient solubility required this dosing
schedule. The second day of dosing was considered the starting point (day 0)
of each experiment. Different total doses were given to groups of 30 to 60 rats.
The various dosage groups were started at least 1 month apart. The doses
administered and the number of animals (in parentheses) were as follows: 10.0
(30), 5.0 (30), 2.5 (30), 3.8 (30), 3.1 (30), 3.4 (32), 4.1 (30), and 2.8 (60)
mg/kg.
TABLE 1
Dose- and Time-Responses of HpCDD-Induced
Wasting/Hemorrhage
Dose
(mg/kg)
Mortality
(%)
Time to death
(days)
c3t
(mg/kg 3 day)
2.5
2.8
3.1
3.4
3.8
4.1
5.0
10.0
0
8.3
31.0
65.6
83.3
96.7
100.0
100.0
N/A
40.2 6 6.3 a
44.3 6 6.6
29.1 6 2.9
23.4 6 1.5
25.2 6 1.9
18.6 6 0.6
10.8 6 0.3
N/A
112.6
137.3
98.9
88.9
103.3
93.0
108.0
Note. Average c 3 t: 106.0 6 6.1; N/A, not applicable.
a
Mean 6 SE.
One rat died of gavage errors in the 3.1 mg/kg dosage group shortly after
dosing and was excluded from the study. The batch of rats ordered for the 3.4
mg/kg dosage group contained 32 rats. All of them were used. The number of
rats in the 2.8 mg/kg dosage group was increased from an average of 30 to 60
rats, for reasons to be discussed.
The first 3 doses were selected for purposes of dose range finding. The 10and 5-mg/kg doses of HpCDD caused 100% mortality due to wasting/hemorrhage, and 2.5 mg/kg represented a NOAEL for this effect. Initially, doses
were calculated on mg/kg basis. Therefore, the next dose (3750 mg/kg) was the
midpoint between 5000 and 2500 mg/kg, which was rounded up to 3.8 mg/kg.
The other doses were selected so that the dose changed by multiples of 312.5
mg/kg. Numbers were rounded up or down to avoid unwieldy calculations of
c 3 t. The sequence of dosing the various groups of rats was carried out in the
order depicted above. This sequence of dosing defined the upper curvature of
the dose-response curve first, which generated the hypothesis that the last dose
(2.8 mg/kg) would cause the death of 2 or 3 rats in a group of 30 rats, as a result
of wasting/hemorrhage.
Observations. Rats were weighed daily and their feed intake measured.
They were also carefully examined daily for signs of hemorrhage. Mortality
was recorded twice daily, mostly between 6 and 8 A.M. and 8 and 10 P.M.,
including weekends. Each of the dead rats was necropsied and macroscopically
examined for intestinal hemorrhage and for the presence or absence of abdominal fat depots.
RESULTS
Table 1 depicts original dose- and time-response information
without any attempt to distinguish between various causes of
death. There are 3 different causes in chlorinated dibenzo-pdioxin (CDD)-treated rats in acute/subchronic studies: wasting,
hemorrhage, and anemia (Viluksela et al., 1997,1998). The
dose-responses for wasting and hemorrhage are overlapping
but not with that of anemia. Anemia is clearly separated from
the two former effects by time, because none of the rats died of
wasting and/or hemorrhage after day 126, which is when the
first rat died of anemia. In addition, rats dying of anemia or
hemorrhage have macroscopically-identifiable fat depots,
whereas rats dying of wasting do not.
There is a very steep dose-response for HpCDD-induced
mortality between 2.8 mg/kg and 4.1 mg/kg. The lowest dose
104
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TABLE 2
Dose and Time Course of Wasting in HpCDD-treated Rats
Dose
(mg/kg)
Death due to
wasting (%)
Time to death
(days)
c3t
(mg/kg 3 day)
2.5
2.8
3.1
3.4
3.8
4.1
5.0
10.0
0
8.3
20.7
56.3
83.3
86.7
100.0
100.0
N/A
40.2 6 6.3 a
33.0 6 4.4
29.2 6 3.2
23.4 6 1.5
23.7 6 1.8
18.9 6 0.7
10.9 6 1.4
N/A
112.6
102.3
94.3
88.9
97.2
94.5
109.0
Note. Average c 3 t: 99.8 6 3.2; N/A, not applicable.
a
Mean 6 SE
(2.5 mg/kg) represents a NOAEL for the delayed acute toxicity
of HpCDD (Table 1). It is remarkable how consistent the
relationship of dose 3 time 5 constant (5106 mg/kg 3 day)
is from supralethal doses, all the way down to a dose of 2.8
mg/kg.
In order to separate the two competing dose responses (wasting and hemorrhage), a body-weight loss of at least 25% was
chosen as an inclusion criterion for rats considered dying
primarily of wasting (Viluksela et al., 1997,1998). Table 2
demonstrates that this reduced the variability (mean 6 SE) of
the dose 3 time 5 constant data from 5.8% to 3.2%.
Figure 1 depicts the dose- and time-response information of
Table 2 graphically. The upper panel displays a typical sigmoid
dose-response curve, whereas the lower panel shows a timeresponse curve of very similar shape. Both the dose- and
time-response curves are highly symmetrical in themselves and
nearly symmetrical, in relation to each other. No error bars are
shown in the lower panel depicting the time-response because
the variability is shown in Table 2. Figure 2 shows that the
arithmetic plot of dose vs. time yields a hyperbola (upper
panel) with a nearly perfect correlation coefficient (r 2 5 0.98)
and that the logarithmic plot (lower panel) of the same data
results in a straight line (r 2 5 0.98), which is more familiar to
toxicologists (Hayes, 1991).
Figure 3 examines the dose-response data at constant times
in a traditional log (dose)/effect plot. With increasing dose,
there is a shift in the dose-response curve towards a liminal
value, which represents the minimum observation period
needed to conduct experiments using HpCDD as the toxic
agent and wasting/hemorrhage as the end point of toxicity.
Figure 4 examines the time-response data at constant doses
in a log(time)/effect plot. It illustrates the flattening of the
time-response curve toward a liminal value, which will be
obtained at the LOAEL, in terms of dose response for this
compound and this effect.
A three-dimensional presentation of the dose- and timeresponse data can be seen in Figure 5. Having two dependent
variables (response and time) increases variability as shown by
irregularities of the surface area. Nevertheless, dose responses
at constant times and time responses at constant doses are also
apparent in this particular perspective.
DISCUSSION
The hypothesis that HpCDD exerts its delayed acute toxicity
according to Haber’s Rule of inhalation toxicology was confirmed (Table 1). Some toxicologists might object to using the
term “acute toxicity” involving an observation period of close
to 100 days. However, the traditional observation period of 14
days in acute toxicity studies is entirely arbitrary. It is the
half-life of a compound and/or the recovery half-life of an
effect that determines the length of an observation period
needed after acute exposure. In this particular instance, a
14-day observation period is not meaningful when the last rat
does not die of wasting/hemorrhage until day 74 after dosing.
FIG. 1. Dose- and time-response in female Sprague-Dawley rats administered different oral doses of HpCDD
HABER’S RULE IS VALID FOR HpCDD TOXICITY
105
FIG. 3. Dose responses depicted at constant times to effect, (E, 15 days;
Œ, 20 days; F, 30 days; }, 40 days; h, 50 days; ƒ, 60 days)
FIG. 2. Correlation between dose and time (upper panel) and log (dose)
and log (time) to effect (lower panel) in female Sprague-Dawley rats administered different oral doses of HpCDD
worthwhile refinement, because only rats that die of the same
cause are part of the same dose and time response (Table 2).
The graphic presentation of the data is particularly useful,
because it allows a direct comparison of these data with those
reported on c 3 t 5 constant by others in previous publications. Entomologists frequently plotted the hyperbolas whereas
toxicologists chose more often the log (dose)/log (time) form
of presentation (Figure 2).
A previous publication reported a remarkably good correlation of the 30-day log LD 50 with log (total body fat content) of
TCDD in some 20 different species and strains of animals
A 5.8% variability of the data can be considered acceptable
in toxicology, particularly in the case of 2 overlapping doseresponses (wasting/hemorrhage). Discrimination between
wasting and hemorrhage is difficult, because both are present
in many animals to some degree. However, some animals die,
usually suddenly without displaying the typical signs of wasting, still possessing some macroscopically identifiable abdominal fat depots and often displaying blood around the nose, but
in all instances their small intestine is filled with blood. Traditional differential diagnosis between wasting, hemorrhage,
and anemia in HpCDD-exposed rats has been conducted in an
earlier study (Viluksela et al., 1997). This was not possible in
these experiments because of the difficulty in obtaining blood
from dead rats. However, our experience with about 1000 rats
suggested that 25% body-weight loss is a reliable criterion for
distinguishing the main cause of death between wasting and
hemorrhage (Viluksela et al., 1997). Reduction of the variability of the results from 5.8 to 3.2% shows that this is a small, but
FIG. 4. Time-responses depicted at constant doses to effect (}, 2.8 mg/kg;
E, 3.1 mg/kg; h, 3.4 mg/kg; Œ, 3.8 mg/kg; F, 4.1 mg/kg; ƒ, 5.0 mg/kg; h,
10.0 mg/kg)
106
FIG. 5.
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Three-dimensional plot of the dose- and time-response surface.
(Geyer et al., 1990). In light of the current experiment, the
most likely explanation of that finding is that the more body fat
a species/strain possesses, the more likely it is to survive the
30-day mark. In that sense, total body fat content is a surrogate
measure of time.
The sequence for starting the various dosage groups deserves some discussion. The first 3 doses represent the dose
range finding whereas the other doses are self-explanatory. It
should be noted that the 2.8 mg/kg dose was chosen as the last
dose to be studied in order to test whether HpCDD-induced
wasting was normally distributed. For that to be the case, the
curvature of the dose-response had to be the same in the low as
in the high dose region. Therefore, the number of rats in that
dosage group had to be increased to 60 to yield an integer (5)
instead of a fractional (2.5) number of expected deaths. The
hypothesis of normal distribution was fully confirmed (5 of 60
rats died of wasting) with implications for population thresholds.
Survivors of wasting and hemorrhage started developing
anemia in all dosage groups. It remains to be seen if the c 3
t 5 constant holds also for anemia, because by the time of its
development, HpCDD-treated rats had or will have excreted 30
to 50% of their body burden. Because this departure from
steady state occurs according to a monotonic function, it is
possible that this effect will still also occur according to c 3
t 5 constant, according to a triangular geometry (c 3 t/2 5
constant).
Thus far, 9 of 30 rats died of squamous cell carcinoma of the
lungs in the 2.5 mg/kg dose group, which is about twice the
incidence rate reported in the Kociba et al., (1978) bioassay,
using TCDD as the test compound. Correcting for relative
potency by a toxic equivalency factor (TEF) of 0.007, (Viluksela et al., 1997) for HpCDD, and using the liver concentrations for HpCDD as reported by Viluksela et al., (1997) and for
TCDD, those reported by Kociba et al., (1978), and as calcu-
lated by Rozman et al., (1993) indicate that the relative area
under the curve (rAUC) of HpCDD in this study is about twice
that of the Kociba et al., (1978) experiment. The 30% lung
cancer incidence in this study vs. 14% in the TCDD study
suggest that c 3 t calculations may be possible across chemicals using the same mechanism of action.
It is difficult to anticipate how much the various dose- and
time-response analyses (Figs. 3–5) will contribute to our understanding of the c 3 t x 5 constant phenomenon, probably a
great deal. It is, though, already apparent that the slope of the
dose-response curve does not seem to be changing at constant
times to effect even if the dose-response curve is truncated by
time (Fig. 3). But the time-response curve keeps flattening
(decreasing slope) as the dose decreases (Fig. 4), as if the
symmetry between dose and time would be disturbed at low
doses during prolonged periods of time. The most likely explanation for this phenomenon is a monotonic departure from
toxicokinetic steady state.
Conceptual Considerations
It is interesting to note that the original statement in German
about the dose response was formulated by Paracelsus in the
form of a denial, which makes it the more all encompassing:
“Was ist das nit gifft ist? alle ding sind gifft/und nichts ohn
gifft/Allein die dosis macht das ein ding kein gift ist. [What is
it that is not a poison? All things are poison/and nothing
without poison /the dose alone makes that a thing is not a
poison.]”
This statement was then paraphrased in the first Latin edition
of his famous Carinthian Trilogy as “Dosis sola fiat (facit)
venenum [The dose alone makes the poison]” by an unknown
translator (Deichmann et al., 1986). Paracelsus did not make
explicit reference to the role of time in toxicology, although
some of his writings indicate that he may have been aware of
it, as in describing chronic inhalation toxicity in miners (Paracelsus, 1990). More likely, though, he was firmly embedded in
the medieval time perception, which made explicit considerations of time as a variable unnecessary.
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 3 t 5
constant to p 3 v 5 constant of ideal gases, the entire issue
was forgotten. Even though c 3 t 5 constant kept surfacing
repeatedly (e.g., Druckrey and Küpfmüller, 1948; Flury and
Wirth, 1934; Littlefield et al.1980; Peto et al., 1991) an analogy to thermodynamics was not contemplated again, at least
not to my knowledge! Having “rediscovered” the c 3 t 5
constant concept in still another context (delayed acute oral
toxicity) requires some reevaluation regarding the role of time
in toxicology in a historical context.
Ostwald and Dernoscheck’s (1910) analogy of toxicity to an
HABER’S RULE IS VALID FOR HpCDD TOXICITY
adsorption isotherm is problematic, because adsorption entails
processes in far from ideal conditions. Much more reasonable
is Warren’s (1900) analogy to p 3 v 5 constant for ideal gases
as a comparison for ideal conditions in toxicology. Reducing
the volume of a gas chamber containing a given number of
molecules of an ideal gas will decrease the time for any given
molecule to collide with the wall of the chamber, leading to
increased pressure, which is just an attribute of the increased
number of molecules per unit-volume, which is concentration.
Thus c 3 t 5 constant and p 3 v 5 constant 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 c 3 t x 5
constant.
These thought experiments and some discussions led to the
recognition that toxicologists and thermodynamicists did everything in opposite ways. Instead of starting out with the
simplest model (ideal gas in thermodynamics corresponds to
ideal conditions in toxicology experiments) and building into it
step by step the increasing complexity of the real world,
toxicologists try to predict from one complex situation to
another. In addition, time is largely ignored, although it is one
of two fundamental variables of toxicology (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 departure
from ideal to real conditions. For example, the standard inhalation toxicity protocols (6 h/5days/week) cannot yield c 3 t 5
constant because, after 6 h of 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 2 additional functions to correct for departure from steady
state. The real life situation is even more complex, where
departures from the ideal condition (steady state) are highly
irregular. Nevertheless, it is reasonable to expect that risk
prediction will be possible for even the most irregular exposure
scenarios, once the reference points are estabalished as dose
and time responses under ideal conditions (toxicodynamic or
toxicokinetic/toxicodynamic steady state) and then to define
departures of increasing complexity.
In 25 years of studying the toxicity of TCDD and related
compounds, the concept of c 3 t 5 constant did not emerge in
any other experimental context except the 2 most recent subchronic/chronic 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 herein presented
line of thinking for many years (Rozman, 1998; Rozman and
Doull, 1998; Rozman et al., 1993, 1996). Most toxicologists
are familiar with Haber’s Rule of inhalation toxicology and its
applicability to some solvents. Much less reference is being
made to Druckrey’s work, which extended the c 3 t concept to
107
lifetime cancer studies by oral rather than inhalation exposure.
And finally, there is very little cross-referencing of the c 3 t 5
constant data generated by entomologists (e.g., Peters and
Ganter, 1935; Busvine, 1938; Bliss, 1940) and those established by toxicologists. Usually, a fundamental relationship in
science keeps reappearing in different contexts, as is the case
with c 3 t 5 constant. Unfortunately, at the same time many
apparent exceptions occur with no satisfactory explanation.
Attempts at generalization fail until a commonality is detected
among all experiments, as in this case among those that yielded
c 3 t 5 constant. This commonality is toxicokinetic steady
state and/or irreversibility of an effect, which of course can be
interrelated. Anesthesia, like intravenous infusion, leads to
rapid and sustained steady state for compounds of short halflife. 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 still underway, i.e., induction of a
protein. Druckrey and the ED 01 Study used feeding as a route
of exposure, which yields a better steady state for compounds
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 a compound
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 HpCDD, which has a
half-life of 314 days (Viluksela et al., 1997) in female rats,
yields a virtual steady state for a 70-day observation period,
after any route of administration, but not TCDD with a half-life
of 20 days. But when TCDD’s toxicity was studied under
steady state conditions, its subchronic/chronic toxicity also
occurred according to c 3 t 5 constant (Rozman et al., 1993).
Toxicity is a function of exposure (Ex) and exposure is a
function of dose and time {T 5 f[Ex(d,t)]}. Consequences of
interactions between a toxic agent and an organism at the
molecular level propagate through toxicodynamic or toxicokinetic/toxicodynamic causality chains all the way to the manifestation of toxicity at the organismic level. If the recovery
(consisting of adaptation, repair, and reversibility) half-life of
an organism is longer than the half-life of the causative agent
in the organism, then toxicodynamics becomes rate-determining (one-compartment model) or rate-limiting (multicompartment model). If the toxicokinetic half-life of the compound is
longer than the recovery half-life, then toxicokinetics will be
rate-determining (-limiting), in which case the toxicokinetic
AUC will be identical to the toxicodynamic AUC. There are
two liminal conditions for c 3 t 5 constant to emerge when the
causality chain propagates through either toxicodynamic or
toxicokinetic processes:
Toxicodynamic. (1) In the case of no recovery (no reversibility, no repair, no adaptation), linear accumulation of injury
will occur according to a triangular geometry (c 3 t/2 5
constant) following repeated doses, or according to a rectan-
108
ROZMAN
gular geometry after a single dose (c 3 t 5 constant), provided
that the c 3 t lifetime threshold has been exceeded. (2) After
recovery (reversibility, repair, adaptation), steady state has
been reached, and injury will occur according to a rectangular
geometry (c 3 t 5 constant), after exceeding the c 3 t lifetime
threshold.
Toxicokinetic. (1) No elimination will lead to linear accumulation of a compound, and as a consequence, to accumulation of injury according to a triangular geometry (c 3 t/2 5
constant) after repeated doses, or according to rectangular
geometry after a single dose (c 3 t 5 constant) above the c 3
t life time threshold. (2) After toxicokinetic (and as a consequence, toxicodynamic) steady state has been reached, injury
will occur above the c 3 t lifetime threshold according to a
rectangular geometry (c 3 t 5 constant).
It must be kept in mind that 90 and 99% of steady state will
be reached after 3.32 and 6.64 toxicodynamic or toxicokinetic/
toxicodynamic half-lives, respectively. During this time, c 3 t
will be constant only if the rate-determining step is of zero
order.
Thus, the various (c 3 t 5 constant) scenarios represent
liminal conditions. The magnitude of the c 3 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 3 t x 5 constant for non-liminal conditions
(Large c 3 t x product indicates either low potency, and/or lack
of susceptibility and/or low exposure).
In conclusion, these data and considerations of a significant body of evidence accumulated over the last 100 years
suggests that c 3 t 5 constant is probably a fundamental
Law of Toxicology, which can be seen only under ideal
conditions. If confirmed using other classes of compounds,
and in the herein described ideal conditions, then Paracelsus’ famous statement may have to be supplemented to read
“Dosis et tempus fiunt (faciunt) 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:
c 3 tx
MOE 5
.
c3t
Above the c 3 t lifetime threshold, this will yield the margin
of safety and its reciprocal, the margin of risk.
ACKNOWLEDGMENTS
The skillful technical assistance of Margitta Lebofsky is gratefully acknowledged. Her devotion to detail and accuracy is legendary in the department.
Stimulating discussions with Drs. John Doull and Robert Kovacs have contributed to the development of the author’s notion about the role of time in
science in general and in toxicology in particular. This research was supported
by GSF-Forschungszentrum für Umwelt und Gesundheit, Neuherberg, Germany.
REFERENCES
Bliss, C. I. (1940). The relation between exposure time, concentration, and
toxicity in experiments on insecticides. Ann. Entomol. Soc. Am. 33, 721–
766.
Busvine, J. R. (1938). The toxicity of ethylene oxide to Calandra oryzae, C.
granaria, Tribolium castaneum, and Cimex lectularius. Ann. Appl. Biol. 25,
605– 635.
Crump, K. S., Hoel, D. G. Langley, C. H., and Peto, R. (1976). Fundamental
carcinogenic processes and their implications for low-dose risk assessment.
Cancer Res. 36, 2973–2979.
Deichmann, W. B., Henschler, D., Holmstedt, B., and Keil, G. (1986). What is
there that is not a poison? A study of the Third Defenses by Paracelsus.
Arch. Toxicol. 58, 207–213.
Druckrey, H. (1967). Quantitative aspects in chemical carcinogenicity. In
Potential Carcinogenic Hazard from Drugs. Evaluation of Risk (R. Truhaut,
Ed.), Vol. 7, pp. 60 –78. UICC Monograph Series, Springer Verlag, Berlin.
Druckrey, H., and Küpfmüller, K. (1948). Quantitative Analyse der Krebsentstehung. Zeitsch. f. Naturforschg. 36, 254 –266.
Flury, F. and Wirth, W. (1934). Zur Toxikologie der Lösungsmittel. Archiv f.
Gewerbepath u. Gewerbehyg. 5, 1–90
Geyer, H. J., Scheunert, I., Rapp, K., Kettrup, A., Korte, F., Greim, H., and
Rozman, K. K. (1990). Correlation between acute toxicity of 2,3,7,8-tetrachlorodibenzo-p-dioxin and total body fat content in mammals. Toxicology
65, 97–107.
Haber, F. (1924). Zur Geschichte des Gaskrieges. In Fünf Vorträge aus den
Jahren 1920 –1923, pp.77–92. Verlag von Julius Springer, Berlin.
Hayes, W. J. (1991). Dosage and other factors influencing toxicity. In Handbook of Pesticide Toxicology (W. J. Hayes and E. R. Laws, Jr., Eds.) Vol.
1, pp. 39 –105. Academic Press, Inc., San Diego.
Kociba, R. J., Keyes, D. G., Beyer, J. E., Carreon, R. M., Wade, C. E.,
Dittenber, D. A., Kalnius, R. P., Franson, L. E., Park, C. N., Barnard, S. D.,
Hummel, R. A., and Humiston, C. G. (1978). Results of a two-year chronic
toxicity and oncogenicity study of 2,3,7,8-tetrachlorodibenzo-p-dioxin in
rats. Toxicol. Appl. Pharmacol. 46, 279 –303.
Littlefield, N. A., Farmer, J. H., and Gaylor, D. W. (1980). Effects of dose and
time in a long-term, low-dose carcinogenic study: Innovations in cancer risk
assessment (ED 01 Study). J. Environ. Pathol. Toxicol. 3, 17–34.
Ostwald, W. and Dernoscheck, A. (1910). Über die Beziehung zwischen
Adsoption und Giftigkeit. Kolloid-Zeitschr. 6, 297–307.
Paracelsus, A. (1990). Die Geheimnisse. In Esoterik (G. Riemann, Ed.), pp.
190 –192. Knaur, Droemersche Verl. München.
Peters, G., and Ganter, W. (1935). Zur Frage der Abtötung des Kornkäfers mit
Blausäure. Zeitsch. f. Angew. Entomol. 21, 547–559.
Peto, R., Gray, R., Brantom, P., and Grasso, P. (1991). Effects on 4080 rats of
chronic ingestion of N-nitrosodimethylamine or N-nitrosodiethylamine: A
detailed dose-response study. Cancer Res. 51, 6415– 6451.
Rozman, K. K. (1998). Quantitative definition of toxicity: A mathematical
description of life and death with dose and time as variables. Med. Hypotheses 51, 175–178.
Rozman, K. K., and Doull, J. (1998). General principles of toxicology. In
Environmental Toxicology. Current Developments (J. Rose, Ed.), pp. 1–11.
Gordon and Breach, Amsterdam.
Rozman, K. K., Kerecsen, L., Viluksela, M. K., Österle, D., Deml, E., Viluksela, M., Stahl, B. U., Greim, H., and Doull, J. (1996). A toxicologist’s view
of cancer risk assessment. Drug Metab. Rev. 28, 29 –52
Rozman, K. K., Roth, W. L., Greim, H., Stahl, B. U., and Doull, J. (1993).
HABER’S RULE IS VALID FOR HpCDD TOXICITY
Relative potency of chlorinated dibenzo-p-dioxin (CDDs) in acute, subchronic and chronic (carcinogenicity) studies: Implications for risk assessment of chemical mixtures. Toxicology 77, 39 –50.
Viluksela, M., Stahl, B. U., Birnbaum, L. S., Schramm, K.-W., Kettrup, A., and
Rozman, K. K. (1997). Subchronic/chronic toxicity of 1,2,3,4,6,7,8-heptachlorodibenzo-p-dioxin (HpCDD) in rats. Part 1. Design, general observations,
hematology and liver concentrations. Toxicol. Appl. Pharmacol. 146, 207–216.
109
Viluksela, M., Stahl, B. U., Birnbaum, L. S., Schramm, K.-W., Kettrup, A.,
and Rozman, K. K. (1998). Subchronic/chronic toxicity of a mixture of
four chlorinated dibenzo-p-dioxins in rats. I. Design, general observations, hematology and liver concentrations. Toxicol. Appl. Pharmacol.
151, 57– 69.
Warren, E. (1900). On the reaction of Daphnia magna (Straus) to certain
changes in its environment. Quart. J. Microsc. Sci. 43, 199 –224.