Vaccari D.A., Strom P.F., Alleman J.E. Environmental Biology for Engineers and Scientists

Подождите немного. Документ загружается.

carcinogen is to keep lifetime risk below 10

6

(0.0001%). However, for practical and

economic reasons, the dosages in laboratory experiments are selected to produce effects

with probability no lower than 10

1

. The biological uncertainties with such an extrapola-

tion are discussed below; here we discuss the mathematical aspects of the problem.

Table 19.5 and Figure 19.3 show a typical situation for the carcinogen dieldrin. The

data are shown in the ﬁrst and second columns of the table. The excess risk (the risk

due to the toxin) is found by subtracting out the spontaneous risk (0.109 in this case).

Cancer bioassays are commonly run at only two or three dosages, plus a control. In

the example, the dosages at the three levels produced tumors in 18%, 43%, and 73%

of the test animals. How, then, should one extrapolate to estimate the dosage that

would produce tumors in 0.0001%? One of the simplest ways would be a linear extrapo-

lation of the two lowest data points, ðP

; d

Þ and ðP

; d

Þ. Thus, to compute the dose, d,

resulting in risk P:

d ¼ d



 P

 d

ðÞ ð19:12Þ

Or, simple linear regression could be used on all the data. Both of these approaches,

however, often produce a threshold below which the probability of harm would be

TABLE 19.5 Data and Model Results for Dieldrin

Dose (ppm) Fraction Having Tumors Excess Risk Predicted P Predicted Excess Risk

0.0 17/156 ¼0.109 0.000 0.107 0.000

1.25 11/60 ¼0.183 0.074 0.213 0.106

2.5 25/58 ¼0.431 0.322 0.389 0.282

5.0 44/60 ¼0.733 0.624 0.746 0.640

Source: Crump et al. (1977); original source Walder et al., 1972, Food Cosmet. Toxicol. Vol. 11, pp. 415–432.

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

0123456

Dosage (ppm)

Fraction having tumors

Background response

Multistage model

Linear model

Linear

Threshold

Figure 19.3 Dose–response curve for a carcinogen and extrapolation to low dosages by linear and

multistage models.

778

DOSE–RESPONSE RELATIONSHIPS

predicted to be zero. For biological reasons described below, this model is ruled out for

carcinogens. The next simpl est model is linear extrapolation of the lowest data point to the

origin:

d ¼

ð19:13Þ

This produces a very conservative result, one producing a low predicted dose for a

given risk. For example, u sing the data from Table 19.5, the lowest excess risk is 0.074

at a dosage of 1.25 ppm. Thus, the dosage that would produce a risk of 10

6

d ¼

6

0:074

ð1:25 ppmÞ¼1:69  10

5

ppm

Even more conservative is to use the upper conﬁdence limit for P

, in place of P

equation (19.13). It is thought that every likely response would be below this line, making

this the most conservative model. Ideally, one of the mechanistic models would apply

instead of these empirical approachs, although two data or three points may be insufﬁcient

to estimate their coefﬁcients.

The major models used by regulatory agencies are the multistage, one-hit, multihit,

logit, probit, and Weibull models. The U.S. Occupational Health and Safety Administra-

tion (OSHA) has rejected the use of any models for setting standards. The U.S. EPA has

selected the linearized multistage (LMS) model. A maximum-likelihood method was

developed by Crump et al. (1977) to estimate the values of the b’s. Crump et al. ﬁtted

the multistage model to the data in Table 19.5, obtaining

P ¼ 1 exp½ð0:11296 þ 0:05148 d þ 0:04007 d

Þ ð19:14Þ

The probability of an animal having tumors computed by this model is shown in the fourth

column of Table 19.5. The rate of spontaneous tumors can be estimated from this model

by setting d equal to zero, yielding 0.107 in the example.

At extremely low concentrations the quadratic term of the multistage model is insig-

niﬁcant, and the model is approximatel y linear with d . The maximum likelihood proce-

dure also yields a 95% conﬁdence interval around the prediction of the model. The upper

conﬁdence limit of the model also is linear with d at low doses. The slope of the upper

conﬁdence interval thus provides a conservative estimate of the sensi tivity of excess risk

to dose:

P ¼ CPF d ð19:15Þ

where CPF, the slope of the upper conﬁdence interval, is called the carcinogenic potency

factor or slope factor. For example, the CPF for chloroform is 0.13 kg day/mg. Thus,

when CPF is found from the slop e of the upper 95% conﬁdence interval of the multistage

model, equation (19.15), constitutes the linearized multistage model.

In 1996, the U.S. EPA proposed changes in its approach to low-dose extrapolation. The

proposed guideline recommends biologically based extrapolation when sufﬁcient data

are available. One method that is part of the proposal is a linear extrapolation based on

the lower 95% conﬁdence level of ED

, which is called LED

BACKGROUND RESPONSE 779

19.3.2 Thresholds

If a straight line is ﬁtted to the three nonzero dosages and corresponding observed frac-

tional incidences from Table 19.5 by least-squares linear regression, the resulting model is

P ¼ 0:0322 þ 0:143 d ð19:16Þ

Extrapolation of this linear model at low doses is shown in Figure 19.3. The dosage at

which the line crosses the background risk is the threshold. The threshold can be com-

puted for this model from equation (19.16) by setting P equal to the background level

of 0.109 and solving for d. The resulting threshold is

threshold

0:109  0:322

0:143

¼ 0:537 ppm

Below the threshold, the linear model predicts that there is no effect. In fact, for reg-

ulatory purposes the U.S. EPA assumes that a threshold exists for all noncarcinogenic tox-

ins. Put another way, it is assumed that for every noncarcinogenic toxin, there exists a

‘‘safe’’ dose at or below which one would expect a zero probability of having an adverse

reaction. At low doses damage becomes progressively small, until it is overwhelmed by

repair mechanisms or compensating factors. However, a tumor can be formed from a sin-

gle cell that has one or very few mutations. The tremendous ampliﬁcation that occurs with

genetic effects makes the threshold assumption unrea sonable in the case of genotoxicity.

Many factors could produce inaccuracy in dose–response extrapolation. The high

doses used in animal studies can overload bioactivation mechanisms, resulting in under-

estimation of risk. One may also overload repair or elimination mechanisms, overestimat-

ing risks. There may be lower tumor incidence in a high-dose group, due to poor survival

among them. However, even if there is overestimation of risk, the notion of a threshold is

not supported.

Even if a threshold exists theoretically, as it may for some epigenetic carcinogens, the

fact that we are exposed not to a single toxin at a time, but to many, may rule out the

argument for assuming a threshold exists in actuality. In general, regulatory agencies

assume that there is no threshold for carcinogenesis.

19.4 INTERACTIONS

Since the environment contains numerous toxins, we are interested in their combined

effect. We worry that two pesticides taken up by the same organism may have a much

greater effect than either one alone. To detect such an effect, we must ﬁrst deﬁne the

situation expected when two toxins act independently.

First, we need to establish the following fact: If d is the dosage of toxin A producing a

given response, 1=d is a direct measure of the toxicity of A. By direct measure we mean a

quantity that is p roportional to toxicity. For example, the LD

is the dosage that results in

50% mortality. However, LD

is inversely related to toxicity. We would consi der a toxin

that is twice as toxic as A to have half the LD

, and one 10 times as toxic to have one-

tenth the LD

. Thus, 1=LD

is a satisfactory measure of toxicity.

Next, let us deﬁne a parameter to describe the mixed dosage of two toxins, A and B,

with LD

50;A

and LD

50;B

, resp ectively. The mixed dosage, d

, will simply be the sum of

780 DOSE–RESPONSE RELATIONSHIPS

the individual dosages, d

and d

, respectively. Then the fraction of the total dosage, l

will be

ð19:17Þ

A similar deﬁnition could be made for l

. Note that l

¼ 1  l

for a binary mixture.

The range of values for l

is 0.0 (pur e B) to 1.0 (pure A).

Now consider an experiment in which the toxicity of a mixture is determined. The

fraction l

is held constant but the total dosage d

is varied to determine the LD

the mixture ðLD

50;M

Þ. In general, LD

50;M

will depend on the fraction l

, and will

equal LD

50;B

when l

is zero and will equal LD

50;A

when l

is 1.0. The question is:

What happens in between?

We can deﬁne the situation expected when the two toxins act independently: Two tox-

ins are said to show additive toxicity when the toxicity of a mixture of them (as measured

by inverse dosage) varies linearly with the mixture fraction. Figure 19.4a shows

this relationship. In the case where the dosage is the LD

, the equation of the straight

line is

50;M

50;B

þ l

50;A



50;B



ð19:18Þ

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0 0.2 0.4 0.6 0.8 1

(a)

100

00.20.40.60.81

(b)

mix

1 / LD

mix

Figure 19.4 ðaÞ Linear relationship for toxicity (the inverse of LD

); ðbÞ effect of mixture

fraction (l) directly on LD

INTERACTIONS 781

This can be rearranged to the following equation, which can be used to predict the

additive LD

50;M

50;A

50;B

ð19:19Þ

Figure 19.4b shows an example of how LD

50;M

will vary with l

according to equation

(19.18).

It is common to multiply equation (19.19) by LD

50;M

to obtain Marking and Dawson’s

(1975) equation for additive toxicity. The result is deﬁned as S, the sum of toxic action,

and will equal 1.0 for additive toxicity:

S ¼

50;A

50;B

ð19:20Þ

If the LD

50;M

measured equals that computed by equation (19.19) (or S ¼ 1:0), one can

conclude that the toxicity is additive.

Example 19.2 If compound A has an LC

of 100 mg/L, and compound B has an LC

of 10 mg/L, what would the additive model predict for the LC

50;M

of a 75 : 25 mixture of

the two?

Answer

¼ 0:75 LD

50;M

0:75=100 þ 0:25=10

¼ 30:8

That is, a mixture of 23.1 mg/L A and 7.7 mg/L B will be expected to cause 50%

mortality.

More than two toxic substances: Equations (19.19) and (19.20) can be applied to any

number of toxins simply by adding similar terms. The sum of the l’s must be 1.0. Thus, a

more general form of equation (19.19), which appl ies to n different toxic substances, is

50;M

i¼1

50;i



ð19:21Þ

where l

¼ d

Example 19.3 What would be the expected EC

and associated individual concentra-

tions, according to the additive model, of a mixture consisting of 10% A, 20% B, and 70%

C? (All percentages are by weight.) The EC

values for the three compounds individually

are 10, 15, and 80 mg/L, respectively.

Answer

10;M

0:1=10 þ 0 :2=15 þ 0:7=80

¼ 31:17 mg=L

¼ð0:10Þð31:17Þ¼3:12 mg=L

¼ð0:20Þð31:17Þ¼6:23 mg=L

¼ð0:70Þð31:17Þ¼21:82 mg=L

782 DOSE–RESPONSE RELATIONSHIPS

Many organophosphate pesticides are additive toxins. This is because they have similar

properties and act by a very similar mechanism—covalent bonding with acetylcholines-

terase.

19.4.1 Nonadditive Interactions

If LD

50;M

measured in the laboratory is less than that computed by equatio n (19.19) (or

S < 1:0), the two toxins interact in a positive way. This is called synergistic interaction,

also called ‘‘more than additive.’’ Another type of positive interaction is when A is essen-

tially nontoxic by itself but causes an increase in the toxicity of B when present. This is

called potentiation (although this term is sometimes also used in the literature to indicate

synergistic interaction).

Unfortunately for the additive model, synergistic interactions are common, as is to be

expected, especially for an effect such as lethality. This is because, even if the two toxins

have completely independent effects, one may sicken the organisms, making them more

vulnerable to the effect of the other. The models of equations (19.19) or (19.21) could be

extended to nonlinear interactions by adding terms involving products of toxicities and

ﬁtting the coefﬁcients by regression. However, data on mixture toxicity are hard to

come by. Furthermore, they may not be consistent at different effect levels. That is, if

there is positive interaction between the LD

s of two compounds, it is not necessarily

true that there will be positive interaction to a similar extent, or at all, in their LD

values,

let alone at the 10

6

risk level.

In an exception to what was noted about organophosphate interactions above,

malathion interacts synergistically with some other organophosphates, as much as 50

times as strong in combination. As Rachel Carson put it in Silent Spring: ‘‘1/100 of the

lethal dose of each compound may be fatal when the two are combined.’’

Ethanol and carbon tetrachloride have a synergistic effect on the liver, and tobacco

smoke and asbestos interact in lung cancer. In the latter case the interaction was deﬁned

differently from that above. It was observed that asbestos workers who did not smoke

experienced a ﬁvefold increase in their risk of lung cancer, and cigarette smokers who

did not work with asbestos had an 11-fold increase. However, asbestos workers who

smoked experienced a 55-fold increase in lung cancer rate. Thus, the interaction here is

deﬁned in terms of additivity of risk instead of additivity of toxicity. An example of poten-

tiation is isopropanol, which does not harm the liver by itself but greatly increases the

toxicity of carbon tetrachloride.

Positive interactions can be caused by a number of mechanisms, including:

 By interfering with an enzyme that detoxiﬁes other compound

 By affecting absorption, blood transport, or excretion

 By reacting to form a more toxic substance (e.g., nitrites and some amines react in

the stomach to form carcinogenic nitrosomines)

 Induction of biotransformation enzymes

If two toxins interact, resulting in a measured toxic effect less than that predicted

by the additive model, this is a negative, or antagonistic, interaction, also called ‘‘less

than additive.’’ Antagonistic interactions are dete cted when the LD

value of a mixture

is greater than predicted by equations (19.19) or (19.21), or S > 1:0. Some antidotes

INTERACTIONS 783

take advantage of antagonistic interactions. Mechanisms causing negative interactions

include:

 Chemical reactions, such as complexation between EDTA and heavy metals

 Inhibition of bioactivation (e.g., toluene competitively inhibits the enzymes that

biotransform benzene)

 Two toxins produce opposite effects, such as central nervous system depressants and

stimulants

 Competition for the same receptor

 Induction of detoxiﬁcation enzymes

Enzyme induction was mentioned above as a mechanism of both positive and negative

interactions. The cytochrome P450 enzymes are a common target of induction. Benzene

can interact positively with other solvents by inducing cytochrome P450.

Example 19.4 Doudoroff (1952) measured the 8-hour LC

of zinc and copper to

fathead minnows (Pimephales promelas), obtaining LC

50;zinc

¼ 8mg=L and LC

50;copper

0:2mg=L. He then tested a mixture with a ﬁxed 1.0 mg/L zinc and varied the copper con-

centration to obtain the LC

50;M

. This was found to occur at a copper concentration of

0.025 mg/L. What kind of interaction is this?

Answer

1:0

1:025

¼ 0:9756 l

0:025

1:025

¼ 0:02439

50;M

expected ¼

0:9756=8:0 þ 0:02439=0:2

¼ 4:1

ratio of observed LC

50;M

to expected LC

50;M

1:025

4:1

¼ 0:25

Therefore, the toxicity of the mixture was four times that predicted by the additive model.

Using Marking and Dawson’s equation (19.20), we obtain S ¼ 0:250, which also indicates

more than additive toxicity.

It is easy to show that Marking and Dawson’s (1975) parameter corresponds to the ratio

S ¼

50;M

observed

additive LD

50;M

ð19:22Þ

Therefore, S < 1:0 indicates positive interaction or synergism, and S > 1:0 indicates less

than addi tive or antagonistic interaction. Despite this simple interpretation for S, toxico-

logists prefer to transform it into an additive toxicity index, I, which eliminates the phy-

sical interpretation:

I ¼

 1 for S < 1:0 ðgreater than additive interactionÞð19:23aÞ

I ¼ 1 S for S > 1:0 ðless than additive interactionÞð19:23bÞ

784 DOSE–RESPONSE RELATIONSHIPS

The resulting index produces a I value of 0.0 for additive toxicity, greater than 0.0 for

positive interaction, and less than 0.0 for negative interaction.

19.5 TIME–RESPONSE RELATIONSHIP

The picture of dose–response relationships we have been describing so far is a static one.

It assumes that all measurements are taken at a ﬁxed interval after the ﬁrst exposure.

Inclusion of time adds another dimension to the response and is an important qualiﬁer

in any toxicity data. A 96-hour LD

may seriously underestimate the risk if the situation

being studied involves chronic, ongoing exposure.

The progress of a toxicity test can be followed by examining the toxicity curve, made

by plotting the logarithm of time vs. the logarithm of the LD

. The toxicity curve indi-

cates when acute lethality has ceased by leveling off parallel to the time axis (Figure

19.5). The LD

associated with the plateau region is called the threshold LD

(denoted

as d

on Figure 19.5), also called asymptotic or incipient LD

. If a plateau is not

reached, the LD

computed will be sensitive to the experimental interval selected, and

it would be advisable to extend the test. The toxicity curve may assume other shapes as

well. This can provide the experimenter with information about how the compound acts or

may indicate the presence of multiple toxic agents in a tested mixture. In Figure 19.5 the

threshold LD

is 5 mg/L. The ﬁgure also indicates that the LD

would be 13.6 if the

organisms were exposed for just 24 hours.

19.6 OTHER MEASURES OF TOXIC EFFECT

Bioassay results are used to compute a variety of parameters related to the toxicity of an

agent. Table 19.6 summarizes some of the more common ones, along with acronyms used

100

1000

0 1 10 100 1000

Time (hrs)

(mg/L)

Figure 19.5 Hypothetical time–toxicity curve.

TIME–RESPONSE RELATIONSHIP 785

for them. The MATC is usually given as a range: NOEC < MATC < LOEC. These para-

meters imply the existence of a toxic threshold. Often, only acute toxicity data, such as

values, are available. One would like to estimate the MATC from acute data.

Although an estimated MATC would be of limited validity for application to the environ-

ment, it would be useful for determining the dosages to use in chronic toxicity tests. The

application factor (AP) is the ratio of acute to chronic toxicity. For example, the applica-

tion factor could be deﬁned as LD

/MATC and would thus be given as a range. Applica-

tion factors for toxicity of xenobiotics to ﬁsh have been found to vary from 0.01 to 0.50.

More extreme cases exist, such as 0.003 for lead and chromium, and even lower for

certain pesticides.

All of the levels ref erred to in Table 19.16 are implicitly linked to an experimental and

statistical procedure for their measurement. For example, unless a compound exhibits a

true threshold effect, it should always be possible to detect adverse effects at a lower

dosage, by increasing the number of organisms in the experiment.

PROBLEMS

19.1. For the following simpliﬁed artiﬁcial toxicity data, plot the response curve and the

estimated tolerance distribution.

Dosage 0% 40% 50% 60% 100%

Mortality 0% 0% 50% 100% 100%

TABLE 19.6 Acronyms Describing Toxic Doses or Concentrations

,LC

Lethal dose (or concentration) Dose or concentration resulting in mor-

tality to x percent of a test population.

,EC

Effective dose (or concentration) Dose or concentration resulting in some

speciﬁed effect in x percent of a

population.

,IC

Inhibitory dose (or concentration) Dose or concentration resulting in a

reduction of the normal response of an

organism (such as growth) by x per-

cent.

NOEL, NOEC No observed effect level

(or concentration)

Level or concentration below which no

effect has been measured experimen-

tally.

NOAEL, NOAEC No observed adverse effect level

(or concentration)

Level or concentration below which no

adverse toxic effect has been mea-

sured.

LOEL, LOEC Lowest observed effect level

(or concentration)

Lowest level or concentration at which an

effect could be observed.

MTC Minimum threshold

concentration

MATC Maximum allowable

toxicant concentration

Greater than NOEC and less than LOEC

as found from chronic toxicity test.

Source: Based on Landis and Yu (1995).

786 DOSE–RESPONSE RELATIONSHIPS

(a) Estimate LC

and LC

by interpolating the response curve. (b) Compute the

mean and standard deviation of the tolerance distribution using the method of

moments, and use these to compute LC

and LC

. (c) Compare the results and

explain any discrepancies. Which do you think is more reliable?

19.2. Many medicinal drugs are effective above a threshold dosage but toxic above a

higher threshold. This range is called the therapeutic window. Consider an

antibiotic being used to treat a potentially fatal infection. How would Figure 19.1

appear for such an antibiotic? What implications does the range between the two

thresholds have for how the drug is administere d (dosage, frequency)? Which

nutrient in Table 19.1 has the smallest ratio between the toxicity and deﬁciency

thresholds?

19.3. In a bioassay experiment, the lowest dose was 20 mg/kg and produced tumors in

three out of 13 animals. By linear extrapolation, what dosage will be expected to

produce a 10

6

risk?

19.4. The LD

of substance A is 10 mg/kg, and for substance B it is 1.5 mg/kg.

Assuming that there is no interaction, what would be the expected LD

of a

mixture that is 70% A and 30% B?

19.5. In the deﬁnition of additive toxicity of mixtures, why not say that com pound B is

twice as toxic as A if it results in double the mortality at the same dosage? (Hint:

Consider what would happen with respect to the dose–response curve if the two

substances, A and B, were the same thing.)

19.6. Two substances, A and B, have LC

values of 80 and 25 mg/L, respectively. A

mixture of the two containing A and B in a 3 : 1 ratio by mass has an LC

40 mg/L. Are the toxins additive, more than additive, or less than additive?

Compute the LC

50;M

predicted and Marking and Dawson’s S.

REFERENCES

Crump, K. S., H. A. Guess, and K. L. Deal, 1977. Conﬁdence intervals and tests of hypothesis

concerning dose response relations inferred from animal carcinogenicity data, Biometrics, Vol. 33,

p. 437.

Doudoroff, P., B. G. Anderson, G. E. Burdick, P. S. Galtsoff, W. B. Hart, R. Patrick, E. R. Strong,

E. W. Surber, and W. M. Van Horn, 1951. Bioassay methods for the evaluation of acute toxicity of

industrial wastes to ﬁsh, Sewage and Industrial Wastes, Vol. 23, p. 1381.

Freidman, G. D., 1987. Primer of Epidemiology, 3rd ed., McGraw-Hill, New York.

Landis, W. G., and Ming-Ho Yu, 1995. Introduction to Environmental Toxicology: Impacts of

Chemicals Upon Ecological Systems, Lewis Publishers, Boca Raton, FL.

Marking, L. L., and V. K. Dawson, 1975. Method for assessment for toxicity or efﬁcacy of mixtures of

chemicals. U.S. Fish Wildl. Serv. Fish Control, Vol. 67, pp. 1–8.

Merck, 2004. Merck Manual, http://www.merck.com/pubs/mmanual/section1/chapter3/3g.htm.

National Research Council, 1980. Recommended Dietary Allowances, Food and Nutrition Board,

NRC, National Academy of Sciences, Washington, DC.

National Toxicology Program. http://ntp-server.niehs.nih.gov/Main_Pages/Chem-HS.html.

World Health Organization, 2004. http://www.who.int/water_sanitation_health/GDWQ/Chemicals/

coppersum.htm.

REFERENCES 787