Quantification of Toxic Effects
for Water Concentration-Based Aquatic Life Criteria
PartB
Section 4: Pentachloroethane Lethality to Juvenile Fathead Minnows
Russell J. Erickson
Mid-Continent Ecology Division
National Health and Environmental Effects Laboratory
Office of Research and Development
U.S. Environmental Protection Agency
Duluth, Minnesota
Final
July 20, 2011
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Section 4. Pentachloroethane Lethality To Juvenile Fathead Minnows
4.1 Overview
Erickson et al. (1991) conducted a series of experiments on the toxicity of
pentachloroethane (PCE) to juvenile fathead minnows. These experiments included evaluations
of bioaccumulation kinetics, the time-course of mortality under both constant and time-variable
exposures, the response offish growth rate to constant and time-variable exposures, and the
relationship of toxic effects to PCE accumulation. This section will examine mortality in these
experiments and evaluate the applicability of the toxicity models discussed in Section 2 of Part A
of this report, first considering the "implicit" models already applied to copper toxicity in Section
3, and then the "explicit" models using information gathered in these experiments regarding PCE
accumulation kinetics and the relationship of effects to PCE accumulation. Both deterministic
and stochastic toxicity models will be evaluated, but only in their simplest forms (Equations 2.1-
2.7, Equations 2.22-2.28), because the data in these experiments are insufficient to consider more
complicated models with multiple processes and/or compartments. Subsequent work will
evaluate growth effects in these experiments.
4.2 Study Description
The study of Erickson et al. (1991) consisted of the following experiments:
(1) A bioconcentration experiment (Experiment Bl) in which ca. 4-week-old fathead minnows were
exposed to five levels of PCE (ranging from 1 mg/L, a no effect concentration for growth and
survival, to 10 mg/L, lethal within 12 h) for 48 h, followed by an elimination period of 24 h in
uncontaminated water. Accumulation of PCE in the fish was monitored at 1, 2, 4, 8, 24, and 48 h
during the exposure period and at 1, 2, 4, 8, and 24 h during the elimination period.
(2) 4-d tests of survival (Experiments Al, A2) with ca. 4-week-old fish. In Experiment Al,
continuous exposures at five concentrations (Test Ale) were evaluated simultaneously with daily 6-
h pulses of five intensities (Test Alp). In Experiment A2, continuous exposure (Test A2c) was
contrasted both to daily 6-h pulses (Test A2p) and to an incrementally increasing ("stepped")
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exposure (Test A2s), in which the five treatments started at the five same concentrations as the
continuous exposure and each was increased daily to the next higher concentration (terminating
each treatment after it reached the highest concentration for one day). Accumulation of PCE was
measured in samples offish that died and in fish surviving at the end of the test.
(3) 28-d tests of survival and growth, starting with 2- to 3-week-old fish. In Experiment Cl,
continuous exposure (Test Clc) and daily 6-h pulses (Test Clp6h) were evaluated. In Experiment
C2, continuous exposure (Test C2c) was contrasted to exposures only during the first 2 weeks (Test
C2b2w) or the final 2 weeks (Test C2f2w). In Experiment C3, continuous exposure (Test C3c),
daily 3-h pulses (Test C3p3h), and daily 8-h pulses (Test C3p8h) were evaluated. In Experiment
C4, continuous exposure (Test C4c) was contrasted with exposures of 1 d per week (Test C4pld)
and 3 d per week (Test C4p3d). The highest exposure concentrations in these tests was set to be
near acutely lethal levels. Growth rates were determined by weighing random samples of test
organisms at weekly intervals. Accumulation of PCE was measured in fish collected for growth
determinations and, for experiments C3 and C4, in subsamples offish that died.
(4) An experiment (Experiment Gl) to determine the time dependence of growth effects, both
during and after exposure. Fish were exposed to five levels of PCE for 7 d and then to clean water
for 11 days. Growth rates were determined by weighing random samples offish at 2-3 d intervals.
Accumulation of PCE was measured in samples offish collected for growth determination.
Accumulation of PCE was also determined in fish dying at the higher exposure concentrations and
in selected live fish collected throughout the period in which mortality occurred.
4.3 Mortality Observations
Figure 4.1 shows cumulative percentage mortality for five continuous exposure
treatments from Experiments A2, Gl, and C2 (left side) and five pulsed and stepped exposure
treatments from Experiments Al and A2 (right side). For Experiment Gl, there was substantial
sampling of surviving organisms throughout periods with high mortality rates. For such a
situation, deaths during different observation intervals will have different effects on cumulative
mortality depending on the number of live samples preceding each interval. Thus, cumulative
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percentage mortality at any time cannot be calculated simply as the sum of the mortalities
observed up to that time divided by the starting number of organisms, even if this starting
number is reduced by the live samples up to that time. Rather, for the "ith" observation period, an
incremental fraction mortality (f\ii) is calculated as the deaths during that period divided by the
actual number of organisms present at the start of the period. Then, the cumulative fraction
mortality is calculated as l-n(l-fm~) (i.e., the Kaplan-Meier estimator). Consider a test
starting with 20 organisms in which 4 died during each of the first two observation intervals and
8 survivors were sampled at the end of the first observation interval. For the first period the
incremental fraction mortality would be 0.20, based on the initial number of organisms. For the
second period, the incremental fraction mortality would be 0.50, based on this period starting
with 8 organisms after both the first period deaths and the sampling. The cumulative fraction
mortality would be 0.60 after the second period, in contrast to 0.67 based simply dividing the
cumulative deaths (8) by the starting number minus the live samples (20-8=12).
Figure 4.1 illustrates how mortality due to PCE has steep relationships to exposure
concentration and time. For the continuous exposures (left panels of Figure 4.1), the highest
concentration (Panel Gl-1) resulted in complete mortality within 14 h, but just a 15% drop in the
exposure concentration (A2c-l) resulted in complete mortality being delayed to 28 h, and an
additional 15% drop (C2c-l) caused mortality to not reach 90% until 4 d and to not reach 100%
within 7 d. Further reduction to about 5.0 mg PCE/L resulted in virtually no mortality over 96 h
(Panel A2c-2) and 48 h (Panel Gl-2), and for the latter exposure just slight increases in
concentration after 48 h was enough to cause 30% mortality to be reached at 7 d. Although not
shown in the figure, for continuous exposures in other experiments, mortality was never
appreciable at exposures concentrations less than 5 mg PCE/L and was generally 100% within
several days for exposure concentrations near and above 7 mg PCE/L.
The time variable exposures (right panels of Figure 4.1) also reveal steep relationships of
mortality to time and concentration. For a 6-h pulse to previously unexposed fish, mortality
exceeded 80% at 9.2 mg PCE/L (A2p-l), but was only 40% at 8.4 mg PCE/L (Alp-1), 12% at
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7.0 mg PCE/L (A2p-2), and absent at 5 mg PCE/L (not shown). After the first 6-h pulse, there
was no additional mortality for pulses of 6-7 mg PCE/L (Panel A2p-2), suggesting rapid
reduction in chemical accumulation and/or stress between pulses, such that later pulses could not
add enough stress to kill additional fish. Higher pulses (Panels Alp-1, A2p-l) did show some
incremental mortality after the first pulse, suggesting that such recovery between pulses is not
complete; however, this incremental mortality is also probably partly attributable to higher
concentrations in the later pulses. Rapid recovery from toxic stress is also indicated by the
absence of mortality during the intervals between the pulses.
For the stepped exposures, mortality was nonexistent when exposure was 5 mg PCE/L or
less, and was 100% within 24 h once exposure was near or over 8 mg PCE/L (Panels A2s-l,
A2s-4 in Figure 4-1). These stepped exposures also suggest prior exposure does not increase
how rapidly mortality occurs once lethal exposures are imposed; rather, the opposite seems to be
true. For A2s-4, despite the fact that the prior exposure should create body burdens more than
halfway to lethal levels, mortality when the exposure is stepped up to over 9.5 mg PCE/L only
reached 25% in 6 h, much lower than the 80% mortality for a 6-h pulse of similar concentration
in Treatment A2p-l, and the 50% mortality for the first 6-h of a lower concentration (7.8 mg
PCE/L) in Treatment A2s-l.
However, although the relationship of mortality to exposure concentration and time is
obviously very steep, care should be taken not to infer too much about the exact relationships,
because of uncertainties in exposure concentrations (due to limited sampling, measurement error,
and/or time variability) and variability in organism susceptibility. Because even a 10-20%
change in concentration appears to have substantial effects on mortality in some cases, analytical
error of just the same amount can confound results and make inferences about differences
between similar exposures uncertain. One example of possible uncertainties in exposure or
variability among experiments is that in exposure A2p-l, mortality reaches 80% in the first 6-h
pulse of 9.2 mg PCE/L, whereas only 50% mortality is reached in the first 6 h in exposure Gl-1,
where the measured concentration is actually slightly higher.
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4.4 Kinetics of PCE Accumulation
Figure 4.2 shows the results for four treatments in the bioconcentration experiment
(Experiment Bl). For each treatment, the dashed line shows the water concentration, which rises
within 2 h to at least 90% of its eventual values, and remains roughly constant until PCE input is
terminated, after which the concentration shows an exponential decline, dropping about 90% in
the subsequent 2 h. The PCE accumulations in sampled fish are shown by the filled circles. For
the lower three concentrations, there is a rather rapid rise in the first 4 h to about half of the
eventual value, and attainment of approximate steady state within 24 h. After the termination of
exposure, accumulation declines similarly - by about half in 4 h and by more than 95% after 24
h. For the highest treatment concentration, fish exhibited toxic responses (lethargy,
disequilibria) starting around 4 h and were all dead by 24 h. Because of this toxicity,
accumulation rate relative to the treatment concentration was slower than in the lower, nonlethal
treatment concentrations.
The simple, single-compartment, first-order accumulation model (Equations 2.1, 2.2) was
parameterized based on the data from the lower three treatment concentrations in Figure 4.2.
Uptake and elimination rate constants were both assumed to vary among individual fish with a
log triangular distribution. Model parameters thus consisted of a mean and standard deviation
for both \og(ku) and log(fe). The accumulation model was integrated across the measured
exposure times-series (using linear interpolation between data points) to provide, for each time at
which accumulation was measured, a model-estimated accumulation as a function of model
parameter values. Mathematical search routines (see Section 3) were then used to determine the
parameter values that maximized the likelihood of the observed accumulations, resulting in
estimated means and standard deviations of 1.619 and 0.226 for \og(ku) and -0.560 and 0.010 for
log(fe). This analysis thus inferred that the variability of the data was almost entirely due to
variation in the uptake constant among individuals. These parameter values correspond to a
median ku of 41.6 ml/g/h and median ks of 0.275/h.
Figure 4.2 also shows the fit of the model to the data, using the parameter estimates to
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Figure 4.2. Measured accumulation (solid circles) versus time for a 48 h exposure and 24 h depuration at four
concentration levels (dashed lines) in Test B1. Solid line denotes median prediction of single compartment, first
order toxicokinetics model (median ku=4l.6 ml/g/h, median fe=0.275/h) fitted to data from lower three
concentration levels (highest level not used because of toxicity). Dashed lines denote 25th and 75th percentiles of
predicted variation among individual organisms.
24 36 48
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randomly generate 1000 pairs of ku and fe values and calculating the model-estimated
accumulation for each pair of parameters. The bold lines denote the median of these
accumulation estimates and the dotted lines denote the 25th and 75th percentiles.
For the lower three treatment concentrations, the median line is consistently near the
middle of the data spread, except at 8 h into both the accumulation and elimination phases. This
suggests the toxicokinetics are more complicated than the single-compartment, first-order
behavior assumed in the model; for example, two-compartment kinetics would show slower
uptake after several hours due to the outer compartment approaching equilibrium, subsequent
uptake reflecting slower accumulation into an inner compartment (see Section 2.1.4). However,
this deviation is relatively minor - at 8 h into accumulation, the deviation of the median model
line from the median data averages less than 15% - and will not be further considered here.
For the highest treatment concentration, the model overestimates accumulation,
presumably due to the toxic effects on metabolic processes leading to reduced uptake. This
illustrates a potential problem in incorporating such accumulation information into time-
dependent effects models - exposures that are of interest because they cause effects will have
different kinetics of accumulation than lower exposures which are often used for accumulation
studies. To account for this aspect of toxicity, a reduction in the accumulation model parameters
would be needed as a function of accumulation. Such possible refinements will not be made
here but rather be a subject for possible later work as deemed appropriate.
4.5 Relationship of Mortality to PCE Accumulation
Figure 4.3 summarizes accumulation in both dead and surviving test organisms as a
function of time and treatment concentration for two tests (A2c, Gl) in which accumulation was
comprehensively documented. It is assumed that accumulation in dead organisms did not change
significantly between the times of death and sampling.
For Test A2c, at the highest concentration (Treatment A2c-l), mortality was complete in
the first day and accumulation was measured in all the dead individuals (Figure 4.3). On
average, accumulation increased with time-to-death, and at 24 h was especially variable. This
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Figure 4.3 Measured PCE accumulation in dead (filled circles) and surviving (open circles) fish for two
concentrations levels in Tests A2c and Gl, contrasted with cumulative mortality (solid line).
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whole-body accumulation. Given the distribution of accumulation observed for dead individuals
in Treatment A2c-l, substantial mortality should have been observed in Treatment A2c-2.
Although not presented here, the lipid content of each fish was measured and the same
problem - of lower PCE accumulation in dead organisms at a high exposure concentration than
in surviving organisms exposed to a lower concentration - is observed for lipid-normalized
whole-body accumulation values. This does not contradict the fundamental importance of
accumulation to toxicity, but rather suggests that whole-body accumulation is not a good
measure of the accumulation relevant to toxicity. A likely contributing factor to this problem is
that toxicity should be related to specific compartments in the individual and accumulation in
such compartments might have a different time course than whole-body accumulation. For
example, PCE in the circulating blood and well-perfused tissues would respond more quickly to
water concentrations, whereas total body accumulation, especially after substantial time, might
mainly reflect chemical partitioned into lexicologically less important tissues. A more
complicated toxicokinetic model and a toxicodynamics model focused on a specific
compartment would thus be necessary to better relate mortality, accumulation, and exposure
(e.g., Section 2.1.4), but such a model cannot be adequately supported with the data obtained in
these experiments.
The results in Test Gl (Figure 4.3) reinforce these difficulties in relating accumulation to
death in the toxicity models being considered. Although it must be acknowledged that some of
the variability in this data is analytical uncertainty, there is clearly a large amount of variability
among individuals, which is inconsistent with the stochastic model. But if just average
accumulations are considered, the fact that the survivors in the later stages of Treatment Gl-2
have accumulation greater than the individuals that died in this exposure also is incompatible
with the tenets of the model. For the deterministic model, this is also a problem, because it is
statistically improbable for the accumulation in the dead organisms to be so much lower than that
of the randomly selected surviving organisms. Again, this does not belie the importance of
accumulation, but rather only the utility of the whole-body accumulation monitored in these
12
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experiments.
Despite these problems regarding the application of these accumulation measurements to
the "explicit" forms of the toxicity models, these data can still be used to estimate model
parameters, and thus be used to evaluate the implications of these problems to model predictions.
For the deterministic model, the desired parameters are the mean and variability of the
distribution of lethal accumulation thresholds. This cannot simply be the mean and standard
deviation of accumulation in dead organisms (unless the data set consists of exposures in which
all the individuals died), because surviving organisms also have useful information in that they
establish minimum values for their lethal accumulations. The data in Figure 4.3 were therefore
subjected to maximum likelihood analyses to estimate the distribution of lethal accumulations, in
which (a) the likelihood of the accumulation measured in a dead individual is the frequency of
that accumulation value within the distribution and (b) the likelihood of the accumulation
measured in a live individual is 1.0 minus the cumulative probability of that accumulation value
within the distribution. For a pooled analysis of all the data in Figure 4.3, this resulted in a mean
and standard deviation for the log(LA) of 2.79 and 0.39. Analyses on the separate tests produced
similar values - 2.68 and 0.34 for Test Ale and 2.86 and 0.42 for Test Gl. Analyses on just the
treatments in which mortality was complete produced slightly lower means and standard
deviations - 2.56 and 0.30 for Treatment Alc-1 and 2.65 and 0.22 for Treatment Gl-1.
For the stochastic model, the toxicodynamic parameters to estimate from the
accumulation data include the lethal accumulation threshold AO and the killing rate d (Equation
2.26). To estimate these parameters, it is necessary to first estimate, for the accumulation
measured in each individual, the time-series of the accumulation leading up to that measurement,
because this model uses the whole times-series to determine the integrated probability of death
(Equations 2.22-2.26). As already noted, the fact that accumulation varies so much among
individuals is inconsistent with the tenets of the stochastic model, but the desired times-series
just depends on the value which was inferred (Section 4.4 above) to not be the source of this
variability, so that the median value for ke of 0.275/h could be used to generate these times-series
13
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for illustrative purposes. Using such accumulation times-series for each individual, the
probability of death can be determined as a function of AO and d, and a likelihood can thus be
computed for the observed combination of dead and surviving organisms with their respective
times and accumulations. However, the problems already noted in the accumulation data
resulted in such an analysis inferring that this likelihood was maximized for a value for AO of 0
(no threshold for effects) with a value for d of 0.000027/h/(mg PCE/g wwt). Constraining AO to
be 100 mg PCE/g wwt (lower than all but a few of the measured accumulations in dead
organisms, Figure 4.3) and estimating just d resulted in a slightly higher value for d of
0.000032/h/(mg PCE/g wwt), which will be used in model calculations below.
4.6 Application of Implicit Deterministic Mortality Model
4.6.1 Model Parameterization
One consequence of both (a) the steep relationships of mortality to time and
concentration and (b) the impact of exposure concentration uncertainties on interpreting these
changes is that this data set does not have the information to support consideration of models of
lethality more complex than the simplest ones in Section 2. In fact, this data set provides a good
test of whether even the simplest model can be parameterized with limited information.
Mortality data from continuous exposures in Tests A2, C2, C3, C4, and Gl (in which the
highest concentrations caused sufficient mortality to support model parameterization), were used
to parameterize model Dl as described in Sections 2 and 3 of part A of this report, with no
consideration being needed for how to treat delayed mortality, which was absent in these PCE
tests. Parameters were estimated based on data from each individual test and on the pooled data
from tests Al, C4, and Gl (in which mortality was monitored multiple times during the 12 h of
exposure, whereas in tests C2 and C3 mortality was not monitored until 24 h). Table 4.1
summarizes the estimated parameter values from all six parameterizations.
The parameterization using the individual tests involves a small amount of information -
often just two concentrations with mortality being complete in a short time at the higher
concentration and being slight or absent at the lower concentration. Nevertheless, parameter
14
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Table 4. 1 . Maximum likelihood estimates for deterministic model Dl parameters (implicit version).
Parentheses denote standard error of estimate.
Tests Used
for Parameter
Estimation
A2, G1,C4
A2c
Gl
C2c
C3c
C4c
Median
Parameter Value
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(mg PCE/L)
6.15
5.65
5.84
6.67
6.65
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k
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0.160
0.155
0.141
0.136
0.104
0.167
Mean
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LCoo
0.789
(0.006)
0.752
0.766
0.824
0.823
0.782
k
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-0.810
-0.852
-0.862
-0.984
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Standard Deviation
logioParameter Value
LCoo
0.058
(0.003)
0.020*
0.023
0.020*
0.022
0.062
k
0.322
(0.021)
0.295
0.224
0.020*
0.020*
0.437
* minimum allowed log standard deviation = 0.02
estimates were successfully derived from each set, although for some sets a minimum variability
among individuals was imposed on LC^ or k (this being a minimum standard deviation of the log
parameter = 0.02, so that the maximum parameter value was at least 25% higher than the
minimum). Despite the limited data, the median parameter estimates varied across the sets only
from 5.65 to 6.05 mg PCE/L for LC^ and 0.141 to 0.167/h for k (Table 4.1) for the three data sets
with early mortality information. For the tests without early mortality observations (C2c and
C3c) parameter estimates were also close to these ranges, but were higher for the LC^ and lower
for &£, which raises the possibility that predicting mortality at short times will be uncertain based
on such data sets.
4.6.2 Model Performance Using Parameterizatiom Based on Tests A2c, Gl, and C4c.
For parameterizations based on tests in which early mortality observations were made
(A2, Gl, and C4), there were good fits to the mortality observed in the continuous exposures
(left panels of Figure 4.4). For the high exposure concentrations (A2c-l and Gl-1), the model
predicts rapid toxicity, including substantially more rapid toxicity when the exposure
concentration is only slightly higher in Gl-1 compared to A2c-l. The observed mortality falls
15
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16
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within 1.0 standard deviation of the mean prediction based on the individual parameterizations.
On average, the model predicts the attainment of 90-100% mortality to be slower than observed,
but uncertainties in such high mortality would be of little importance to risk assessments.
When exposure is reduced to about 7 mg PCE/L (C2c-l), the model predicts well the
degree to which mortality slows down, with the observed mortality again bracketed by the
uncertainty of predictions based on the individual parameterizations. For the pooled
parameterization, the eventual degree of predicted mortality is 15% low, further illustrating the
underestimation of high mortality already noted. This underestimation of mortality for the more
tolerant individuals can occur due to overestimation of the variability of Co and/or ks among
individuals, resulting in a subset of organisms estimated to be more tolerant than appropriate.
For the pooled parameterization, this can occur due to variation across experiments being
interpreted by the model as variability across individuals.
Consistent with the observed mortality, model-estimated mortality for exposure Gl-2
shows little mortality at early times when exposures are near 5 mg PCE/L and also shows
moderate mortality as exposure lengthens and concentrations increase to about 5.5 mg PCE/L.
For the parameterizations based on the individual data sets, substantial variability exists, but this
is to be expected because the steepness of the response relationships causes small uncertainties in
exposure concentrations and model parameters to have large effects on partial mortality
predictions. For exposure A2c-2, the model predicts little or no mortality when exposure
concentrations remain near 5 mg PCE/L, consistent with what was observed.
Large uncertainties of effects at concentrations in a steep section of the effects versus
concentration curve are to be expected and are not generally of concern for risk assessments, for
which the uncertainty of the concentration causing a particular effect is of more interest. With
regard to this, the estimated effect concentration (EC) ranges across the different
parameterizations are very small - 5.7 to 6.2 mg PCE/L for the 96-h ECso, 5.0-5.4 mg PCE/L for
the 96-h ECio, and 5.9-6.6 for the 24-h EC5o - despite the limited data.
Although these good fits to the continuous exposures indicate that the model captures the
17
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important features of the relationship of mortality to PCE concentration and exposure duration,
model predictions for the pulsed and stepped exposures in the right panels of Figure 4.4 are also
important for establishing the merits of the model. The model underestimates mortality for the
most intense pulse exposure (A2p-l), even in the first pulse, by nearly a factor of 2.0. This is
partly due to the underestimation already noted regarding the quickness of mortality for the more
tolerant organisms, but also probably reflects the uncertainty issues also noted regarding steep
toxicity relationships. For exposure Alp-1, the prediction for the first pulse is good, but the
model fails to predict the observed incremental mortality in subsequent pulses. One possible
reason for this is that the single kinetic constant in the model can cause an overestimation of the
degree of recovery between pulses for this intense exposure (e.g., >90% reduction in
accumulation and/or damage). In contrast, for the less intense pulse of A2p-2, the model does
predict well both the degree of mortality in the first pulse and the absence of mortality in
subsequent pulses.
Again, data presentations such as Figure 4.4 highlight uncertainties in effects at a
particular exposure concentration, which are informative, but typically of less interest to risk
assessments than the uncertainties in effect concentrations. For a single 6-h pulse, the average
predicted EC50 is 9.8 mg PCE/L, whereas the observed EC50 is 8.5 mg PCE/L, just 13% lower.
For four daily pulses, the observed EC50 is 7.5 mg PCE/L based on average pulse
concentrations, 20% less than the average predicted EC50 of 9.4 mg PCE/L. Thus, the model
underestimation of the risk of pulsed exposures is relatively minor.
For the stepped exposures, the good predictions for A2s-l are expected because this is no
different than the first day of the continuous exposures already discussed. The model does
predict well that there will be total mortality when exposures are stepped up to lethal levels on
later days after previous nonlethal exposures (A2s-4, and also A2s-2 and A2s-3, not shown, in
which lethal exposures were on the second and third day). However, the slower rate of mortality
in such incrementally increasing exposures, that appears to come from the prior nonlethal
exposure, is not predicted. This suggests some importance of toxicokinetic or toxicodynamic
18
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processes that are not included in the model. However, again, these have relatively little
importance to the exposure concentrations predicted to be lethal for any particular exposure
times-series shape.
4.6.3 Model Performance Using Parameterizations Based on Tests C2c and C3c.
When the model is parameterized based on tests in which early mortality is not
monitored, predictions are worse. For continuous exposures with high concentrations, the
average predicted mortality for parameterizations based on Tests C2 and C3 is delayed
substantially from that observed (Gl-1, A2c-l, C2c-l, A2s-l in Figure 4.4). At the lower
exposures of 5.0-5.6 mg PCE/L, the moderate mortality observed in Treatment Gl-2 is not
predicted at all, despite this occurring over a timeframe consistent with the observations in C2
and C3 used to parameterize the model. Little or no mortality is predicted for the pulsed
exposures (A2p-l, Alp-1, A2p-2 in Figure 4.4). This emphasizes the need for at least some
mortality information over a broad range of timeframes if these models are to be effective.
4.7 Application of Implicit Stochastic Mortality Model
4.7.1 Model Parameterization
As for the deterministic model, mortality data from continuous exposures in Tests A2c,
C2c, C3c, C4c, and Gl were used to parameterize the implicit version of stochastic model SI, as
previously described in Sections 2 and 3 in Part A of this report. Again, parameters were
estimated based on data from each individual test and on the pooled data from Tests Al, C4, and
Gl. Table 4.2 summarizes the estimated parameter values from all six parameterizations.
Although parameter estimates were successfully obtained, the estimates for fe in four of the
parameterizations were at a maximum allowed value (1.0/h, beyond which this parameter has no
practical consequences), about 4-fold greater than the value estimated directly from
bioaccumulation data in Section 4.4, and were more than 2-fold higher or lower in the other two
parameterizations. This difficulty in the model parameterization reflects the fact that both fe and
d represent aspects of the kinetics of the toxicity response (fe regards accumulation of chemical
or damage and d addresses the mortality rate for a given accumulation), and the data must
19
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Table 4.2. Maximum likelihood estimates for stochastic model SI parameters (implicit version).
Tests Used
for Parameter
Estimation
A2, G1,C4
A2c
Gl
C2c
C3c
C4c
Parameter Value
C0
5.25
5.14
5.28
6.35
6.58
4.68
d
0.030
0.040
0.040
0.054
0.079
0.014
fe
1.0*
1.0*
0.604
1.0*
0.3*
1.0*
logioParameter Value
CO
0.718
0.711
0.723
0.803
0.719
0.670
d
-1.528
-1.401
-1.399
-1.270
-1.596
-1.848
fe
0.000*
0.000*
-0.219
0.000*
-0.898*
0.000*
* log mean k constrained to be <0.0
contain at least some indication of two-phase kinetics for mortality for the model to partition the
kinetics between these two processes. That ks is so much greater than the known kinetics of
accumulation is indicative of the model parameters not actually describing what they purport to.
4.7.2 Model Performance
When parameterized using Tests Gl, A2c, and/or C4c, stochastic model mortality
estimates show both limitations and merits of the model. As for the deterministic model, the
rapid, high mortality in Treatments Gl-1 and A2c-l is predicted well (Figure 4.5), although with
some underestimation of the death rate as mortality nears 100%. The model also predicts the
slower and approximately complete toxicity for Treatment C2c-l. However, it greatly
overestimates the mortality in Treatment Gl-2. This is due to this model assuming no
differences in sensitivity among individuals, so that once one individual dies, all the others will
eventually die if exposure does not decrease below the threshold. Regarding this, the apparent
leveling off of mortality for Treatment A2c-2 at the upper range of the predictions is due to such
declining exposure. That this model lacks consideration of differences among organisms and
treats partial mortality only as an issue of insufficient time to reach complete mortality is a
limitation, and results in vanishingly small differences in ECs for different effect levels (an "all
20
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Figure 4. 5. C
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21
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or nothing" response) for prolonged exposures with constant, or regularly fluctuating,
concentrations. However, for the PCE toxicity of concern here, this results in little error because
the steep toxicity relationships of PCE already result in a narrow EC range. The ECs estimated
using the stochastic model are similar to those for the deterministic model and do not vary much
among the different parameterizations, being 5.3-5.5 mg PCE/L for the 96-h ECso, 4.8-5.3 mg
PCE/L for the 96-h ECio, and 6.0-6.9 for the 24-h EC50
Regarding the pulsed exposures, like the deterministic model, the stochastic model
underestimates mortality in the first pulse at the high exposure in Treatment A2p-l. Unlike the
deterministic model, the stochastic model does predict substantial incremental mortality across
multiple pulses, which results in good predictions for Treatment Alp-1, but incorrectly predicts
substantial mortality after the first pulse for Treatment A2p-2, where none was observed.
Overall, this incremental mortality predicted by the stochastic model is of questionable merit
because it reflects again that this model assumes all organisms have the same susceptibility and
that the partial mortality in an initial pulse just reflects the finite probability within a finite time
of any individual dying; thus, those individuals that survive the first pulse will eventually all
succumb to subsequent pulses of sufficient magnitude. It thus does not allow for partial
mortality that persists across pulses, as is evident in Treatment A2p-2 in Figure 4.5 and was also
evident for copper in Section 3. However, this does not necessarily mean that this model does
not provide mortality estimates that would still be useful in risk assessments. For a single 6-h
pulse, the stochastic model estimates an ECso (11.0 mg PCE/L) only 30% greater than what was
observed (8.5 mg PCE/L), and, for four daily pulses, an ECso of 6.9 mg PCE/L, within 10% of
what was observed (7.5 mg PCE/L).
For the stepped exposures, the stochastic model successfully predicts that mortality will
be heavy when exposure increases from about 5 mg PCE/L to about 9 mg PCE/L, and it better
predicts the rate of mortality during the lethal step because the parameter d makes this rate less
sensitive to prior exposure than for the deterministic model. However, like the deterministic
model, it does not address how prior exposure might actually slow the mortality rate, as was
22
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apparent in the data.
As for the deterministic model, in most cases, predictions are worse when the stochastic
model is parameterized with tests lacking mortality observations at early times (Figure 4.5). This
again emphasizes that these toxicity models require information on mortality across a reasonable
broad range of time scale. Although the required data would require only modest additional
effort in standard tests and already is often collected, this does create some problems in
exploiting reported test results, which do not typically provide results across multiple exposure
times, even when these data are collected.
4.8 Application of Explicit Deterministic Mortality Model
The parameter estimates needed for application of the version of deterministic mortality
model Dl that explicitly addresses accumulation were already reported in Sections 4.4 and 4.5.
For toxicokinetics, the estimated means and standard deviations were 1.619 and 0.226 for \og(ku)
and -0.560 and 0.010 for log(fe), where the units of ku are ml/g/h and those of ks 1/h. For
toxicodynamics, log(,L4) was estimated based on the pooled data from Treatments A2c-l, A2c-2,
Gl-1, and Gl-2 to have a mean 2.79 and a standard deviation of 0.39, where the units of LA are
jig PCE/g wwt. With these parameter estimates, model predictions were made based on
generating 1000 sets of values for ku, fe and LA and calculating fraction mortality as a function
of time and exposure concentration based on 1000 model simulations using these sets.
The performance for this explicit implementation of the deterministic model is poor
(Figure 4.6). For the continuous exposures, mortality is underestimated at high concentrations
and overestimated at low concentrations. This poor performance is also apparent in the time-
variable exposures on the right side of Figure 4.6, with mortality from pulsed Treatments Alp-1
and A2p-2 being overestimated. Problems with model estimates are particularly evident for
Treatment A2s-4, where substantial mortality is predicted in the earlier steps, where no mortality
was observed.
This poor performance reflects the problems noted earlier in Sections 4.4 and 4.5:
specifically, the wide variability of model parameters resulting in predictions of a wide range of
23
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Figure 4.6. Observed mortality (bold solid lines) and predicted mortality (bold dashed line) as a function of
water concentration time-series (narrow solid lines) for continuous exposures from Tests A2, Gl, and C2 (left
side) and time-variable exposures from Tests Al and A2 (right side). All predictions are for the explicit version
of deterministic model Dl and use toxicokinetics parameters from Experiment Bl and lethal accumulations
estimated from the pooled data of Tests A2c and Gl.
r 10 100
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60
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.n 0
0 24 48 72 96 120 144 168
24
48
72
96
Time (h)
24
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sensitivity of individuals to specific exposures, so that some individuals survive the high
exposures and some succumb to lower exposures, contrary to what was observed. This does not
belie the importance of accumulation to toxicity, but rather that these relationships are more
complex than expressed in these models, and that this oversimplification can result in erroneous
predictions, especially in the face of various uncertainties in parameterization data (e.g.,
accumulation measurements).
4.9 Application of Explicit Stochastic Mortality Model
The explicit form of the stochastic mortality model can be implemented based on the
median ku (41.6 ml/g/h) and fe (0.275/h) estimated in Section 4.4, and the values specified in
Section 4.5 of 100 |ig PCE/g for the lethal accumulation threshold and 0.000032/h/(mg PCE/g
wwt) for the killing rate d. Figure 4.7 provides the resultant model estimates of mortality time-
series. Although the mortality patterns are much different than for the explicit deterministic
model, there is again consistent underestimation of mortality for the higher exposures and
overestimation for lower exposures.
The poor model performance again is due to problems already noted regarding the
relationship of mortality to accumulation and the large variability among individuals in the
measured accumulation and in the relationship of mortality to accumulation. As already noted,
such variability is inherently inconsistent with the stochastic model. Using average parameter
estimates based on variable data results in this model estimating mortality to occur at much
lower concentrations than it actually does and for the mortality at high concentrations to occur
more slowly than observed. Again, this does not refute the basic concepts of the model, but
rather reflects errors that can occur when an overly simple model formulation is combined with
uncertain data used for parameterization.
25
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Figure 4.7. Observed mortality (bold solid lines) and predicted mortality (bold dashed lines) as a function of
water concentration time-series (narrow solid lines) for continuous exposures from Tests A2, Gl, and C2 (left
side) and time-variable exposures from Tests Al and A2 (right side). All predictions are for the explicit version
of stochastic model SI and use median toxicokinetics parameters from Experiment Bl and a killing rate
estimated from pooled data of Tests A2c and Gl, using a lethal accumulation threshold of 100 |j,g PCE/g wwt.
(D
(D
Q_
0)
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O
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24
48
72
96
0 24 48 72 96 120 144 168
100
80
60
40
20
0
0 24 48 72 96 120 144 168
Time (h)
26
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4.10 Summary and Implications to Aquatic Life Criteria
This analysis of mortality of juvenile fathead minnows exposed to pentachloroethane has
further demonstrated that the toxicity models discussed in Section 2, when used in their
"implicit" form and parameterized directly on the observed relationships between the time-series
of mortality and continuous water exposure, can effectively describe these relationships and
make useful predictions regarding time-variable exposures. These models are simple depictions
of the toxicity processes and thus do not fully describe the mortality relationships. However,
when direct data are lacking, they provide estimates for the effects of exposures that are accurate
enough to be of use in aquatic life criteria applications and other aquatic risk assessments where
information on the relationship of magnitude of effects to different exposure time-series is
needed.
However, although these models rely on theoretical relationships of effects to
accumulation, using versions of these models explicitly based on relationships of accumulation
to exposure and mortality to accumulation did not provide good predictions for this case study.
This was likely due to an oversimplification of the relationship of mortality to accumulation and
to uncertainties and variability of data used in model parameterization. This does not argue
against the importance of accumulation in toxicity relationships or in the utility of accumulation
for more simple risk assessments. However, for predicting magnitude of toxicity across various
exposure times-series, better models and data are needed.
It should finally be emphasized that the data and analyses of this section only relate to
mortality in an acute timeframe and to toxicity mechanisms that operate with this timeframe.
Actual criteria applications regarding even just mortality would need to also consider longer-
term survival data, including the possibility of different mechanisms operating in different
timeframes. Furthermore, the analyses here would be most relevant to highly variable exposure
situations in which transient high exposures would make acute mortality relevant. For other
exposures scenarios, chronic survival and other endpoints would be more of a concern.
Subsequent reports in this series will be addressing longer exposures.
27
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4.11 References
Erickson R, Kleiner C, Fiandt J, Highland T. 1991. Use of toxicity models to reduce uncertainty
in aquatic hazard assessments: Effects of exposure conditions on pentachloroethane toxicity
to fathead minnows. Internal report, U.S. Environmental Protection Agency, Mid-Continent
Ecology Division, Duluth, MN, USA. 37 p.
Kaplan, E.L., Meier, P. 1958. Nonparameteric estimation from incomplete observations. J Am
StatAssoc 53:457-481.
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