Calculation of chemical elimination half-life from blood with an ongoing exposure source: The example of perfluorooctanoic acid (PFOA)

Calculation of chemical elimination half-life from blood with an ongoing

exposure source: The example of perﬂuorooctanoic acid (PFOA)

Mark H. Russell

⇑

, Robert L. Waterland

, Fiona Wong

DuPont Haskell Global Centers for Health and Environmental Sciences, S320/214, P.O. Box 50, Newark, DE 19714-0050, United States

DuPont Central Research & Development, Experimental Station, E320/314, Rt 141 and Henry Clay, Wilmington, DE 19880, United States

Department of Applied Environmental Science, Stockholm University, Svante Arrhenius väg 8, SE-10691 Stockholm, Sweden

article info

Article history:

Received 14 March 2014

Received in revised form 17 July 2014

Accepted 20 July 2014

Available online 20 August 2014

Handling Editor: I. Cousins

Keywords:

Elimination

Perﬂuorooctanoic acid

Half-life

Background exposure

abstract

Determination of the chemical clearance rate from human blood is a critical component of toxicokinetic

exposure assessment. Analysis of temporal biomonitoring data without consideration of ongoing expo-

sure results in calculation of apparent elimination half-life values that are longer than the intrinsic value.

The intrinsic elimination half-life is solely a function of the rate of elimination while the apparent elim-

ination half-life reﬂects the processes of both elimination and ongoing exposure. Confusion between

intrinsic and apparent half-life values can lead to misinterpretation of biomonitoring data and can result

in exaggerated predictions in subsequent modeling efforts. This work provides a review of the ﬁrst-order

equations that have been developed to calculate intrinsic and apparent half-life values and the potential

bias that can result from confusing these two values. Published human biomonitoring data for perﬂuoro-

octanoic acid (PFOA) are analyzed using these equations to provide examples of low, medium and high

bias in determination of the intrinsic elimination half-life from plasma or serum, the components of

blood typically analyzed for PFOA. An approach is also provided to estimate the extent of exposure

reduction that is indicated by declining longitudinal or cross-sectional biomonitoring data. Based on

the evaluation methodology presented in this work, the intrinsic elimination half-life of PFOA in humans

is 2.4 years, representing the average of independent estimates of 2.5 years (95% CI, 2.4–2.7) and 2.3 years

(95% CI, 2.1–2.4). The declining concentration of PFOA in blood of the general USA adult population

represents an estimated exposure reduction of 20–30% over the period 1999–2008.

1. Introduction

One of the critical parameters in toxicokinetic assessment of

chemical exposure is determination of the rate of clearance from

the body via a combination of metabolism, conjugation and

physical elimination. In biomonitoring studies, internal chemical

concentrations are routinely determined as a longitudinal or

cross-sectional series of samples from a readily accessible tissue

such as blood, plasma or serum. After the cessation of exposure,

the rate of elimination can then be determined from mathematical

analysis of the time course of the samples. However, in many situ-

ations there is some level of ongoing exposure which results in an

‘apparent’ rather than the ‘intrinsic’ elimination half-life.

Researchers have previously pointed out that apparent half-life

values are functions of both the ongoing rate of uptake as well as

the rate of elimination, resulting in biased estimation of the intrin-

sic elimination half-life (Shirai and Kissel, 1996). However, failure

to explicitly account for ongoing exposure is common in the

published literature. The rate of intrinsic elimination can be deter-

mined if the inﬂuence of ongoing exposure and changes in physi-

ology (such as body weight) are accounted for. Population-based

pharmacokinetic models have been developed (Ritter et al., 2011)

to calculate the intrinsic elimination half-lives of polychlorinated

biphenyls in the U.K. population and perﬂuorooctane sulfonic acid

in the U.S. population (Wong et al., 2014). The following discourse

provides a review of simple ﬁrst-order equations for analysis of

apparent and intrinsic half-life values, similar to the relationships

http://dx.doi.org/10.1016/j.chemosphere.2014.07.061

Abbreviations: PFOA, perﬂuorooctanoic acid; Intrinsic elimination half-life, the

ﬁrst-order elimination half-life obtained from the depuration of a chemical from

biota when the effects of ongoing exposure are not present or are negligible;

Apparent elimination half-life, the ﬁrst-order elimination half-life obtained from

the depuration of a chemical from biota when the effects of ongoing exposure are

neglected; Bias, the difference between the apparent elimination half-life and the

intrinsic half-life, typically expressed as a normalized percent of the intrinsic value.

⇑

Corresponding author. Tel.: +1 (302) 366 6020; fax: +1 (302) 451 4531.

E-mail address: [email protected] (M.H. Russell).

Chemosphere 129 (2015) 210–216

Contents lists available at ScienceDirect

Chemosphere

journal homepage: www.elsevier.com/locate/chemosphere

originally developed by Shirai and Kissel. These equations are then

used to assess the potential bias in using apparent half-life values

to represent intrinsic half-life and to estimate the extent of

exposure reduction from temporal biomonitoring data. Similar

equations are applicable to environmental systems such as lakes

and soil which have simultaneous chemical inputs (i.e., inﬂow or

deposition) and outputs (i.e., outﬂow, degradation or leaching)

(Schnoor, 1996).

The application of these equations is illustrated through exam-

ination of three sets of published biomonitoring results for perﬂu-

orooctanoic acid (PFOA, CAS 000335-67-1) in human plasma and

serum samples. The developed kinetic equations are equally valid

for analysis of biomonitoring data for concentrations in blood,

plasma or serum. Human biomonitoring for PFOA currently repre-

sents one of the most robust datasets available and provides an

excellent example of the issue of potential bias in the calculation

of elimination rates.

2. Methods: Derivation of equations

2.1. Calculation of blood concentration in response to a constant

exposure source

The following equations are similar to mathematical relation-

ships that were originally developed to clarify differences between

the intrinsic (‘true’) and apparent elimination half-lives of PCBs

from humans (Shirai and Kissel, 1996). Continuous exposure to a

chemical contaminant and subsequent uptake and distribution of

that chemical into body tissues commonly leads to an increasing

concentration C of the chemical in human blood (or plasma or

serum). When chemical exposure is constant or nearly constant

and elimination is ﬁrst order, the rate of change of concentration

with time (ng L

1

) is given by:

dC=dt ¼ I

=ðV

MÞk

C ð1Þ

where I

is the rate of chemical exposure (ng d

1

), E

is a dimen-

sionless chemical uptake fraction which accounts for the fraction

of the chemical exposure that is absorbed into blood, V

is the vol-

ume of distribution (L kg

1

) of the chemical and M is body mass

(kg). k

is the intrinsic elimination rate constant (d

1

) which

describes the underlying rate of chemical loss due to the combina-

tion of physical elimination and metabolism. This equation

accounts for the difference between constant chemical exposure

and ﬁrst order chemical loss from blood.

Approximate values of V

include 0.08 L kg

1

for a chemical that

is distributed solely to human blood and 0.20 L kg

1

for distribu-

tion to extracellular ﬂuid (i.e. blood, lymph and other ﬂuids)

(Wagner, 1975; Brown et al., 1997). Integration of Eq. (1) yields:

CðtÞ¼C

k

þ C

ð1  e

k

Þð2Þ

where C

= I

/(k

M) and C

is the chemical concentration in

blood at any given initial time taken to be t = 0 for convenience.

2.2. Calculation of steady-state blood concentration for initial chemical

exposure

If no chemical is initially present in blood, C

= 0 and the blood

concentration increases with time, asymptotically approaching a

steady-state value C

after an extended period of constant expo-

sure (Fig. 1a). Eventually, the rate of chemical elimination

approaches the rate of chemical uptake and the blood concentra-

tion stabilizes at the steady-state concentration C

lim

t!1

CðtÞ¼C

¼ I

=ðk

MÞð3Þ

Eq. (3) is a simple, one-compartment toxicokinetic (TK) model

that is routinely used to calculate the chemical concentration in

blood in response to a constant or chronic chemical exposure rate

. This model can be applied if the fractional chemical uptake (E

the rate of elimination and metabolism (k

), the volume of distribu-

tion (V

) and body mass (M) are known or can be reliably

estimated. One-compartment TK models have been applied to

estimate human blood concentrations of a wide variety of environ-

mental contaminants that result in chronic, constant or near-con-

stant exposure including pesticides (Timchalk, 2010), brominated

ﬂame retardants (Quinn and Wania, 2012; Bjerregaard et al.,

2013), perﬂuoroalkyl substances (Egeghy and Lorber, 2011),

dioxin-like chemicals (Olsen, 2012) and polycyclic aromatic hydro-

carbons (Li et al., 2012).

2.3. Calculation of blood concentration when constant exposure ceases

When constant chemical exposure has continued for a consider-

able amount of time, the chemical concentration in blood C(t)

approaches its steady state concentration, C

. Now consider the

transient response in blood concentration if chemical exposure

suddenly stops or is very signiﬁcantly reduced. This situation

may occur for a number of reasons. A factory worker with high

occupational exposure may retire or move to a new assignment

with little or no exposure. A person may move from a city with

signiﬁcant local exposure to a different city with no further

exposure or they may remain in the same location but exposure

is suddenly eliminated by a treatment method (e.g. a carbon ﬁlter

is placed on drinking water).

If chemical uptake abruptly ceases, the subsequent elimination

of the contaminant from blood is given by:

dC=dt ¼k

C ð4Þ

The solution of this ﬁrst-order differential equation is:

CðtÞ¼C

k

ð5Þ

Fig. 1. Example proﬁles of blood concentrations in response to (a) a constant exposure source, (b) cessation of steady-state exposure and (c) fractional reduction of steady-

state exposure. Dashed line is steady-state concentration and solid line is transient concentration.

M.H. Russell et al. / Chemosphere 129 (2015) 210–216

211

where C

is deﬁned as the chemical concentration in blood at the

time when exposure ends, again taken to be t = 0 for convenience.

This behavior is illustrated in Fig. 1b where C is constant during

the period of exposure but then follows a ﬁrst order decline towards

zero when exposure ceases.

2.4. Calculation of blood concentration when exposure is reduced but

not fully eliminated

Suppose as before that constant exposure has produced a con-

stant blood concentration C

ss0

. At time t

exposure is markedly

reduced but not completely eliminated. When chemical exposure

is reduced from an initial constant value (I

) to a lower but non-

zero constant value (I

), the following expression can easily be

derived from Eq. (2):

CðtÞ¼C

ss1

þðC

ss0

 C

ss1

Þe

k

ð6Þ

where C(t) is the chemical concentration in blood at any time t sub-

sequent to t

and C

ss1

is the new asymptotic steady-state blood con-

centration associated with the reduced constant exposure input I

ss0

and C

ss1

are easily obtained from Eq. (3) if I

and I

are known.

If the exposures are not known, C

ss0

can be taken to be the initial

blood concentration C(t

) of the more highly exposed sub-popula-

tion being studied and C

ss1

as the background blood concentration

measured in the general public. Uncertainty in the values of C

ss0

and/or C

ss1

results in uncertainty in the calculated concentration

values, C(t), especially when the magnitude of change is small.

Eq. (6) shows that reducing the chemical dose rate from I

to I

leads to an exponential decrease in blood concentration from an

initial steady-state value C

ss0

to a new, lower steady-state value

ss1

. This behavior is illustrated in Fig. 1c. Solving Eq. (6) for k

yields the following expression:

¼ ln

ss0

 C

ss1

CðtÞC

ss1



=t ð7Þ

is the intrinsic elimination rate constant for blood and reﬂects the

actual rate at which chemical is removed from blood via the combi-

nation of metabolism and physical elimination. The corresponding

intrinsic elimination half-life is t

1=2

¼ ln ð2Þ=k

In many studies, the rate of elimination is evaluated without

considering the potential impact of any ongoing source of expo-

sure. Therefore, a conventional ﬁrst-order equation analogous to

Eq. (5) is typically applied:

CðtÞ¼C

ss0

k

ð8Þ

where k

is the apparent elimination rate constant, the best

estimate of the chemical elimination rate constant when ongoing

exposure is neglected. Solving Eq. (8) for k

gives

¼ ln

ss0

CðtÞ



=t ð9Þ

and a corresponding apparent elimination half-life t

1=2

¼ ln ð2Þ=k

Values of k

are frequently estimated from only two data points:

an initial blood concentration (i.e. C

ss0

) and a concentration at some

later time, i.e. C(t). If there is no ongoing source of exposure, C

ss1

and k

= k

. However, if exposure is decreased but not eliminated

then k

< k

that is, the apparent rate of elimination is slower than

the intrinsic rate of elimination. As a result, the apparent elimina-

tion half-life is always longer than the intrinsic half-life. Proof of

this relationship is provided in the Supplementary Data (SD).

2.5. Bias in calculation of intrinsic elimination half-life

When the contribution of an ongoing source of exposure is

ignored, the bias in calculating accurate values of the intrinsic

blood elimination half-life can range from minor to extreme. The

bias can be estimated from the following relationship:

Biasð%Þ100

 k



¼ 100 1 

1=2

ð10Þ

Estimated values of k

and the percent bias depend on the

sampling time t. In contrast, k

is an intrinsic quantity and can gen-

erally be assumed to be invariant with time (see later discussion

for possible longer-term variation in k

). Estimation of k

using k

values from the ﬂawed model described by Eq. (9) leads to two dif-

ﬁculties: k

systematically underestimates k

, and the degree of

underestimation depends on the times at which blood samples

are taken.

For highly exposed individuals who are subsequently removed

from any further signiﬁcant exposure (i.e. C

ss0

 C

ss1

), the calcu-

lated percent bias in the elimination half-life is low throughout

the initial period of depuration. When the initial steady-state con-

centration C

ss0

is 100 times greater than the ﬁnal steady-state con-

centration C

ss1

, the percent bias varies in the range of 1.4–2.2% for

sampling times which range over 1–2 intrinsic half-lives (i.e. for

the ﬁrst 50–75% of the change to the new steady-state) (Calcula-

tion provided in SD). When the initial to ﬁnal steady-state ratio

is small, the percent bias increases rapidly: if C

ss0

is 5 times larger

than C

ss1

, the bias increases to 29–50% for the same time frame. In

each case where there is an ongoing source, the intrinsic elimina-

tion half-life is shorter than the apparent elimination half-life.

This analysis shows that the most accurate estimations of blood

elimination half-lives for xenobiotic chemicals will be obtained by

examining highly exposed individuals who are subsequently

exposed to only minor background concentrations, or from more

marginally exposed individuals who are completely removed from

any further exposure. The bias in these half-life calculations is gen-

erally negligible or is within experimental error. In contrast,

attempts to determine intrinsic chemical elimination half-lives

from evaluations of moderate to minor reductions in the blood

concentrations of the general population will be highly biased

and will result in excessively long estimates of intrinsic elimina-

tion half-lives.

3. Results: Applying the bias equations to human biomonitoring

of PFOA

Bias in calculation of intrinsic elimination half-life values is best

illustrated with actual examples. Blood monitoring studies can

provide datasets useful for estimation of intrinsic elimination

half-lives, especially if information on the relative contribution of

ongoing exposure sources is also available. The extensive human

biomonitoring data for PFOA provide a unique set of results to

demonstrate the potential bias in estimation of intrinsic elimina-

tion half-lives inherent in different types of temporal biomonitor-

ing studies.

3.1. Example of minimal bias in intrinsic half-life calculation of PFOA

The results summarized in Table 1 are from a study of recently

retired workers who were occupationally exposed to PFOA and

other ﬂuorinated chemicals (Olsen et al., 2007). The initial serum

concentrations of these individuals ranged between 72 and

5100 ng mL

1

PFOA and many workers had initial concentrations

greater than 100 times the population background concentration

of 4.06 ng mL

1

estimated from NHANES data for the general pop-

ulation in the USA during the same time frame (CDC, 2012). For

workers with initial serum concentrations >500 ng mL

1

, the

estimated calculation bias between the apparent and intrinsic

elimination half-lives is less than 1.2% indicating that correction

212 M.H. Russell et al. / Chemosphere 129 (2015) 210–216

of the observed serum concentrations for background exposure has

a negligible effect. However, for those individuals with lower initial

serum concentrations, the calculation bias ranges up 13%. It should

be noted that minimal bias values (i.e. <10–15%) are likely to be

similar to the uncertainty in analytical measurements.

The apparent geometric mean elimination half-life for all work-

ers reported by Olsen et al. was 3.5 years (95% CI, 3.0–4.1) (Olsen

et al., 2007). However, if the calculations are restricted to only

those workers with initial serum concentrations greater than

500 ng mL

1

, a less-biased estimate of the intrinsic half-life of

PFOA is 3.0 years (95% CI, 2.4–3.8). Due to the highly elevated ini-

tial concentration and the extended sampling duration (almost two

half-lives), the intrinsic elimination half-life determined from

these highly exposed individuals is expected to provide an accurate

estimate of the elimination rate of PFOA from this population of

male adults.

3.2. Example of moderate bias in intrinsic half-life calculation of PFOA

An example of moderate calculation bias in elimination

half-lives can be found in the recent study of residents of Arnsberg,

Germany who were environmentally exposed to PFOA through

drinking water during the period 2006–2008 (Brede et al., 2010).

The geometric mean PFOA apparent elimination half-life for the

adult participants in Arnsberg was 3.2 years (95% CI, 2.9–3.5)

(Table 2). Adjusting for background exposure from the reported

control population provides a geometric mean intrinsic elimination

half-life of 2.5 years (95% CI, 2.4–2.7) for adults. In this case the

initial plasma PFOA concentrations were 5–8 times higher than

the estimated background plasma concentrations in the control

population and the sampling interval was less than one half-life.

For the Arnsberg study, neglecting to correct for the observed back-

ground concentrations resulted in a mean calculation bias of 21%

for the adult population.

In a similar study of adult residents in the Mid-Ohio Valley of

the USA who were exposed to PFOA in drinking water, the appar-

ent elimination half-life was observed to vary with both time

and concentration, leading to an initial conclusion that the clear-

ance of PFOA may be concentration dependent or the result of

ongoing background exposure (Seals et al., 2011). When the

observed biomonitoring results were analyzed using a statistical

model that accounted for ongoing exposure, the mean elimination

half-life was estimated to be 2.3 years (95% CI, 2.1–2.4) (Bartell

et al., 2010). This half-life result is in excellent agreement with

the value determined above for the Arnsberg population. An aver-

age intrinsic elimination half-life of 2.4 years from the results from

the Arnsberg and Ohio Valley studies provides a reasonable

estimate to be used for comparison with other temporal biomoni-

toring studies of PFOA for the general population.

3.3. Example of high bias in intrinsic half-life calculation of PFOA

An example of high bias in estimated PFOA elimination

half-lives is shown in Table 3. These cross-sectional data were

Table 1

Example of negligible calculation bias between apparent and intrinsic elimination half-life values for PFOA (data from Olsen et al., 2007).

Population and sample

collection period

Serum concentration (ng mL

1

) Elapsed

time (yr)

1=2

, apparent

elimination

half-life, (yr)



1=2

, intrinsic

elimination

half-life (yr)

Estimated

calculation

bias (%)

Initial Final Bkgd

Retired workers with

occupational exposure to

PFOA, 1998–2004

5100 2435 4.06 4.78 4.48 4.47 0.12

1833 486 4.06 5.33 2.78 2.77 0.46

1622 577 4.06 5.33 3.57 3.56 0.44

1180 145 4.06 4.74 1.57 1.55 1.18

1077 404 4.06 4.74 3.35 3.33 0.64

883 266 4.06 5.33 3.08 3.05 0.89

702 248 4.06 4.18 2.78 2.75 1.02

549 235 4.06 4.74 3.87 3.83 1.17

496 284 4.06 5.27 6.56 6.48 1.10

490 129 4.06 5.27 2.74 2.69 1.74

474 162 4.06 5.33 3.44 3.39 1.54

430 108 4.06 5.33 2.67 2.62 2.04

425 162 4.06 5.33 3.83 3.77 1.61

390 61 4.06 4.18 1.56 1.51 3.05

356 244 4.06 5.33 9.78 9.64 1.39

306 188 4.06 5.33 7.58 7.45 1.71

254 150 4.06 3.12 4.11 4.02 2.11

247 104 4.06 5.33 4.27 4.16 2.62

212 84 4.06 5.33 3.99 3.86 3.16

183 50 4.06 5.33 2.85 2.72 4.58

181 65 4.06 5.33 3.61 3.47 3.92

167 78 4.06 5.33 4.85 4.67 3.65

142 51 4.06 5.33 3.61 3.43 5.00

131 45 4.06 5.33 3.46 3.26 5.57

74 26 4.06 5.33 3.53 3.19 9.78

72 17 4.06 5.33 2.56 2.23 12.96

Workers with initial serum concentration > 500 ng mL

1

- Geomean: 3.06 3.04} 0.6

95% CI: (2.46–3.81) (2.44–3.79)

All workers - Geomean: 3.56 3.46} 2.8

95% CI: (3.06–4.16) (2.96–4.05)

Background PFOA plasma values are geomean averages of NHANES data for 1999–2004: Geomean of adults 60+, 1999–2004 = 4.06 ng mL

1



Calculated with Eq. (9). Values differ slightly from Olsen et al. values which were determined by linear regression with multiple data points.

Calculated with Eq. (7).

Calculated with Eq. (10).

M.H. Russell et al. / Chemosphere 129 (2015) 210–216

213

compiled by the U. S. Centers for Disease Control and Prevention

(CDC) as a part of the National Health and Nutritional Evaluation

Survey (NHANES) (Kato et al., 2011). NHANES data from the

years of 1999–2008 showed a general downward trend in PFOA

serum concentrations for the U.S. general population. Geometric

mean PFOA concentrations in males 12 years of age or older fell

from 5.71 ng mL

1

in 1999–2000 to 4.47 ng mL

1

in 2003–2004

but remained largely unchanged from 2003 to 2008. Serum PFOA

concentrations in females 12 years of age or older were lower

than those found for males but followed the same general trend.

These changes reﬂect a general reduction in exposure to poly-

ﬂuoroalkyl chemicals which is most likely due to changes in

manufacturing practices and product formulation that began in

2002.

PFOA is a persistent chemical and there is direct, ongoing

exposure to legacy PFOA in the environment. In addition, ongoing

indirect sources of PFOA have been identiﬁed such as formation

from precursor chemistry (Prevedouros et al., 2006). The NHANES

data indicate that PFOA uptake has been reduced since 1999 but

ongoing exposure to legacy and indirect sources remains. As a

result, calculation of the apparent elimination half-life of PFOA

from the gradual decline observed in the general population pro-

vides a misleading estimate of the intrinsic elimination half-life

with a mean calculation bias of 91% (95% CI, 87–95) (Table 3).

The Mexican–American (MA) sub-population shows a PFOA con-

centration decline of less than 10% (geomean values of

3.89 ng mL

1

declining to 3.53 ng mL

1

) which leads to a highly

biased (and highly inaccurate) value of the intrinsic elimination

half-life for this sub-population. The calculation biases summa-

rized in Table 3 result almost entirely from neglecting ongoing

PFOA exposure as concentrations in the general population are

observed to slowly decline.

3.4. Using biomonitoring data to estimate chemical exposure reduction

Eq. (6) describes how a partial reduction in chemical exposure

leads to a reduction in blood concentration. In the derivation of

Eq. (6) it was noted that the initial and ﬁnal steady state concentra-

tions (C

ss0

and C

ss1

) can be readily obtained from the generic

expression C

= IE

/(k

M) when the initial and ﬁnal chemical

exposure rates (I

and I

) are known. The inverse proposition also

holds: initial and ﬁnal chemical exposures can be obtained if initial

and ﬁnal steady state blood concentrations are known. In fact, the

ratio of the initial and ﬁnal exposure rates is equal to the ratio of

the initial and ﬁnal steady state concentrations, that is

¼ C

ss1

ss0

ð11Þ

The ratio of C

ss1

to C

ss0

can be obtained from Eq. (6) and the

resulting percentage exposure reduction (ER) is then given by:

ER ð%Þ100 1  I

ðÞ¼100 1 

CðtÞ

ss0



= 1  e

k





ð12Þ

In Eq. (12), t is the time that has elapsed since exposure was

reduced. Eq. (12) shows that, within the limitations of this simple

model, exposure reduction can be calculated directly from mea-

surements of C(t) if the intrinsic elimination rate constant, k

, the

initial steady state concentration, C

ss0

, and the elapsed time since

exposure reduction, t, are known. In practice, C

ss0

and t can be esti-

mated by examination of the time history of blood concentration

to ﬁnd the onset of reduction in C(t): C

ss0

can be taken as the mean

value of C(t) before the blood concentration changed and t can be

taken as the elapsed time since the onset of reduction of C(t).

The derivation of Eqs. (11) and (12) is given in the SD. Eq. (12)

can be used to estimate the exposure reduction of many additional

environmental contaminants such as lead, cotinine and benzene

Table 2

Example of moderate calculation bias between apparent and intrinsic elimination half-life values for PFOA (from Brede et al., 2010 ).

Population and sample

collection period

Sub-population

Plasma concentration (ng mL

1

) Elapsed

time (yr)

Apparent

elimination

half-life, (yr)

Intrinsic

elimination

half-life (yr)

Calculation

bias (%)

Initial Final Bkgd



Arnsberg residents, 2006–2008 Children (20) 23.4 13.2 5.0 2.00 2.42 1.72 29.2

Mothers (22) 23.6 13.3 2.9 2.00 2.42 2.01 16.7

Men (23) 30.3 21.7 6.3 2.00 4.15 3.13 24.6

All sub-populations: {Geomean: 2.93 2.24 23.5

95% CI: (2.75–3.12) (2.10–2.39)

Adults only: {Geomean: 3.19 2.52 20.9

95% CI: (2.94–3.45) (2.36–2.69)

Number of individuals in the population given in parentheses.



Background PFOA plasma values are the geomean of the control population in Siegen Germany.

Table 3

Example of high calculation bias between apparent and intrinsic elimination half-life values for PFOA (from Kato et al., 2011).

Population and sample collection period Sub-Population

Serum concentration (ng mL

1

) Elapsed

time (yr)

Apparent

elimination

half-life (yr)

Intrinsic

elimination

half-life



(yr)

Calculation

bias (%)

Initial Final

USA general population, 1999–2008 Males 5.71 4.80 8.0 31.9 2.4 92

Females 4.80 3.56 8.0 18.6 2.4 87

nHW

5.60 4.38 8.0 22.6 2.4 89

3.89 3.53 8.0 57.1 2.4 96

nHB

4.80 3.86 8.0 25.4 2.4 91

Mean bias: 91

95% CI: (87–95)

All individuals in the study were >12 years old.



The intrinsic elimination half-life was determined to be 2.4 years, the average of the general population data of Bartell et al. (2010) and Brede et al. (2010).

Key: nHW (non-Hispanic Whites); MA (Mexican–Americans); nHB (non-Hispanic Blacks).

214 M.H. Russell et al. / Chemosphere 129 (2015) 210–216

for which extensive biomonitoring data have been collected and

reported in studies such as NHANES.

3.5. Estimating exposure reduction of PFOA in USA general population

As discussed above, the intrinsic PFOA half-life for the general

population is 2.4 years resulting in k

= ln(2)/2.4 = 0.289 yr

1

. The

NHANES data summarized for males and females in Table 3 were

collected over an eight year period (i.e. t = 8). When these values

are substituted into Eq. (12), the estimated exposure reduction

for the general US male population is 18% and the corresponding

ﬁnal steady-state serum concentration is 4.7 ng mL

1

. For

females 12 and older, a similar calculation results in an esti-

mated exposure reduction of 29% and a corresponding ﬁnal

steady state serum concentration of 3.4 ng mL

1

. Apparent

sex-based differences in PFOA exposure reduction may reﬂect

differences in exposure scenarios, limitations in the modeling

assumptions, uncertainty and bias in the monitoring data as well

as actual differences in intrinsic elimination rates for men and

women. Based on these inverse calculations, it is reasonable to

conclude that PFOA exposure in the general US adult population

decreased by 20–30% over the period 1999–2008. The estimated

exposure reduction is similar to the change in male and female

body burdens of PFOA over this period, as reﬂected in the

decrease in serum concentrations, i.e. 16% and 26% for males

and females, respectively. Due to the multi-year intrinsic elimi-

nation half-life of PFOA, the observed decline in serum concen-

tration lags the estimated reduction in external exposure over

the nine period of biomonitoring.

4. Discussion

As demonstrated in the examples described above, accurate

determination of intrinsic chemical elimination half-life values

is a function of the magnitude of observed concentration decline

as well as the level of ongoing exposure (Eq. (7)). Accurate cal-

culation of intrinsic elimination half-life values requires both

an extended period of sampling (i.e. more than 1–2 half-lives)

and appropriate correction for ongoing exposure. Alternatively,

intrinsic elimination half-life values can be derived from multi-

ple cross-sectional biomonitoring and intake data by using pop-

ulation-level pharmacokinetic modeling as demonstrated for

human exposure to polychlorinated biphenyls (Ritter et al.,

2011).

The intrinsic elimination half-life is not necessarily the same in

all sub-populations. For chemicals such as PFOA which are elimi-

nated almost exclusively via urinary excretion, it is important to

consider the age and gender of the population being studied. The

glomerular ﬁltration rate (GFR) of the kidney typically decreases

with age (Sun et al., 2009; Musso and Oreopoulos, 2011). In addi-

tion, differences in the elimination half-life of PFOA have been

noted between males and females. Enhanced elimination of PFOA

in menstruating women is possible as several studies have

reported lower PFOA levels in women than men (Harada et al.,

2005; Yeung et al., 2006; Kato et al., 2011). Furthermore, mean

elimination half-lives of PFOA have been estimated to be slower

for young females (2.1 yr) than for males or older females

(2.6 yr) (Zhang et al., 2013). These factors may help explain the dif-

ferences observed between the intrinsic elimination half-lives cal-

culated for PFOA in older, predominantly male workers (Table 1)

and for the general population (Table 2). Thus, for chemicals such

as PFOA, it is important to consider potential confounding factors

such as age and gender when evaluating bioelimination half-lives

from biomonitoring data to ensure appropriate application in

subsequent toxicokinetic modeling.

5. Conclusions

Perﬂuorooctanoic acid (PFOA) is a persistent and widely dis-

persed environmental pollutant that has been detected in biota

and humans worldwide. Based on evaluation of two biomonitoring

studies of the general population, the intrinsic plasma elimination

half-life of PFOA in humans is estimated to be 2.4 years, represent-

ing the average of the results from Brede et al. (2.5 years, 95% CI

2.4–2.7) and Bartell et al. (2.3 years, 95% CI 2.1–2.4). The accurate

determination of intrinsic chemical elimination half-lives from

longitudinal or cross-sectional studies of human blood, plasma or

serum requires careful consideration of the magnitude of the

observed concentration changes as well as evaluation of the extent

of ongoing levels of exposure. Calculation of intrinsic chemical

elimination half-life values clariﬁes the actual rate of metabolism

and elimination and permits improved understanding and predic-

tion of the fate of xenobiotic chemicals in humans.

Determination of the bioelimination rate of xenobiotics is a crit-

ical component of toxicokinetic modeling and subsequent risk

assessments. Failure to account for ongoing exposure results in

calculation of biased elimination rates and produces exaggerated

estimates of chemical elimination half-lives. Care should be taken

in calculating and reporting elimination data to minimize misun-

derstanding and potential misuse of experimental kinetic results.

For some chemicals, factors such as age or gender may impact

intrinsic elimination half-life values for speciﬁc subpopulations

and additional values may be needed to enable accurate toxicoki-

netic modeling of subpopulations.

Evaluation of elimination kinetics from biomonitoring data

without explicitly compensating for the effects of ongoing

exposure can lead to speculation involving nonlinear elimination

kinetics and novel retention mechanisms, especially when moni-

tored concentrations approach background values (Costa et al.,

2009; Yali and Yaqi, 2014). Evaluation of accurate intrinsic elimi-

nation rates for PFOA from humans can contribute to improved

exposure assessments, more reliable risk assessments and more

complete understanding of the behavior of persistent chemicals

in the environment. Kinetic equations similar to those described

in this study can be developed to differentiate between intrinsic

and apparent rates of chemical decline in environmental media

such as lakes and soil where input sources occur simultaneously

with various elimination mechanisms.

Appendix A. Supplementary material

Supplementary data associated with this article can be found, in

the online version, at http://dx.doi.org/10.1016/j.chemosphere.

2014.07.061.

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