Physiologically-Based Pharmacokinetic Models Of 

Pyrethroids: Bayesian Calibration And Their Use In 

Interpreting Probabilistic Exposure Data 

Rogelio Tornero-Velez1

, Jimena Davis2, Jianping Xue1, R. Woodrow Setzer2 

1

National Exposure Research Laboratory, Office of Research and Development, U.S. 

Environmental Protection Agency, Research Triangle Park, NC 

2

National Center for Computational Toxicology, Office of Research and Development, 

U.S. Environmental Protection Agency, Research Triangle Park, NC 
2

Table of Contents 

PHYSIOLOGICALLY-BASED PHARMACOKINETIC MODELS OF PYRETHROIDS: BAYESIAN 

CALIBRATION AND THEIR USE IN INTERPRETING PROBABILISTIC EXPOSURE DATA..................1

OVERVIEW ................................................................................................................................................................3

A GENERIC PBPK MODEL OF PYRETHROIDS TO EVALUATE AGGREGATE EXPOSURES TO 

PYRETHROIDS..........................................................................................................................................................4

BACKGROUND ON PBPK MODELING ..........................................................................................................4

MODELING GOALS.......................................................................................................................................6

EXTRAPOLATION BY PARALLELOGRAM ......................................................................................................7

DELTAMETHRIN PBPK MODELS .................................................................................................................7

EXTENSION OF THE DELTAMETHRIN PBPK MODEL TO OTHER PYRETHROIDS ............................................11

PERMETHRIN PBPK MODEL......................................................................................................................12

CONSIDERING AGGREGATE EXPOSURE .....................................................................................................13

Ingestion Exposure ..............................................................................................................................18

Inhalation Exposure.............................................................................................................................18

Dermal Exposure .................................................................................................................................19

BIOMARKER MODEL..................................................................................................................................20

BAYESIAN CALIBRATION OF PBPK MODELS...............................................................................................20

MODEL STRUCTURE ..................................................................................................................................21

Population Model ................................................................................................................................21

Measurement Error Model ..................................................................................................................21

PRIORS ......................................................................................................................................................22

Informative Priors ...............................................................................................................................23

Weakly Informative Priors...................................................................................................................24

COMPUTATIONAL ISSUES ..........................................................................................................................24

MODEL EVALUATION ................................................................................................................................25

EXTRAPOLATION OF ANIMAL-CALIBRATED MODELS TO HUMANS...................................................25

CONSIDERATIONS FOR EXTRAPOLATION ...................................................................................................25

PARAMETER EXTRAPOLATION...................................................................................................................27

Physiological Parameters....................................................................................................................27

Chemical Specific Parameters.............................................................................................................27

CHARACTERIZING UNCERTAINTY IN THE EXTRAPOLATED MODEL ...........................................................28

UNCERTAINTY IN THE LINKED SHEDS – PBPK MODEL ...........................................................................28

PERMETHRIN CASE-STUDY: PROBABILISTIC MODELING OF DIETARY AND RESIDENTIAL 

PERMETHRIN EXPOSURE, INTERPRETATION WITH PBPK MODELING, AND COMPARISON 

WITH NHANES DATA............................................................................................................................................29

OVERVIEW ................................................................................................................................................29

SIMULATION..............................................................................................................................................29

COMPARISONS BETWEEN MODEL PREDICTED DCCA CONCENTRATIONS AND MEASURED QUANTILES FROM 

NHANES ................................................................................................................................................................30

SUMMARY................................................................................................................................................................33

REFERENCES ..........................................................................................................................................................34

APPENDIX A. ORD RESEARCH RELATED TO PYRETHROID PBPK MODELING.................................38

APPENDIX B: EQUATIONS OF THE AGGREGATE PERMETHRIN PBPK MODEL ...............................41

SYMBOLS ..................................................................................................................................................41

Chemical Abbreviations.......................................................................................................................41

Compartment Abbreviations ................................................................................................................41
3

Primary Symbols..................................................................................................................................41

MODEL EQUATIONS ..................................................................................................................................42

Tissue Distribution...............................................................................................................................42

Venous blood .......................................................................................................................................43

Arterial Blood and Absorption Processes............................................................................................43

Dermal Absorption ..............................................................................................................................44

Oral Absorption...................................................................................................................................44

Single Compartment PK Model of DCCA metabolite..........................................................................45

APPENDIX C: PBPK MODEL PARAMETER VALUES ...................................................................................47

ESTIMATION OF STOICHIOMETRIC COEFFICIENTS......................................................................................48

Overview 

We describe the application of physiologically-based pharmacokinetic (PBPK) modeling to 

interpret simulated exposure profiles of the Stochastic Human Exposure and Dose Simulation 

(SHEDS) model. These approaches are being developed to evaluate dietary and residential 

exposures to pyrethroid pesticides in the population. SHEDS is a stochastic exposure model 

coupled with a single compartment pharmacokinetic model designed to estimate bodily dose. In 

the current application, the SHEDS dietary and residential exposure profiles are processed with a 

PBPK model. The SHEDS-PBPK simulations render a population distribution of tissue dosemetrics (e.g., peak brain concentration of permethrin) and a corresponding population 

distribution of predicted biomarkers. Urinary concentrations of excreted metabolites are 

estimated concurrent to the tissue simulations, allowing comparison with NHANES 

measurements to evaluate the reasonableness of the models. Given reasonable agreement with 

NHANES, these simulations permit further investigation of the exposure pathways (e.g., dietary 

exposure to permethrin). We demonstrate the SHEDS-PBPK simulation for population exposure 

to permethrin, comparing a simulated distribution of a permethrin metabolite with NHANES 

data for this metabolite. 

We propose Bayesian hierarchical modeling to characterize the uncertainty in PBPK model 

parameters. The uncertainty in describing rat kinetics is quantified through this process and, 

combined with methods using the parallelogram principle for extrapolating from animals to 

humans, used as a measure of uncertainty of the estimated human dose metrics. We propose the 

use of Monte Carlo methods to propagate parameter uncertainty through the linked simulations 

(SHEDS-PBPK), providing an understanding of the influence of parameter uncertainty (e.g., the 

rate constant for oral absorption of permethrin) and the influence of key population variables 

(e.g, the distribution of hand-to-mouth frequency among 4 year olds). 
4

A generic PBPK model of pyrethroids to evaluate aggregate 

exposures to pyrethroids 

Background on PBPK Modeling 

EPA has on-going efforts to develop physiologically based pharmacokinetic (PBPK) 

models for pyrethroid pesticides. Pyrethroids are synthetic chemical compounds similar to the 

natural pyrethrins produced by certain flowers of the genus Chrysanthemum. These compounds 

now constitute a substantial portion of the synthetic insecticide market. Model development is 

an important component of the research effort at the Agency to evaluate the toxicity, disposition, 

mode of action, and exposure to pyrethroids. The breadth of these efforts is highlighted in 

Appendix A. PBPK models have advantages over "classical" pharmacokinetic models, which 

are less grounded in physiology. PBPK models predict internal body concentrations of 

chemicals or their metabolites. These estimates may be used for risk assessment purposes, and 

the same models may be used to predict concentrations of excreted metabolites for comparison 

with biomarker data (e.g., NHANES). PBPK models are suited for developing pharmacokinetic 

models for a class of chemical (e.g., pyrethroids) because they leverage the structural 

information, and reconcile disparate yet informative data. These data include physicochemical 

properties, in vitro measures, and in vivo experiment. Several types of extrapolation are feasible 

with PBPK modeling: 

• Dose extrapolation (e.g., from high to low dose) 

• Route of administration (e.g., from oral exposures to dermal) 

• Species and age extrapolation (e.g., from rodents to human, and adult to young) 

• Exposure duration (e.g., from continuous to discontinuous, or single to multiple 

exposures) 

The FIFRA Scientific Advisory Panel (SAP) met on August 16 - 17, 2007, to address science 

issues on approaches to model pyrethroids1

. To guide discussions, charge questions were 

developed on the following issues: 

I. Common Model Structure. The Agency believes that the important PK 

properties relevant for PBPK modeling are common among all or most members of this 

class, such that a ‘generic’ or family model structure with chemical specific adjustments, 

as needed, can be used. Please comment on the evidence which does and does not support 

the concept of using a generic model structure for the pyrethroid pesticides. 

II. Parallelogram Approach. The Agency is planning to develop equivalent rodent 

and human in vitro databases for metabolic and physiological parameters. The rodent in 

vitro parameters will be assessed by comparing model predictions to in vivo data. It is 

likely that scaling factors will be used in order incorporate these in vitro parameters into 

the rodent model. When calibrating the human data, the scaling factors used in the rodent 

models will be used in the human models. Please comment on this approach and other 

 1 http://www.epa.gov/scipoly/sap/meetings/2007/august/pyrethroidpbpk_sap_2007_finalv1.pdf
5

approaches that could be taken to calibrate and assess these models for use in human 

risk assessment. 

III. Dose Metric Considerations. The Agency’s issue paper and data provided in 

Appendix C show that blood and brain concentrations of parent compound in the rat 

correlate with pyrethroid toxicity as measured by motor activity. At present time, the 

Agency plans to evaluate additional metrics (e.g., area under the curve) with additional 

pyrethroids. Moreover, the Agency plans to test other behavioral measures (e.g., startle 

response). Please comment on the available database to assess the dose metric for 

pyrethroids. Please also comment on what additional experiments, if any, that could 

further inform the dose metric 

IV. Stereochemistry Considerations. Pyrethroids may have one or more chiral 

centers resulting in potentially multiple stereoisomers. Some products, such as 

deltamethrin, are relatively pure single steroisomers. Others such as cypermethrin may 

contain as many as eight stereoisomers. There is limited information on the toxicity and 

pharmacokinetics of the different stereoisomers. The Agency is proposing to evaluate 

three modeling assumptions. The first approach combines all stereoisomers as one 

chemical. The second approach includes modeling all the diastereomers and ignores the 

enantiomers; the third approach includes only the toxic stereoisomers. To evaluate these 

approaches, the Agency is using permethrin as a model chemical. Please comment on 

these three approaches. Are there additional modeling assumptions or approaches that 

the Agency should consider or that could simplify the modeling? 

A full commentary on these charge questions was provided.2

 To summarize, the panel 

agreed that a generic model (Question I) should be pursued: “An evolving family of PBPK 

models that undergo continuous iterations, as each pyrethroid is studied, seems appropriate and a 

logical approach to tackle the pyrethroid family”. Given the emergence of a generic PBPK 

model for pyrethroids, the panel noted that the parameters could be conceptualized as speciesspecific parameters (rat or human) and compound specific elements (Table I). 

Table 1. Panel’s View on Fixed and Varying Parameters for a Generic PBPK Model 

of Pyrethroids 

Fixed Elements Compound-Specific Elements 

 Tissue compartment Volumes Tissue-plasma PC 

 Blood flow to compartments Tissue permeability coefficients 

 GI uptake rate constants 

 Elimination clearance constants 

 P-glycoprotein transport 

 Liver, intestinal, and plasma clearance rate 

constants 

 Reversible binding to blood components 

 

2 Transmittal of Meeting Minutes of the FIFRA Scientific Advisory Panel Meeting Held August 16-17, 

2007 on Assessing Approaches for the Development of PBPK models of Pyrethroid Pesticides. November 13, 2007
6

The panel commented that Bayesian model selection approaches along with sensitivity 

and uncertainty analysis (both structural and parametric) are important components of the family 

modeling approach. With respect to elements in Table I, the panel highlighted the need to fill 

critical data gaps, notably concerning (1) the plasma protein binding and (2) P-glycoprotein 

transport. The panel noted that some of the apparent diffusion-limitation in pharmacokinetic 

time-course simulation in the fat and brain tissues may result from plasma protein binding or Pglycoprotein transport. If so, these processes could have direct impact on species extrapolation 

from rats to humans (Question II). The panel considered that the parallelogram approach focuses 

heavily on enzyme activity in liver microsomes and cautioned that metabolizing activity could be 

found in (a) liver cytosol and (b) organs outside the liver. Regarding (a), the panel suggested 

using hepatocytes instead of liver microsomes. 

On the issue of dose metric selection (Question III), the panel was in agreement with 

using blood and brain pyrethroid concentration profiles as dose-metrics for pyrethroid 

neurotoxicity. Both peak concentration and AUC are informative; however, the panel was most 

concerned with how these dose-metrics might be affected in species extrapolation; for example, 

what is the influence of transporters in the brain capillary endothelium; e.g. Pgp (Pglycoprotein). 

On matters related to stereochemistry (Question IV) the panel took the pragmatic view 

that it was important to consider the differential toxicity of the various isomers, yet recognized 

that consideration of stereochemistry is driven by analytical capabilities, time and costs. The 

panel endorsed modeling cis and trans diastereomers because these sets of isomers exhibit 

different pharmacokinetic behavior. In summary, the panel was in favor of the approaches 

outlined by the Agency to describe pyrethroid disposition with a generic PBPK modeling 

approach. To date several model have been elaborated, including the in-vitro measures of 

metabolic clearance to develop additional models (refer to Appendix A). We are currently 

elaborating methods based on Bayesian sampling which make use of the existing model 

structures to develop additional PBPK models for pyrethroids. The benefit of these approaches 

(see ‘Bayesian Calibration of PBPK models’) is that they permit characterization of the 

uncertainty of model predictions. The current SAP3

 will consider and review a set of scientific 

issues related to SHEDS-Multimedia version 4, the Bayesian calibration of PBPK models, the 

interpretation of aggregate exposure data, and a SHEDS-PBPK permethrin study. 

Modeling goals 

The effects of pyrethroids are well described for the insects they were designed to 

control. To anticipate possible adverse health effects to humans, rodent models have been used 

to evaluate dose-response relationships and determine the relative potencies of the pyrethroids 

(Soderlund et al., 2002; Wolansky et al., 2006; Wolansky et al., 2009). The question is how to 

extrapolate these findings to humans. Andersen (2003) has proposed that the key to successful 

extrapolation to humans is the reliability of target-tissue dose estimations across species. PBPK 

models allow calculations of tissue doses of chemicals and their metabolites over a wide range of 

exposure conditions (Chiu et al., 2007; Chiu and White 2006; Keys et al., 2003). By 

incorporation of anatomy and biological processes, the models allow adaptation to different 

organisms (Medinsky and Valentine, 2001). Because the rate constants in PBPK models 

represent known or hypothesized biological processes, they may be acquired using in vitro

 3 http://www.epa.gov/scipoly/sap/meetings/2010/index.html
7

models or in silico models of the relevant processes. The ability to project from in vitro or in 

silico measures to in vivo kinetics using PBPK models is evaluated with an animal model and 

considered in forecasting human in vivo kinetics. This procedure is known as the parallelogram 

approach. 

Figure 1 Parallelogram scheme for species extrapolation

Extrapolation by Parallelogram 

The optimal way to conduct the extrapolation is through a parallelogram approach (Fig. 

1) (Sobels, 1989) incorporating a PBPK/PD model (Andersen, 2003). The steps are as follows. 

(1) Develop a hypothesis based model that includes descriptions of the proposed PK and PD 

determinants. (2) The influence of the PK and PD determinants (rodent in vitro) on the surrogate 

mammalian system (rodent in vivo) is understood through this PBPK/PD model. If the scaled in 

vitro constants render predictions that depart from the in vivo data, an empirical correction factor 

may be applied. Such an adjustment reflects systems unknowns. This procedure is further 

described in the section on Extrapolation of Animal-Calibrated Models to Humans. (3) The in 

vitro determinants are compared with one another in the human and surrogate mammalian 

system (e.g., Godin et al., 2006); species differences may be apparent. (4) The human in vitro

data is then incorporated in the PBPK/PD model with the pertinent human 

anatomical/physiological data. Empirical adjustments for in vitro to in vivo scaling derived from 

the mammalian surrogate are applied, establishing the human PBPK/PD model. 

To apply the method to risk assessments, population distributions of exposure, either 

measured or modeled (e.g., SHEDS) are interpreted by the human PBPK/PD model rendering 

population distributions of dose-metrics pertinent to central nervous system (CNS) effects of 

pyrethroids (e.g., peak brain concentration, time above a threshold brain concentration). The 

dose metrics are interpreted based on dose response relationships understood in the rodent 

system. 

Deltamethrin PBPK Models 

In recent years, PBPK models have been developed for the type II pyrethroid, 

deltamethrin (DLM) (Mirfazaelian et al., 2006, Godin et al., 2010, Tornero-Velez et al., 2010), 

allowing for assessment of internal dose levels in various organs and tissues. Pyrethroids may be 

roughly categorized into two groups, type I and type II. Both groups target nerve membrane 

sodium channels, prolonging the open state, resulting in abnormal discharge of targeted neurons. 

In mammals, Type I (non-cyano pyrethroids) cause tremors (T-syndrome) at high doses, whereas 

type II (α-cyano pyrethroids) give rise to choreoathetosis and salivation (CS-syndrome). The 

recent study of Weiner et al. (2009) applies principal component analysis to a functional 

observational battery study of twelve type I and type II pyrethroids to discern the extent to which 

these compounds tend to segregate along the historic categorizations. The results confirm the 

validity of the T (type I) and CS (type II) categories, providing a basis for two common 

Rodent (in vivo) Human (in vivo)

Rodent (in vitro) Human (in vitro)
8

mechanism groups. Notwithstanding these finding, both type I and type II pyrethroids 

demonstrate dose-dependent decrease in motor activity, with the type II tending to be more 

potent (Wolansmky et al., 2006). The FIFRA Scientific Advisory Panel (SAP) met on June 16 - 

18, 2009, to evaluate common mechanism of action of pyrethroid pesticides. 4

 

As a starting point for developing PBPK models for pyrethroids, DLM was selected for 

exploring the fundamentals of pyrethroid disposition because it is formulated as a single isomer 

(( S)-cyano-3-phenoxybenzyl (1R, 3R)-cis-3-(2,2-dibromovinyl)-2,2-dimethylcyclopropane 

carboxylate)- thus minimizing complications introduced by the presence of multiple isomers. To 

better understand the dosimetry of DLM in the central nervous system, Mirfazaelian et al. (2006) 

developed a PBPK model for DLM for the adult male Sprague-Dawley rat that employed both 

flow-limited (brain, gastrointestinal [GI] tract, liver, and rapidly perfused tissues) and diffusionlimited (fat, blood/plasma, and slowly perfused tissues) rate equations. The blood was divided 

into plasma and erythrocytes. Cytochrome P450-mediated metabolism was modeled in the liver. 

Carboxylesterase (CaE)-mediated metabolism was described in the plasma and liver. Serial 

blood, brain, and fat samples were taken for DLM analysis for up to 48 h after adult rats received 

2 or 10 mg DLM/kg po. Hepatic biotransformation was estimated to account for approximately 

78% of these administered doses. Plasma CaEs accounted for biotransformation of 

approximately 8% of each dosage. Model predictions compared favorably to the 2- and 10-

mg/kg po blood, plasma, brain, and fat DLM profiles, as well as profiles subsequently obtained 

from adult rats given 1 mg/kg iv. 

An advantage of PBPK models over classical data-based pharmacokinetic models is the 

ability to update and revise portions of the model, as more information is available. Sensitivity 

analysis can help identify parameters that influence the dose metrics of concern and, thus, guide 

model refinement (Clewell et al., 1994). Godin et al. (2010) made an important change to the 

Mirfazaelian model based on the finding that no difference in the bioavailability from single oral 

doses of 0.3 and 3.0 mg DLM /kg were observed in the Long Evans Rat. The Mirfazaelian 

PBPK model was modified, simplifying the absorption process. Mirfazaelian had hypothesized 

that efflux transport in the GI process was operative, consistent with a hypothesis of efflux 

transport in the blood brain barrier which explained the low distribution of DLM into the brain. 

Other changes to the Mirfazaelian model included describing all tissue compartments with 

diffusion-limited kinetics and a single blood compartment. These changes improved model 

predictions of deltamethrin tissue concentration data from the present study and the literature. 

The rat model was then scaled to humans. The model predicted a 2-fold greater peak DLM brain 

concentration and 3-fold greater area under the curve (AUC(0-48h)) for humans following an 

oral exposure of 1 mg/kg. Based on these findings, humans would have greater distribution of 

deltamethrin to the brain for the same administered oral dose compared to rats. 

Based on the models of Mirfazaelian et al. (2006) and Godin et al. (2010), Tornero-Velez 

et al. (2010) developed a model of deltamethrin PK in the maturing rat (Fig 2). 

 4 http://www.epa.gov/scipoly/sap/meetings/2009/061609meeting.html
9

clearance (CaEP)

QB 

QF 

QS 

QR 

QL 

clearance (CaE)

clearance (CYP)

QPL

 p.o. dosing

 fecal excretion of parent

RBC

Plasma

Brain 

Fat

Slowly 

Rapidly 

Liver 

 Ksi

GI tissue 

 Ki 

 Ksi 

Ks

Figure 2. PBPK model for age-dependent disposition of deltamethrin

Age-specific organ weights and age-dependent changes in the oxidative (CYP) and 

hydrolytic (CaE) clearance of DLM were modeled with a generalized Michaelis-Menten model 

for growth and the summary equations incorporated into the PBPK model. The model's 

simulations compared favorably with empirical DLM time-courses in plasma, blood, brain and 

fat for the four age-groups evaluated (10, 21, 40 and 90 days old) (Fig. 3). Post-natal-day 

(PND)10 pups' area under the 24-h brain concentration time curve (AUC(0-24h)) was 3.8-fold 

higher than that of the PND 90 adults. This work emphasizes the importance of metabolism as a 

clearance mechanism of pyrethroids. 
10

Figure 3 Model predictions and measured levels of DLM in the blood, plasma, brain and fat of PND 10, 21, 40, and 90 male 

SD rats. In each graph, time is in h (x-axis) and tissue concentrations in μg/g (y-axis). From top to bottom, the simulation lines represent 

the 10, 2, and 0.4 mg/kg administered doses. Corresponding laboratory data are represented by circles, triangles, and squares.
11

Extension of the deltamethrin PBPK model to other pyrethroids 

Generally, pyrethrins and pyrethroids have similar physical properties: low vapor 

pressures, low Henry’s law constants, and large octanol/water coefficients (Kow), and are not 

very soluble in water (ATSDR, 2003). As such, we expect PBPK model parameters reflecting 

physicochemical properties (e.g., partition coefficients, and permeability coefficients) to be 

similar among the pyrethroids. On the other hand, we expect divergence in biochemical 

parameters (i.e., metabolic rate constants). Although pyrethroids are metabolized at different 

rates, they follow the same detoxification pathways. These features support a common model 

structure for pyrethroids. 

Pyrethroids are metabolized through oxidative and hydrolytic pathways. Fig. 4 shows the 

structural similarity of pyrethroids bearing derivative structures of the chrysanthemic acid and 

phenoxybenzoic acid moieties. The predominance of either pathway in their clearance depends 

on their stereochemistry, determined by the acid moiety (cis/trans) and, for type II pyrethroids, 

by the R/S configuration of alpha-cyano group on the alcohol moiety. Generally, compounds in 

the cis configuration are more resistant to hydrolysis than trans compounds, and generally type I 

compounds are more rapidly metabolized than type II compounds. Scollon et al., (2009) 

evaluated rat/human differences in the intrinsic clearance (CLint). The pyrethroids bifenthrin, Sbioallethrin, bioresmethrin, β-cyfluthrin, cypermethrin, cis-permethrin, and trans-permethrin 

were incubated in rat and human hepatic microsomes. The CLint of the pyrethroids was 5- to 15-

fold greater in rat relative to human microsomes except for trans-permethrin, which was 

approximately 45% greater in human microsomes. The metabolism of bifenthrin, S-bioallethrin, 

and cis-permethrin in rat and human hepatic microsomes was solely the result of oxidative 

processes. The metabolism of bioresmethrin and cypermethrin in human hepatic microsomes was 

solely the result of hydrolytic processes. 

Name R1 R2 R3 R4

Cypermethrin: Cl Cl CN H

Permethrin: Cl Cl H H

Cyfluthrin: Cl Cl CN F

Phenothrin: CH3 CH3 H H

Cyphenothrin: CH3 CH3 CN H

Cyhalothrin Cl CF3 CN H

Deltamethrin Br Br CN H

R1

R2

O

H3C

H3C O

O

R3

R4

R1

R2

O

H3C

H3C OH

O

R4

HO

+

A.

B.

R1

R2

O

H3C

H3C O

O

R3

R4 OH

trans 

or cis

hydrolytic

products

oxidation

product

ester cleavage

Figure 4. Scheme of the oxidative and hydrolytic biotransformation of pyrethroids, for those pyrethroids 

with structure based on chrysanthemic acid and phenoxybenzoic acid moieties.
12

Permethrin PBPK Model 

Following the modeling of deltamethrin, permethrin was the next logical pyrethroid to 

model to better understand the influence of cis/trans configurations in pyrethroid disposition. 

Permethrin (PM) is a broad-spectrum Type I pyrethroid insecticide and among the most widely 

used in residential and agricultural settings. Using PBPK modeling, a model of PM disposition 

in rats was developed to consider aggregate exposure (oral, dermal, inhalation). The model 

structure (Fig.5) is based on the model of Mirfazaelian et al. 2006, and includes two important 

refinements introduced by Godin et al. 2010; namely, simple rate constants for absorption and 

collapse of the plasma and red blood cell (RBC) compartments into a single blood compartment. 

Furthermore, uptake structures were added for inhalation and dermal exposure. Deltamethrin 

consists of a single isomer; however, PM is formulated as a blend of cis and trans isomers. To 

better understand the role of stereochemistry in the pharmacokinetics, we assessed time courses 

for cis and trans isomers in several tissues (brain, blood, liver, and fat) following oral 

administration of 1 and 10 mg/kg PM (cis/trans : 40/60) to rats. Accurate simulation in brain 

and blood and parallels with the pharmacokinetics of deltamethrin suggests a ‘chemical familyoriented’ approach for modeling is valid. Human in vitro data and appropriate anatomical 

information were used to develop a human model of PM disposition and used to interpret limited 

data on human dermal exposure and oral ingestion. 
13

inhaled

permethrin 

Qc Ca QcCv

QBRN CBRN

dermal exposure

Kds

 

Kdv

Qskin CVVE

QF CVF

QS CVS

QR CVR

QL CVL

 CVG I metabolic clearance

Kel

QG I

 Ks Ki

 p.o. dosing

Kfec 

indicates 

diffusion 

limited 

compartment

GI Lumen

metabolic 

clearance

fecal 

excretion 

of parent

urinary 

excretion of 

metabolites

art

blood

rapidly 

 

 

IL

 

 

IL

 Ksi

brain

slowly 

liver 

GI 

ven

blood

VE 

SC 

lung blood eq 

fat 

alv vent

central comp.

Figure 5

Considering Aggregate Exposure 

The PBPK model should be able to consider the important routes of exposure. 

Individuals can be exposed to pyrethroids via air, water, soil, house dust, diet and from medical 

applications (specifically for permethrin only). Inhalation exposure to pyrethroids can result 

from their application in agricultural fields or in residential homes. Oral exposure to pyrethroids 

can occur by ingesting food, water, or household dust. Dermal exposure to pyrethroids can result 

from surface contact or from the treatment of lice (Naeher et al., 2009). Important pathways of 

exposure may depend on age-dependent behaviors. For example, young children would be more 

likely to ingest pyrethroid-contaminated dust or soil from hand-to-mouth motions. 

Although PK studies of pyrethroids are not available for humans, a limited number of 

human dose-excretion studies involving pyrethroids have been published. These studies are 

useful to inform the uptake processes in human PBPK models. The parallelogram is not replaced 

for informing tissue distribution. Human dose-excretion studies in accordance with Agency 

policy on human subjects research as defined in 40 C.F.R. PART 26 can be used to calibrate 
14

absorption parameters. Table 2 provides a list of such studies and the chemical. Urinary 

metabolites accounted for 35-60% of the oral dose of permethrin or cypermethrin. In contrast, 

urinary metabolites accounted for 0.1-1.2% of the applied dermal dose of these pyrethroids 
15

Table 2. Human Dose Excretion Studies of Pyrethroids 

(Studies provided indication of independent oversight and informed consent) 

Pyrethroid Route N Concentration Eliminated 

in Urine 

(% Dose) 

t 1/2 (h) trans-

:cisDCCA 

ratio 

Human 

Studies 

Issues 

Source 

cypermethrin oral 6 3.3 mg; 

subjects: 61-80 

kg 

36% 13 2 PK, IC, IRB Woollen et al., 1992 

alphacypermethrin oral 6 0.25-0.75 mg in 

0.2 ml cornoil 

43.0% 24 nd PK, IC, IRB Eadsforth et al., 1988 

pyrethrin oral 3 3.3-5.4 mg/kg 

in 50:50 

ethanol:water 

60.0% 4.2 nd PK, IC, IRB Leng et al., 2006 

permethrin dermal 6 5% prescription 

cream 

0.47% 28.8 nd PK, IC, IRB Tomalik-Scharte et al., 

2005 

cypermethrin dermal 2 25 mg/ 50 cm2 0.10% nd nd PK, IC, IRB Eadsforth et al., 1988 

cypermethrin dermal 6 31 mg/ 800cm2;

subjects: 62-82 

kg 

1.2% 16.5 1.2 PK, IC, IRB Woollen et al., 1992 

cyfluthrin aerosol 

inhalation 

9 40 and 160 

mg/m3; subjects: 

51-91.3 kg 

51.45% cis: 6.9h; 

trans: 6.2

h

1.9 PK, IC, IRB Leng et al., 1997 

PK- pharmacokinetic endpoint; IC- informed consent; IRB- Involvement of independent oversight 
16

Fig. 6 shows the uptake mechanism of the PM PBPK model for aggregate exposure. 

These data are provided through a CSV text file containing SHEDS output simulation. Fig. 7 

shows a 15 hour SHEDS PM exposure simulation for a child weighing 14.7 Kg. Process A 

includes dietary and non-dietary exposure to PM. Columns 8 and 9 indicate hour-by-hour 

dietary and non-dietary ingestion exposure to PM (micro-g), respectively. Process B is 

inhalation exposure, and is described by column 10, the ventilation rate (m3

/min), and column 

12, the airborne concentration of PM (micro-g/m3). Process C is dermal exposure, and is 

captured by column 3, area exposure (cm2

)- a whole body dermal exposure- and column 11, the 

amount of PM on the skin surface (micro-g). All values are updated hourly. Unit conversions 

take place in the PBPK models (Matlab, R) to run the model in units of micro-moles, L, and h. 

A B

C

Figure 6 Interface of the exposure model and PBPK model. Blue Arrows indicate 

exposure processes described by SHEDS. The solid dark arrows indicate absorption processes 

described by the PBPK model.
person weight height area_dermal age_group gender date hour diet_Tperm Dose_ingest Vent_inhal run

1 76.02703 180.4788 19940.50349 20-49 years M 12-Jul-10 19 2.438650909 0 0.01261814 1 76.02703 180.4788 19940.50349 20-49 years M 14-Jul-10 20 0.470288 0 0.0250942 1 76.02703 180.4788 19940.50349 20-49 years M 16-Jul-10 12 34.73421336 0 0.00798151 1 76.02703 180.4788 19940.50349 20-49 years M 17-Jul-10 12 0.000267955 0 0.0265954 1 76.02703 180.4788 19940.50349 20-49 years M 18-Jul-10 19 0.1057536 0 0.00872869 1 76.02703 180.4788 19940.50349 20-49 years M 19-Jul-10 15 0.760508364 0 0.02090339 1 76.02703 180.4788 19940.50349 20-49 years M 21-Jul-10 16 21.76421433 0 0.01682962 1 76.02703 180.4788 19940.50349 20-49 years M 24-Jul-10 10 0.00842688 0 0.00918217 1 76.02703 180.4788 19940.50349 20-49 years M 25-Jul-10 17 0.37670115 0 0.00539541 1 76.02703 180.4788 19940.50349 20-49 years M 26-Jul-10 19 1.4 0 0.00524947 1 76.02703 180.4788 19940.50349 20-49 years M 27-Jul-10 16 9.45E-06 0 0.01151972 1 76.02703 180.4788 19940.50349 20-49 years M 27-Jul-10 18 0.002605122 0 0.00863456 1 76.02703 180.4788 19940.50349 20-49 years M 29-Jul-10 21 0.000483694 0 0.00521797 1 76.02703 180.4788 19940.50349 20-49 years M 30-Jul-10 11 5.51304E-05 0 0.00903805 2 82.32053 185.465 21022.05396 20-49 years M 10-Jul-10 1 0 0 0.00419841 2 82.32053 185.465 21022.05396 20-49 years M 10-Jul-10 2 0 0 0.00414598 

Figure 7 Sample SHEDS exposure aggregate data. 
18

The full set of equations for the aggregate PM model is provided in Appendix B. Here 

we highlight the equations that pertain to uptake by the different routes. 

Ingestion Exposure 

Two compartments are used to describe the rate of absorption of PM from the lumen into 

GI tissue. Ks and Ki represent the stomach and intestinal absorption rate constants, respectively, 

while the gastric-emptying rate constant is represented by Ksi. Separate sets of equations are 

applied for cis-PM and trans-PM. 

 KsAs KsiAs

dt

dAs = − − (A.1) 

 KsiAs KiAi rFEC

dt

dAi = − − (A.2) 

The terms As and Ai represent the amount of PM in stomach and intestine, respectively. 

Once absorbed the cis-PM and trans-PM are available to the GI tissue. Refer to the Appendix 

for the subsequent processes (metabolism, distribution, excretion) 

In the sample simulation shown in Fig.7, SHEDS was configured to simulate dietary (Fig 

7, column 8) or non-dietary ingestion (Fig.7 column 9). A cis:trans ratio of 40:60 was assumed. 

With each new hour, cis-PM is assigned to ‘stomach_1’ in the sample code below (Figure 8), and 

trans-PM to ‘stomach_2’. The current unabsorbed quantities of cis and trans are specified by the 

terms derivs(3,1) and derivs(4,1), respectively. These terms represent the initial state values 

pertinent to the stomach lumen for the next one hour ODE simulation. 

 derivs(3,1) = derivs(3,1) + stomach_1; % update oral

 derivs(4,1) = derivs(4,1) + stomach_2

Inhalation Exposure 

The concentration of PM in arterial lung blood (Cart) is computed according to the 

venous equilibration model (Reddy, 2005): 

 

Palv

Qp Qc

Qp Cinh Qc Cv Cart

+

× + × = (B.1) 

Where QP indicates rate of pulmonary ventilation (L/h), Cinh is the breathing-zone 

concentration of PM (micro-mole/L) during exposure, and Cv is the venous blood. Palv is the 

equilibrium blood:air partition coefficient, estimated at 4564:1 based on the quantitative structure 

Figure 8 Hourly updating of oral exposure in PM model (Matlab) occurs by adding the unabsorbed mass of

PM in the GI to the new oral dose of PM and resetting the initial state vector for the next hour ODE simulation. This 

stream of inputs is provided as output from the SHEDS model. The top equation pertains to cis-PM, the bottom to 

trans-PM. 
19

property model of Beliveau et al. (2003). The magnitude of this estimated parameter indicates 

that inhaled permethrin greatly favors the blood phase upon equilibration. Refer to the Appendix 

B for the subsequent processes (metabolism, distribution, excretion). 

Dermal Exposure 

SHEDS models dermal exposure as a combination of deposition and removal processes, 

updated hourly. SHEDS rate constants are expressed in inverse time h-1; therefore, a dermal 

absorption process was developed for the PBPK model with equivalent unit (h-1), and provided 

to the SHEDS simulation team in order to account for this removal process (in conjunction with 

other removal processes) at each hourly interval. This formulation for a dermal rate constant is 

akin to the oral absorption rate constants (h-1) used in PBPK models; however, this approach 

departs from the conventional approach for describing dermal uptake in PBPK models using the 

permeability coefficient, Kp (cm/hr). Furthermore, Kp is derived under conditions of aqueous 

dermal exposure which are not typically the case for residential dermal exposure to pyrethroids. 

The empirical rate constant was fit from the study of Tomalik-Scharte et al. (2005) who 

evaluated dermal exposure in human volunteers from excretion of DCCA in urine (acid moiety 

derivative of PM after hydrolysis), following the topical application of PM-based ointments for 

lice and scabies. 

Dermal absorption of PM through the skin is modeled with two compartments for the 

uptake and distribution of PM through the stratum corneum (SC) and the viable epidermis (VE), 

based on such models from Kim et al. (2006). This structure was applied to facilitate the 

interpretation of tape strip data (assessed in the SC) should it be available in the future. The rate 

of change of PM in the stratum corneum is governed by the equation: 

 SC

SC Kds Asurf Kdv A

dt

dA = × − × (C.1) 

where Asurf is the amount of PM on the exposed surface area of the skin which enters the 

stratum corneum at the rate Kds. The term Kdv indicates mass transport through the VE and 

was set to Kds x 100, such that Kds was effectively the critical rate-limiting step for dermal 

absorption. In order to calibrate the SC for biomarker-tape stripping purposes, Kdv would need 

proper calibration. The rate of change of PM in the viable epidermis is then given by: 

.

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛ = × + −

VE

VE

SC

VE

PC

C Kdv A Qskn Ca

dt

dA (C.2) 

The rate of removal of PM from the skin surface is assessed: 

dAsurf Kds Asurf dt

=− × (C.3) 

As shown in the sample simulation in Fig.7, SHEDS was configured to simulate dermal 

exposure as a running exposure, thus the current amount on the surface is updated as shown in 

Fig.9, where cis-PM on the skin surface is specified as amtsurf_1, and trans-PM as amtsurf_2. A 

cis:trans ratio of 40:60 was assumed. 
20

 derivs(47,1) = amtsurf_1; % update dermal

 derivs(48,1) = amtsurf_2

Figure 9 Hourly updating of dermal exposure in the permethrin PBPK model (Matlab) occurs by resetting 

the initial state vector to the new mass of cis-PM and trans-PM for the next hour ODE simulation. This stream of 

inputs is provided as output from the SHEDS model.

Biomarker Model 

Single compartment model of cis- and trans-DCCA. Ester cleavage of cis- and transPM occurs via hydrolysis catalyzed by CaE (see Fig. 4) and renders phenoxybenzyl alcohol 

(PBA) and (cis- and trans-DCCA). We modeled cis- and trans-DCCA, as these are specific to 

permethrin, cypermethrin, and cyfluthrin, whereas 3-phenoxybenzoic acid (3-PBA) is common 

to a larger set of pyrethroids. The study of Gaughan et al. provided information relating oral 

absorption of cis- and trans-PM in the rat and the stoichiometric production of cis- and transDCCA in the urine. The study of Woollen et al. (1993) provided information on rates of 

excretion of cis- and trans-DCCA in urine, in humans, following controlled oral exposure to 

cypermethrin, the type II analog of permethrin. The details of the one-compartment metabolite 

model are described in Appendix-B. 

Bayesian Calibration of PBPK Models 

Parameter uncertainty and variability on multiple levels (parameters that vary among 

individuals as well as variation in studies) must be addressed correctly in a statistical framework 

for the resulting estimates to be correct. Hierarchical Bayesian statistical models lend 

themselves easily to the usage of multiple data sets from different sources and evaluate both 

uncertainty and variability for a large number of unknown parameters. 

Although data from different sources can be used to calibrate PBPK models in a Bayesian 

statistical framework, there is often limited in vivo data available for estimating the large number 

of parameters associated with PBPK models. However, many PBPK model parameters reflect 

biological characteristics, so parameter and model values and their uncertainties can still be 

determined even in the absence of in vivo experimental pharmacokinetic data. Uncertainties can 

be derived from prior knowledge about model parameters that can be obtained from data sets of 

measured physiological parameters (e.g., tissue volumes and cardiac output), computational 

predictors (e.g., QSAR methods for partition coefficients), and in vitro assays (e.g., 

measurements of intrinsic hepatic clearance rates). This prior information is easily included in 

hierarchical Bayesian analyses of PBPK models through the use of prior distributions (priors) 

that reflect what is known about parameters before evaluating observed data. Prior distributions 

are then coupled with experimental data in Bayesian analysis to determine posterior distributions 

(as opposed to point estimates with confidence intervals) that characterize both the uncertainty 

and variability associated with PBPK model parameters and predictions. 

Hierarchical Bayesian analysis is not only advantageous because it allows prior 

information to be incorporated easily through the use of priors and provides a thorough 

assessment of both uncertainty and variability in model parameters, but it also addresses the 

issue of parameter identifiability. Parameter identifiability is often a problem in dynamic 

computational (e.g., PBPK) models with large parameter spaces and limited available data for 

determining some of the parameters exactly. Garcia et al. (in preparation) observed that 

statistical identifiability of PBPK parameters cannot be determined a priori. However, 
21

specifying proper prior distributions (i.e., distributions that have a finite integral) for parameters 

results in proper posteriors, which are necessary for valid statistical analysis of PBPK models. 

Therefore, inferences based on Bayesian analyses that result in proper posteriors are valid even 

though the PBPK model may not be identifiable. For a given data set, parameters that are not 

identifiable can be characterized by comparing the priors to the posterior distributions; the 

posterior for parameters that are not identifiable will be the same as the prior. 

These features have made hierarchical Bayesian methods a standard approach for 

analyzing PBPK models [Bois et al., 1996; Gelman et al., 1996; Hack et al., 2006; Wambaugh et 

al., 2008]. We are currently using this framework to calibrate the rat permethrin model 

(discussed earlier and given in Appendix B) with data from oral exposure studies; however, we 

did not have final results in time to include in this background paper. In the following 

discussion, we give an overview of the Bayesian method for calibrating PBPK models and 

present some approaches that we have developed to address some of the issues that are 

associated with these types of computational efforts. We begin by discussing the model structure 

that must be formulated for a hierarchical Bayesian analysis of a PBPK model. 

Model Structure 

Deterministic and stochastic models must be defined for a Bayesian calibration of a 

PBPK model in a hierarchical statistical framework. The deterministic portion involves 

developing the PBPK model, which describes the uptake and disposition of chemicals or drugs 

throughout the body for an individual. The model for permethrin has already been described 

above. Two additional models must be formulated for the stochastic portion in a hierarchical 

Bayesian analysis: a population model and a measurement error model. These models will now 

be described. 

Population Model 

One of the advantages to using a hierarchical Bayesian statistical framework to calibrate 

PBPK models is that one not only gets estimates of the individual-specific parameters but also 

estimates of the population parameters (e.g., means and variances) quantifying the distribution 

for the individual pharmacokinetic parameters. The population model describes how the 

individual parameters vary across the population. We assume the individual pharmacokinetic 

parameters are log-normally distributed with two population parameters: mean μ and variance 

Σ2. Truncated log-normal distributions (mean ± 2 or 3 standard deviations) are used to constrain 

the parameters to biologically reasonable values, thereby avoiding some computational issues 

that can arise when solving the PBPK model. Prior distributions are assigned to the population 

parameters for the pharmacokinetic parameters. The priors are described in more detail in the 

Priors section. 

Measurement Error Model 

The measurement error model describes the distribution of the error or difference in the 

PBPK model predictions and observed data for each individual. Let yijk denote the concentration 

of cis- or trans-permethrin measured for individual i at time tij in compartment k. We assume 

that the log of the measurement log yijk is normally distributed with mean log Yijk, the log of the 

model predicted concentration, and variance 2 σ k for each compartment k

2 log ~ (log , ) ijk ijk k yNY σ
22

where ) ( | , 2 N ⋅ μ σ is the density of a normally distributed random variable with mean μ and 

variance σ

2

. 

With the deterministic and stochastic model components defined, prior distributions 

specified (see the next section), and observed data from various sources compiled, Bayesian 

calibration efforts can be carried out. These efforts result in estimates of the uncertainty 

distributions for the unknown parameters (e.g., population parameters, each individual’s 

pharmacokinetic parameters, and the measurement variances for each PBPK compartment). The 

uncertainty distribution, or posterior distribution, for the unknown parameters θ is given by 

p( | ) ( | )() θ y Ly p ∝ θ θ , 

where p(|) θ y , the posterior distribution, is proportional to the product of the likelihood of the 

data given the model parameters L y(|) θ and the prior distribution ( ) p θ .

Priors 

As previously stated, one of the major advantages to using hierarchical Bayesian analysis 

to calibrate PBPK models is the ability to use prior knowledge about the unknown model 

parameters along with experimental data to determine posterior distributions that reflect all of 

what is known about the parameters for a given data set. Hence, priors are important because 

they reflect what is known about parameters and their uncertainties before data is observed. 

Furthermore, if a data set does not contain information that can be used to estimate some 

parameters and their associated uncertainties, then the uncertainties in those model parameters 

will be determined solely by the priors. This is a contributing factor to the overall uncertainty 

analysis of the model predictions, so it is important to specify priors that reflect what is known 

based on information that can be obtained from valid sources. 

There are different types of priors that can be assigned to parameters for Bayesian 

calibration efforts, such as point estimates (“perfect knowledge”), weakly informative (diffuse) 

priors, and informative priors. Point estimates are sometimes used to reduce the large number of 

parameters that must be estimated in hierarchical Bayesian statistical analyses. In this case, the 

parameter estimates and model predictions are dependent upon these point estimates or fixed 

values, which could result in misleading or incorrect conclusions. Furthermore, the uncertainty 

associated with the model predictions is underestimated as a result of using a point estimate 

without any measure of the uncertainty in its value. At the opposite extreme are weakly 

informative priors, such as broad uniform distributions with every value in some range being 

equally likely. If the data contains no information on parameters that are assigned diffuse priors, 

then the posteriors are equal to the priors, which can lead to much larger uncertainty in model 

predictions. Computations for parameter estimation can also be inefficient due to algorithms 

exploring areas of the parameter space that are highly unlikely as a result of very broad, 

uninformed distributions. The optimal case is informative priors that are truly reflective of what 

can be derived from the literature in regards to the unknown parameters of interest with regards 

to mean values and plausible ranges. 

Specifying priors for PBPK model parameters can be addressed separately for 

physiological parameters and chemical-specific parameters based on the different types of prior 

information available in the literature. In the following, we discuss approaches for developing 

informative priors for PBPK model parameters, specifically chemical-specific parameters. 
23

Informative Priors 

Physiological Parameters 

Physiological parameters include body weight, cardiac output, tissue volumes, and blood 

flows. Values for body weight are usually measured during experiments. For the remaining 

physiological parameters not observed experimentally, mean values for these parameters are 

typically found in the literature [Brown et al., 1997]. Standard deviations or coefficients of 

variation (CVs) are also based on information derived from the literature. CVs are usually small, 

indicating less uncertainty in the mean values obtained from the literature for these parameters. 

Reference values found in the literature for physiological parameters usually provide informative 

priors for these parameters [Bernillon et al., 2000]. For our calibration efforts with the rat 

permethrin model, we use informative priors for all of the physiological parameters (e.g., cardiac 

output, fractional blood flows, fractional tissues volumes, and blood volume fractions) with 

values for the mean and uncertainty derived from the literature. 

Chemical-specific Parameters 

Chemical-specific parameters, such as partition coefficients, oral absorption rates, 

diffusion-limited tissue permeability rates, and metabolic parameters, are oftentimes assigned 

weakly informative priors as a result of more uncertainty in the values for these parameters. 

While values obtained from the literature are used in many PBPK calibration efforts for 

physiological parameters with less uncertainty, there seems to be less consensus in the literature 

on the uncertainty one should use when specifying priors for chemical-specific parameters. In 

many cases, large CVs are used for these parameters due to more uncertainty being associated 

with the values for these parameters [Bernillon et al., 2000; Gelman et al., 1996]. 

We have developed approaches that can be used to specify more informative priors for 

chemical-specific parameters based on information that can be found in the literature, such as 

various computational models that predict chemical-specific parameters based on chemical 

structure properties, experimental in vivo measurements of these parameters for a number of 

chemicals, and in vitro methods that can be used to make in vivo predictions for some parameters 

(e.g., metabolic parameters) [Davis et al., in preparation]. We discuss and illustrate these 

approaches with the following two examples. 

Partition Coefficients 

In an effort to standardize the approach used in specifying priors for tissue-plasma 

partition coefficients, we surveyed the literature for computational predictors that can be used to 

predict these parameters. There are a number of mechanistic models based on a small number of 

physicochemical properties that have been developed to predict tissue-plasma partition 

coefficients [Poulin et al., 2000; Rodgers et al., 2005; Schmitt, 2008]. In particular, Schmitt’s 

model combines principles from the models of Poulin et al. (2000) and Rodgers et al. (2005). 

Schmitt (2008) showed that his model does a good job of predicting the partition coefficients for 

several tissues for a diverse set of compounds. 

After identifying a reasonable computational predictor, we compiled an extensive data 

set, including the data from Schmitt as well as additional in vivo measured values for tissueplasma partition coefficients for a number of tissues. The relationship between the experimental 

and predicted values was determined by using regression analysis on the log scale. Regression 

analysis is used to adjust for any bias that may exist in the predictor for partition coefficients. 
24

The regression corrected value from the computational predictor is then used as the mean for the 

prior for the tissue-plasma partition coefficient. The variance from the experimental versus the 

predicted regression lines (or the root mean square error) is used as the variance (or standard 

deviation) of the prior. Using this approach, we computed log standard deviations that 

correspond to CVs in the range of 50 – 70% for most of the tissue-plasma partition coefficients 

in the permethrin model. This is an improvement over CVs of 150% that have been used in 

vague priors for partition coefficients in some PBPK modeling efforts [Bois et al., 1996, Gelman 

et al., 1996]. 

This same approach can be used to develop informative priors for other chemical-specific 

parameters, such as oral absorption rates and dermal permeability, based on computational 

predictors that exist provided that substantial data sets can be compiled via thorough surveys of 

the literature. While this general approach allows one to use readily available data from the 

literature to construct more informative priors for chemical-specific parameters, one must note 

that the priors developed via this approach are very much dependent on how well the chemicals 

included in the data set for the regression analysis cover chemical space (in particular, 

compounds are included that have similar physicochemical properties to the chemical of 

interest). 

Metabolism 

We use a more empirical approach in developing informative priors for the metabolic 

parameters in the permethrin model. Instead of using computational predictors and in vivo

measurements of metabolic, or clearance, rates, we use in vitro measures of intrinsic clearance 

rates for both cis- and trans-permethrin. Means and standard deviations are provided in Scollon 

et al. (2009) for the intrinsic clearance measured in rat hepatic microsomes along with the 

hydrolytic and oxidative proportions. Then, utilizing the parallelogram approach outlined 

previously in the Extrapolation by Parallelogram section and discussed in Chiu et al. (2007) as a 

method for estimating metabolic parameters in PBPK models, we apply an in vitro-in vivo

scaling factor to the intrinsic clearance from the in vitro measurements. The in vitro-in vivo

scaling factor is then assigned a weakly informative prior due to no information being available 

for this factor (see the next section), which is refined via the Bayesian calibration efforts. 

Weakly Informative Priors 

While specifying informative priors for all of the PBPK model parameters that we are 

estimating would be ideal, we are not able to do so due to lack of computational predictors, 

limited in vivo data, or lack of information in the literature for some parameters (e.g., in vitro-in 

vivo scaling factor). In these cases, weakly informative priors must still be used. We use weakly 

informative parameters for the absorption rates, diffusion-limited parameters, and scaling factors 

in the hierarchical Bayesian analysis of the rat permethrin model. Since there is little prior 

knowledge with regards to the mean and uncertainty in these parameters, truncated uniform 

priors are used for these parameters. 

Computational Issues 

Although Bayesian analysis offers several advantages in regards to calibration efforts and 

uncertainty analyses of PBPK models, there are some issues that can make these efforts 

challenging. One major drawback is the long computational runtimes often required when these 

models are implemented via Markov Chain Monte Carlo (MCMC) methods. MCMC methods 
25

are typically used in Bayesian analyses of PBPK models to determine posterior distributions; 

however, it is not uncommon for Markov chains to require weeks to converge to the posterior 

due to the high dimensionality of the parameter space. The large number of parameters that must 

be estimated for PBPK models coupled with the iterative procedures of MCMC techniques 

makes hierarchical Bayesian analyses very time-consuming. Another issue that arises when 

using MCMC is determining whether or not MCMC chains have converged to the posterior 

distribution. There are several metrics that are typically used to determine if a MCMC chain 

appears to have converged, but there are cited cases wherein these metrics proved not to be 

correct in suggesting convergence [Gelman et al., 1996, Chiu et al., 2006]. 

Many implementations of the various sampling algorithms that exist (e.g., MetropolisHastings and Gibbs sampling) are rather slow. Wambaugh, et al. (in preparation) discuss an 

approach developed in R that decreases computational runtimes for MCMC sampling based on 

parallelizing the likelihood computations where most of the time is spent for hierarchical models. 

The speed-ups obtained with this sampler are a result of allowing the likelihood computations for 

each individual to be computed in parallel since these computations are independent of each 

other. We are currently using this sampler, which is able to produce 10000 simulations in less 

than 2 hours on clusters at the National Computer Center in Research Triangle Park, NC, to 

calibrate the rat permethrin model. This makes calibration of the human permethrin model as 

well as model evaluation (discussed in the next section) much more feasible. 

Model Evaluation 

Bayesian analysis also allows one to evaluate how well a model fits data as well as 

quantitatively compare alternative model structures. Model fits can be evaluated by analyzing 

posterior predictive distributions [Gelman et al., 2004] and using metrics such as the Deviance 

Information Criterion (DIC) to compare the results. This process often involves visually 

inspecting and comparing different PBPK model predictions to observed data in an effort to 

determine which model structure provides the most adequate fit to the data (see examples in 

Chiu et al., 2007). For simple linear regression models, standard statistical techniques, such as 

residual plots, are often used to assess how well a model fits a data set. However, interpretation 

of these results is not as straightforward in applications with complicated statistical model 

structures (e.g., PBPK models). Furthermore, the difficulty with using the standard tests for 

goodness of fit that exist in the statistical literature for linear models is that these approaches are 

not always applicable to PBPK models (Chiu et al., 2007). Therefore, additional guidelines, 

such as those discussed in Clark et al. (2004), need to be formally developed in order to address 

the issue of model evaluation and comparison of PBPK models. 

Extrapolation of Animal-Calibrated Models to Humans 

Considerations for Extrapolation 

For a given exposure input, PBPK models generate a time-dependent stream of tissue 

concentrations. The inputs, such as dietary or non-dietary ingestion, air concentration, or dermal 

dose of permethrin, can themselves be time-dependent, so the pharmacokinetic system, and the 

PBPK model that mimics it, can be thought of as a filter that takes as input a time-dependent 

sequence of exposures, and produces, as output, a time-dependent constellation of tissue-specific 

concentrations. However, our effects models do not, at this point, handle time-dependent inputs, 

so we need to summarize that time-changing concentration into a single, scalar, dose-metric. 
26

There are many different ways to do that. Some examples are peak concentration over a given 

time interval, average area under the curve (AUC), average AUC above a given toxicological 

threshold, how long the concentration exceeds a given threshold value; in general, we compute 

the integral () ( ) , (.)

T

c t w t c dt ∫ over a time interval T, where c(t) describes how the concentration 

of the molecule in question changes over time in a critical tissue, and w(t,c(.)) is a weighting 

function which may depend on time t and the function c(). Put in this form, the PBPK model’s 

role is to produce the function c(t) for a given input. The dose-metric is characterized by the 

function w() and interval T, and is mainly determined by an understanding of the biological 

processes relating internal dose to the health effect. 

One of the important uses of PBPK models in risk assessment is to provide a framework 

for extrapolating pharmacokinetic behavior, in general, and dose-metrics, in particular, from 

animal models to humans. For this extrapolation to be successful, the PBPK model derived from 

animals must contain all the elements thought to be necessary for accounting for 

pharmacokinetic processes in people, and there must be a way to assign values to the model 

parameters that are appropriate to humans. A strength of the physiologically-based modeling 

approach is that many of the parameters needed can be linked to independently measurable 

physiological parameters, which greatly facilitates extrapolating parameter values from the 

animal to human model. However, the model contains other parameters which are specific to the 

chemical(s) under consideration. We try to find ways to measure such parameters directly that 

are appropriate for the human model, or, if that is difficult, to find rules that allow us to 

extrapolate such parameter values from the animal model to humans. 

While laboratory animal populations are fairly homogeneous, humans are quite variable, 

and this variability affects pharmacokinetics. It is important to attempt to characterize what we 

know about variability of target dose measures among members of target populations with a 

given exposure. Since direct measurements of the pharmacokinetics of pesticides in humans are 

rare, the only way to quantify both aspects of variability is indirectly, through knowledge of how 

basic physiological and biochemical characteristics vary in a population. This means both 

targeting the model to the appropriate subpopulation (for example, by age or gender), and 

attempting to characterize the variability of pharmacokinetic characteristics expected in that 

population. Through Monte Carlo sampling from a distribution of parameter values thought to 

characterize population variability, the model is then used to transduce that variability into 

variability in target dose. 

Finally, one of the goals for this model development has always been to be able to 

quantitatively characterize the remaining uncertainty about human pharmacokinetics of the 

pyrethroids. While it is probably not possible to characterize all the uncertainty convincingly, it 

is certainly possible to identify major sources of uncertainty, characterize them, and evaluate the 

effects of that uncertainty on target dose measures. Since the human model is based almost 

exclusively on rat data, the uncertainty about human dose measures includes both the uncertainty 

about parameter values derived from rat data and uncertainty about the rules we use to 

extrapolate those values to humans. This latter uncertainty is generally difficult to quantify. In 

what follows, we discuss general approaches to incorporating such uncertainty, but delay until 

later quantification of that uncertainty. 
27

Parameter Extrapolation 

Physiological Parameters 

Tissue volumes, cardiac output, and fractions of cardiac output allocated to each tissue 

are estimated in the rodent model using strongly informative priors. To extrapolate the 

physiological part of the model from animals to humans, we assume the same basic model 

structure, but use human-appropriate physiological values. Price et al. (2003) published a set of 

relationships to predict tissue volumes and perfusion rates. Tissue volumes are computed as 

functions of sex, age, weight, and height, and so can vary across the population. Tissue 

perfusion rates are modeled as functions of tissue weight. In addition, since it is desired to 

simulate other than resting physiology, blood flows to specific tissues are modified to account 

for activity following the methods of Jonsson et al. (2001). Variability of physiological 

parameters over the population then is driven by variability in the anthropometric measures, such 

as weight, height, age and sex. While there is uncertainty in the relationships described in these 

papers, it is likely to be dominated by the variability over the simulated population, and is 

ignored in this analysis. 

Chemical Specific Parameters 

The permethrin model has four general groups of chemical-specific parameters: partition 

and permeability-area coefficients, metabolic clearances, oral absorption, and dermal absorption. 

These are all treated differently. 

Permeability-area coefficients. We have little basis for treating permeability-area 

coefficients from animals or humans differently, and adopt the values estimated from the rodent 

data directly into the human model. 

Partition Coefficients. Partition coefficients are influenced by tissue lipid content, 

which differs to an extent between rodents and humans. To account for the differences, tissuespecific partition coefficients are computed using the method of Schmitt (2008) based on both rat 

and human lipid compositions: PCr and PCh. The PC estimated from the rat data is then adjusted 

by multiplying by the ratio PCh/PCr. 

Metabolic parameters. The parallelogram approach is used to extrapolate from rat to 

human metabolic parameters. Metabolism in the pyrethroid model is characterized by a hepatic 

clearance term, which includes both oxidative and hydrolytic clearance processes. As discussed 

earlier, the rodent clearance is computed as the product of oxidative and hydrolytic clearance 

terms based on in vitro measurements (Scollon et al., 2009) using rat tissue and a term that 

adjusts the in vitro clearance term for in vivo use. Only the in vitro to in vivo adjustment term is 

estimated, and the estimation process yields a distribution of values for that term, which 

characterizes the uncertainty in the in vitro to in vivo extrapolation. To extrapolate to humans, 

the rat in vitro term is replaced with a human in vitro term (Scollon et al., 2009). The adjustment 

factor estimated from the rodent data is used to adjust from human in vitro to human in vivo. 

Oral absorption. Absorption rate parameters estimated for the GI tract from rat data are 

used unadjusted in the human model. 

Dermal absorption. Dermal absorption parameters will be used as estimated from 

human data. 
28

Characterizing Uncertainty in the Extrapolated Model 

The baseline uncertainty for all the chemical-specific parameters is the uncertainty, 

quantified by the joint posterior distribution, inherent in the parameters as estimated from the rat 

data. The uncertainty in the final extrapolation to humans includes that baseline uncertainty and 

the uncertainty about the extrapolation itself. Extrapolation for permeability-area and partition 

coefficients, and oral and dermal absorption parameters are accomplished by multiplying a 

constant (‘one’ for all but partition coefficients). An approach to characterizing the uncertainty 

of such extrapolation is to replace the constant with a distribution, say a log-normal distribution, 

whose median equals that constant, but with a positive coefficient of variation that reflects 

uncertainty about the value. While it may be difficult to specify particular values for the 

coefficient of variation for a given uncertainty extrapolation, such a formulation allows ‘what if’ 

sorts of experiments, to examine the consequence of varying levels of uncertainty about model 

elements on the overall uncertainty of predictions of dose-metric distributions. 

Uncertainty in the Linked SHEDS – PBPK Model 

In order to develop predictions of population distributions of relevant dose-metrics, given 

a set of exposure scenarios, SHEDS is used to predict time courses of the amount or 

concentration of chemicals ingested, inhaled, or on the skin. These are used as inputs to a PBPK 

model, which translates those inputs into time courses of tissue concentrations, and, ultimately, 

estimates of dose-metrics for the chemical in question. 

The output of SHEDS can be formalized as a table of values, with rows as observations 

and columns for replication number, subject id, other subject-specific characteristics (age, 

gender, weight, height), time, activity level, and exposure measures (see Fig. 7). We have 

developed an implementation of the PBPK model described here that runs in a combination of 

interpreted R code and compiled code, using the R package deSolve (Soetaert et al., 2010) to 

integrate the system of differential equations. This implementation can take as exposure inputs 

matrices of times exposure concentrations or amounts as appropriate for the route, and other 

time-dependent features. Thus, the exposure and dose systems can be linked through a defined 

SHEDS output file format, and run asynchronously on different platforms. This latter feature 

allows some time efficiency, as PBPK simulations can be run on earlier SHEDS outputs while 

additional SHEDS outputs are being produced. 

The interesting output of the linked SHEDS-PBPK model is a population distribution of a 

particular dose-metric. In this mode, SHEDS is used to produce realizations of exposure patterns 

for individuals from a defined population over a specified period of time. The exposure patterns 

for each individual are used as inputs to a human-specific PBPK model with parameters tuned as 

appropriate for that individual (that is, adjusted for the given age, gender, height and weight of 

the individual). The output of the PBPK model is processed to yield the desired dose-metric, and 

the corresponding dose-metric for all the individuals are aggregated to estimate a population 

distribution. Two-stage Monte Carlo sampling is used to characterize the uncertainty in the 

characterizations of quantiles of the population distribution. A sample of parameter values is 

drawn from the joint uncertainty distribution for the SHEDS and PBPK model parameters, then a 

population of individuals is drawn and exposed, using those parameter values, and population 

percentiles, say 50th, 90th, and 95th percentiles, of the dose-metric computed. This is repeated for 

multiple samples from the uncertainty distribution, resulting in a distribution of the desired 

percentiles, which characterizes their uncertainty. 
29

It is of interest to identify the extent to which uncertainty in individual parameters and 

correlated sets of parameters contributes to the overall uncertainty about population percentiles 

of dose-metrics. This is accomplished through a sensitivity analysis based on using regression 

methods to partition the variance of the distributions of percentiles into components contributed 

by individual parameters. 

Permethrin Case-Study: Probabilistic Modeling of Dietary and 

Residential Permethrin Exposure, Interpretation with PBPK 

Modeling, and Comparison with NHANES Data 

Overview 

The goal of this simulation was to quantify dietary and residential exposure to permethrin 

and to compare model predictions with observed biomarker data. Probabilistic exposure 

modeling for dietary and residential permethrin exposure was conducted with the Stochastic 

Human Exposure and Dose Simulation Model for Multimedia, Multipathway Chemicals 

(SHEDS-Multimedia):Dietary Module and the SHEDS-Multimedia Residential Module. 

The SHEDS-PBPK biomarker simulation was conducted by processing the SHEDS 

output exposure profiles through the permethrin PBPK model described in this white paper. 

What we present is preliminary with respect to scope of proposed methods in this paper: (a) the 

PBPK model was fit by eye (we intend to use a Bayesian-calibrated PBPK model in future 

evaluations); (b) variability sampling was not fully conducted for PK (we considered variability 

in body weight as informed by SHEDS, but did not consider population variability conditional 

on body weight); (c) uncertainty sampling of PBPK parameter space was not conducted; (d) 

uncertainty sampling of the SHEDS parameter space was not conducted. In spite of the short 

comings, we provide the first account of a population simulation of excreted levels of urinary 

DCCA following residential and dietary exposure to permethrin. Model evaluation was 

conducted by comparing the percentiles of the cumulative distribution function (CDF) of 

simulated cis- and trans-DCCA excreted urinary biomarker with the percentiles of the cis- and

trans-DCCA reported in the ’99-’00 and ’01-02 survey years of the National Health and 

Nutrition Examination Survey (NHANES). 

Simulation 

Residential and dietary exposures to permethrin were simulated for 8994 persons of 6 

years age and older. For each person, hour-by-hour exposures were simulated for 21 days (504 

hours). These 8994 persons represent the satisfactory merger within SHEDS of dietary and 

residential simulations, each consisting of 10000 persons. For the 6-12 year old group there 

were 978 persons simulated, 1025 persons for the13-19 year old group, 4407 persons for 20-49 

year, and 2584 for the 50+ group. The aggregate exposure matrix served as input for the PBPK 

model. Each row of this matrix provided an hourly update of the aggregate exposure vector, 

providing starting conditions to inform the initial state vector (ISV) for a one-hour PBPK 

simulation. Upon completion of the hour simulation, the model state variables provided 

information that was combined with information in the next row of the exposure vector to reset 

the ISV for the next hour of simulation. Studies evaluating the length of time to achieve pseudo 

steady-state conditions indicated that a 5-day simulation provided a reasonably stationary 

distribution of dose-metrics. Upon completion of a 6-day simulation, dose metrics pertaining to 
30

the individual were retrieved and stored. This was performed for all 8994 individuals, providing 

a distribution of dose-metrics for the population. 

Comparisons between model predicted DCCA concentrations and 

measured quantiles from NHANES 

NHANES measurements provide an integrated measure of exposure across routes. 

Exposure information does not accompany the NHANES measurements. Therefore, it is with 

the coupled SHEDS-PBPK system that hypotheses may be developed and tested in conjunction 

with NHANES to ask questions regarding important exposure pathways. It is important to 

appreciate the limits of NHANES in this context. NHANES is perhaps the largest database of 

population urine DCCA measurements; however, the lack of accompanying exposure data 

indicate that care must be taken in interpreting results. 

Two different approaches were used to estimate cis- and trans-DCCA urine 

concentrations in model outputs. In the first approach, DCCA urine concentration is the average 

concentration over a 24-hour period. The simulation was run for 5 days, sufficient for the 

distribution to be reasonably stationary, and measurements taken on the sixth. The estimated 

DCCA concentration for a person is the total DCCA excreted over that 24 hours, divided by the 

total volume of urine excreted over 24 hours. The second approach is an attempt to simulate the 

natural process of urine voids. The simulation was run for 5 days, as in the previous method, 

and a random time selected between 9 am and 5 pm (uniformly over that time). Next, an interval 

duration between 0.5 and 2 hours was selected to represent the time since the last void. The 

amount of DCCA created over that interval divided by the urine excreted over that interval, is the 

estimate of concentration. These two approaches gave similar results such that we report the 

findings from the first approach. 

Figures 10 and 11 provide comparison of the simulated urine concentrations of cis- and

trans-DCCA with measured values from NHANES. In both figures, the upper region provides 

comparisons for entire age range, and towards the bottom, comparisons for children, teens, and 

adults, respectively. Comparisons are provided for the 75th, 90th, and 95th percentile of each 

distribution. The NHANES data includes a line though the percentile denoting a 95% 

confidence interval. The 95% confidence intervals (CI) on the simulated percentiles are based 

on sample theory. These CI relate to the uncertainty of projecting from a finite number of 

simulated individuals to a population of infinite size and assume that parameters are measured 

without error. As such, these CI underestimate the true uncertainty (introduced by parameter 

uncertainty). In spite of this bias, these CI are informative in quantifying the uncertainty 

introduced purely from sample size; consider that the CI for children 6-12 is the largest of any 

group precisely because this age group was under-sampled relative to the other age groups. 

Future plans are to provide uncertainty bound based on uncertainty sampling (Monte Carlo) of 

the parameters in the SHEDS and PBPK models. Therefore, in these future simulations, it may 

be apparent if the computational expense of increased sample size may help to narrow CI, or 

whether parameter uncertainties are disproportionately contributing to the large CI. 

Overall, simulated DCCA is in good agreement with sampled DCCA, suggesting that 

permethrin exposure is the primary contributor to the NHANES sampled DCCA. Future 

investigations are intended to understand the contributions from the dietary and residential 

pathways. Furthermore, since DCCA arises from metabolism of cypermethrin and cyfluthrin, 

these exposures need to be investigated. Interestingly, the SHEDS-PBPK simulation indicated 
31

the highest exposures occurred for children 6-12. This was consistent with the 95th percentile of 

the NHANES ‘99-‘00 cis-DCCA measurements for children 6-11 (and within the confidence 

interval for the corresponding trans-DCCA result). 

Figure 10 SHEDS-PBPK simulated and NHANES sampled cis-DCCA.
32

Figure 11 SHEDS-PBPK simulated and NHANES sampled trans-DCCA.

PBPK modeling allows prediction of tissue dose metrics concurrent to biomarker 

predictions. This is an important feature of PBPK modeling over classical PK. Interestingly, 

urine and tissue-based metrics may not be strongly correlated with each other. PBPK modeling 

provides a tool to further explore reasons why. Figure 12 shows a scatter plot of peak daily brain 

cis-permethrin (μmol/L) and 24-hour average cis-DCCA in urine (μg/L). The moderate 

correlation may be caused by exposures that occur through different routes (inhalation, oral, 

dermal) and net the same 24-hour average urine concentration, but do not achieve the same peak 

levels (because of varying absorption rates). 
33

Figure 12 Relationship, in simulations, of peak brain cis-permethrin and average cis-DCCA concentration 

in urine for the same time interval.

Summary 

PBPK modeling has become an important tool for research and analysis in toxicology 

and risk assessment. We describe the application of PBPK modeling to help translate exposure 

simulations of the SHEDS probabilistic exposure model both into measures of dose relevant to 

risk assessment, and to predict population distributions of biomarkers. The approach described 

here is particularly useful for probabilistic exposure assessments (and risk assessments) 

involving chemical groups, such as the pyrethroids, in which the benefits of chemical-tochemical extrapolation are best realized. Our hope is to spawn a dialogue between practitioners 

in the fields of exposure science and PBPK modeling, to the benefit and additional applicability 

of both disciplines. We have just presented preliminary results for population exposure 

assessment of permethrin based on a single population sampling within SHEDS. Future 

directions include iterative sampling in SHEDS and the PBPK model to investigate the 

propagation of exposure and PBPK modeling uncertainty and variability and its impact on 

biomarker estimates and tissue dose metrics. 
34

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38

Appendix A. ORD Research Related To Pyrethroid PBPK 

Modeling 

PYRETHROID PBPK MODELING RESEARCH SUMMARY 

Mirfazaelian A, Kim KB, Anand SS, Kim HJ, 

Tornero-Velez R, Bruckner JV, Fisher JW. 

Development of a physiologically based 

pharmacokinetic model for deltamethrin in the 

adult male Sprague-Dawley rat. Toxicol Sci. 

2006 Oct;93(2):432-42. 

First published PBPK model of a pyrethroid. 

Model employed both flow-limited and 

diffusion-limited rate equations to describe 

disposition of deltamethrin in the adult, male 

Sprague-Dawley rat. Cytochrome P450-

mediated metabolism was accounted for in 

the liver and carboxylesterase (CaE)-

mediated metabolism in plasma and liver. 

Tornero-Velez R, Mirfazaelian A, Kim KB, 

Anand SS, Kim HJ, Haines WT, Bruckner JV, 

Fisher JW. Evaluation of deltamethrin kinetics 

and dosimetry in the maturing rat using a PBPK 

model. Toxicol Appl Pharmacol. 2010 Apr 

15;244(2):208-17. 

PBPK model of deltamethin for the Maturing 

Rat. Age-dependent parameters (metabolism, 

compartment sizes) are continuously updated 

in the model to account for age-dependence 

in the pharmacokinetics of deltamethrin. 

Godin SJ, DeVito MJ, Hughes MF, Ross DG, 

Scollon EJ, Starr JM, Setzer RW, Conolly RB, 

Tornero-Velez R. Physiologically based 

pharmacokinetic modeling of deltamethrin: 

development of a rat and human diffusionlimited model. Toxicol Sci. 2010 

Jun;115(2):330-43. 

Proposed an alternative model structure 

describing all tissue compartments with 

diffusion-limited kinetics and a single blood 

compartment. This model also revises the 

incorrect GI absorption model of 

Mirfazaelian et al. (2006). 

Tornero-Velez R, Scollon EJ, Starr JM, Hughes 

MF, DeVito MJ, Dary CC. Pharmacokinetic/ 

Pharmacodynamic Modeling of Permethrin in 

the Rat. Presented at the 46th Annual Meeting of 

the Society of Toxicology. 

Applied the structure of Mirfazaelian et al. 

(2006) to describe time-course of cis- and

trans-permethrin in the rat. Paper is in 

progress. 

Harrill JA, Li Z, Wright FA, Radio NM, Mundy 

WR, Tornero-Velez R, Crofton KM. 

Transcriptional response of rat frontal cortex 

following acute in vivo exposure to the 

pyrethroid insecticides permethrin and 

deltamethrin. BMC Genomics. 2008 

Nov 18;9:546 

Pyrethroids induced changes in gene 

expression in the frontal cortex near the 

threshold for decreases in ambulatory motor 

activity in vivo. PBPK modeling was used to 

evaluate tissue dose where these changes take 

place. 

METABOLISM OF PYRETHROIDS RESEARCH SUMMARY 

Godin SJ, Scollon EJ, Hughes MF, Potter PM, 

DeVito MJ, Ross MK. Species differences in the 

in vitro metabolism of deltamethrin and 

This study examined the elimination of 

esfenvalerate and deltamethrin from rat and 

human liver microsomes. 
39

esfenvalerate: differential oxidative and 

hydrolytic metabolism by humans and rats. 

Drug Metab Dispos. 2006 Oct;34(10):1764-71. 

Godin SJ, Crow JA, Scollon EJ, Hughes MF, 

DeVito MJ, Ross MK. Identification of rat and 

human cytochrome p450 isoforms and a rat 

serum esterase that metabolize the pyrethroid 

insecticides deltamethrin and esfenvalerate. 

Drug Metab Dispos. 2007 Sep;35(9):1664-71. 

Using a parent depletion approach, rat and 

human cytochromes P450 (P450s) were 

screened for their ability to eliminate 

deltamethrin or esfenvalerate during in vitro 

incubations. 

Scollon EJ, Starr JM, Godin SJ, DeVito MJ, 

Hughes MF. In vitro metabolism of pyrethroid 

pesticides by rat and human hepatic microsomes 

and cytochrome p450 isoforms. Drug Metab 

Dispos. 2009 Jan;37(1):221-8. 

Species differences in the intrinsic clearance 

and the enzymes involved in the metabolism 

of pyrethroid pesticides were examined in rat 

and human hepatic microsomes. The 

pyrethroids investigated included bifenthrin, 

S-bioallethrin, bioresmethrin, beta-cyfluthrin, 

cypermethrin, cis-permethrin, and transpermethrin 

UNCERTAINTY ANALYSIS RESEARCH SUMMARY 

Davis JL, Wambaugh JF, Garcia RI, Setzer RW. 

Methodology for Uncertainty Analysis of 

Dynamic Computational Toxicology Models. 

Presented at the 2009 Board of Scientific 

Counselors Computational Toxicology 

Subcommittee Meeting. 

Discussion of issues related to quantifying 

the uncertainty in PBPK model parameters, 

including assessing uncertainty in the 

absence of data, decreasing long 

computational runtimes, and evaluating 

model uncertainty 

Davis JL, Tornero-Velez R, Setzer RW. A 

General Approach for Specifying Informative 

Prior Distributions for PBPK Model Parameters. 

Presented at the 49th Annual Society of 

Toxicology Meeting. 

Presentation of proposed approach for 

quantifying uncertainties in chemical-specific 

PBPK model parameters using prior 

knowledge based on chemical structure, 

computational predictors, and information 

from in vitro assays (paper in progress) 

Davis JL, Tornero-Velez R, Setzer RW. 

Quantifying uncertainty in Bayesian calibrated 

animal-to-human PBPK models with 

informative prior distributions. Air Force 

Institute of Technology Department of 

Mathematics and Statistics Colloquium, Dayton, 

OH (invited). May 20, 2010 

Discussion of hierarchical Bayesian analysis 

for PBPK models and preliminary results of 

parameter estimation for permethrin (paper in 

progress) 

Wambaugh, JF, Barton, HA, Setzer, RW. (2008) 

Comparing models for perfluorooctanoic acid 

pharmacokinetics using Bayesian analysis, 

Journal of Pharmacokinetics and 

Pharmacodynamics 35, 683 – 712. 

Bayesian analysis using Markov Chain 

Monte Carlo (MCMC) provides tools to 

calibrate PK model as well as quantitative 

diagnostics to evaluate and discriminate 

between models
40

COMPUTATIONAL APPROACHES RESEARCH SUMMARY 

D.T. Chang, M.-R. Goldsmith, R. TorneroVelez, R. Rabinowitz and C.C. Dary. 2007. 

Utilizing In Silico Techniques to Elucidate the 

Stereoselective Behaviour of Pyrethroids within 

Carboxylesterase. 234th ACS National 

Meeting, Modern Chiral Agrochemicals: the 

Importance of Enantioselectivity in Fate and 

Effects Symposium, Boston, MA (invited). 

In silico model to estimate relative rates of 

metabolism of pyrethroid stereoisomers via 

carboxylesterase mediated hydrolysis 

Chang, D. T.; Goldsmith, M-.R.; Tornero-Velez, 

R.; Rabinowitz, J.; Knaak, J. B.; Johnson, J. C.; 

Peterson S. D., Dary C. C.; An in Silico 

Consensus Docking Approach towards 

Elucidating the Stereoselective Activity of 

Pyrethroid and Pyrethroid-Like Compounds in 

Carboxylesterase. - 4th Pan-Pacific Conference 

on Pesticide Science– 06/2008, Hawaii

In silico model to estimate relative rates of 

metabolism of pyrethroid stereoisomers via 

carboxylesterase mediated hydrolysis 

DOSE ADDITIVE EFFECTS OF 

PYRETHROIDS 

RESEARCH SUMMARY 

Wolansky MJ, Gennings C, Crofton KM. 

Relative potencies for acute effects of 

pyrethroids on motor function in rats. Toxicol 

Sci. 2006 Jan;89(1):271-7. 

The objective of this work was to 

characterize individual dose-response curves 

for in vivo motor function and calculate 

relative potencies for 11 commonly used 

pyrethroids. 

Wolansky MJ, Gennings C, DeVito MJ, Crofton 

KM. Evidence for dose-additive effects of 

pyrethroids on motor activity in rats. Environ 

Health Perspect. 2009 Oct;117(10):1563-70. 

A mixture of 11 pyrethroids was 

administered to rats. First in vivo evidence 

on pyrethroid cumulative effects supporting 

the default assumption of dose addition. 
41

Appendix B: Equations of the Aggregate Permethrin PBPK 

Model 

Symbols 

Chemical Abbreviations 

 PM: permethrin 

Compartment Abbreviations 

 BRN: brain 

 F: fat 

 GI: gastrointestinal 

 L: liver 

 S: slowly perfused tissue 

 R: rapidly perfused tissue 

 SC: stratum corneum 

 VE: viable epidermis 

Primary Symbols 

 Ca: Concentration of PM in arterial blood (μmol/L) 

 Cv: Concentration of PM in venous blood (μmol/L)

 AIJ: amount of PM in intracellular tissue space j (μmol)

AEj: amount of PM in extracellular tissue space j (μmol) 

 Aj: amount of PM in tissue j (μmol) 

 Vj: volume of tissue j (L) 

 Qj: flow in tissue j (L/h) 

 Qp: alveolar ventilation (m3/h) 

 PCj: tissue/blood partition coefficient of PM in tissue j 

 Palv: blood/air partition coefficient of PM 

 PAj: permeability-surface area product of tissue j (L/h) 

 BVj: blood volume fraction of tissue j 

 Ks: gastric absorption rate constant (h-1) 

 Ki: intestinal absorption rate constant (h-1) 

 Ksns: non-specific absorption rate constant (h-1) 

 Ksi: GI transfer rate constant (h-1) 

 Kds: diffusion rate constant across stratum corneum (h-1) 

 Kdv: diffusion rate constant across viable epidermis (h-1) 
42

Model Equations 

The following PBPK model equations describe the kinetics of both cis and trans isomers 

of PM with appropriate values for the chemical-specific parameters for each isomer. 

Tissue Distribution 

The rapidly perfused tissues were modeled as flow-limited compartments, 

indicating that the rate of transfer of PM to the j-th tissue is limited by the rate at which 

the chemical in blood reaches the compartment 

Q ( ) Ca CVj , dt

dA

dt

dC

V j

j j

j = = − (B.1) 

where concentration of PM in venous blood leaving tissue is: 

. PCj

Cj CVj = (B.2) 

The brain, fat, and slowly perfused tissues were modeled as diffusion-limited 

compartments. Assuming the rate of transfer of PM to the j-th tissue is limited by the 

rate of transfer across the cellular membrane, the following equations describe the 

movement in and out of the extracellular space (B.3) 

 Q ( ) Ca CVj PAj(CIj CVj) dt

dAEj = j − + − (B.3) 

where the concentration in venous blood leaving tissue is: 

 CVj = AEj (Vj × BVj) (B.4) 

Specifying this variable “CVj” instead of “CEj” applies the same terminology as 

the flow-limited case so that equation for venous return B.8 is kept the same regardless 

if compartments change structure (diffusion-limited → flow-limited and vice-versa). 

Mass transfer into the intracellular space (B.5) is mediated by the permeability surfacearea product (PAj): 

 PA ( ) CVj CIj / PCj . dt

dAIj = j − (B.5) 

The concentration of PM in the intracellular tissue space is defined: 

 CIj = AIj (Vj × (1− BVj) (B.6) 
43

The concentration of PM in a homogenized tissue compartment (j) is: 

 

 Cj = (AIj + AEj) Vj (B.7) 

Venous blood 

Having defined the concentration of PM in venous blood exiting the flow- and 

diffusion-limited tissues, we weight their contribution to the venous blood pool according 

to organ blood flow, Qj. Blood flow from the liver is the sum of portal and arterial supply 

to the liver: 

( )

QC

Qj CVj QL QGI CVL

Cven j

× + + ×

=

∑ (B.8)

To interpret rodent venous iv injection studies, a differential equation is specified: 

QC Cven Cv rIV

dt

dAAVB = ( − ) + (B.9)

Where rIV is the rate of i.v. injection, and the concentration of PM in the venous 

blood, Cv, is defined as: 

.

VB

VB

V

A

Cv = (B.10) 

Arterial Blood and Absorption Processes 

The concentration in of PM in arterial lung blood (Cart) is computed according to 

the venous equilibration model: 

Palv

Qp Qc

Qp Cinh Qc Cv Cart

+

× + × = (B.11) 

Where QP indicates rate of pulmonary ventilation (m3

/h), and Cinh is the 

breathing-zone concentration of PM (umole/m3) during exposure, and Palv is the 

equilibrium blood:air partition coefficient. 

Additional processes impact the arterial blood, these are accounted for as: 

 

QP Cart Ca rCaEP

dt

dAAB = ( − ) − (B.12) 
44

The concentration of PM in the arterial blood, Ca, is defined as: 

AB

AB

V

A Ca = (B.13) 

and rCaEP corresponds to hydrolytic clearance in the plasma: 

rCaEP = Kbld ×Ca (B.14)

Dermal Absorption 

Dermal absorption of PM through the skin is modeled with two compartments for 

the uptake and distribution of PM through the stratum corneum and the viable 

epidermis. The rate of change of PM in the stratum corneum is governed by the 

equation: 

 SC

SC Kds Asurf Kdv A

dt

dA = × − × (B.15) 

where Asurf is the amount of PM on the exposed surface area of the skin which 

enters the stratum corneum at the rate Kds. The rate of change of PM in the viable 

epidermis is then given by: 

 .

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛ = × + −

VE

VE

SC

VE

PC

C Kdv A Qskn Ca

dt

dA (B.16) 

The rate of removal of PM from the skin surface is assessed: 

dAsurf Kds Asurf dt

=− × (B.17) 

Oral Absorption 

Two compartments are used to describe the rate of absorption of PM from the 

lumen into the blood supply of the GI tract. The terms Ks and Ki represent the stomach, 

intestinal absorption rate constants, respectively, while the gastric-emptying rate 

constant is represented by Ksi. The rate of change in the stomach (B.18) and intestine 

(B.19) are as follows: 

 KsAs KsiAs

dt

dAs = − − (B.18) 

 KsiAs KiAi rFEC

dt

dAi = − − (B.19) 
45

where As and Ai are the amount of PM in stomach and intestine, respectively. 

The rate of fecal excretion rFEC (μmol/h) is in terms of the fecal excretion rate constant 

Kfec 

 rFEC = Kfec × Ai. (B.20) 

The rate of change in the GI compartment is thus: 

KsAs KiAi rCaEGI

PC

C Q Ca

dt

dA

dt

dC V

GI

GI

GI

GI gi

GI + + − ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛ = = − (B.21) 

where rCaEGI, which corresponds to hydrolytic clearance in the GI tract, is 

proportional to the concentration of PM in the GI tract 

 . CLestGI CGI rCaEGI = × (B.22) 

Ingested PM is primarily absorbed from the GI tract into the portal vein and 

transported directly to the liver. The movement of compound in and out of the liver is 

described by the equation: 

rCYP rCaE

PC

C

PC

C Q PC

C Q Ca

dt

dA

dt

dC V

L

L

GI

GI

GI

L

L

L

L L

L − − ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

+ − ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛ = = − (B.23) 

where rCYP and rCaE correspond to oxidative and hydrolytic clearance in the 

liver: 

CLox CL rCYP = × , (B.24) 

. CLest CL rCaE = × (B.25) 

Single Compartment PK Model of DCCA metabolite 

Metabolism renders several metabolites, which manifest in urine, feces, or both. 

Carboxyl esterases catalyze the hydrolysis of PM yielding DCCA and 3-PBA. 

Oxidation via CYP P450 produces hydroxyl derivatives of PM (PM-OH), but is also 

hypothesized to contribute to ester cleaveage. In the equations below DCCAfrac 

(cisDCCAfrac or transDCCAfrac) represent stoichiometric coefficients specifying the 

relationship between metabolized PM and urinary DCCA. 

These stoichiometric coefficients are derived from a radiocarbon study and 

account for metabolism and excreta and thus have a broader context than reaction 

stoichiometry. DCCA from these sources arrive at a central plasma compartment 

eliminated at a rate Kel into the urine. Kel was obtained from human dose-excretion 
46

studies of Woollen et al. (1992) that determine the half-life urinary excretion of DCCA; 

Kel= ln(2)/t1/2 . In the model, separate equations are specified for cis-PM and trans-PM. 

DCCAfrac rCYP rCaE rCaEP rCaEGI Kel Ahyd dt

dAhyd = × ( + + + ) − ×

 (B.26)

Kel Ahyd dt

dExcr = × (B.27)
47

Appendix C: PBPK Model Parameter Values 

Rat Human Rat Human Rat Human

BVBRN 0.03 0.04 QBRNC 0.02 0.12 PR_2 0.44 0.44

BVF 0.02 0.02 QCC 14.1 13.4 PVEB_2 1 1

BVS 0.04 0.01 QFC 0.07 0.05 QBRN 0.11288 38.91433

BW 0.295 70 QGIC 0.151 0.19 QC 5.643982 324.2861

c_DCCA_frac 0.26 0.26 QLC 0.024 0.06 QF 0.395079 16.2143

cfactor 1 1 QP 0 0 QGI 0.852241 61.61436

Clr1C_1 7.6 1.86 QRC 0.211 0.255 QL 0.135456 19.45717

Clr1C_2 6.4 8 QSKNC 0.058 0.05 QR 1.19088 82.69295

Clr2C_1 0 0 SA 5.6 800 QSC 0.524 0.325

Clr2C_2 11.9 5.6 TSA 401.328 15410.21 QS 2.952879 104.5512

Dinf 12 12 stratumTC 10 10 QSKN 0.004568 0.841743

frac_derm_abs 1 1 t_DCCA_frac 0.73 0.73 stratumT 0.001 0.001

frac_derm_cis 0.25 0.25 tfactor 1 1 VABL 0.010915 2.765

frac_derm_trans 0.75 0.75 Tinf 0.005 0.005 VVBL 0.010915 2.765

frac_iv_cis 1 1 VABLC 0.037 0.0395 VBRN 0.00177 1.4

frac_iv_trans 0 0 VVBLC 0.037 0.0395 VF 0.02065 14.98

frac_oral_cis 0.4 0.4 VBRNC 0.006 0.02 VGI 0.007965 1.19

frac_oral_trans 0.6 0.6 VDISTC_1 1 1 VL 0.01003 1.82

Kds_1 0.01 0.001 VDISTC_2 1 1 volbal 100 100

KEL_1 0.0586 0.0586 VFC 0.07 0.214 VolSC 0.000401 0.01541

KEL_2 0.0586 0.0586 VGIC 0.027 0.017 VolVE 0.055649 2.57459

Kfec_1 0.59 0.4 VLC 0.034 0.026 VR 0.004425 1.19

Kfec_2 0.59 0.4 VRC 0.015 0.017 VSC 0.594 0.437

KGI_1 0.04 0 VSKNC 0.19 0.037 VS 0.174448 30.45554

KGI_2 0.4 0.78 CLest_1 0 0 VSKN 0.05605 2.59

Ki_1 0.9 0.9 CLest_2 3.5105 392

Ki_2 0.9 0.9 CLestGI_1 0.0118 0

Ks_1 0.01 0.01 CLestGI_2 0.118 0.78

Ks_2 0.01 0.01 CLox_1 2.242 130.2

Ksi_1 0.7 0.7 CLox_2 1.888 560

Ksi_2 0.7 0.7 EXP_DERM 0.000782103 0.134456

Ksns_1 0 0 EXP_VSC 5.60E-06 8.00E-04

Ksns_2 0 0 EXP_VVE 0.000776503 0.133656

MW 391.3 391.3 flowbal 100 100

PABRNC_1 0.003 0.003 Kbld_1 0.0236 0

PABRNC_2 0.003 0.5 Kbld_2 0.09027 0

PAFC_1 0.1 0.1 Kds_2 0.01 0.001

PAFC_2 0.1 0.1 Kdv_1 1 0.1

Palv_1 200 200 Kdv_2 1 0.1

PASC_1 0.7 0.7 mol 2.555583951 2.555584

PASC_2 0.7 0.7 PABRN_1 0.000338639 0.116743

PBRN_1 1.5 1.5 PABRN_2 0.000338639 19.45717

PBRN_2 0.4 0.75 PAF_1 0.039507874 1.62143

PF_1 150 150 PAF_2 0.039507874 1.62143

PF_2 50 50 Palv_2 200 200

PL_1 0.44 0.44 PAS_1 2.067015196 73.18587

PL_2 0.44 0.44 PAS_2 2.067015196 73.18587

PS_1 5.59 5.64 PGI_1 0.44 0.44

PS_2 5.59 5.64 PGI_2 0.44 0.44

PVEB_1 1 1 PR_1 0.44 0.44

Table C-1 Values of PBPK parameters for humans used in the NHANES comparison. 

Parameter values for rats are included for reference. 
48

Estimation of Stoichiometric Coefficients 

The relationship between metabolized cis- and trans-PM and cis- and transDCCA in urine was estimated from the study of Gaughan et al. (1977). The one 

compartment model applies stoichiometric coefficients to relate metabolism of cis-PM 

and trans-PM to corresponding moles of cis-DCCA and trans-DCCA in urine. It was thus 

important to quantify DCCA as a fraction of metabolized PM rather than administered 

PM because oral absorption was already accounted for in the model. 

Rats were administered 14C labeled permethrin orally and radiocarbon was 

assessed in tissues, urine and feces. By day 12, almost all the radioactivity had 

completely exited the tissues (low ppb level). By day 12, 98.5% of trans-PM related 

radioactivity and 99.5% cis-PM related radioactivity now resided in urine or feces. 

The authors determined DCCA in urine with thin layer chromatography and 

reported this as DCCA fraction of urine radiocarbon at 1 day. For trans-PM, 57% of the 

radiocarbon was excreted in urine in 1 day and 82% in 12 days. We used this 

proportion to estimate the total excreted DCCA excreted in urine by 12 days. The 

coefficient is computed as [DCCA in urine / metabolized PM]. This calculation was 

performed for cis- and trans-PM. Metabolized PM was estimated as [total radiocarbonPM]. Calculations are shown in the table below. Lines 1-12 indicate % of administered 

radio carbon, and lines 13 and 14 are the coefficients that are applied to the term 

‘DCCAfrac’ in B.26 (cis and trans). 
49

Table C-2. 14C-Labeled Compounds (% of administered radiocarbons) in the urine and in feces 

of rats at 1 day and 12 days after oral administration of 14C-acid labeled preparations of [1RS, trans] and 

[1RS, cis]- permethrin. Data are from Gaughan et al., 1977. Additional calculations are indicated at lines 

3, 8, 10, 12, 13, 14. 

 trans-permethrin cis-permethrin

 

 Urine Feces Urine Feces 

 1RS 1RS 1RS 1RS 

Line 1 day calculations 

1 DCCA ("Cl2CA") free 5.6 2.7 0.7 0.5 

2 DCCA ("Cl2CA") gluc 41.9 13.8 

3 DCCA ("Cl2CA") line1 + line 2 total 47.5 14.5 

4 total urine radiocarbon 57 34 

5 parent PM in feces 2.8 6.7 

6 total fecal radiocarbon 9 27 

 

 12 days 

7 total fecal radiocarbon 16 45 

8 

estimated parent in 

feces line 5 x line 7/ line 6 4.98 11.17 

9 total urine radiocarbon 82.0 54 

10 

estimated DCCA in 

urine line 3 x line 9/ line 4 68.3 23.0 

11 Total radiocarbon 98.5 99.5 

12 total metabolized PM line 11- line 8 93.5 88.3 

 

 stoichiometric coefficients 

13 trans_DCCA_frac line 10/ line 12 0.73 

14 cis_DCCA_frac line 10/ line 12 0.26