## Physiologically-Based Pharmacokinetic Models Of Pyrethroids: Bayesian Calibration And Their Use In Interpreting Probabilistic Exposure Data

Rogelio Tornero-Velez 1 , Jimena Davis 2 , Jianping Xue 1 , R. Woodrow Setzer 2

1 National Exposure Research Laboratory, Offi ce of Research and Development, U.S. Environmental Protection Agenc y, Research Triangle Park, NC

2 National Center for Computa tional Toxicology, Office of Re search and Development, U.S. Environmental Protection Agency, Research Triangle Park, NC2 

## 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

B ACKGROUND ON PBPK M ODELING ..........................................................................................................4

M ODELING GOALS

............................................................................................................................... ........6

E XTRAPOLATION BY P ARALLELOGRAM ......................................................................................................7

D ELTAMETHRIN PBPK M ODELS .................................................................................................................7

E XTENSION OF THE DELTAMETHRIN PBPK MODEL TO OTHER PYRETHROIDS ............................................11

P ERMETHRIN PBPK M ODEL ......................................................................................................................12
C ONSIDERING A GGREGATE E XPOSURE .....................................................................................................13 Ingestion Exposure ............................................................................................................. .................18
Inhalation Exposure............................................................................................................ .................18 Dermal Exposure ................................................................................................................ .................19

B IOMARKER M ODEL

............................................................................................................................... ...20

BAYESIAN CALIBRATIO N OF PBPK MODELS............................................................................................ ...20

M ODEL S TRUCTURE

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

Measurement E rror Model ........................................................................................................ ..........21

P RIORS

............................................................................................................................... .......................22 Informati ve Priors ............................................................................................................. ..................23 Weakly Informa tive Pr iors...................................................................................................... .............24
C OMPUTATIONAL I SSUES ..........................................................................................................................24

M ODEL E VALUATION

............................................................................................................................... .25

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

C ONSIDERATIONS FOR E XTRAPOLATION ...................................................................................................25

P ARAMETER E XTRAPOLATION ...................................................................................................................27 Physiological Parameters....................................................................................................... .............27 Chemical Specific Parameters................................................................................................... ..........27
C HARACTERIZING U NCERTAINTY IN THE E XTRAPOLATED M ODEL ...........................................................28

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

PERMETHRIN CASE-STUDY: PROBABILISTIC MO DELING OF DIETARY AND RESIDENTIAL PERMETHRIN EXPOSURE, INTERPRETATION WI TH PBPK MODELING, AND COMPARISON
WITH NHANES DATA............................................................................................................... .............................29

O VERVIEW

............................................................................................................................... .................29
S IMULATION

............................................................................................................................... ...............29
C OMPARISONS 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 AG GREGATE PERMETHRIN PBPK MODEL ...............................41

S YMBOLS

............................................................................................................................... ...................41
Chemical Ab breviations......................................................................................................... ..............41 Compartment Ab breviations ...................................................................................................... ..........413 Primary Symbols................................................................................................................ ..................41

M ODEL E QUATIONS

............................................................................................................................... ...42

Tissue Dist ributio n............................................................................................................ ...................42
Venous blood ................................................................................................................... ....................43
Arterial Blood and Ab sorption Processes........................................................................................ ....43 Dermal Absorption .............................................................................................................. ................44 Oral Absorption................................................................................................................ ...................44 Single Compartment PK M odel of DCCA metabolite..........................................................................45

APPENDIX C: PBPK MOD EL PARAMETER VALUES ...................................................................................47

E STIMATION OF S TOICHIOMETRIC C OEFFICIENTS ......................................................................................48



## Overview

We describe the application of physiologica lly-based pharmacokinetic (PBPK) modeling to interpret simulated exposure prof iles of the Stochastic Huma n Exposure and Dose Simulation (SHEDS) model. These approaches are being de veloped to evaluate di etary and residential exposures to pyrethroid pesticid es 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. Urinar y 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 investig ation of the exposure pathways (e.g., dietary exposure to permethrin). We demonstrate th e SHEDS-PBPK simulation for population exposure to permethrin, comparing a simulated distri bution of a permethrin metabolite with NHANES
data for this metabolite.

We propose Bayesian hierarchical modeling to characterize the uncerta inty in PBPK model parameters. The uncertainty in describing rat ki netics is quantified thr ough this process and, combined with methods using the parallelogram principle for extrapolating from animals to humans, used as a measure of uncertainty of th e estimated human dose metrics. We propose the use of Monte Carlo methods to propagate para meter uncertainty through the linked simulations (SHEDS-PBPK), providing an unders tanding of the influence of pa rameter uncertainty (e.g., the rate constant for oral absorption of permethr in) 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 physiolo gically based pharmacokinetic (PBPK) models for pyrethroid pesticides. Pyrethroids are synthetic ch emical 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. Th e breadth of these efforts is highlighted in Appendix A. PBPK models ha ve advantages over "classical" pharmacokinetic models, which are less grounded in physiology. PBPK models predict internal body concentrations of
chemicals or their metabolites. These estimate s may be used for risk assessment purposes, and the same models may be used to predict concen trations of excreted metabolites for comparison with biomarker data (e.g., NHANES). PBPK mo dels are suited for developing pharmacokinetic models for a class of chemical (e.g., pyrethroi ds) because they leverage the structural information, and reconcile disparate yet informa tive 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 pyrethroids 1 . 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 st ructure for the pyrethroid pesticides.

II. Parallelogram Approach . The Agency is planning to develop equivalent rodent
and human in vitro databases for metabolic and physio logical parameters. The rodent in

vitro parameters will be assessed by co mparing 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 da ta, 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.pdf5 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 concen trations of parent compound in the rat correlate with pyrethroid toxi city as measured by motor activity. At present time, the Agency plans to evaluate additional metric s (e.g., area under the curve) with additional pyrethroids. Moreover, the Agency plans to te st other behavioral measures (e.g., startle response). Please comment on the available dat abase 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 steroi somers. Others such as cypermethrin may contain as many as eight stereoisomers. Ther e is limited information on the toxicity and pharmacokinetics of the different stereoisomer s. The Agency is proposing to evaluate three modeling assumptions. The first approa ch combines all stereoisomers as one chemical. The second approach includes mode ling 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 additiona l modeling assumptions or approaches that the Agency should consider or t hat could simplify the modeling?

A full commentary on these ch arge 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 it erations, as each pyret hroid is studied, seems appropriate and a logical approach to tackle the pyrethroid fam ily”. Given the emergence of a generic PBPK model for pyrethroids, the panel no ted 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 Varyin g 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 Scien tific Advisory Panel Meeting Held August 16-17, 2007 on Assessing Approaches for the Development of PBPK models of Pyrethroid Pesticides. November 13, 20076 The panel commented that Bayesian model se lection approaches al ong with sensitivity and uncertainty analysis (both st ructural and parametric) are impor tant 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) th e plasma protein binding and (2) P-glycoprotein transport. The panel noted that some of th e 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 co uld have direct impact on species extrapolation from rats to humans (Question II). The panel cons idered 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 (Ques tion III), the panel was in agreement with using blood and brain pyrethro id 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 a ffected 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 (Que stion IV) the panel took the pragmatic view that it was important to consider the differential toxicity of th e 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 behavi or. In summary, the panel was in favor of the approaches outlined by the Agency to describe pyrethro id disposition with a generic PBPK modeling approach. To date several model ha ve been elaborated, including the in-vitro measures of metabolic clearance to develop additional mode ls (refer to Appendix A). We are currently elaborating methods based on Bayesian samp ling which make use of the existing model structures to develop additional PBPK models for pyrethroids. The benefit of these approaches (see ‘Bayesian Calibration of PB PK models’) is that they permit characterization of the uncertainty of model pred ictions. The current SAP 3 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 descri bed for the insects they were designed to control. To anticipate possible a dverse health effects to humans, rodent models have been used to evaluate dose-response relationships and dete rmine the relative potenc ies 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 targ et-tissue dose estimations across species. PBPK
models allow calculations of tissu e doses of chemicals and their me tabolites over a wide range of exposure conditions (Chiu et al., 2007; Chiu and White 2006; Keys et al., 2003). By incorporation of anatomy and bi ological processes, the models allow adaptation to different organisms (Medinsky and Valentine, 2001). B ecause the rate consta nts 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.html7 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 ev aluated 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 Extrapolati on of Animal-Calibrated Models to Humans . (3) The in

vitro determinants are compared with one anot her in the human and surrogate mammalian system (e.g., Godin et al., 2006); species diffe rences may be apparent. (4) The human in vitro data is then incorporated in the PB PK/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, popul ation distributions of exposure, either measured or modeled (e.g., SH EDS) are interpreted by the human PBPK/PD model rendering population distributions of dose-me trics 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 res ponse relationships understood in the rodent
system.



### Deltamethrin PBPK Models

In recent years, PBPK models have b een developed for the type II pyrethroid, deltamethrin (DLM) (Mirfazaelian et al., 2006, G odin 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 ope n state, resulting in abnormal di scharge 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 choreoat hetosis and salivati on (CS-syndrome). The recent study of Weiner et al. (2009) applies principal compon ent 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 histor ic 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 fi nding, both type I and type II pyrethroids demonstrate dose-dependent decrease in motor ac tivity, with the type II tending to be more potent (Wolansmky et al., 2006). The FIFRA Scien tific 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 mode ls for pyrethroids, DLM was selected for exploring the fundamentals of pyrethroid disposition because it is formulated as a single isomer (( S )-cyano-3-phenoxybenzyl (1 R

, 3 R )- cis -3-(2,2-dibromovinyl)-2,2-dimethylcyclopropane carboxylate)- thus minimizing complications introdu ced by the presence of multiple isomers. To better understand the dosimetry of DLM in the ce ntral nervous system, Mi rfazaelian et al. (2006) developed a PBPK model for DLM for the adu lt male Sprague-Dawley rat that employed both flow-limited (brain, gastrointestinal [GI] tract, liver, and rapidly perfus ed tissues) and diffusionlimited (fat, blood/plasma, and slowly perfused tissues) rate equations . The blood was divided into plasma and erythrocytes. Cytochrome P450-me diated 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 biotransformati on was estimated to account for approximately
78% of these administered doses. Plasma CaEs accounted for biotransformation of approximately 8% of each dosage. Model predic tions 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 ph armacokinetic models is the ability to update and revise porti ons of the model, as more information is available. Sensitivity analysis can help identify parameters that infl uence 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 diffe rence 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 absorp tion process. Mirfaza elian had hypothesized that efflux transport in the GI process was ope rative, consistent with a hypothesis of efflux transport in the blood brain barrier which explaine d the low distribution of DLM into the brain. Other changes to the Mirfazaelian model include d 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 pres ent 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 th e curve (AUC(0-48h)) for humans following an oral exposure of 1 mg/kg. Based on these finding s, humans would have greater distribution of
deltamethrin to the brain for the same admi nistered 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 deltameth rin PK in the maturing rat (Fig 2).

4 http://www.epa.gov/scipoly/sap/meetings/2009/061609meeting.html9 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-depende nt changes in the oxidative (CYP) and hydrolytic (CaE) clearance of DLM were modele d with a generalized Michaelis-Menten model for growth and the summary equations incorp orated into the PBPK model. The model's simulations compared favorably with empirica l 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 concentr ation 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 μ g/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 pyr ethroids have similar physic al 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 suc h, we expect PBPK model parameters reflecting physicochemical properties (e.g., partition coeffi cients, and permeability coefficients) to be similar among the pyrethroids. On the othe r hand, we expect divergence in biochemical parameters (i.e., metabolic rate constants). Al though pyrethroids are metabolized at different rates, they follow the same detoxification path ways. These features support a common model structure for pyrethroids. Pyrethroids are metabolized through oxidative and hydrolytic pathways. Fig. 4 shows the structural similarity of pyrethr oids 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 (CL int ). The pyrethroids bifenthrin, S

bioallethrin, bioresmethrin, β -cyfluthrin, cypermethrin, cis -permethrin, and trans -permethrin
were incubated in rat and huma n hepatic microsomes. The CL int 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 micros omes 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: CH 3 CH 3 H H

Cyphenothrin: CH 3 CH 3 CN H

Cyhalothrin Cl CF 3 CN H

Deltamethrin Br Br CN H

R 1

R 2 O

C H 3

C H 3 O O R 3

R 4 R 1

R 2 O

C H 3

C H 3 OH
O

R 4 O H + A.

B.

R 1

R 2 O

C H 3

C H 3 O O R 3

R 4 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 chrysanthemi c acid and phenoxybenzoic acid moieties.12 

### Permethrin PBPK Model

Following the modeling of deltamethrin, permet hrin 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 cons ider aggregate exposure (oral, dermal, inhalation). The model structure (Fig.5) is based on the model of Mi rfazaelian et al. 2006, and includes two important refinements introduced by Godin et al. 2010; name ly, simple rate constants for absorption and collapse of the plasma and red blood cell (RBC) co mpartments 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 tissu es (brain, blood, liver, a nd 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 m odeling 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 exposur e and oral ingestion.13 inhaled permethrin

Q
c C
a Q
c C

v

Q BRN C BRN

dermal exposure

Kds

Kdv

Q skin C VVE

Q F C VF

Q S C VS

Q R C VR

Q L C VL

C VG I metabolic clearance

Kel

Q G 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

r apidly

IL IL Ks i brain

s lowly

liver

G I ven blood

V E SC lung blood eq

fat alv vent

central com p.

Figure 5



### Considering Aggregate Exposure

The PBPK model should be able to consid er the important routes of exposure. Individuals can be exposed to pyr ethroids 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 du st. Dermal exposure to pyrethroids can result
from surface contact or from the treatment of li ce (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 pyrethroi ds are not available for hum ans, a limited number of
human dose-excretion studies i nvolving pyrethroids have been published. These studies are useful to inform the uptake processes in human PB PK models. The parallelogram is not replaced for informing tissue distribution. Human dose-ex cretion studies in ac cordance with Agency policy on human subjects research as defined in 40 C.F.R. PART 26 can be used to calibrate14 absorption parameters. Table 2 provides a lis t 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 pyrethroids15 Table 2. Human Dose Excretion Studies of Pyrethroids (Studies provided indicati on 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, I RB Tomalik-Scharte et al.,
2005 cypermethrin dermal 2 25 mg/ 50 cm 2 0.10% nd nd PK, IC, IRB Eadsforth et al., 1988

cypermethrin dermal 6 31 mg/ 800cm 2; 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/m 3; 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 oversight16 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 ingesti on exposure to PM (micro-g), respectively. Process B is inhalation exposure, and is described by column 10, the ventilation rate (m 3 /min), and column 12, the airborne concentration of PM (micro-g/m 3 ). Process C is dermal exposure, and is captured by column 3, area exposure (cm 2 )- a whole body dermal exposure- and column 11, the amount of PM on the skin surface (micro-g). A ll values are updated hourly. Unit conversions take place in the PBPK models (M atlab, R) to run the model in units of micro-moles, L, and h. A B

C

Figure 6 Interface of the exposure model and PB PK model. Blue Arrows indicate exposure processes described by SHEDS. The solid dark arrows indi cate absorption processes described by the PBPK model.17person weight height area_dermal age_group gender date hour diet_Tperm Dose_ingest Vent_inhal runexp_dermal Expo_inhal diet_wt1 76.02703 180.4788 19940.50349 20-49 years M 12-Jul-10 19 2.438650909 0 0.01261814 0 0 67.858951 76.02703 180.4788 19940.50349 20-49 years M 14-Jul-10 20 0.470288 0 0.0250942 0 0 67.858951 76.02703 180.4788 19940.50349 20-49 years M 16-Jul-10 12 34.73421336 0 0.00798151 0 0 67.858951 76.02703 180.4788 19940.50349 20-49 years M 17-Jul-10 12 0.000267955 0 0.0265954 0 0 67.858951 76.02703 180.4788 19940.50349 20-49 years M 18-Jul-10 19 0.1057536 0 0.00872869 0 0 67.858951 76.02703 180.4788 19940.50349 20-49 years M 19-Jul-10 15 0.760508364 0 0.02090339 0 0 67.858951 76.02703 180.4788 19940.50349 20-49 years M 21-Jul-10 16 21.76421433 0 0.01682962 0 0 67.858951 76.02703 180.4788 19940.50349 20-49 years M 24-Jul-10 10 0.00842688 0 0.00918217 0 0 67.858951 76.02703 180.4788 19940.50349 20-49 years M 25-Jul-10 17 0.37670115 0 0.00539541 0 0 67.858951 76.02703 180.4788 19940.50349 20-49 years M 26-Jul-10 19 1.4 0 0.00524947 0 0 67.858951 76.02703 180.4788 19940.50349 20-49 years M 27-Jul-10 16 9.45E-06 0 0.01151972 0 0 67.858951 76.02703 180.4788 19940.50349 20-49 years M 27-Jul-10 18 0.002605122 0 0.00863456 0 0 67.858951 76.02703 180.4788 19940.50349 20-49 years M 29-Jul-10 21 0.000483694 0 0.00521797 0 0 67.858951 76.02703 180.4788 19940.50349 20-49 years M 30-Jul-10 11 5.51304E-05 0 0.00903805 0 0 67.858952 82.32053 185.465 21022.05396 20-49 years M 10-Jul-10 1 0 0 0.00419841 8.967995176 0.050230767 65.099932 82.32053 185.465 21022.05396 20-49 years M 10-Jul-10 2 0 0 0.00414598 8.963511178 0.050163719 65.09993Figure 7Sample 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 pertai n to uptake by the different routes.



### Ingestion Exposure

Two compartments are used to describe the ra te 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 c onstant is represented by Ksi. Separate sets of equations are applied for cis -PM and trans -PM.

KsiAs KsAs dt dAs

− − = (A.1)

rFEC KiAi KsiAs 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 ti ssue. Refer to the Appendix for the subsequent processes (met abolism, distribution, excretion)

In the sample simulation shown in Fig.7, SHEDS was configured to simulate dietary (Fig 7, column 8) or non-dietary i ngestion (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 th e sample code below (Figure 8), and

trans -PM to ‘stomach_2’. The curre nt unabsorbed quantities of cis and trans are specified by the terms derivs(3,1) and derivs(4,1 ), respectively. These terms repr esent 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 Cv Qc Cinh Qp Cart

+ × + ×

= (B.1)

Where Q P indicates rate of pulmonary ventilat ion (L/h), Cinh is the breathing-zone concentration of PM (micro-mole/L) during expo sure, and Cv is the venous blood. Palv is the equilibrium blood:air partition coe fficient, estimated at 4564:1 ba sed on the quantitative structure Figure 8 Hourly updating of oral exposure in PM model (Matlab) occurs by adding the unabsorbed mass o f 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 ma gnitude of this estimated parameter indicates that inhaled permethrin greatly favors the blood phase upon equilibr ation. Refer to the Appendix B for the subsequent processes (met abolism, distribution, excretion).



### Dermal Exposure

SHEDS models dermal exposure as a combin ation of deposition and removal processes, updated hourly. SHEDS rate constant s are expressed in inverse time h -1 ; therefore, a dermal absorption process was developed for th e PBPK model with equivalent unit (h -1 ), and provided
to the SHEDS simulation team in order to accoun t for this removal proce ss (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 desc ribing dermal uptake in PBPK models using the permeability coefficient, Kp (cm/hr). Furtherm ore, Kp is derived under conditions of aqueous dermal exposure which are not typically the case fo r residential dermal exposure to pyrethroids. The empirical rate constant was fit from the study of Tomalik-Schar te et al. (2005) who evaluated dermal exposure in human volunteers fro m excretion of DCCA in urine (acid moiety derivative of PM after hydrolysis), following th e 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 A Kdv Asurf Kds dt dA

×

− × = (C.1)

where Asurf is the amount of PM on the exposed surf ace area of the skin which enters the
stratum corneum at the rate Kds. The term Kdv indicates mass tran sport through the VE and was set to Kds x 100, such that Kds was effectiv ely the critical rate- limiting step for dermal absorption. In order to calibrate the SC for bi omarker-tape stripping pu rposes, 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 Ca Qskn A Kdv 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 curren t 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 trans

PM occurs via hydrolysis catalyzed by CaE (s ee Fig. 4) and renders phenoxybenzyl alcohol (PBA) and (c is- and trans -DCCA). We modeled cis- and trans -DCCA, as these are specific to permethrin, cypermethrin, and cyfluthrin, wh ereas 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 st oichiometric 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, followi ng 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 mu ltiple levels (parameters that vary among
individuals as well as variation in studies) must be addressed corre ctly 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 la rge number of unknown parameters. Although data from different sources can be used to calibrate PBPK m odels 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 m odel 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., tissu e volumes and cardiac output), computational predictors (e.g., QSAR methods fo r partition coefficients), and in vitro assays (e.g., measurements of intrinsic hepatic clearance rates). This prior in formation 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 obs erved data. Prior distributions are then coupled with experimental data in Bayesi an analysis to determine posterior distributions (as opposed to point estimates with confidence in tervals) that characte rize 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 thr ough 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 identifiabili ty. Parameter identifiability is often a problem in dynamic computational (e.g., PBPK) models with large para meter spaces and limited available data for determining some of the parameters exactly. Garcia et al. (in prep aration) 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 fo r valid statistical analysis of PBPK models. Therefore, inferences based on Bayesian analyses that result in proper post eriors are valid even though the PBPK model may not be identifiable. Fo r a given data set, parameters that are not
identifiable can be characteri zed by comparing the priors to the posterior distributions; the posterior for parameters that are not identif iable will be the same as the prior.
These features have made hierarchical Ba yesian 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 framew ork 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 tim e to include in this background paper. In the following discussion, we give an overvi ew of the Bayesian method fo r calibrating PBPK models and present some approaches that we have devel oped to address some of the issues that are associated with these types of computational effo rts. 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, whic h describes the uptake and dispos ition 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 onl y gets estimates of the individu al-specific parameters but also estimates of the population parameters (e.g., m eans and variances) quantifying the distribution for the individual pharmacokinetic parameters . The population model describes how the individual parameters vary across the populati on. We assume the individual pharmacokinetic parameters are log-normally distributed with two population parameters: mean μ and variance

Σ 2 . Truncated log-normal distributions (mean ± 2 or 3 standard deviations) are used to constrain the parameters to biologically reasonable values, thereby avoi ding some computational issues that can arise when solving the PBPK model. Prior distributi ons are assigned to the population parameters for the pharmacokinetic parameters. Th e priors are described in more detail in the
Priors section.



### Measurement Error Model

The measurement error model describes the dist ribution of the error or difference in the PBPK model predictions and observed data for each individual. Let y ijk denote the concentration
of cis- or trans- permethrin measured for individual i at time t ij in compartment k . We assume that the log of the measurement log y ijk is normally distributed with mean log Y ijk , the log of the model predicted concentration, and variance 2

k σ for each compartment k

2 log ~ (log , ) ijk ijk k yNY σ22 where )

, | ( 2 σ μ ⋅ N is the density of a normally distri buted random variable with mean μ and

variance σ 2

. With the deterministic and stochastic m odel components defined, prior distributions specified (see the next section), and observed data from various sources compiled, Bayesian
calibration efforts can be carried out. These e fforts 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 y Ly p θ θ θ ∝ , where (|) p y θ , the posterior distribution, is proportiona l 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 advantag es 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 determ ine posterior distributions that reflect all of what is known about the parameters for a given da ta set. Hence, priors are important because they reflect what is known about parameters an d their uncertainties before data is observed. Furthermore, if a data set does not contain in formation that can be used to estimate some parameters and their associated uncertainties, th en 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 importa nt to specify priors th at 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 ar e 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 misl eading or incorrect c onclusions. Furthermore, the uncertainty associated with the model predic tions is underestimated as a result of using a point estimate without any measure of the uncer tainty in its value. At th e opposite extreme are weakly informative priors, such as broad uniform distri butions with every value in some range being equally likely. If the data contains no informa tion on parameters that ar e assigned diffuse priors, then the posteriors are equal to the priors, whic h can lead to much larger uncertainty in model predictions. Computations for parameter estimati on can also be inefficient due to algorithms exploring areas of the paramete r space that are highly unlikely as a result of very broad, uninformed distributions. The optim al 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 parame ters can be addressed separately for physiological parameters and chemical-specific pa rameters 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 wei ght, cardiac output, tissue volumes, and blood flows. Values for body weight are usually meas ured during experiments. For the remaining physiological parameters not observed experiment ally, mean values for these parameters are typically found in the literature [Brown et al., 19 97]. 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 obta ined from the literature for these parameters. Reference values found in the literature for physio logical parameters usually provide informative priors for these parameters [Bernillon et al., 2000]. For our calibrati on 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 part ition coefficients, oral absorption rates, diffusion-limited tissue permeability rates, and me tabolic parameters, are oftentimes assigned weakly informative priors as a result of more un certainty 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 [B ernillon 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 ch emical-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 fo r 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 de veloped 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 dive rse 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 tis sues. The relationship between the experimental and predicted values was determined by using re gression 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 computationa l 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 mo st of the tissue-plasm a partition coefficients in the permethrin model. This is an improve ment over CVs of 150% that have been used in vague priors for partition coefficients in some PBPK modeling efforts [Boi s 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 a nd 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 allo ws 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 ar e very much dependent on how well the chemicals included in the data set for the regression an alysis cover chemical space (in particular, compounds are included that have similar physic ochemical 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. Inst ead of using computa tional 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, u tilizing the parallelog ram approach outlined previously in the Extrap olation by Parallelogram section and discussed in Chiu et al. (2007) as a method for estimating metabolic paramete rs 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 inform ative prior due to no info rmation 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 pr iors 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. Sin ce there is little prior knowledge with regards to the mean and uncerta inty in these parameters, truncated uniform priors are used for these parameters.



### Computational Issues

Although Bayesian analysis offers several adva ntages 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 co mputational runtimes of ten required when these models are implemented via Markov Chain M onte Carlo (MCMC) methods. MCMC methods25 are typically used in Bayesian analyses of PB PK models to determine posterior distributions; however, it is not uncommon for Markov chains to require weeks to conve rge to the posterior due to the high dimensionality of the parameter sp ace. 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 MC MC chains have converged to the posterior
distribution. There are several metrics that ar e typically used to dete rmine 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 sampli ng 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 com putational runtimes for MCMC sampling based on parallelizing the likelihood computa tions 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 si nce 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 make s 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 eval uate how well a model fits data as well as quantitatively compare alternativ e model structures. Model fits can be evaluated by analyzing posterior predictive distributi ons [Gelman et al., 2004] and using metrics such as the Deviance Information Criterion (DIC) to compare the resu lts. This process of ten involves visually inspecting and comparing different PBPK model predictions to obs erved 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 lin ear regression models, standard st atistical 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 th at these approaches are not always applicable to PBPK models (Chiu et al., 2007). Th erefore, 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 ge nerate a time-dependent stream of tissue concentrations. The inputs, such as dietary or no n-dietary ingestion, air c oncentration, or dermal dose of permethrin, can themselves be time-de pendent, 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 cons tellation of tis sue-specific concentrations. However, our effects models do not , at this point, handle time-dependent inputs, so we need to summarize that time-changing con centration 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 gi ven 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 extrapolati on 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 mu st be a way to assign values to the model parameters that are appropriate to humans. A strength of the physiolo gically-based modeling approach is that many of the parameters need ed can be linked to independently measurable physiological parameters, which gr eatly facilitates extrapolati ng parameter values from the animal to human model. However, the model cont ains 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 populati ons 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 targ et dose measures among members of target populations with a given exposure. Since direct measurements of th e pharmacokinetics of pest icides in humans are rare, the only way to quantify both aspects of va riability is indirectly , through knowledge of how basic physiological and biochemi cal characteristics vary in a population. This means both targeting the model to the appropriate subpopul ation (for example, by age or gender), and attempting to characterize the va riability of pharmacokinetic characteristics expected in that population. Through Monte Carlo sa mpling from a distribution of parameter values thought to characterize population variability, the model is th en used to transduce that variability into variability in target dose. Finally, one of the goals for this model deve lopment has always been to be able to quantitatively characterize the remaining uncer tainty about human pha rmacokinetics 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 meas ures. Since the human model is based almost exclusively on rat data, the uncer tainty 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 allo cated to each tissue are estimated in the rodent model using str ongly 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 tissu e weight. In addition, since it is desired to simulate other than resting physiology, blood flow s 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 clearan ces, oral absorption, a nd 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 infl uenced by tissue lipid content,
which differs to an extent between rodents and humans. To account for the differences, tissuespecific partition coefficients are computed us ing the method of Schmitt (2008) based on both rat and human lipid compositions: PC
r and PC h . The PC estimated from the rat data is then adjusted by multiplying by the ratio PC h /PC
r . 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 cleara nce processes. As discussed earlier, the rodent clearance is computed as th e product of oxidative a nd 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 da ta 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 chemi cal-specific parameters is the uncertainty, quantified by the joint posterior distribution, inhere nt 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 repl ace 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 di fficult to specify part icular values for the coefficient of variation for a given uncertainty ex trapolation, such a form ulation allows ‘what if’ sorts of experiments, to examine the consequen ce of varying levels of uncertainty about model elements on the overall uncertainty of pr edictions 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 c ourses of tissue concentrat ions, 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-specifi c characteristics (age, gender, weight, height), time, activity level, and exposure measures (s ee Fig. 7). We have developed an implementation of the PBPK model de scribed here that runs in a combination of interpreted R code and compiled code, using th e 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 am ounts as appropriate fo r the route, and other time-dependent features. Thus, the exposure a nd 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 simula tions can be run on earlier SHEDS outputs while additional SHEDS outputs are being produced. The interesting output of the linked SHEDS-PB PK model is a populati on distribution of a particular dose-metric. In this mode, SHEDS is used to produce realizatio ns of exposure patterns for individuals from a defined population over a sp ecified 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 yi eld the desired dose-metric, and the corresponding dose-metric for all the indivi duals are aggregated to estimate a population distribution. Two-stage Monte Carlo sampling is used to char acterize the uncertainty in the characterizations of quantiles of the population distribution. A sample of parameter values is drawn from the joint uncertainty distribution fo r the SHEDS and PBPK model parameters, then a population of individuals is drawn and exposed, using those parameter values, and population percentiles, say 50 th , 90 th , and 95 th percentiles, of the dose-metric computed. This is repeated for multiple samples from the uncertainty distributi on, 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 i ndividual parameters and correlated sets of parameters co ntributes to the over all 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 distributi ons 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 di etary and residential exposure to permethrin and to compare model predictions with obser ved biomarker data. Pr obabilistic exposure modeling for dietary and reside ntial 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 th e permethrin PBPK model descri bed in this white paper. What we present is preliminary with respect to sc ope 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 fu lly 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 sp ace was not conducted. In spite of the short comings, we provide the first account of a populat ion simulation of excreted levels of urinary DCCA following residential and dietary expos ure to permethrin. Model evaluation was conducted by comparing the percentiles of th e cumulative distributi on function (CDF) of
simulated cis- and trans- DCCA excreted urinary biomarke r with the percentiles of the cis- and

trans -DCCA reported in the ’99-’0 0 and ’01-02 survey years of the National Health and Nutrition Examination Survey (NHANES).



### Simulation

Residential and dietary exposures to permet hrin were simulated for 8994 persons of 6 years age and older. For each person, hour-by-ho ur exposures were simulated for 21 days (504 hours). These 8994 persons represent the satisf actory 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 th e13-19 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 matr ix provided an hourly update of the aggregate exposure vector, providing starting conditions to inform the init ial 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. Studi es 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. U pon completion of a 6-day simulati on, dose metrics pertaining to30 the individual were retrieved a nd stored. This was performed for all 8994 individuals, providing
a distribution of dose-metr ics 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 NHA NES measurements. Th erefore, 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 ap proach, DCCA urine concentration is the average concentration over a 24-hour period. The simu lation was run for 5 days, sufficient for the distribution to be reasonably st ationary, and measurements taken on the sixth. The estimated DCCA concentration for a person is the total D CCA excreted over that 24 hours, divided by the
total volume of urine excreted over 24 hours. Th e second approach is an attempt to simulate the natural process of urine voids. Th e 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 excr eted 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 th e 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. Compar isons are provided for the 75 th , 90 th , and 95 th percentile of each
distribution. The NHANES data includes a line though the per centile denoting a 95%
confidence interval. The 95% confidence interv als (CI) on the simulated percentiles are based on sample theory. These CI relate to the unc ertainty 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-s ampled relative to the other age groups. Future plans are to provide uncertainty bound ba sed 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 in creased sample size may help to narrow CI, or whether parameter uncertainties are disproportionately contri buting to the large CI. Overall, simulated DCCA is in good agr eement with sampled DCCA, suggesting that permethrin exposure is the primary contribu tor to the NHANES sampled DCCA. Future investigations are inte nded to understand the contributions from the dietary and residential pathways. Furthermore, since DCCA arises fr om metabolism of cypermethrin and cyfluthrin, these exposures need to be inve stigated. Interestingly, the SHEDS-PBPK simulation indicated31 the highest exposures occurred for children 6-12. This was consistent with the 95 th 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 predic tion of tissue dose metrics concurrent to biomarker predictions. This is an importa nt 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 pl ot of peak daily brain

cis- permethrin ( μ mol/L) and 24-hour average cis -DCCA in urine ( μ g/L). The moderate correlation may be caused by exposures that occu r through different routes (inhalation, oral, dermal) and net the same 24-hour average urine c oncentration, 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 anal ysis in toxicology and risk assessment. We describe the applica tion of PBPK modeling to help translate exposure simulations of the SHEDS probabi listic exposure model both into measures of dose relevant to risk assessment, and to predict population distribu tions 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 dialogu e between practitioners in the fields of exposure scienc e and PBPK modeling, to the bene fit and additional applicability of both disciplines. We have just presen ted preliminary results for population exposure assessment of permethrin based on a single population sampling within SHEDS. Future directions include iterative sampling in SH EDS and the PBPK model to investigate the propagation of exposure and PBPK modeling uncertainty and va riability and its impact on
biomarker estimates and tissue dose metrics.34 

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## 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 mode l of a pyrethroid. Model employed both flow-limited and
diffusion-limited rate e quations 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 ma turing 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 alternat ive 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 46 th 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 deple tion 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 Computa tional 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 49 th Annual Society of Toxicology Meeting. Presentation of proposed approach for quantifying uncertainties in chemical-specific PBPK model parame ters using prior knowledge based on chemical structure, computational predicto rs, 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 pr eliminary 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 models40 COMPUTATIONAL APPROACHES RESEARCH SUMMARYD.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 Ag rochemicals: 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 fo r 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

C a : Concentration of PM in arterial blood ( μ mol/L)
C v : Concentration of PM in venous blood ( μ mol/L)

AI J : amount of PM in intr acellular tissue space j ( μ mol) AEj: amount of PM in ex tracellular tissue space j ( μ mol) Aj: amount of PM in tissue j ( μ mol) Vj: volume of tissue j (L) Qj: flow in tissue j (L/h) Qp: alveolar ventilation (m 3 /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 fr action 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 par ameters 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



## ( )

, CVj Ca Q 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 fo llowing equations describe the
movement in and out of the extracellular space (B.3)



## ( ) ) ( CVj

CIj PAj CVj Ca Q dt dAEj

j − +

− = (B.3)

where the concentration in v enous blood leaving tissue is:



## ( ) BVj Vj AEj CVj × = (B.4)

Specifying this variable “CVj” instead of “CEj” applies the same terminology as the flow-limited case so that equation for ven ous return B.8 is kept the same regardless if compartments change stru cture (diffusion-limited → flow-limited and vice-versa). Mass transfer into the intracellular space (B .5) is mediated by the permeability surfacearea product (PAj):



## ( )

. / PCj CIj CVj PA dt dAIj

j − = (B.5)

The concentration of PM in the in tracellular tissue space is defined:

) 1 ( ( BVj Vj AIj CIj

− × = (B.6)43 The concentration of PM in a hom ogenized tissue compartment (j) is:

Vj AEj AIj Cj ) ( + = (B.7)



### Venous blood
Having defined the concentration of PM in venous blood exiting the flow- and diffusion-limited tissues, we weight their co ntribution 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 CVL QGI QL CVj Qj

Cven j × + + ×

= 

## ∑

(B.8)

To interpret rodent venous iv injection studi es, a differential equation is specified:

rIV Cv Cven QC dt dA AVB +

− = ) ( (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 Cv Qc Cinh Qp Cart

+ × + ×

= (B.11)

Where QP indicates rate of pulmonary ventilation (m 3 /h), and Cinh is the breathing-zone concentrat ion of PM (umole/m 3 ) during exposure, and Palv is the equilibrium blood:air par tition coefficient.

Additional processes impact the arteri al blood, these are accounted for as:

rCaEP Ca Cart QP dt dA AB

− − = ) ( (B.12)44 The concentration of PM in the ar terial blood, Ca, is defined as:

AB AB V A Ca = (B.13)

and rCaEP corresponds to hydrolytic clearance in the plasma:

Ca Kbld rCaEP × = (B.14)



### Dermal Absorption
Dermal absorption of PM through the ski n is modeled with two compartments for the uptake and distribution of PM thr ough the stratum corneum and the viable epidermis. The rate of change of PM in the stratum corneum is governed by the equation:

SC SC A Kdv Asurf Kds dt dA

×

− × = (B.15)

where Asurf is the amount of PM on the expo sed 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 Ca Qskn A Kdv 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, res pectively, while the gastric-emptying rate constant is represented by Ksi. The rate of change in the stomac h (B.18) and intestine (B.19) are as follows:

KsiAs KsAs dt dAs

− − = (B.18)

rFEC KiAi KsiAs 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 ( μ mol/h) is in terms of the fe cal excretion rate constant
Kfec

. Ai Kfec rFEC × = (B.20)

The rate of change in the GI compartment is thus:

rCaEGI KiAi KsAs PC

C Ca Q 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 concentrati on of PM in the GI tract

. GI C CLestGI rCaEGI × = (B.22)

Ingested PM is primarily absorbed from the GI tract into the portal vein and transported directly to the liver. The movem ent of compound in and out of the liver is described by the equation:

rCaE rCYP PC

C

PC

C Q PC

C Ca Q 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:

L C CLox rCYP × = , (B.24)

. L C CLest rCaE × = (B.25)



### Single Compartment PK Model of DCCA metabolite

Metabolism renders several metabolites, which m anifest in urine, fe ces, or both. Carboxyl esterases catalyze the hydrol ysis 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 t hus 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 obt ained from human dose-excretion46 studies of Woollen et al. ( 1992) that determine the half-lif e urinary excretion of DCCA; Kel= ln(2)/t 1/2 . In the model, separate equations are specified for cis- PM and trans- PM.

Ahyd Kel rCaEGI rCaEP rCaE rCYP DCCAfrac dt dAhyd

×

− + + + × = ) ( (B.26)

Ahyd Kel 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 Stoich iometric Coefficients

The relationship between metabolized cis- and trans- PM and cis - and trans

DCCA in urine was estimated from t he 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 14 C 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 es timated 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 coe fficients that are ap plied to the term

‘ DCCAfrac ’ in B.26 ( cis and trans ).49 Table C-2. 14 C-Labeled Compounds ( % of administered radiocarbons ) in the urine and in feces of rats at 1 day and 12 days after oral administration of 14 C-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