httk: r package for high-throughput toxicokinetics and hepatic clearance), ... set of mass balance...

JSS Journal of Statistical SoftwareJuly 2017 Volume 79 Issue 4 doi 1018637jssv079i04

httk R Package for High-Throughput Toxicokinetics

Robert G PearceUS EnvironmentalProtection Agency

R Woodrow SetzerUS EnvironmentalProtection Agency

Cory L StropeUS EnvironmentalProtection Agency

Nisha S SipesNational Institute of

Environmental Health Sciences

John F WambaughUS EnvironmentalProtection Agency

Abstract

Thousands of chemicals have been profiled by high-throughput screening programssuch as ToxCast and Tox21 these chemicals are tested in part because most of themhave limited or no data on hazard exposure or toxicokinetics Toxicokinetic modelsaid in predicting tissue concentrations resulting from chemical exposure and a ldquoreversedosimetryrdquo approach can be used to predict exposure doses sufficient to cause tissue con-centrations that have been identified as bioactive by high-throughput screening We havecreated four toxicokinetic models within the R software package httk These models aredesigned to be parameterized using high-throughput in vitro data (plasma protein bind-ing and hepatic clearance) as well as structure-derived physicochemical properties andspecies-specific physiological data The package contains tools for Monte Carlo samplingand reverse dosimetry along with functions for the analysis of concentration vs time sim-ulations The package can currently use human in vitro data to make predictions for 553chemicals in humans rats mice dogs and rabbits including 94 pharmaceuticals and 415ToxCast chemicals For 67 of these chemicals the package includes rat-specific in vitrodata This package is structured to be augmented with additional chemical data as theybecome available Package httk enables the inclusion of toxicokinetics in the statisticalanalysis of chemicals undergoing high-throughput screening

Keywords high-throughput ToxCast httk toxicokinetics pharmacokinetics

1 Introduction

Humans are exposed to thousands of chemicals from the environment and consumer productsmost of which have not been tested for toxicity (Park et al 2012 Wambaugh et al 2013b

2 httk High-Throughput Toxicokinetics in R

Egeghy et al 2011 Judson et al 2008) In order to screen for potential bioactivity in vitrodata have been generated in the Tox21 (Bucher 2008) and ToxCast (Judson et al 2010)programs using high-throughput screening systems Over 8500 chemicals have been tested inat least 50 assays (Tox21) and a subset of around 1800 have had nearly 1200 assay endpointsmeasured (ToxCast) Recently high-throughput exposure modeling has provided estimates ofdaily human exposure for thousands of environmental contaminants (Wambaugh et al 2014)However linking these hazard and exposure predictions to estimate risk requires developmentand use of high-throughput toxicokinetics The terms ldquopharmacokineticrdquo ldquotoxicokineticrdquoand ldquobiokineticrdquo models have been used somewhat interchangeably in the scientific literatureHowever since this package is intended to provide dose context to high-throughput toxicityscreening projects we have selected the term ldquotoxicokineticrdquo even though we include severalcompounds with known therapeutic benefits and many others that may not cause adversityfor the highest plausible dose

Toxicokinetics is a field of study for determining the absorption distribution metabolismand excretion of substances in the body (OrsquoFlaherty 1981) The necessary data for toxicoki-netics are commonly collected in rats and other animals but the collection of these data forthousands of chemicals is costly in time money and animals (Rovida and Hartung 2009)Creating computational predictive models parameterized with more easily obtained in vitrodata may help address these problems Inputting estimated exposures into toxicokinetic mod-els yields information about the steady state and time course concentrations in various partsof the body These concentrations can then be compared to concentrations that cause bio-logical activity in in vitro assays The models can also be used in a reverse manner knownas reverse toxicokinetics by predicting the dose needed to produce a specific concentrationof interest such as the in vitro AC50 or other levels of biological activity as done in Wet-more et al (2012) and Wetmore (2015) Thus chemicals can be ranked based on the ratioof the predicted exposure dose to the back-calculated bioactive dose (Thomas et al 2013)which due to the linearity of these models is equal to the ratio of the predicted steady stateconcentration to the in vitro bioactive concentration

Many basic toxicokinetic models (Wetmore et al 2012 Wetmore 2015 Pelekis et al 1997)only predict steady state plasma concentrations (Css) assuming a dose rate that is bothcontinuous and constant (eg infusion dose) With a more dynamic model such as a phys-iologically based toxicokinetic (pbtk) model we can simulate discrete doses to reach steadystate which we observe to oscillate around the infusion dose prediction Our pbtk modelsinclude multiple compartments with partition coefficients These models are expressed as aset of mass balance differential equations describing the rate of change of the amount of asubstance in each compartment Chemical-specific physicochemical data and species-specificin vitro and physiological data are used in calculating the partition coefficients clearancetissue volumes and blood flows These in vitro data consist of the intrinsic hepatic clearanceClint and the plasma protein binding fub httk provides tools for Monte Carlo sampling andreverse dosimetry (Tan et al 2006) along with functions that solve for concentration vs timecurves steady state concentrations the number of days to steady state and other toxicoki-netic summary statistics for chemicals as shown in Tables 4 and 5 with the correspondingabbreviations in Table 1 With this R package we provide data models and examples toallow the inclusion of toxicokinetics in statistical analysis of chemical exposure and toxicityfor 553 chemicals The package is structured to be modular and expandable to allow newmodeling approaches and chemical data to be added as they become available

Journal of Statistical Software 3

Variable Name1compartment One compartment model (OrsquoFlaherty 1981) shown in Figure 13compartment Three compartment model (Jamei et al 2009) shown in Figure 13compartmentss Three compartment steady state model (Wetmore et al 2012 Wetmore

2015)BW Body weightCss Average plasma concentration of a chemical at steady stateClint In vitro intrinsic hepatic clearanceClmetabolism Whole liver hepatic clearance scaled from Clint Clwellminusstirred Hepatic clearance modeled with well-stirred approximation using

Clmetabolism fub Fraction unbound in vitro ratio of unbound to total concentration in

plasmahttk High-throughput toxicokineticskelim Elimination ratekgutabs Gut absorption rate default of 1 hminus1logP Logarithm (base 10) of octanol to water partition coefficientpbtk Physiologically based toxicokinetic model shown in Figure 1PM Poor metabolizersQcardiac Cardiac output blood flow through the heart and lungsQgfr Glomerular filtration rateQrest The difference between Qcardiac and the flow to the liver kidney and gutQtissue Blood flow to a tissueQSAR Quantitative structure-activity relationshipRblood2plasma Ratio of the blood concentration of a chemical to the plasma concentra-

tionSBML Systems biology markup languageSMILES Simplified molecular-input line-entry systemVdist Volume of distribution the weighted sum of all partition coefficients

Table 1 List of abbreviations

2 MethodsVersion 17 of httk (Wambaugh et al 2017) is used in this manuscript The package isavailable from the Comprehensive R Archive Network (CRAN) at httpsCRANR-projectorgpackage=httk

21 Models included

The four models in httk include ldquopbtkrdquo ldquo3compartmentrdquo ldquo3compartmentssrdquo and ldquo1com-partmentrdquo the predictions and parameters of these models are compared in Table 2 Allmodels currently use only oral and intravenous (iv) dosing The models pbtk and 3com-partment shown in Figure 1 use tissue to unbound plasma partition coefficients calculatedwith a modified version of Schmittrsquos model (Schmitt 2008b) (using octanol-water partition-ing membrane affinity acidbase dissociation constants tissue compositions and adjustedfub) to simulate chemical concentrations over time for multiple tissue compartments The


Model Hepatic

clearance

Partitio

ncoeffi

cients

Fractio

nunbound

Hematocrit

Mole

cular

weigh

tRa

tioofbloodto

plasma

Elimination

rate

Volume o

f distrib

ution

Dynamicprediction

Steady

state

prediction

pbtk Yes Yes Yes Yes Yes Yes No No Yes Yes1compartment No No No No Yes No Yes Yes Yes Yes3compartment Yes Yes Yes Yes Yes Yes No No Yes Yes3compartmentss Yes No Yes No Yes No No No No Yes

Table 2 Model parameter and prediction comparison Partition coefficients are needed incalculating Vdist Clearances and fub are needed in calculating kelim

model pbtk contains separate tissue compartments for the gut liver lungs arteries veinsand kidneys while the model 3compartment only contains compartments for the liver and gutand is essentially a condensed form of the model pbtk The tissues contained in tissuedatathat are unused in each of these models are aggregated into a single compartment termedldquorestrdquo whose partition coefficient is calculated by averaging the remaining partition coeffi-cients weighted by their species-specific tissue volumes Absorption from the gut lumen intogut tissue is modeled as a first order process with an arbitrary ldquofastrdquo absorption rate of 1hminus1 The fraction of the dose absorbed into the system through the gut wall is set to 1 whenmeasured data are unavailable The gut blood flows directly into the liver where the hepaticclearance Clmetabolism is calculated with a unit conversion of Clint using the density of hep-atocytes in the liver (11 times 108 hepatocytes per gram of liver from Ito and Houston 2004 anda liver density of 105 gmL from Snyder et al 1975) Both models also feature renal elim-ination by passive glomerular filtration through the kidneys We assume perfusion-limitedtissue (ie tissue red blood cells and plasma come to equilibrium rapidly with respect tothe flow of blood) and a constant Rblood2plasma is used throughout the body predicted usinghematocrit and the predicted partitioning between red blood cells and plasma when in vivovalues are unavailableThe models 3compartmentss and 1compartment both contain only plasma without separatecompartments for blood and tissue (and thus no individual partition coefficients) The model3compartmentss ldquossrdquo standing for steady state is a single equation for the Css of the rest-of-body compartment in the model 3compartment resulting from iv dosing This is thesame equation used for determining Css in previous work (Rotroff et al 2010 Wetmore et al2012 Wetmore 2015 Wilkinson and Shand 1975) but with a modification adjusting for themisuse of hepatic blood flow in determining plasma clearance (Yang et al 2007) The model1compartment features an absorption compartment and a total clearance equal to the sumof the metabolism of the parent compound in the liver modeled with the adjusted ldquowell-stirredrdquo approximation (Wilkinson and Shand 1975 Houston and Carlile 1997) and the renalclearance by passive glomerular filtration The elimination rate ke is equal to the totalclearance divided by the volume of distribution Vdist Vdist is used as the volume of thecompartment and is calculated by summing the plasma volume and the products of eachtissue to unbound plasma partition coefficient its corresponding volume and fub (Schmitt


A B

Qgfr

Qliver

Qgut

QgutGut Blood

Liver Blood

Liver Tissue

Clmetabolism

Body Blood

Rest of Body

Gut Tissue

Gut Lumen

Qliver + Qgut

Qliver + Qgut

Clwell-stirred + Qgfr

Gut Lumen

Primary Compartment

C

kgutabs

kgutabs

Lung BloodQcardiac

Qliver

Qgut

QkidneyKidney Blood

Gut Blood

Gut Lumen

Qgfr

Kidney Tissue

Liver Blood

Liver Tissue

Qrest

Lung Tissue

Clmetabolism

Body Blood

Rest of Body

Qgut

Arteria

l Blo

odV

enou

s B

lood

Gut Tissue

kgutabs

Figure 1 Models (A) 1compartment (B) 3compartment and (C) pbtk In order to preservemass-balance Qrest is defined as the difference between Qcardiac and the flow to the liverkidney and gut Variable names are defined in Table 1

2008b) Css resulting from infusion dosing for the model 1compartment is equivalent to3compartmentssAmong the four models in the package the simplest model 3compartmentss is applicable tothe largest number of chemicals specifically those which are missing information needed toparameterize the other models It is the only model that does not use partition coefficientsand thus does not require logP and when fub is below the limit of detection the model can beused with Monte Carlo to simulate Css distributions Thus fub below the limit of detection(set to zero in chemphysical_and_invitrodata and 0005 in default parameter lists) andClint are the minimum data requirements for running a model The model 1compartment isincluded to compare our predictions with in vivo experiments which are often characterizedby one compartment model parameters (Vdist and kelim) We note that fully understand-ing the kinetics of a given chemical might require additional data on features currently notaccessible with high-throughput in vitro approaches such as bioavailability transportersprotein-binding kinetics and extra-hepatic or strongly saturable metabolism (Rotroff et al2010)

22 Model equations

The differential equations below describe changes in the concentrations or amounts of a sub-stance within the model compartments Although the models are written as changes intissue concentrations except for the gut lumen the equations actually express changes inthe amount of substance in the blood of each tissue divided by the tissue volume with theblood and tissue concentrations related through the out-flowing concentration in blood A


blood flow Q (Lday) multiplied by a concentration C (molL) is equal to the amountof the substance entering or leaving a compartment through the blood QC (molday) Wedefine partition coefficients as the ratio of the concentration in a tissue to the unbound con-centration in plasma of that tissue Ktissue2pu = Ctissue(fubCplasma) Thus dividing Ctissue byKtissue2pu and fub and then multiplying by Rblood2plasma yields the blood concentration of thecompartment at equilibrium CtissueRblood2plasma(fubKtissue2pu) Assuming perfusion-limitedtissue we substitute this term for the out-flowing blood concentrations (Campbell Jr et al2012) and assume negligible blood volume fractions in all tissues to justify dividing by thetissue volume without a blood volume fraction and partition coefficient dependency Theflow to the rest-of-body Qrest is calculated by subtracting the sum of all the other tissueflows (ie gut liver and kidney) from the total cardiac output The glomerular filtrationrate Qgfr and the hepatic clearance Clmetabolism (both in Lday) are both multiplied bythe unbound plasma concentrations CtissueKtissue2pu in the kidney and liver to express theamount of the substance leaving the system Note that although the units of the clearancesflows and absorption rate are in days being consistent with the model outputs they areinitially entered in units of hours The model 3compartmentss assumes a constant dose ratekdose (mgkg BWday) and the other models use discrete changes in the amount in the gutlumen or venous concentration depending on which type of dose is specified The functionthat is part of the gut lumen equation g(t) describes the oral dosing schedule MCSim (Boisand Maszle 1997) was used for converting the model equations into C code which is usedwith deSolve (Soetaert et al 2016) in solving each system of equations

pbtk equations

d

dtAgutlumen = minuskgutabsAgutlumen + g(t)

d

dtCgut =

(kgutabsAgutlumen +Qgut

(Cart minus Rblood2plasma

Kgut2pufubCgut

))Vgut

d

dtCliver =

(QliverCart + QgutRblood2plasma

Kgut2pufubCgutminus

(Qliver +Qgut)Rblood2plasmaKliver2pufub

Cliver minus ClmetabolismKliver2pu

Cliver

)Vliver

d

dtCven =

((Qliver +QgutKliver2pu

Cliver + QkidneyKkidney2pu

Ckidney+

QrestKrest2pu

Crest

)Rblood2plasma

fubminusQcardiacCven

)Vven

d

dtClung = Qcardiac

(Cven minus Rblood2plasma

Klung2pufubClung

)Vlung

d

dtCart = Qcardiac

(Rblood2plasmaKlung2pufub

Clung minus Cart

)Vart

d

dtCrest = Qrest


Krest2pufubCrest

)Vrest

d

dtCkidney =

(QkidneyCart minus QKidneyRblood2plasma

Kkidney2pufubCkidney minus Qgfr

Kkidney2puCkidney

)Vkidney


3compartment equations

d


d

dtCgut =

(kgutabsAgutlumen + QgutRblood2plasma

Krest2pufubCrest minus QgutRblood2plasma

Kgut2pufubCgut

)Vgut

d

dtCliver =

(QgutRblood2plasma

Kgut2pufubCgut + QliverRblood2plasma

Krest2pufubCrestminus((Qliver +Qgut)Rblood2plasma

fubKliver2pu+ Clmetabolism

Kliver2pu

)Cliver

)Vliver

d

dtCrest =

((Qgut +Qliver)Rblood2plasmafubKliver2pu

Cliverminus(Rblood2plasma

fub

(Qgut +Qliver

)+Qgfr

)Crest

Krest2pu

)Vrest


d


d

dtCrest = kgutabs

VdistAgutlumen minus kelimCrest

3compartmentss equation

Css = kdose(

fubQgfr + (Qliver +Qgut)fubClmetabolism(Qliver +Qgut) + fubClmetabolismRblood2plasma

)

23 In vitro chemical data

In vitro experiments provide empirical data for two model parameters The first Clint the intrinsic hepatic clearance of the parent compound by primary hepatocytes (substratedepletion approach) was measured in a well on a multi-compound plate (Shibata et al 2002)This was determined by dividing the in vitro clearance of the unbound parent chemical bythe fraction of chemical unbound in the hepatocyte intrinsic clearance assay provided in theparameter lists which was estimated using a distribution coefficient calculated from pKaand the method of Kilford et al (2008) The second in vitro measurement is fub assessedusing rapid equilibrium dialysis (RED) in which two wells are separated by a membrane thatis permeable by smaller molecules but prevents the plasma protein added to one well frommigrating to the other well (the relative chemical concentration in the two linked wells givesthe free fraction of chemical Waters et al 2008) However the default value used in themodels is adjusted for absent binding in vitro (Poulin and Haddad 2012)


Data table DescriptioncheminvivoPKdata This data set includes time and dose specific measurements of

chemical concentrations in tissues taken from animals administeredcontrol doses of the chemicals either orally or intravenously Theseplasma concentration-time data are from rat experiments reportedin public sources Toxicokinetic data were retrieved from thosestudies by the Netherlands Organisation for Applied Scientific Re-search (TNO) using curve stripping (TechDig v2) These data areprovided for statistical analysis as in Wambaugh et al (2015)

cheminvivoPK-summarydata

This data set summarizes the time course data in thecheminvivoPKdata table Maximum concentration (Cmax)time integrated plasma concentration for the duration of treat-ment (AUCtreatment) and extrapolated to zero concentration(AUCinfinity) as well as half-life are calculated Summary val-ues are given for each study and dosage

chemphysical_and_-invitrodata

This data set contains the necessary information to make basichigh-throughput toxicokinetic predictions for compounds includ-ing fub Clint molecular weight logP logMA (membrane affinity)and pKa

tissuedata This data set contains values from Ruark et al (2014) describingthe composition of specific tissues and from Snyder et al (1975)and Birnbaum et al (1994) describing volumes of and blood flowsto those tissues allowing parameterization of toxicokinetic modelsfor human mouse rat dog or rabbit

physiologydata This data set contains additional physiological values necessary toparameterize a toxicokinetic model for human mouse rat dog orrabbit

Wetmoredata This data set gives the chemical-specific predictions for serum con-centration at steady state resulting from infusion exposure at aconstant rate as published in a series of papers from Barbara Wet-morersquos group (Wetmore et al 2012 2013 Wetmore 2015) at theHamner Institutes for Life Sciences Predictions include the me-dian and 90 interval in microM and mgL Calculations were madeusing the 1 and 10 microM in vitro measured clearances

Table 3 List of data tables in the package In Ring et al (2017) a series of tables for gen-erating populations based on variation in human physiology were added They are describedin that manuscript and vignettes

For non-pharmaceutical chemicals in vitro experimental data were obtained primarily fromWetmore et al (2012) Wetmore (2015) and Tonnelier et al (2012) for humans and Wet-more et al (2013) for rats For pharmaceutical compounds these values are compiled fromObach (1999) Jones et al (2002) Naritomi et al (2003) Ito and Houston (2004) Ri-ley et al (2005) Schmitt (2008a) and Obach et al (2008) These data are contained inchemphysical_and_invitrodata


24 Physicochemical properties

Physicochemical properties were collated from various sources Molecular weight and struc-ture are determined from the DSStox database (httpwwwepagovncctdsstox) andoctanol to water partitioning is predicted for most compounds with EPArsquos estimation pro-gram interface (EPI) suite (httpwwwepagovtsca-screening-toolsepi-suitetm-estimation-program-interface) EPI suite quantitative structure activity relationships(QSARs) were used to estimate octanol to water partitioning (logP) if simplified molecularinput line entry system (SMILES) descriptions of chemical structure were available and theQSARs did not fail for that structure In addition to QSAR model estimates EPI suitecontains a database of experimentally obtained octanol to water partition coefficients thatwere used in place of estimated values when available Where available ionization asso-ciationdissociation equilibrium constants (pKa) were curated from the literature otherwisepredictions were made from structure using the SPARC (which performs automated reasoningin chemistry) model (Hilal et al 1995) Membrane affinities (ie lipid-bilayer to water con-centration ratios) are predicted using a regression from Yun et al (2014) based on octanolto water partitioning and membrane affinity values from Schmitt (2008b) when measuredvalues are unavailable These data are contained in chemphysical_and_invitrodata

25 Physiological and tissue data

The tissue data needed for calculating partition coefficients in human and rat taken fromRuark et al (2014) include cellular and water fractions of total volume lipid and proteinfractions of cellular volume lipid fractions of the total lipid volume the pH of each tissueand the fractional volume of protein in plasma A default plasma pH of 74 is taken fromSchmitt (2008b) in calculating ionization The partition coefficient for the mass and volumeof the body unaccounted for by the tissues included in Schmitt (2008b) is calculated with theaverages of the fractional volumes and pH of these tissues excluding red blood cells Tissuevolumes and liver density are taken from Snyder et al (1975) Blood flows are from Birnbaumet al (1994) Tissue volumes are scaled linearly to body weight while the flows includingglomerular filtration are scaled by body weight to the 34 power (Campbell Jr et al 2012)The available data for the fraction of a dose absorbed into the gut lumen are taken fromNaritomi et al (2003) The remaining data are taken from Davies and Morris (1993) Thesedata are included in the physiologydata and tissuedata tables that are accessible in thepackage

26 Determination of steady state

Although the discrete dosing in our models produces an oscillating steady state we use thesteady state resulting from equivalent oral infusion dosing at a constant rate calculated byanalytically solving the differential equations at steady state to determine when steady stateis reached The day a chemical reaches steady state is found by determining when the averageconcentration of the numerically solved solution for a given day falls within a specified percentof the analytic solution from oral infusion dosing calc_css defaulting to 1

27 Monte Carlo sampler

The package contains a Monte Carlo sampler HTTK-Pop (Ring et al 2017) used in


calc_mc_css for probabilistically simulating human biological variability and measurementuncertainty in parameters determining Css (Thomas et al 1996) HTTK-Pop uses physiologiesbased on distributions of demographic and anthropometric quantities from the most recentUS Centers for Disease Control and Prevention National Health and Nutrition ExaminationSurvey (NHANES) data (Johnson et al 2014) This allows incorporation of inter-individualvariability including variability across relevant demographic subgroups which can be speci-fied through the arguments gendernum agelim_yearsagelim_months weight_categorygfr_category and reths respectively specifying the relative numbers of genders age rangesbody weights kidney function and racial ethnicity for the simulated population By defaultthe total US population is represented (Johnson et al 2014) HTTK-Pop accounts forthe correlation structure in physiological parameters (Ring et al 2017) Two methods forsampling individuals are available the default direct resampling (method=dr) uses actualindividuals from the NHANES If the number of individuals for a specific demographic groupis small larger numbers of virtual individuals (method=vi) can be generated Prior toversion 15 the package relied upon a Monte Carlo sampler that used uncorrelated normaldistributions that were truncated to ensure positive values The distributions can be changedbut default to a mean equal to the model parameter estimate and a coefficient of variationof 03 For humans setting httkpop to FALSE allows the original uncorrelated Monte Carlosampler to be used HTTK-Pop is only used for humans and so for all non-human speciesthe original sampler is still used

Body weight liver volume and blood flow cellular density in the liver andQgfr are all varied asdescribed above HTTK-Pop varies Clmetabolism by varying three quantities Hepatocellularity(106 cellsg liver) and liver weight (kg) are varied based on NHANES biometrics (Ring et al2017) The chemical specific in vitro measured Clint is varied according to a Gaussian mixturedistribution to represent the population proportions of poor metabolizers (PMs) and non-PMsof each substance With probability 095 Clint was drawn from a non-PM distribution anormal distribution truncated below at zero centered at the value measured in vitro with acoefficient of variation of 03 With probability 005 Clint was drawn from a PM distributiona truncated normal distribution centered on one-tenth of the in vitro value with coefficientof variation 03 fub is drawn from a censored distribution with identical properties to theother distributions where values are sampled from a uniform distribution between 0 and thelimit of detection (default of 1 unbound) at a rate proportional to the number of samplesfrom the truncated normal distribution below the limit of detection fub below the limitof detection (set to zero in chemphysical_and_invitrodata) is set to a default value of0005 in the model parameters For each chemical a default of 1000 different combinationsof parameters are used to determine Css These concentrations are determined with dosesof 1 mgkg BWday but given the linear concentration response of the models can beextrapolated to other doses with calc_mc_css Using calc_mc_oral_equiv we can in areverse manner back-calculate the dose for a given concentration and quantile The functionsget_wetmore_css and get_wetmore_oral_equiv perform the same operations on doses andconcentrations using the published Css results from Wetmore et al (2012) Wetmore et al(2013) and Wetmore (2015) contained in the Wetmoredata table which used the same invitro data as contained in the package However these data only contain the 5 medianand 95 quantiles for humans and the median for rats These results were obtained withthe SimCYP population simulator (Jamei et al 2009) in a manner identical to the defaultsimulation in calc_mc_css with two exceptions The Wetmore data assumed fub = 0005 for


chemicals with fub below the limit of detection instead of sampling the value from a censoreddistribution and the Clmetabolism values were accepted as nonzero if the p value was less than01 instead of 005 as used in our sampler

3 ExamplesThe following examples are run with version 17 and may not generate the same outputs asother versions New versions of the package typically correspond to submission to or revisionof manuscripts for peer-reviewed scientific journals (Wambaugh et al 2015 Wetmore 2015Ring et al 2017) If using httk for regulatory purposes a copy of the version used should bearchived To check if the version installed is 17 or greater

Rgt packageVersion(httk) gt= 17

31 Accessing and changing model parametershttk allows the user to access and change the parameters used in each of the models Each ofthe models contains their own parameterize function that generates a list of the parametersrequired by the model For example to get a list of parameters for the pbtk model of triclosanin a rat

Rgt parameters lt- parameterize_pbtk(chemname = triclosan species = rat)

To see the effect a change in parameters has on the model we can modify the desired entries inthe list and use the new parameter list as an input for the parameters argument of a functionthat uses that model For example to change the fub in the previous parameters list to 01from the default of 0005 (noting the warning that fub is below the limit of detection) anduse it in a simulation of the pbtk model for a single dose of 1 mgkg BW of triclosan in a rat

Rgt parameters[Funboundplasma] lt- 01Rgt out lt- solve_pbtk(parameters = parameters)

Individual parameters such as Rblood2plasma total clearance Vdist metabolic clearance andkelim can also be calculated using the functions with the prefix calc followed by the parametername and the same arguments as the above parameterize function

32 Making data frames and tablesIn order to compare predictions or models we can construct tables or data frames Supposewe want to look at how Css at 1 mgkg BWday compares for the model pbtk the medianof the Monte Carlo simulation and the Wetmore data We can construct a data frame(used with ggplot2 Wickham 2009 in the following examples) containing these data witha for loop The intersection of get_wetmore_cheminfo and get_cheminfo contains all theCAS numbers that will work for all three functions In the example below setting modelto pbtk in get_cheminfo removes the chemicals from the list with fub below the limit ofdetection This is the same as setting excludefubzero to TRUE However we could includethese chemicals by using the default model option of 3compartmentss and fub would thenautomatically be set to 0005


Function Descriptionadd_chemtable Adds chemical data for HTTK analysisavailable_rblood2plasmaRetrieves Rblood2plasma (measured preferred over predicted))calc_analytic_css Calculates Css and blood concentrations for the four models used

in the package from infusion dosing at a constant ratecalc_css Calculates the maximum and average steady state concentra-

tions along with the day steady state is reachedcalc_elimination_rate Calculates kelim for a one compartment model due to the liver

and kidneys dividing the total clearance by Vdist calc_hepatic_clearance Calculates the hepatic clearance for a well-stirred model or other

type if specified (Ito and Houston 2004)calc_mc_css Calculates Css using Monte Carlo simulation defaulting to

HTTK-Pop simulator (Ring et al 2017)calc_mc_oral_equiv Calculates an oral equivalent dose using Css from calc_mc_csscalc_rblood2plasma Calculates the bloodplasma chemical concentration ratiocalc_stats Calculates the area under the curve mean and peak values for

the blood or plasma concentration of either a specified chemicalor all chemicals for a given simulation

calc_total_clearance Calculates the total clearance rate for a one compartmentmodel where clearance is equal to the sum of the well-stirredmetabolism by the liver and glomerular filtration in the kidneys

calc_vdist Calculates the one compartment volume of distributionexport_pbtk_jarnac Exports the model pbtk to Jarnac (Sauro and Fell 2000)export_pbtk_sbml Exports the model pbtk to SBML (Hucka et al 2003)get_cheminfo Provides a list of CAS numbers along with compound names

logP pKa molecular weight Clint and its p value and fub ifspecified for chemicals with sufficient data for a given model

get_httk_params Converts table generated by httkpop_generate to the corre-sponding table of httk model parameters

get_rblood2plasma Retrieves in vivo Rblood2plasmaget_wetmore_cheminfo Provides the names and CAS numbers of chemicals with infor-

mation from Wetmore et al (2012) Wetmore et al (2013) andWetmore (2015)

get_wetmore_css Retrieves Css as a result of oral infusion dosing from Wetmoreet al (2012) Wetmore et al (2013) and Wetmore (2015)

get_wetmore_oral_equiv

Calculates an oral equivalent dose using Css from Wetmore et al(2012) Wetmore et al (2013) and Wetmore (2015)

httkpop_generate Generates a virtual populationlump_tissues Lumps tissue flows volumes and input partition coefficients

based on specified grouping

Table 4 List of functions in the package ndash Part I Models are described in Table 2 Parametersare defined in Table 1 Jarnac and SBML are external languages for systems biology models


Function Descriptionmonte_carlo Runs a Monte Carlo simulation of a given modelparameterize_1comp Parameterizes the model 1compartmentparameterize_3comp Parameterizes the model 3compartmentparameterize_pbtk Parameterizes the model pbtkparameterize_schmitt Parameterizes predict_partitioning_schmittparameterize_steadystate

Parameterizes the model 3compartmentss used in Wetmoreet al (2012) and Wetmore (2015)

predict_partitioning_schmitt

Predicts partition coefficients using Schmittrsquos method (Schmitt2008b)

solve_1comp Solves the model 1compartmentsolve_3comp Solves the model 3compartmentsolve_pbtk Solves the model pbtk

Table 5 List of functions in the package ndash Part II Models are described in Table 2 Param-eters are defined in Table 1 Jarnac and SBML are external languages for systems biologymodels

Rgt table lt- NULLRgt for (thiscas in intersect(get_cheminfo(model = pbtk)+ get_wetmore_cheminfo())) + thisrow lt- asdataframe(thiscas)+ thisrow lt- cbind(thisrow asdataframe(calc_analytic_css(+ chemcas = thiscas model = pbtk outputunits = mgL)))+ thisrow lt- cbind(thisrow asdataframe(get_wetmore_css(+ chemcas = thiscas whichquantile = 050)))+ thisrow lt- cbind(thisrow asdataframe(calc_mc_css(+ chemcas = thiscas whichquantile = 050)))+ table lt- rbind(table thisrow)+ Rgt colnames(table) lt- c(CAS PBTK Wetmore MC)

33 Plotting

Concentration vs time

The function solve_pbtk has the option of returning plots for the compartment concentra-tions vs time but to see how Css resulting from discrete dosing deviates from the averagesteady state concentration we can make a plot with ggplot2 that includes a horizontal linethrough the y axis at the predicted Css for oral infusion dosing (Figure 2) We calculate theanalytic Css and enter it into geom_hline as the y intercept and add all the other options toour lsquoggplotrsquo object

Rgt library(ggplot2)Rgt out lt- solve_pbtk(chemname = Bisphenol A days = 50 dosesperday = 3)Rgt plotdata lt- asdataframe(out)


00

05

10

15

20

25

0 10 20 30 40 50Day

Pla

sma

Con

cent

ratio

n (u

M)

Bisphenol A

Figure 2 Css at 3 doses per day 1 mgkg BWday

Rgt css lt- calc_analytic_css(chemname = Bisphenol A)Rgt cvst lt- ggplot(plotdataaes(time Cplasma)) + geom_line() ++ geom_hline(yintercept = css) + ylab(Plasma Concentration (uM)) ++ xlab(Day) + theme(axistext = element_text(size = 16)+ axistitle = element_text(size = 16)+ plottitle = element_text(size = 17 hjust = 05)) ++ ggtitle(Bisphenol A)Rgt cvst

This example plots the concentration vs time of 1 mgkg BWday of Bisphenol A broken intothree doses per day The same plots can be made for the other models by substituting one ofthe other two solve functions solve_3comp or solve_1comp for solve_pbtk and setting themodel argument of calc_analytic_css to the corresponding model These three functionsalso have the option of simulating a single oral or iv dose and setting the initial values ofeach compartment with units matching the specified output units (default is microM)

Days to steady state histogramCreating histograms can allow us to visualize how a given value varies across all the chemicalscontained within the package To create a histogram using ggplot2 of the number of days tosteady state we must first set up a for loop with get_cheminfo and calc_css to generate avector containing the data Vectors containing the average and maximum concentrations atsteady state are also generated in this example avg and max The data contained in the daysvector are then plotted as a histogram (Figure 3) We can just as easily create a histogramcontaining the average or maximum steady state concentrations by substituting avg or maxfor days


0

20

40

60

80

10 1000Days

Num

ber

of C

hem

ical

s

Figure 3 Days to steady state histogram

Rgt library(ggplot2)Rgt days lt- NULL avg lt- NULL max lt- NULLRgt for (thiscas in get_cheminfo(model=pbtk)) + cssinfo lt- calc_css(chemcas = thiscas dosesperday = 1+ suppressmessages = TRUE)+ days[[thiscas]] lt- cssinfo[[theday]]+ avg[[thiscas]] lt- cssinfo[[avg]]+ max[[thiscas]] lt- cssinfo[[max]]+ Rgt daysdata lt- asdataframe(days)Rgt hist lt- ggplot(daysdata aes(days)) ++ geom_histogram(fill = blue binwidth = 14) + scale_x_log10() ++ ylab(Number of Chemicals) + xlab(Days) + theme(axistext =+ element_text(size = 16) axistitle = element_text(size = 16))Rgt hist

Average vs maximum concentration

We can compare the average and maximum concentrations at steady state using the averageand maximum concentration at steady state vectors avg and max from the previous exampleThe vectors are bound into a data frame and plotted with a line through the origin with aslope of 1 (Figure 4)

Rgt library(ggplot2)Rgt avgmaxdata lt- dataframe(avg max)


1eminus01

1e+01

1e+03

1eminus02 1e+00 1e+02 1e+04Average Concentration at Steady State (uM)

Max

Con

cent

ratio

n at

Ste

ady

Sta

te (

uM)

Figure 4 Average vs maximum concentration at steady state for 1 dose per day 1 mgkgBWday

Rgt avgvsmax lt- ggplot(avgmaxdata aes(avg max)) + geom_point() ++ geom_abline() + scale_x_log10() + scale_y_log10() ++ xlab(Average Concentration at Steady State (uM)) ++ ylab(Max Concentration at Steady State (uM)) ++ theme(axistext = element_text(size = 16)+ axistitle = element_text(size = 16))Rgt avgvsmax

34 Calculating AUC peak and mean valuesThe function calc_stats calculates the area under the curve (AUC) peak and mean concen-trations of any of the solve functions If a chemical name or CAS number is specified it willcalculate the specified statistics for that chemical and if not it will calculate the values forall chemicals with sufficient data To calculate the peak statistics for all chemicals simulatedfor 10 days at 1 mgkg BWday with 3 doses per day and a list containing the AUC peakand mean for a single 1 mg dose of triclosan over 10 days we have

Rgt allpeakstats lt- calc_stats(days = 10 dosesperday = 3 stats = peak)Rgt triclosanstats lt- calc_stats(days = 10 chemname = triclosan)

35 Monte Carlo samplerThe functions calc_mc_css and get_wetmore_css generate Css vectors of Monte Carlosamples and their quantiles While calc_mc_css generates new values using the sampler


get_wetmore_css retrieves literature values from Wetmoredata Below are examples of thesetwo functions comparing the medians of the Wetmore data in humans for 1 mgkg BWdayof Bisphenol A with the calc_mc_css simulation with probability distributions containing athird of the standard deviation half the limit of detection for fub and double the number ofsamples of the parameters used in Wetmore et al (2012) and Wetmore (2015) These exam-ples do not make use of HTTK-Pop but vignettes describing the use of HTTK-Pop MonteCarlo sampler for human variability (Ring et al 2017) are included in the package

Rgt get_wetmore_css(chemcas = 80-05-7 dailydose = 1+ whichquantile = 05 outputunits = uM)Rgt calc_mc_css(chemcas = 80-05-7 dailydose = 1 whichquantile = 05+ censoredparams = list(Funboundplasma = list(cv = 01 lod = 0005))+ varyparams = list(BW = 015 Vliverc = 015 Qgfrc = 015+ Qtotalliverc = 015 millioncellspergliver = 015 Clint = 015)+ outputunits = uM samples = 2000 httkpop = FALSE)

The oral equivalent functions convert Css into a dose Below is an example of a 50 microMCss of Bisphenol A converted to an oral equivalent dose using the Wetmore data for the95th quantile of human Css We can call calc_mc_oral_equiv in the same manner passingadditional arguments to calc_mc_css within the function and specifying any quantile wewant

Rgt get_wetmore_oral_equiv(50 chemcas = 80-05-7)

We can also use the original Monte Carlo sampler used in calc_mc_css monte_carlo toperform the same simulations using another model Setting the returnsamples argumentof the calc_mc or monte_carlo functions to TRUE we can generate the sampling distributionfor the Monte Carlo simulation from which the quantiles are calculated To perform a MonteCarlo simulation on zoxamide (Figure 5) with the model pbtk with the same limit of detectionand coefficients of variation of two thirds the size of those used in calc_mc_css we have

Rgt varyparams lt- NULLRgt params lt- parameterize_pbtk(chemname = Zoxamide)Rgt for (thisparam in names(subset(params+ names(params) = Funboundplasma))) varyparams[thisparam] lt- 02Rgt censoredparams lt- list(Funboundplasma = list(cv = 02 lod = 001))Rgt setseed(1)Rgt out lt- monte_carlo(params cvparams = varyparams+ censoredparams = censoredparams returnsamples = TRUE+ model = pbtk suppressmessages = TRUE)Rgt zoxamide lt- ggplot(asdataframe(out) aes(out)) ++ geom_histogram(fill = blue binwidth = 16) + scale_x_log10() ++ ylab(Number of Samples) + xlab(Steady State Concentration (uM)) ++ theme(axistext = element_text(size = 16)+ axistitle = element_text(size = 16))Rgt zoxamide


0

50

100

150

200

1e+03 1e+05Steady State Concentration (uM)

Num

ber

of S

ampl

es

Figure 5 Sampling distribution of zoxomide Css from the model pbtk

The out vector is then plotted in a similar way to the days vector in the previous histogramexample This can also be performed with the new sampler in calc_mc_css by simply settingmodel to pbtk

36 Adding a tissueThe fractional volumes and pH values from Schmitt (2008a) needed to calculate the partitioncoefficients are contained in tissuedata New tissues can be added to this table to generatetheir partition coefficients We can add thyroid to the tissue data by making a row containingits data subtracting the volumes and flows from the rest-of-body and binding the row totissuedata Here we assume it contains the same partition coefficient data as the spleenand a tenth of the volume and blood flow

Rgt newtissue lt- subset(tissuedataTissue == spleen)Rgt newtissue[ Tissue] lt- thyroidRgt newtissue[newtissue$variable in c(Vol (Lkg)+ Flow (mLminkg^(34)))value] lt- newtissue[newtissue$variable+ in c(Vol (Lkg)Flow (mLminkg^(34)))value] 10Rgt tissuedata[tissuedata$Tissue == rest value] lt-+ tissuedata[tissuedata$Tissue == rest value] -+ newtissue[newtissue$variable in c(Vol (Lkg)+ Flow (mLminkg^(34)))value]Rgt tissuedata lt- rbind(tissuedata newtissue)

We can also choose what tissues we want lumped together or in the rest-of-body compartmentThe tissuelist argument in parameterize_pbtk contains a list of the desired compartment


names each containing a vector of the names of the tissues in tissuedata to be lumpedtogether in that compartment All unspecified tissues in tissuedata are lumped togetherin the rest-of-body Lumped flows and volumes are calculated through addition of the indi-vidual component flows and volumes while the lumped partition coefficients are calculatedthrough dividing the sum of the products of the partition coefficients and their correspondingcompartment volumes by the new lumped volume To generate the parameters for a modelwith kidneys thyroid a liver compartment combining the liver and gut and a rest-of-bodycompartment

Rgt compartments lt- list(liver = c(liver gut) kidney = kidney+ thyroid = thyroid)Rgt parameterize_pbtk(chemname = Nicotine tissuelist = compartments)

No matter which compartments we specify the liver volume as well as the gut liver andkidney flows are returned for the calculation of clearance and metabolism

37 Export functions

Jarnac (Sauro and Fell 2000) and SBML (Hucka et al 2003) are commonly used languages forsystems biology models of cellular and physiological processes In the event that a modelerwishes to couple such a model to a toxicokinetic model we provide functions to exportmodel equations and chemical-specific parameters to these languages The two functionsexport_pbtk_sbml and export_pbtk_jarnac have the same arguments and only differ inthe file extension names (xml and jan) entered into the filename argument Both use litersas the units for volume but the amounts are unitless and to be determined by the user Ifwe suppose that we enter an initial amount of 1 mg in the gut lumen then all the othercompartments will contain amounts in mg Below is a call of an export function for a doseof 1 given to a rat

Rgt export_pbtk_sbml(chemname = Bisphenol A species = Rat+ initialamounts = list(Agutlumen = 1) filename = PBTKmodelxml)

4 Concluding remarksThe R software platform is increasingly being used for the statistical analysis of mathemat-ical models (Wambaugh et al 2015 Gelman et al 2013) With the launch of the packageodesolve (Setzer 2001) which was expanded and replaced by deSolve (Soetaert et al 2010)R can be used to solve models consisting of systems of differential equations R further al-lows organization and handling of large data sets making it especially suitable for analyzingthe results from high-throughput experiments (Judson et al 2010) Given the reliance onmathematical models and in vitro testing to prioritize investigation of the large number ofrelatively untested environmental chemicals (Wetmore et al 2012 Wetmore 2015) softwareplatforms such as R allow the systematic statistical evaluation of the performance of thesetechnologies (Wambaugh et al 2015) httk allows the simulation of four toxicokinetic modelsfor 553 chemicals (including 415 ToxCast chemicals and 94 pharmaceuticals) in humans ratsmice dogs and rabbits


All models in httk are parameterized using data on key determinants of toxicokinetics thatcan be measured in vitro using relatively high-throughput methods (Wetmore et al 2012Wetmore 2015) The package includes toxicokinetic models ranging from a one compartmentmodel to a PBTK model but even the PBTK model is relatively spare with most tissueslumped into a rest-of-body compartment Rowland (2004) argued that the ldquobestrdquo model isthe one that most reliably answers the question at hand (Rowland et al 2004) Thus themost parsimonious model ndash that is the simplest most easily understood model allowing usefulpredictions ndash should be preferred (Chiu and White 2006) However since PBTK models allowthe incorporation of additional physiological information we may expect our model pbtk tobe the most accurate on average We hope these models provide predictions of chemical-specific toxicokinetics as informed by in vitro data and physicochemical properties withoutintroducing errors from unnecessary assumptions (Rowland et al 2004 Chiu and White 2006)The parameterize_pbtk function provides parameter estimates for more complex models asneeded (Yang and Lu 2007) though our solvers are currently limited to the four modelstructures In future versions we expect to have the ability to add new compartments usingthese parameters and simulate dermal and inhalation exposure

The httk package provides functions for the application of Monte Carlo methods in vitro-invivo extrapolation and reverse dosimetry httk links exposure scenarios including constantoral infusion a single dose or multiple discrete doses to predicted tissue and plasma concen-trations Standard toxicokinetic statistics including peak concentration and time-integratedplasma concentration (area under the curve or AUC) can be predicted facilitating dosimetricanchoring (Wambaugh et al 2013a) for comparing in vivo toxicity studies where toxicokineticdata were not collected (Wetmore et al 2013) Important aspects of the steady-state behav-ior of the chemicals can be predicted for use in analysis of biomonitoring data including thetime to steady-state and Css (Wetmore et al 2012 Wetmore 2015 Aylward and Hays 2011Wambaugh et al 2013b 2014) Finally as ongoing in vitro experiments allow parameteri-zation of the models for additional chemicals these new data can be easily distributed asupdates to the package on the CRAN repository

Acknowledgments

The authors appreciate editorial comments from Nicole Kleinstreuer and Kevin M Croftonhelp with the Schmitt algorithm from Jimena Davis help with Jarnac from James Sluka andchemical properties and in vivo data provided by the Netherlands Organization for AppliedScientific Research (TNO) through Sieto Bosgra

Disclaimer

The views expressed in this publication are those of the authors and do not necessarilyrepresent the views for policies of the US Environmental Protection Agency Reference tocommercial products or services does not constitute endorsement


References

Aylward LL Hays SM (2011) ldquoConsideration of Dosimetry in Evaluation of ToxCastTM

Datardquo Journal of Applied Toxicology 31(8) 741ndash751 doi101002jat1626

Birnbaum L Brown R Bischoff K Foran J Blancato J Clewell H Dedrick R (1994) ldquoPhysi-ological Parameter Values for PBPK Modelsrdquo Technical report International Life SciencesInstitute Risk Science Institute Washington

Bois F Maszle D (1997) ldquoMCSim A Monte Carlo Simulation Programrdquo Journal of StatisticalSoftware 2(1) 1ndash60 doi1018637jssv002i09

Bucher JR (2008) ldquoGuest Editorial NTP New Initiatives New Alignmentrdquo EnvironmentalHealth Perspectives 116(1) A14ndashA15 doi101289ehp11100

Campbell Jr JL Clewell RA Gentry PR Andersen ME Clewell III HJ (2012) ldquoPhysiolog-ically Based PharmacokineticToxicokinetic Modelingrdquo In B Reisfeld AN Mayeno (eds)Computational Toxicology volume 929 of Methods in Molecular Biology pp 439ndash499 Hu-mana Press doi101007978-1-62703-050-2_18

Chiu WA White P (2006) ldquoSteady-State Solutions to PBPK Models and Their Applicationsto Risk Assessment I Route-to-Route Extrapolation of Volatile Chemicalsrdquo Risk Analysis26(3) 769ndash780 doi101111j1539-6924200600762x

Davies B Morris T (1993) ldquoPhysiological Parameters in Laboratory Animals and HumansrdquoPharmaceutical Research 10(7) 1093ndash1095 doi101023a1018943613122

Egeghy PP Vallero DA Hubal EAC (2011) ldquoExposure-Based Prioritization of Chemicalsfor Risk Assessmentrdquo Environmental Science amp Policy 14(8) 950ndash964 doi101016jenvsci201107010

Gelman A Carlin JB Stern HS Dunson DB Vehtari A Rubin DB (2013) Bayesian DataAnalysis CRC Press

Hilal SH Karickhoff SW Carreira LA (1995) ldquoA Rigorous Test for SPARCrsquos Chemical Re-activity Models Estimation of More Than 4300 Ionization pKasrdquo Quantitative Structure-Activity Relationships 14(4) 348ndash355 doi101002qsar19950140405

Houston JB Carlile DJ (1997) ldquoPrediction of Hepatic Clearance from Microsomes Hep-atocytes and Liver Slicesrdquo Drug Metabolism Reviews 29(4) 891ndash922 doi10310903602539709002237

Hucka M Finney A Sauro HM Bolouri H Doyle JC Kitano H Arkin AP Bornstein BJ BrayD Cornish-Bowden A others (2003) ldquoThe Systems Biology Markup Language (SBML) AMedium for Representation and Exchange of Biochemical Network Modelsrdquo Bioinformatics19(4) 524ndash531

Ito K Houston JB (2004) ldquoComparison of the Use of Liver Models for Predicting DrugClearance Using in Vitro Kinetic Data from Hepatic Microsomes and Isolated HepatocytesrdquoPharmaceutical Research 21(5) 785ndash792 doi101023bpham0000026429121147d


Jamei M Marciniak S Feng K Barnett A Tucker G Rostami-Hodjegan A (2009) ldquoTheSimcypreg Population-Based ADME Simulatorrdquo Expert Opinion on Drug Metabolism ampToxicology 5(2) 211ndash223 doi10151717425250802691074

Johnson CL Dohrmann SM Burt VL Mohadjer LK (2014) ldquoNational Health and NutritionExamination Survey Sample Design 2011ndash2014rdquo Vital and Health Statistics ndash Series 2Data Evaluation and Methods Research 162 1ndash33

Jones OA Voulvoulis N Lester JN (2002) ldquoAquatic Environmental Assessment of the Top25 English Prescription Pharmaceuticalsrdquo Water Research 36(20) 5013ndash5022 doi101016s0043-1354(02)00227-0

Judson R Richard A Dix DJ Houck K Martin M Kavlock R Dellarco V Henry T Hol-derman T Sayre P Tan S Carpenter T Smith E (2008) ldquoThe Toxicity Data Landscapefor Environmental Chemicalsrdquo Environmental Health Perspectives 117(5) 685ndash695 doi101289ehp0800168

Judson RS Houck KA Kavlock RJ Knudsen TB Martin MT Mortensen HM Reif DMRotroff DM Shah I Richard AM Dix DJ (2010) ldquoIn Vitro Screening of EnvironmentalChemicals for Targeted Testing Prioritization The ToxCast Projectrdquo Environmental HealthPerspectives 118(4) 485ndash492 doi101289ehp0901392

Kilford PJ Gertz M Houston Brian J Galetin A (2008) ldquoHepatocellular Binding of DrugsCorrection for Unbound Fraction in Hepatocyte Incubations Using Microsomal Bindingor Drug Lipophilicity Datardquo Drug Metabolism and Disposition 36(7) 1194ndash1197 doi101124dmd108020834

Naritomi Y Terashita S Kagayama A Sugiyama Y (2003) ldquoUtility of Hepatocytes in Pre-dicting Drug Metabolism Comparison of Hepatic Intrinsic Clearance in Rats and Hu-mans in Vivo and in Vitrordquo Drug Metabolism and Disposition 31(5) 580ndash588 doi101124dmd315580

Obach RS (1999) ldquoPrediction of Human Clearance of Twenty-Nine Drugs from HepaticMicrosomal Intrinsic Clearance Data An Examination of in Vitro Half-Life Approach andNonspecific Binding to Microsomesrdquo Drug Metabolism and Disposition 27(11) 1350ndash1359

Obach RS Lombardo F Waters NJ (2008) ldquoTrend Analysis of a Database of IntravenousPharmacokinetic Parameters in Humans for 670 Drug Compoundsrdquo Drug Metabolism andDisposition 36(7) 1385ndash405 doi101124dmd108020479

OrsquoFlaherty EJ (1981) Toxicants and Drugs Kinetics and Dynamics John Wiley amp SonsNew York

Park YH Lee K Soltow QA Strobel FH Brigham KL Parker RE Wilson ME SutliffRL Mansfield KG Wachtman LM Ziegler TR Jones DP (2012) ldquoHigh-PerformanceMetabolic Profiling of Plasma from Seven Mammalian Species for Simultaneous Environ-mental Chemical Surveillance and Bioeffect Monitoringrdquo Toxicology 295(1ndash3) 47ndash55doi101016jtox201202007

Pelekis D Krewski K Krishnan M (1997) ldquoPhysiologically Based Algebraic for PredictingSteady-State Toxicokinetics of Inhaled Vaporsrdquo Toxicology Mechanisms and Methods 7(3)205ndash226 doi101080105172397243169


Poulin P Haddad S (2012) ldquoAdvancing Prediction of Tissue Distribution and Volume ofDistribution of Highly Lipophilic Compounds from a Simplified Tissue-Composition-BasedModel as a Mechanistic Animal Alternative Methodrdquo Journal of Pharmaceutical Sciences101(6) 2250ndash2261 doi101002jps23090

Riley RJ McGinnity DF Austin RP (2005) ldquoA Unified Model for Predicting Human Hep-atic Metabolic Clearance from in Vitro Intrinsic Clearance Data in Hepatocytes and Micro-somesrdquo Drug Metabolism and Disposition 33(9) 1304ndash11 doi101124dmd105004259

Ring CL Pearce RG Setzer RW Wetmore BA Wambaugh JF (2017) ldquoIdentifying Pop-ulations Sensitive to Environmental Chemicals by Simulating Toxicokinetic VariabilityrdquoEnvironment International 106 105ndash118 doi101016jenvint201706004

Rotroff DM Wetmore BA Dix DJ Ferguson SS Clewell HJ Houck KA Lecluyse EL An-dersen ME Judson RS Smith CM Sochaski MA Kavlock RJ Boellmann F Martin MTReif DM Wambaugh JF Thomas RS (2010) ldquoIncorporating Human Dosimetry and Ex-posure into High-Throughput in Vitro Toxicity Screeningrdquo Toxicological Sciences 117(2)348ndash358 doi101093toxscikfq220

Rovida C Hartung T (2009) ldquoRe-Evaluation of Animal Numbers and Costs for in VivoTests to Accomplish REACH Legislation Requirements for Chemicals ndash a Report by theTransatlantic Think Tank for Toxicology (t4)rdquo Altex 26(3) 187ndash208 doi1014573altex20093187

Rowland M Balant L Peck C (2004) ldquoPhysiologically Based Pharmacokinetics in DrugDevelopment and Regulatory Science A Workshop Report (Georgetown University Wash-ington DC May 29ndash30 2002)rdquo AAPS PharmSci 6(1) 56ndash67 doi101208ps060106

Ruark CD Hack CE Robinson PJ Mahle DA Gearhart JM (2014) ldquoPredicting Passive andActive TissuePlasma Partition Coefficients Interindividual and Interspecies VariabilityrdquoJournal of Pharmaceutical Sciences 103(7) 2189ndash2198 doi101002jps24011

Sauro HM Fell D (2000) ldquoJarnac A System for Interactive Metabolic Analysisrdquo In Animatingthe Cellular Map Proceedings of the 9th International Meeting on BioThermoKinetics pp221ndash228 Stellenbosch University Press

Schmitt W (2008a) ldquoCorrigendum to ldquoGeneral Approach for the Calculation of Tissue toPlasma Partition Coefficientsrdquo [Toxicology in Vitro 22 (2008) 457ndash467]rdquo Toxicology inVitro 22(6) 1666 doi101016jtiv200804020

Schmitt W (2008b) ldquoGeneral Approach for the Calculation of Tissue to Plasma PartitionCoefficientsrdquo Toxicology in Vitro 22(2) 457ndash467 doi101016jtiv200709010

Setzer RW (2001) ldquoThe odesolve Package Solvers for Ordinary Differential EquationsrdquoR package version 01-1 URL httpsCRANR-projectorgsrccontribArchiveodesolve

Shibata Y Takahashi H Chiba M Ishii Y (2002) ldquoPrediction of Hepatic Clearance andAvailability by Cryopreserved Human Hepatocytes An Application of Serum IncubationMethodrdquo Drug Metabolism and Disposition 30(8) 892ndash896 doi101124dmd308892


Snyder WS Cook M Nasset E Karhausen L Howells G Tipton I (1975) ldquoReport of the TaskGroup on Reference Manrdquo ICRP Publication 23 International Commission on RadiologicalProtection Elmsford

Soetaert K Petzoldt T Setzer RW (2010) ldquoSolving Differential Equations in R PackagedeSolverdquo Journal of Statistical Software 33(9) 1ndash25 doi1018637jssv033i09

Soetaert K Petzoldt T Setzer RW (2016) deSolve Solvers for Initial Value Problems ofDifferential Equations (ODE DAE DDE) R package version 114 URL httpsCRANR-projectorgpackage=deSolve

Tan YM Liao KH Clewell III HJ (2006) ldquoReverse Dosimetry Interpreting TrihalomethanesBiomonitoring Data Using Physiologically Based Pharmacokinetic Modelingrdquo Journal ofExposure Science amp Environmental Epidemiology 17(7) 591ndash603 doi101038sjjes7500540

Thomas RS Lytle WE Keefe TJ Constan AA Yang RSH (1996) ldquoIncorporating MonteCarlo Simulation into Physiologically Based Pharmacokinetic Models Using Advanced Con-tinuous Simulation Language (ACSL) A Computational Methodrdquo Toxicological Sciences31(1) 19ndash28

Thomas RS Philbert MA Auerbach SS Wetmore BA Devito MJ Cote I Rowlands JCWhelan MP Hays SM Andersen ME others (2013) ldquoIncorporating New Technologies intoToxicity Testing and Risk Assessment Moving from 21st Century Vision to a Data-DrivenFrameworkrdquo Toxicological Sciences 136(1) 4ndash18 doi101093toxscikft178

Tonnelier A Coecke S Zaldivar JM (2012) ldquoScreening of Chemicals for Human Bioaccumu-lative Potential with a Physiologically Based Toxicokinetic Modelrdquo Archives of Toxicology86(3) 393ndash403 doi101007s00204-011-0768-0

Wambaugh J Pearce R Ring C Davis J Sipes N Setzer RW (2017) httk High-ThroughputToxicokinetics R package version 17 URL httpsCRANR-projectorgpackage=httk

Wambaugh JF Setzer RW Pitruzzello AM Liu J Reif DM Kleinstreuer NC Wang NCYSipes N Martin M Das K others (2013a) ldquoDosimetric Anchoring of In Vivo and InVitro Studies for Perfluorooctanoate and Perfluorooctanesulfonaterdquo Toxicological Sciences136(2) 308ndash327

Wambaugh JF Setzer RW Reif DM Gangwal S Mitchell-Blackwood J Arnot JA JolietO Frame A Rabinowitz J Knudsen TB others (2013b) ldquoHigh-Throughput Models forExposure-Based Chemical Prioritization in the ExpoCast Projectrdquo Environmental Scienceamp Technology 47(15) 8479ndash8488 doi101021es400482g

Wambaugh JF Wang A Dionisio KL Frame A Egeghy P Judson R Setzer RW (2014) ldquoHighThroughput Heuristics for Prioritizing Human Exposure to Environmental Chemicalsrdquo En-vironmental Science amp Technology 48(21) 12760ndash12767 doi101021es503583j

Wambaugh JF Wetmore BA Pearce R Strope C Goldsmith R Sluka JP Sedykh A TropshaA Bosgra S Shah I others (2015) ldquoToxicokinetic Triage for Environmental ChemicalsrdquoToxicological Sciences 147(1) 55ndash67 doi101093toxscikfv118


Waters NJ Jones R Williams G Sohal B (2008) ldquoValidation of a Rapid Equilibrium DialysisApproach for the Measurement of Plasma Protein Bindingrdquo Journal of PharmaceuticalSciences 97(10) 4586ndash4595 doi101002jps21317

Wetmore BA (2015) ldquoQuantitative in Vitro-to-in Vivo Extrapolation in a High-ThroughputEnvironmentrdquo Toxicology 332 94ndash101 doi101016jtox201405012

Wetmore BA Wambaugh JF Ferguson SS Li L Clewell HJ Judson RS Freeman K BaoW Sochaski MA Chu TM Black MB Healy E Allen B Andersen ME Wolfinger RDThomas RS (2013) ldquoRelative Impact of Incorporating Pharmacokinetics on PredictingIn Vivo Hazard and Mode of Action from High-Throughput In Vitro Toxicity AssaysrdquoToxicological Sciences 132(2) 327ndash346 doi101093toxscikft012

Wetmore BA Wambaugh JF Ferguson SS Sochaski MA Rotroff DM Freeman K Clewell IIIHJ Dix DJ Andersen ME Houck KA Allen B Judson RS Singh R Kavlock RJ RichardAM Thomas RS (2012) ldquoIntegration of Dosimetry Exposure and High-ThroughputScreening Data in Chemical Toxicity Assessmentrdquo Toxicological Sciences 125(1) 157ndash174 doi101093toxscikfr254

Wickham H (2009) ggplot2 Elegant Graphics for Data Analysis Springer-Verlag New York

Wilkinson GR Shand DG (1975) ldquoCommentary A Physiological Approach to HepaticDrug Clearancerdquo Clinical Pharmacology amp Therpeutics 18(4) 377ndash390 doi101002cpt1975184377

Yang J Jamei M Yeo KR Rostami-Hodjegan A Tucker GT (2007) ldquoMisuse of the Well-Stirred Model of Hepatic Drug Clearancerdquo Drug Metabolism and Disposition 35(3) 501ndash502 doi101124dmd106013359

Yang RSH Lu Y (2007) ldquoThe Application of Physiologically Based Pharmacokinetic (PBPK)Modeling to Risk Assessmentrdquo In MG Robson WA Toscano (eds) Risk Assessment forEnvironmental Health pp 85ndash120 John Wiley amp Sons

Yun YE Cotton CA Edginton AN (2014) ldquoDevelopment of a Decision Tree to Classifythe Most Accurate Tissue-Specific Tissue to Plasma Partition Coefficient Algorithm fora Given Compoundrdquo Journal of Pharmacokinetics and Pharmacodynamics 41(1) 1ndash14doi101007s10928-013-9342-0

AffiliationJohn F Wambaugh Robert G Pearce R Woodrow Setzer Cory L StropeUS Environmental Protection Agency109 TW Alexander DrMail Code D143-02Research Triangle Park NC 27711 United States of AmericaE-mail wambaughjohnepagovURL httpwwwepagovncct


Nisha S SipesDivision of the National Toxicology ProgramNational Institute of Environmental Health Sciences111 TW Alexander Dr ML K2-17Research Triangle Park NC 27709 United States of AmericaURL httpwwwniehsnihgovresearchatniehslabsbmsb

Journal of Statistical Software httpwwwjstatsoftorgpublished by the Foundation for Open Access Statistics httpwwwfoastatorg

July 2017 Volume 79 Issue 4 Submitted 2015-05-06doi1018637jssv079i04 Accepted 2016-06-24

Introduction

Methods

Models included

Model equations

pbtk equations




In vitro chemical data

Physicochemical properties

Physiological and tissue data

Determination of steady state

Monte Carlo sampler

Examples

Accessing and changing model parameters

Making data frames and tables

Plotting


Days to steady state histogram


Calculating AUC peak and mean values

Monte Carlo sampler

Adding a tissue

Export functions

Concluding remarks


Egeghy et al 2011 Judson et al 2008) In order to screen for potential bioactivity in vitrodata have been generated in the Tox21 (Bucher 2008) and ToxCast (Judson et al 2010)programs using high-throughput screening systems Over 8500 chemicals have been tested inat least 50 assays (Tox21) and a subset of around 1800 have had nearly 1200 assay endpointsmeasured (ToxCast) Recently high-throughput exposure modeling has provided estimates ofdaily human exposure for thousands of environmental contaminants (Wambaugh et al 2014)However linking these hazard and exposure predictions to estimate risk requires developmentand use of high-throughput toxicokinetics The terms ldquopharmacokineticrdquo ldquotoxicokineticrdquoand ldquobiokineticrdquo models have been used somewhat interchangeably in the scientific literatureHowever since this package is intended to provide dose context to high-throughput toxicityscreening projects we have selected the term ldquotoxicokineticrdquo even though we include severalcompounds with known therapeutic benefits and many others that may not cause adversityfor the highest plausible dose

Toxicokinetics is a field of study for determining the absorption distribution metabolismand excretion of substances in the body (OrsquoFlaherty 1981) The necessary data for toxicoki-netics are commonly collected in rats and other animals but the collection of these data forthousands of chemicals is costly in time money and animals (Rovida and Hartung 2009)Creating computational predictive models parameterized with more easily obtained in vitrodata may help address these problems Inputting estimated exposures into toxicokinetic mod-els yields information about the steady state and time course concentrations in various partsof the body These concentrations can then be compared to concentrations that cause bio-logical activity in in vitro assays The models can also be used in a reverse manner knownas reverse toxicokinetics by predicting the dose needed to produce a specific concentrationof interest such as the in vitro AC50 or other levels of biological activity as done in Wet-more et al (2012) and Wetmore (2015) Thus chemicals can be ranked based on the ratioof the predicted exposure dose to the back-calculated bioactive dose (Thomas et al 2013)which due to the linearity of these models is equal to the ratio of the predicted steady stateconcentration to the in vitro bioactive concentration

Many basic toxicokinetic models (Wetmore et al 2012 Wetmore 2015 Pelekis et al 1997)only predict steady state plasma concentrations (Css) assuming a dose rate that is bothcontinuous and constant (eg infusion dose) With a more dynamic model such as a phys-iologically based toxicokinetic (pbtk) model we can simulate discrete doses to reach steadystate which we observe to oscillate around the infusion dose prediction Our pbtk modelsinclude multiple compartments with partition coefficients These models are expressed as aset of mass balance differential equations describing the rate of change of the amount of asubstance in each compartment Chemical-specific physicochemical data and species-specificin vitro and physiological data are used in calculating the partition coefficients clearancetissue volumes and blood flows These in vitro data consist of the intrinsic hepatic clearanceClint and the plasma protein binding fub httk provides tools for Monte Carlo sampling andreverse dosimetry (Tan et al 2006) along with functions that solve for concentration vs timecurves steady state concentrations the number of days to steady state and other toxicoki-netic summary statistics for chemicals as shown in Tables 4 and 5 with the correspondingabbreviations in Table 1 With this R package we provide data models and examples toallow the inclusion of toxicokinetics in statistical analysis of chemical exposure and toxicityfor 553 chemicals The package is structured to be modular and expandable to allow newmodeling approaches and chemical data to be added as they become available









21 Models included



Model Hepatic

clearance

Partitio

ncoeffi

cients

Fractio

nunbound

Hematocrit

Mole

cular

weigh

tRa

tioofbloodto

plasma

Elimination

rate

Volume o

f distrib

ution

Dynamicprediction

Steady

state

prediction





A B

Qgfr

Qliver

Qgut

QgutGut Blood

Liver Blood

Liver Tissue

Clmetabolism

Body Blood

Rest of Body

Gut Tissue

Gut Lumen

Qliver + Qgut

Qliver + Qgut


Gut Lumen

Primary Compartment

C

kgutabs

kgutabs

Lung BloodQcardiac

Qliver

Qgut

QkidneyKidney Blood

Gut Blood

Gut Lumen

Qgfr

Kidney Tissue

Liver Blood

Liver Tissue

Qrest

Lung Tissue

Clmetabolism

Body Blood

Rest of Body

Qgut

Arteria

l Blo

odV

enou

s B

lood

Gut Tissue

kgutabs



22 Model equations




pbtk equations

d


d

dtCgut =



Kgut2pufubCgut

))Vgut

d

dtCliver =


Kgut2pufubCgutminus



Cliver

)Vliver

d

dtCven =



Ckidney+

QrestKrest2pu

Crest

)Rblood2plasma


)Vven

d

dtClung = Qcardiac


Klung2pufubClung

)Vlung

d

dtCart = Qcardiac


Clung minus Cart

)Vart

d

dtCrest = Qrest


Krest2pufubCrest

)Vrest

d

dtCkidney =



Kkidney2puCkidney

)Vkidney



d


d

dtCgut =



Kgut2pufubCgut

)Vgut

d

dtCliver =

(QgutRblood2plasma




Kliver2pu

)Cliver

)Vliver

d

dtCrest =



fub

(Qgut +Qliver

)+Qgfr

)Crest

Krest2pu

)Vrest


d


d

dtCrest = kgutabs



Css = kdose(


)

































































33 Plotting





00

05

10

15

20

25

0 10 20 30 40 50Day

Pla

sma

Con

cent

ratio

n (u

M)

Bisphenol A






0

20

40

60

80

10 1000Days

Num

ber

of C

hem

ical

s







1eminus01

1e+01

1e+03


Max

Con

cent

ratio

n at

Ste

ady

Sta

te (

uM)














0

50

100

150

200


Num

ber

of S

ampl

es










37 Export functions







Acknowledgments


Disclaimer



References





































































Introduction

Methods

Models included

Model equations

pbtk equations








Monte Carlo sampler

Examples



Plotting





Monte Carlo sampler

Adding a tissue

Export functions

Concluding remarks









21 Models included



Model Hepatic

clearance

Partitio

ncoeffi

cients

Fractio

nunbound

Hematocrit

Mole

cular

weigh

tRa

tioofbloodto

plasma

Elimination

rate

Volume o

f distrib

ution

Dynamicprediction

Steady

state

prediction





A B

Qgfr

Qliver

Qgut

QgutGut Blood

Liver Blood

Liver Tissue

Clmetabolism

Body Blood

Rest of Body

Gut Tissue

Gut Lumen

Qliver + Qgut

Qliver + Qgut


Gut Lumen

Primary Compartment

C

kgutabs

kgutabs

Lung BloodQcardiac

Qliver

Qgut

QkidneyKidney Blood

Gut Blood

Gut Lumen

Qgfr

Kidney Tissue

Liver Blood

Liver Tissue

Qrest

Lung Tissue

Clmetabolism

Body Blood

Rest of Body

Qgut

Arteria

l Blo

odV

enou

s B

lood

Gut Tissue

kgutabs



22 Model equations




pbtk equations

d


d

dtCgut =



Kgut2pufubCgut

))Vgut

d

dtCliver =


Kgut2pufubCgutminus



Cliver

)Vliver

d

dtCven =



Ckidney+

QrestKrest2pu

Crest

)Rblood2plasma


)Vven

d

dtClung = Qcardiac


Klung2pufubClung

)Vlung

d

dtCart = Qcardiac


Clung minus Cart

)Vart

d

dtCrest = Qrest


Krest2pufubCrest

)Vrest

d

dtCkidney =



Kkidney2puCkidney

)Vkidney



d


d

dtCgut =



Kgut2pufubCgut

)Vgut

d

dtCliver =

(QgutRblood2plasma




Kliver2pu

)Cliver

)Vliver

d

dtCrest =



fub

(Qgut +Qliver

)+Qgfr

)Crest

Krest2pu

)Vrest


d


d

dtCrest = kgutabs



Css = kdose(


)

































































33 Plotting





00

05

10

15

20

25

0 10 20 30 40 50Day

Pla

sma

Con

cent

ratio

n (u

M)

Bisphenol A






0

20

40

60

80

10 1000Days

Num

ber

of C

hem

ical

s







1eminus01

1e+01

1e+03


Max

Con

cent

ratio

n at

Ste

ady

Sta

te (

uM)














0

50

100

150

200


Num

ber

of S

ampl

es










37 Export functions







Acknowledgments


Disclaimer



References





































































Introduction

Methods

Models included

Model equations

pbtk equations








Monte Carlo sampler

Examples



Plotting





Monte Carlo sampler

Adding a tissue

Export functions

Concluding remarks


Model Hepatic

clearance

Partitio

ncoeffi

cients

Fractio

nunbound

Hematocrit

Mole

cular

weigh

tRa

tioofbloodto

plasma

Elimination

rate

Volume o

f distrib

ution

Dynamicprediction

Steady

state

prediction





A B

Qgfr

Qliver

Qgut

QgutGut Blood

Liver Blood

Liver Tissue

Clmetabolism

Body Blood

Rest of Body

Gut Tissue

Gut Lumen

Qliver + Qgut

Qliver + Qgut


Gut Lumen

Primary Compartment

C

kgutabs

kgutabs

Lung BloodQcardiac

Qliver

Qgut

QkidneyKidney Blood

Gut Blood

Gut Lumen

Qgfr

Kidney Tissue

Liver Blood

Liver Tissue

Qrest

Lung Tissue

Clmetabolism

Body Blood

Rest of Body

Qgut

Arteria

l Blo

odV

enou

s B

lood

Gut Tissue

kgutabs



22 Model equations




pbtk equations

d


d

dtCgut =



Kgut2pufubCgut

))Vgut

d

dtCliver =


Kgut2pufubCgutminus



Cliver

)Vliver

d

dtCven =



Ckidney+

QrestKrest2pu

Crest

)Rblood2plasma


)Vven

d

dtClung = Qcardiac


Klung2pufubClung

)Vlung

d

dtCart = Qcardiac


Clung minus Cart

)Vart

d

dtCrest = Qrest


Krest2pufubCrest

)Vrest

d

dtCkidney =



Kkidney2puCkidney

)Vkidney



d


d

dtCgut =



Kgut2pufubCgut

)Vgut

d

dtCliver =

(QgutRblood2plasma




Kliver2pu

)Cliver

)Vliver

d

dtCrest =



fub

(Qgut +Qliver

)+Qgfr

)Crest

Krest2pu

)Vrest


d


d

dtCrest = kgutabs



Css = kdose(


)

































































33 Plotting





00

05

10

15

20

25

0 10 20 30 40 50Day

Pla

sma

Con

cent

ratio

n (u

M)

Bisphenol A






0

20

40

60

80

10 1000Days

Num

ber

of C

hem

ical

s







1eminus01

1e+01

1e+03


Max

Con

cent

ratio

n at

Ste

ady

Sta

te (

uM)














0

50

100

150

200


Num

ber

of S

ampl

es










37 Export functions







Acknowledgments


Disclaimer



References





































































Introduction

Methods

Models included

Model equations

pbtk equations








Monte Carlo sampler

Examples



Plotting





Monte Carlo sampler

Adding a tissue

Export functions

Concluding remarks


A B

Qgfr

Qliver

Qgut

QgutGut Blood

Liver Blood

Liver Tissue

Clmetabolism

Body Blood

Rest of Body

Gut Tissue

Gut Lumen

Qliver + Qgut

Qliver + Qgut


Gut Lumen

Primary Compartment

C

kgutabs

kgutabs

Lung BloodQcardiac

Qliver

Qgut

QkidneyKidney Blood

Gut Blood

Gut Lumen

Qgfr

Kidney Tissue

Liver Blood

Liver Tissue

Qrest

Lung Tissue

Clmetabolism

Body Blood

Rest of Body

Qgut

Arteria

l Blo

odV

enou

s B

lood

Gut Tissue

kgutabs



22 Model equations




pbtk equations

d


d

dtCgut =



Kgut2pufubCgut

))Vgut

d

dtCliver =


Kgut2pufubCgutminus



Cliver

)Vliver

d

dtCven =



Ckidney+

QrestKrest2pu

Crest

)Rblood2plasma


)Vven

d

dtClung = Qcardiac


Klung2pufubClung

)Vlung

d

dtCart = Qcardiac


Clung minus Cart

)Vart

d

dtCrest = Qrest


Krest2pufubCrest

)Vrest

d

dtCkidney =



Kkidney2puCkidney

)Vkidney



d


d

dtCgut =



Kgut2pufubCgut

)Vgut

d

dtCliver =

(QgutRblood2plasma




Kliver2pu

)Cliver

)Vliver

d

dtCrest =



fub

(Qgut +Qliver

)+Qgfr

)Crest

Krest2pu

)Vrest


d


d

dtCrest = kgutabs



Css = kdose(


)

































































33 Plotting





00

05

10

15

20

25

0 10 20 30 40 50Day

Pla

sma

Con

cent

ratio

n (u

M)

Bisphenol A






0

20

40

60

80

10 1000Days

Num

ber

of C

hem

ical

s







1eminus01

1e+01

1e+03


Max

Con

cent

ratio

n at

Ste

ady

Sta

te (

uM)














0

50

100

150

200


Num

ber

of S

ampl

es










37 Export functions







Acknowledgments


Disclaimer



References





































































Introduction

Methods

Models included

Model equations

pbtk equations








Monte Carlo sampler

Examples



Plotting





Monte Carlo sampler

Adding a tissue

Export functions

Concluding remarks



pbtk equations

d


d

dtCgut =



Kgut2pufubCgut

))Vgut

d

dtCliver =


Kgut2pufubCgutminus



Cliver

)Vliver

d

dtCven =



Ckidney+

QrestKrest2pu

Crest

)Rblood2plasma


)Vven

d

dtClung = Qcardiac


Klung2pufubClung

)Vlung

d

dtCart = Qcardiac


Clung minus Cart

)Vart

d

dtCrest = Qrest


Krest2pufubCrest

)Vrest

d

dtCkidney =



Kkidney2puCkidney

)Vkidney



d


d

dtCgut =



Kgut2pufubCgut

)Vgut

d

dtCliver =

(QgutRblood2plasma




Kliver2pu

)Cliver

)Vliver

d

dtCrest =



fub

(Qgut +Qliver

)+Qgfr

)Crest

Krest2pu

)Vrest


d


d

dtCrest = kgutabs



Css = kdose(


)

































































33 Plotting





00

05

10

15

20

25

0 10 20 30 40 50Day

Pla

sma

Con

cent

ratio

n (u

M)

Bisphenol A






0

20

40

60

80

10 1000Days

Num

ber

of C

hem

ical

s







1eminus01

1e+01

1e+03


Max

Con

cent

ratio

n at

Ste

ady

Sta

te (

uM)














0

50

100

150

200


Num

ber

of S

ampl

es










37 Export functions







Acknowledgments


Disclaimer



References





































































Introduction

Methods

Models included

Model equations

pbtk equations








Monte Carlo sampler

Examples



Plotting





Monte Carlo sampler

Adding a tissue

Export functions

Concluding remarks



d


d

dtCgut =



Kgut2pufubCgut

)Vgut

d

dtCliver =

(QgutRblood2plasma




Kliver2pu

)Cliver

)Vliver

d

dtCrest =



fub

(Qgut +Qliver

)+Qgfr

)Crest

Krest2pu

)Vrest


d


d

dtCrest = kgutabs



Css = kdose(


)

































































33 Plotting





00

05

10

15

20

25

0 10 20 30 40 50Day

Pla

sma

Con

cent

ratio

n (u

M)

Bisphenol A






0

20

40

60

80

10 1000Days

Num

ber

of C

hem

ical

s







1eminus01

1e+01

1e+03


Max

Con

cent

ratio

n at

Ste

ady

Sta

te (

uM)














0

50

100

150

200


Num

ber

of S

ampl

es










37 Export functions







Acknowledgments


Disclaimer



References





































































Introduction

Methods

Models included

Model equations

pbtk equations








Monte Carlo sampler

Examples



Plotting





Monte Carlo sampler

Adding a tissue

Export functions

Concluding remarks































































33 Plotting





00

05

10

15

20

25

0 10 20 30 40 50Day

Pla

sma

Con

cent

ratio

n (u

M)

Bisphenol A






0

20

40

60

80

10 1000Days

Num

ber

of C

hem

ical

s







1eminus01

1e+01

1e+03


Max

Con

cent

ratio

n at

Ste

ady

Sta

te (

uM)














0

50

100

150

200


Num

ber

of S

ampl

es










37 Export functions







Acknowledgments


Disclaimer



References





































































Introduction

Methods

Models included

Model equations

pbtk equations








Monte Carlo sampler

Examples



Plotting





Monte Carlo sampler

Adding a tissue

Export functions

Concluding remarks


00

05

10

15

20

25

0 10 20 30 40 50Day

Pla

sma

Con

cent

ratio

n (u

M)

Bisphenol A






0

20

40

60

80

10 1000Days

Num

ber

of C

hem

ical

s







1eminus01

1e+01

1e+03


Max

Con

cent

ratio

n at

Ste

ady

Sta

te (

uM)














0

50

100

150

200


Num

ber

of S

ampl

es










37 Export functions







Acknowledgments


Disclaimer



References





































































Introduction

Methods

Models included

Model equations

pbtk equations








Monte Carlo sampler

Examples



Plotting





Monte Carlo sampler

Adding a tissue

Export functions

Concluding remarks


0

20

40

60

80

10 1000Days

Num

ber

of C

hem

ical

s







1eminus01

1e+01

1e+03


Max

Con

cent

ratio

n at

Ste

ady

Sta

te (

uM)














0

50

100

150

200


Num

ber

of S

ampl

es










37 Export functions







Acknowledgments


Disclaimer



References





































































Introduction

Methods

Models included

Model equations

pbtk equations








Monte Carlo sampler

Examples



Plotting





Monte Carlo sampler

Adding a tissue

Export functions

Concluding remarks


1eminus01

1e+01

1e+03


Max

Con

cent

ratio

n at

Ste

ady

Sta

te (

uM)














0

50

100

150

200


Num

ber

of S

ampl

es










37 Export functions







Acknowledgments


Disclaimer



References





































































Introduction

Methods

Models included

Model equations

pbtk equations








Monte Carlo sampler

Examples



Plotting





Monte Carlo sampler

Adding a tissue

Export functions

Concluding remarks









0

50

100

150

200


Num

ber

of S

ampl

es










37 Export functions







Acknowledgments


Disclaimer



References





































































Introduction

Methods

Models included

Model equations

pbtk equations








Monte Carlo sampler

Examples



Plotting





Monte Carlo sampler

Adding a tissue

Export functions

Concluding remarks





37 Export functions







Acknowledgments


Disclaimer



References





































































Introduction

Methods

Models included

Model equations

pbtk equations








Monte Carlo sampler

Examples



Plotting





Monte Carlo sampler

Adding a tissue

Export functions

Concluding remarks




Acknowledgments


Disclaimer



References





































































Introduction

Methods

Models included

Model equations

pbtk equations








Monte Carlo sampler

Examples



Plotting





Monte Carlo sampler

Adding a tissue

Export functions

Concluding remarks


References





































































Introduction

Methods

Models included

Model equations

pbtk equations








Monte Carlo sampler

Examples



Plotting





Monte Carlo sampler

Adding a tissue

Export functions

Concluding remarks























































Introduction

Methods

Models included

Model equations

pbtk equations








Monte Carlo sampler

Examples



Plotting





Monte Carlo sampler

Adding a tissue

Export functions

Concluding remarks

httk: r package for high-throughput toxicokinetics and hepatic clearance), ... set of mass balance...

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