Nothing
Pearce et al. (2017): Updated v79i04.R Examples"
In httk: High-Throughput Toxicokinetics
from "httk: R Package for High-Throughput Toxicokinetics"
Robert G Pearce, R Woodrow Setzer, Cory L Strope, Nisha S Sipes, and John F Wambaugh
Journal of Statistical Software 2017 Jul 17; 79(4): 1-26.
https://doi.org/10.18637%2Fjss.v079.i04
Please send questions to wambaugh.john@epa.gov
Abstract
Thousands of chemicals have been profiled by high-throughput screening programs
such as ToxCast and Tox21; these chemicals are tested in part because most of
them have limited or no data on hazard, exposure, or toxicokinetics.
Toxicokinetic models aid in predicting tissue concentrations resulting from
chemical exposure, and a "reverse dosimetry" approach can be used to predict
exposure doses sufficient to cause tissue concentrations that have been
identified as bioactive by high-throughput screening. We have created four
toxicokinetic models within the R software package httk. These models are
designed to be parameterized using high-throughput in vitro data (plasma
protein binding and hepatic clearance), as well as structure-derived
physicochemical properties and species-specific physiological data. The package
contains tools for Monte Carlo sampling and reverse dosimetry along with
functions for the analysis of concentration vs. time simulations. The package
can currently use human in vitro data to make predictions for 553 chemicals in
humans, rats, mice, dogs, and rabbits, including 94 pharmaceuticals and 415
ToxCast chemicals. For 67 of these chemicals, the package includes rat-specific
in vitro data. This package is structured to be augmented with additional
chemical data as they become available. Package httk enables the inclusion of
toxicokinetics in the statistical analysis of chemicals undergoing
high-throughput screening.
This vignette was created from the
R replication code v79i04.R
for the
2017 paper that introduced httk.
HTTK Version
The
R replication code v79i04.R
was created with httk v1.7. It was
updated to a vignette using httk v2.2.2 in 2022. Although we attempt to
maintain
backward compatibility, if you encounter issues with the latest release of
httk
and cannot easily address the changes, historical versions of httk are
available from: https://cran.r-project.org/src/contrib/Archive/httk/
Prepare R to run the vignette
R package knitr generates html and PDF documents from this RMarkdown file,
Each bit of code that follows is known as a "chunk". We start by telling
knitr how we want our chunks to look.
knitr::opts_chunk$set(collapse = TRUE, comment = '#>')
options(rmarkdown.html_vignette.check_title = FALSE)
Clear the memory
It is a bad idea to let variables and other information from previous R
sessions float around, so we first remove everything in the R memory.
rm(list=ls())
eval = execute.vignette
If you are using the RMarkdown version of this vignette (extension, .RMD) you
will be able to see that several chunks of code in this vignette
have the statement "eval = execute.vignette". The next chunk of code, by default,
sets execute.vignette = TRUE. If execute.vignette = FALSE that would mean that the code is included (and necessary) but was
not run when the vignette was built.
# Set whether or not the following chunks will be executed (run):
execute.vignette <- TRUE
Load the relevant libraries
We use the command 'library()' to load various R packages for our analysis.
If you get the message "Error in library(X) : there is no package called 'X'"
then you will need to install that package:
From the R command prompt:
install.packages("X")
Or, if using RStudio, look for 'Install Packages' under 'Tools' tab.
library(ggplot2)
library(httk)
Check what version of httk is installed:
packageVersion("httk")
Control run speed
To speed up how fast these examples run, we only simulate every $N^{th}$ chemical
(currently 15) -- to get all chemicals with data set SKIP.CHEMS to 1:
NUM.CHEMS <- length(get_cheminfo(model="pbtk", suppress.messages = TRUE))
SKIP.CHEMS <- 25
Similarly, portions of this vignette use Monte Carlo sampling to simulate variability and
propagate uncertainty. The more samples that are used, the more stable the
results are (that is, the less likely they are to change if a different random
sequence is used). However, the more samples that are used, the longer it takes
to run. So, to speed up how fast these examples run, we specify here that we
only want to use 25 samples, even though the actual httk default is 1000.
Increase this number to get more stable (and accurate) results:
NSAMP <- 25
Examples
To get a list of parameters for the pbtk model of Triclosan in a rat:
parameters <- try(parameterize_pbtk(chem.name = "triclosan", species = "rat"))
We do not have a full set of in vitro parameters for rat for Triclosan,
so we fill in the in vitro measured values with human-derived measurements and
use rat physiological parameters by setting "default.to.human = TRUE":
parameters <- parameterize_pbtk(chem.name = "triclosan",
species = "rat",
default.to.human = TRUE)
To change the $f_{up}$ in the previous parameters list to 0.001 from the
human value of 0.003044 and use it in a simulation of the PBTK model for
a single dose of 1 mg/kg BW of Triclosan in a rat:
parameters["Funbound.plasma"] <- 0.001
out <- solve_pbtk(parameters = parameters, suppress.messages = TRUE)
Making a table
In the example below, setting model to "pbtk"
in "get_cheminfo" removes the chemicals from the list with $f_{up}$ below
the limit of detection which have been set to zero because the
model uses partition coefficients that are calculated with
$f_{up}$. However, we could include all chemicals that work with the
models without partition coefficients by using the default option of
"3compartmentss" or setting exclude.fup.zero to false, and $f_{up}$
would then automatically be set to 0.005.
First we make up a list of chemicals with both literature $C_{ss}$ values and HTTK data for making new $C_{ss}$ predictions:
chem.list <- intersect(get_cheminfo(model = "pbtk",
suppress.messages = TRUE)[seq(
1, NUM.CHEMS, SKIP.CHEMS)],
get_wetmore_cheminfo())
Then we initialize a NULL table and build it up one row at a time:
css.table <- NULL
for (this.cas in chem.list)
{
ids <- get_chem_id(chem.cas=this.cas)
this.row <- data.frame(Compound=ids$chem.name,
DTXSID=ids$dtxsid,
CAS=this.cas)
this.row <- cbind(this.row,
as.data.frame(calc_analytic_css(chem.cas = this.cas,
model = "pbtk",
output.units = "uM",
suppress.messages=TRUE)))
this.row <- cbind(this.row,
as.data.frame(get_wetmore_css(chem.cas = this.cas,
which.quantile = 0.50,
output.units = "uM",
suppress.messages=TRUE)))
this.row <- cbind(this.row,
as.data.frame(calc_mc_css(chem.cas = this.cas,
which.quantile = 0.50,
output.units = "uM",
samples = NSAMP,
suppress.messages=TRUE)))
css.table <- rbind(css.table, this.row)
}
colnames(css.table) <- c("Compound","DTXSID","CAS", "PBTK", "Wetmore", "MC")
Now display the table and plot two columns against each other:
knitr::kable(css.table, caption = "Literature and HTTK Plasma Css",
floating.environment="sidewaystable",
row.names=FALSE,
digits=3)
litvshttkcss <- ggplot(css.table, aes(Wetmore, MC)) +
geom_point() + geom_abline() +
scale_x_log10() + scale_y_log10() +
xlab(bquote("Literature"~C[ss]~"("*mu*"M)")) +
ylab(bquote("HTTK"~C[ss]~"("*mu*"M)")) +
theme(axis.text = element_text(size = 16),
axis.title = element_text(size = 16))
print(litvshttkcss)
Plotting example
To see how $C_{ss}$ resulting from discrete dosing deviates from the
average steady state concentration, we can make a plot with ggplot2
that includes a horizontal line through the $y$-axis at the predicted
$C_{ss}$ for oral infusion dosing (Figure 2 in Pearce et al., 2017).
out <- solve_pbtk(chem.name = "Bisphenol A",
days = 50,
doses.per.day = 3,
daily.dose=1,
output.units = "uM")
plot.data <- as.data.frame(out)
css <- calc_analytic_css(chem.name = "Bisphenol A",
output.units = "uM")
c.vs.t <- ggplot(plot.data, aes(time, Cplasma)) +
geom_line() + geom_hline(yintercept = css) +
ylab(bquote("Plasma Concentration ("*mu*"M)")) +
xlab("Day") +
theme(axis.text = element_text(size = 16),
axis.title = element_text(size = 16),
plot.title = element_text(size = 17, hjust=0.5)) +
ggtitle("Bisphenol A")
print(c.vs.t)
Suppressing Messages
Note that since in vitro-in vivo extrapolation (IVIVE) is built upon
many, many assumptions, httk* attempts to give many warning messages
by default. These messages do not usually mean something is wrong, but
are rather intended to make the user aware of the assumptions involved.
However, they quickly grow annoying and can be turned off with the
"suppress.messages=TRUE" argument. Proceed with caution...
out <- solve_pbtk(chem.name = "Bisphenol A",
days = 50,
doses.per.day = 3,
daily.dose=1,
output.units = "uM",
suppress.messages = TRUE)
css <- calc_analytic_css(chem.name = "Bisphenol A",
output.units = "uM",
suppress.messages = TRUE)
TK Study Summary Statistics
"calc_tk_stats" allows summary TK statistics to be calculated for a specific
study design (including dose regiment, duration, and species).
The following code calculates the peak plasma concentration for all chemicals in
httk simulated for 10 days at 1 mg/kg BW/day with 3 doses per day.
Note that the function "calc_stats" was renamed "calc_tk_stats" in a later release
of httk.
all.peak.stats <- calc_stats(days = 10, doses.per.day = 3, stats = "peak")
The same function can be used for a single chemical. For example,
the AUC, peak, and mean for a single 1 mg dose of Triclosan over 10
day:
triclosan.stats <- calc_stats(days = 10, chem.name = "triclosan")
Steady-state Plasma Concentration
Below are examples of two functions,comparing the medians of
the Wetmore data in humans for 1 mg/kg BW/day of Bisphenol A with
the "calc_mc_css" simulation with probability distributions
containing a third of the standard deviation, half the limit of
detection for $f_{up}$, and the same number of samples of the
parameters used in Wetmore et al. (2012).
We use make use of the default
Monte Carlo sampler by setting argument "httkpop=FALSE" to turn off
httk-pop (Ring et al., 2017) and
"invitrouv=FALSE" to turn off uncertainty/variability
for the in vitro parameters (Wambaugh et al., 2019).
Note that the function "get_wetmore_css" was renamed "get_lit_css" in a later release
of httk.
get_wetmore_css(chem.cas = "80-05-7", daily.dose = 1,
which.quantile = 0.5, output.units = "uM")
set.seed(654321)
calc_mc_css(chem.cas = "80-05-7",
daily.dose = 1,
which.quantile = 0.5,
censored.params = list(
Funbound.plasma = list(cv = 0.1, lod = 0.005)),
vary.params = list(
BW = 0.15,
Vliverc = 0.15,
Qgfrc = 0.15,
Qtotal.liverc = 0.15,
million.cells.per.gliver = 0.15,
Clint = 0.15),
output.units = "uM",
samples = NSAMP,
httkpop=FALSE,
invitrouv=FALSE,
suppress.messages = TRUE)
Using more sophisticated Monte Carlo
httk uses Monte Carlo to simulate population variability and propagate
parameter uncertainty. The algorithm for population variability, "httk-pop"
(Ring et al., 2017)
simulates population variability in TK by
predicting distributions of physiological parameters based on
distributions of demographic and biometric quantities from the
National Health and Nutrition Examination Survey (NHANES),
conducted by the U.S. Centers for Disease Control and Prevention
(CDC). MEthods for propagating uncertainty in in vitro measurements were
described by Wambaugh et al. (2019).
Both httk-pop and in vitro uncertainty/variability simulation, are on by default:
set.seed(654321)
calc_mc_css(chem.cas = "80-05-7",
daily.dose = 1,
which.quantile = 0.5,
output.units = "uM",
samples = NSAMP,
suppress.messages = TRUE)
Controlling the random number generator
Any of the Monte Carlo functions in httk, often indicated by the
inclusion of "mc" in the function name, make use of random draws from
distributions to simulate uncertainty and variability. The random number
generator in any computer is actually a pseudo-random number generator
that creates a sequence of nearly uncorrelated numbers, but that sequence
can be recreated at any time if we set a random number generator "seed".
In R we control the seed with the function "set.seed", which allows us
to get the same Monte Carlo output again and again (and in many cases
on different computers). The seed can take any value, and if you use the
same seed followed by the same functions called in the same order with the
same arguments, you will get the same answer again and again:
# Random number generator seed 1:
set.seed(654321)
calc_mc_css(chem.cas = "80-05-7",
daily.dose = 1,
which.quantile = 0.5,
output.units = "uM",
samples = NSAMP,
suppress.messages = TRUE)
# Continuing to draw random numbers without resetting the seed:
calc_mc_css(chem.cas = "80-05-7",
daily.dose = 1,
which.quantile = 0.5,
output.units = "uM",
samples = NSAMP,
suppress.messages = TRUE)
# Random number generator seed 2:
set.seed(123456)
calc_mc_css(chem.cas = "80-05-7",
daily.dose = 1,
which.quantile = 0.5,
output.units = "uM",
samples = NSAMP,
suppress.messages = TRUE)
# Continuing to draw random numbers without resetting the seed:
calc_mc_css(chem.cas = "80-05-7",
daily.dose = 1,
which.quantile = 0.5,
output.units = "uM",
samples = NSAMP,
suppress.messages = TRUE)
# Random number generator seed 2 gives the same answer as it did above:
set.seed(123456)
calc_mc_css(chem.cas = "80-05-7",
daily.dose = 1,
which.quantile = 0.5,
output.units = "uM",
samples = NSAMP,
suppress.messages = TRUE)
# Random number generator seed 1 gives the same answer as it did above:
set.seed(654321)
calc_mc_css(chem.cas = "80-05-7",
daily.dose = 1,
which.quantile = 0.5,
output.units = "uM",
samples = NSAMP,
suppress.messages = TRUE)
IVIVE with HTTK
Simple "reverse dosimetry" in vitro-in vivo extrapolation (IVIVE) determines
an administered equivalent dose (AED) by taking an in vitro concentration $C_{\text{in vitro}}$
(50 uM in the example below) and dividing it by the steady-state plasma
concentration $C_{ss}$ produced by a dose rate of 1 mg/kg bw/day:
$$ AED = \frac{C_{\text{in vitro}}}{C_{ss}}$$
We can also calculate the AED using literature values or sampling with httk:
get_wetmore_oral_equiv(50, chem.cas = "80-05-7")
set.seed(654321)
calc_mc_oral_equiv(50, chem.cas = "80-05-7", samples = NSAMP)
Monte Carlo Simulation of $C_{ss}$
We can perform a Monte Carlo simulation on Zoxamide with the
model pbtk with the same limit of detection and coefficients of
variation (cv).
Note, the function "monte_carlo" was replaced with a similar function
"calc_mc_tk" for simulation concentration timecourses, while arguments were
added to "calc_mc_css" that allowed the functionality seen in the 2017 paper.
Separately, a new function
"monte_carlo" was created to complement "httkpop_mc" and "invitro_mc" as
part of "create_mc_samples". "monte_carlo" varies parameters according to
a normal distribution with given mean and coefficient of variation or according
to a censored distribution with an additional limit of detection parameter.
Note that we again turn off httkpop and invitrouv to replicate the 2017 version
of Monte Carlo.
First we create a list of parameters and then assign a coefficient of variation
to each parameter we wish to vary:
vary.params <- NULL
params <- parameterize_pbtk(chem.name = "Zoxamide")
for (this.param in names(subset(params, names(params) != "Funbound.plasma")))
# Only want to vary numerical parameters:
if (is.numeric(params[[this.param]]))
vary.params[this.param] <- 0.2
We can draw $f_{up}$ from a censored distribution with a limit of dextion (LOD)
of 0.01:
censored.params <- list(Funbound.plasma = list(cv = 0.2, lod = 0.01))
Solve the full TK time-course
set.seed(1)
out <- calc_mc_tk(parameters=params,
vary.params = vary.params,
censored.params = censored.params,
return.samples = TRUE,
model = "pbtk",
suppress.messages = TRUE,
httkpop = FALSE,
invitrouv = FALSE,
samples = NSAMP,
solvemodel.arg.list = list(times = seq(0,0.5,0.025))
)
Make a table of concentration vs. time with confidence intervals:
zoxtable <- cbind(out[["means"]][,"time"],
out[["means"]][,"Cplasma"],
out[["means"]][,"Cplasma"] - 1.96*out[["sds"]][,"Cplasma"],
out[["means"]][,"Cplasma"] + 1.96*out[["sds"]][,"Cplasma"])
colnames(zoxtable) <- c("time","Cplasma","lcl","ucl")
knitr::kable(zoxtable, caption = "Zoxamide plasma concentration vs. time",
floating.environment="sidewaystable")
Plot Monte Carlo analysis of concentration vs. time:
zoxamide1 <- ggplot(as.data.frame(zoxtable), aes(x=time,y=Cplasma)) +
geom_line(color = "dark blue",size=2) +
geom_ribbon(aes(ymin=lcl, ymax=ucl), alpha = 0.3,
fill = "light blue", color="black", linetype="dotted")+
ylab("Plasma concentration") +
xlab("Time (days)") +
theme(axis.text = element_text(size = 16),
axis.title = element_text(size = 16))
print(zoxamide1)
Examine $C_{ss}$
out <- calc_mc_css(parameters=params,
vary.params = vary.params,
censored.params = censored.params,
return.samples = TRUE,
model = "pbtk",
suppress.messages = TRUE,
httkpop = FALSE,
samples = NSAMP,
invitrouv = FALSE)
zoxamide2 <- ggplot(as.data.frame(out), aes(out)) +
geom_histogram(fill = "blue", binwidth = 1/6) +
scale_x_log10() + ylab("Number of Samples") +
xlab(bquote(C[ss]~"("*mu*"M)")) +
theme(axis.text = element_text(size = 16),
axis.title = element_text(size = 16))
print(zoxamide2)
Adding a tissue
The httk package contains a data.frame called tissue.data that describes the
composition of various tissues in terms of the
Schmitt (2008)
mechanistic model for deriving tissue:plasma partition coefficients. Once described,
these tissues are available for use as compartments in new models or to be lumped
into the rest of body in existing models (using function "lump_tissues"). We can add
a new tissue (for example, mammary) to the tissue data by replicating the data
from another tissue and adjusting as appropriate.
new.tissue <- subset(tissue.data,Tissue == "adipose" & Species =="Human")
new.tissue[, "Tissue"] <- "mammary"
new.tissue[new.tissue$variable=="Vol (L/kg)","value"] <-
320/1000/60 # Itsukage et al. (2017) PMID: 29308107
new.tissue[new.tissue$variable %in% c('Flow (mL/min/kg^(3/4))'),'value'] <-
# We'll arbitrarily set flow to a tenth of total adipose:
new.tissue[new.tissue$variable %in% c('Flow (mL/min/kg^(3/4))'),'value']/10
tissue.data <- rbind(tissue.data, new.tissue)
knitr::kable(subset(tissue.data,Tissue=="mammary"),
caption = "Approximate Mamary Tissue Parameters",
floating.environment="sidewaystable",
row.names=FALSE,
digits=3)
If we thought this tissue had been included in the rest of body total
previously we could consider removing it from those volumes and flows, but
we won't do that here (Note eval=FALSE):
# If we thought this tissue was included in the rest of the bod
tissue.data[tissue.data$Tissue == "rest", 'value'] <-
tissue.data[tissue.data$Tissue == "rest", 'value'] -
new.tissue[new.tissue$variable %in% c(
'Vol (L/kg)',
'Flow (mL/min/kg^(3/4))'),
'value']
To generate the parameters for a model with kidneys, thyroid, brain,
breast, liver compartment combining the liver and gut, and a rest of body
compartment:
compartments <- list(liver = c("liver", "gut"), kidney = "kidney",
breast = "mammary", brain = "brain",
thyroid = "thyroid")
tissues.to.include <- unique(tissue.data$Tissue)
tissues.to.include <- tissues.to.include[!(tissues.to.include=="placenta")]
Kp <- predict_partitioning_schmitt(
chem.name = "Nicotine",
tissues = tissues.to.include,
suppress.messages = TRUE)
lumped.params <- lump_tissues(Kp, tissuelist=compartments)
knitr::kable(as.data.frame(lumped.params),
caption = "PCs, Volumes, and Flows for Lumped Tissues",
floating.environment="sidewaystable",
row.names=FALSE,
digits=3)
Adding a species
The httk package contains a data.frame called physiology.data that describes
the species-specific aspects of physiology necessary to parameterize a PBTK
model. We can add a new species (for example, wolverines) to the physiology.data by
replicating the data from another species and adjusting as appropriate.
new.species <- physiology.data[,"Rabbit"]
names(new.species) <- physiology.data[,"Parameter"]
rabbit.BW <- new.species["Average BW"]
new.species["Average BW"] <- 31.2 # Rausch and Pearson (1972) https://doi.org/10.2307/3799057
new.species["Average Body Temperature"] <- 38.5 # Thiel et al. (2019) https://doi.org/10.1186/s12983-019-0319-8
physiology.data <- cbind(physiology.data, new.species)
colnames(physiology.data)[length(colnames(physiology.data))] <- "Wolverine"
knitr::kable(physiology.data[,c("Parameter","Units","Wolverine")],
caption = "Approximate Wolverine Physiological Parameters",
floating.environment="sidewaystable",
row.names=FALSE,
digits=3)
The tissue volumes and flows are stored separately in tissue.data
new.tissue.data <- subset(tissue.data,Species=="Rabbit")
new.tissue.data$Species <- "Wolverine"
tissue.data <- rbind(tissue.data,new.tissue.data)
Now we can make predictions for wolverines!
calc_mc_css(chem.cas="80-05-7",species="wolverine",
parameterize.arg.list=list(default.to.human=TRUE),
suppress.messages=TRUE,
samples = NSAMP)
Export functions
Jarnac (Sauro and Fell 2000)
and SBML (Hucka et al. 2003) are commonly used languages for
systems biology models of cellular and physiological processes. In the event that a modeler
wishes to couple such a model to a toxicokinetic model, we provide functions to export
model equations and chemical-specific parameters to these languages. The two functions,
"export_pbtk_sbml" and "export_pbtk_jarnac", have the same arguments and only differ in
the file extension names (.xml and .jan) entered into the filename argument. Both use liters
as the units for volume, but the amounts are unitless and to be determined by the user. If
we suppose that we enter an initial amount of 1 mg in the gut lumen, then all the other
compartments will contain amounts in mg.
Below is a call of an export function for a dose
of 1 given to a rat:
export_pbtk_sbml(chem.name = "Bisphenol A", species = "Rat",
initial.amounts = list(Agutlumen = 1),
filename = "PBTKmodel.xml")
Days to steady state histogram
Creating histograms can allow us to visualize how a given value varies across
all the chemicals
contained within the package. To create a histogram using ggplot2 of the
number of days to
steady state, we must first set up a for loop with "get_cheminfo" and "calc_css"
to generate a
vector containing the data. Vectors containing the average and maximum concentrations at
steady state are also generated in this example, avg and max. The data contained
in the days
vector are then plotted as a histogram (Pearce et al., (2017) Figure 3). We can
just as easily create a histogram
containing the average or maximum steady state concentrations by substituting
avg or max
for days.
css.data <- data.frame()
chem.list <- get_cheminfo(model='pbtk', suppress.messages = TRUE)[seq(
1, NUM.CHEMS, SKIP.CHEMS)]
for (this.cas in chem.list) {
css.info <- calc_css(chem.cas = this.cas,
doses.per.day = 1,
suppress.messages = TRUE)
css.data[this.cas,"days"] <- css.info[["the.day"]]
css.data[this.cas,"avg"] <- css.info[["avg"]]
css.data[this.cas,"max"] <- css.info[["max"]]
}
hist <- ggplot(css.data, aes(days+0.1)) +
geom_histogram(fill = "blue", bins=5) +
scale_x_log10() + ylab("Number of Chemicals") + xlab("Days") +
theme(axis.text = element_text(size = 16),
axis.title = element_text(size = 16))
print(hist)
Average vs. maximum concentration
We can compare the average and maximum concentrations at steady state using the average
and maximum concentration at steady state vectors, avg and max, from the
previous example.
The vectors are bound into a data frame and plotted with a line through the
origin with a
slope of 1 (Pearce et al. (2017) Figure 4).
avg.vs.max <- ggplot(css.data, aes(avg, max)) +
geom_point() + geom_abline() +
scale_x_log10() + scale_y_log10() +
xlab(bquote("Avg. Conc. at Steady State ("*mu*"M)")) +
ylab(bquote("Max. Conc. at Steady State ("*mu*"M)")) +
theme(axis.text = element_text(size = 16),
axis.title = element_text(size = 16))
print(avg.vs.max)
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from "httk: R Package for High-Throughput Toxicokinetics"
Robert G Pearce, R Woodrow Setzer, Cory L Strope, Nisha S Sipes, and John F Wambaugh
Journal of Statistical Software 2017 Jul 17; 79(4): 1-26.
https://doi.org/10.18637%2Fjss.v079.i04
Please send questions to wambaugh.john@epa.gov
Abstract
Thousands of chemicals have been profiled by high-throughput screening programs such as ToxCast and Tox21; these chemicals are tested in part because most of them have limited or no data on hazard, exposure, or toxicokinetics. Toxicokinetic models aid in predicting tissue concentrations resulting from chemical exposure, and a "reverse dosimetry" approach can be used to predict exposure doses sufficient to cause tissue concentrations that have been identified as bioactive by high-throughput screening. We have created four toxicokinetic models within the R software package httk. These models are designed to be parameterized using high-throughput in vitro data (plasma protein binding and hepatic clearance), as well as structure-derived physicochemical properties and species-specific physiological data. The package contains tools for Monte Carlo sampling and reverse dosimetry along with functions for the analysis of concentration vs. time simulations. The package can currently use human in vitro data to make predictions for 553 chemicals in humans, rats, mice, dogs, and rabbits, including 94 pharmaceuticals and 415 ToxCast chemicals. For 67 of these chemicals, the package includes rat-specific in vitro data. This package is structured to be augmented with additional chemical data as they become available. Package httk enables the inclusion of toxicokinetics in the statistical analysis of chemicals undergoing high-throughput screening.
This vignette was created from the R replication code v79i04.R for the 2017 paper that introduced httk.
HTTK Version
The R replication code v79i04.R was created with httk v1.7. It was updated to a vignette using httk v2.2.2 in 2022. Although we attempt to maintain backward compatibility, if you encounter issues with the latest release of httk and cannot easily address the changes, historical versions of httk are available from: https://cran.r-project.org/src/contrib/Archive/httk/
Prepare R to run the vignette
R package knitr generates html and PDF documents from this RMarkdown file, Each bit of code that follows is known as a "chunk". We start by telling knitr how we want our chunks to look.
knitr::opts_chunk$set(collapse = TRUE, comment = '#>') options(rmarkdown.html_vignette.check_title = FALSE)
Clear the memory
It is a bad idea to let variables and other information from previous R sessions float around, so we first remove everything in the R memory.
rm(list=ls())
eval = execute.vignette
If you are using the RMarkdown version of this vignette (extension, .RMD) you will be able to see that several chunks of code in this vignette have the statement "eval = execute.vignette". The next chunk of code, by default, sets execute.vignette = TRUE. If execute.vignette = FALSE that would mean that the code is included (and necessary) but was not run when the vignette was built.
# Set whether or not the following chunks will be executed (run): execute.vignette <- TRUE
Load the relevant libraries
We use the command 'library()' to load various R packages for our analysis. If you get the message "Error in library(X) : there is no package called 'X'" then you will need to install that package:
From the R command prompt:
install.packages("X")
Or, if using RStudio, look for 'Install Packages' under 'Tools' tab.
library(ggplot2) library(httk)
Check what version of httk is installed:
packageVersion("httk")
Control run speed
To speed up how fast these examples run, we only simulate every $N^{th}$ chemical (currently 15) -- to get all chemicals with data set SKIP.CHEMS to 1:
NUM.CHEMS <- length(get_cheminfo(model="pbtk", suppress.messages = TRUE)) SKIP.CHEMS <- 25
Similarly, portions of this vignette use Monte Carlo sampling to simulate variability and propagate uncertainty. The more samples that are used, the more stable the results are (that is, the less likely they are to change if a different random sequence is used). However, the more samples that are used, the longer it takes to run. So, to speed up how fast these examples run, we specify here that we only want to use 25 samples, even though the actual httk default is 1000. Increase this number to get more stable (and accurate) results:
NSAMP <- 25
Examples
To get a list of parameters for the pbtk model of Triclosan in a rat:
parameters <- try(parameterize_pbtk(chem.name = "triclosan", species = "rat"))
We do not have a full set of in vitro parameters for rat for Triclosan, so we fill in the in vitro measured values with human-derived measurements and use rat physiological parameters by setting "default.to.human = TRUE":
parameters <- parameterize_pbtk(chem.name = "triclosan", species = "rat", default.to.human = TRUE)
To change the $f_{up}$ in the previous parameters list to 0.001 from the human value of 0.003044 and use it in a simulation of the PBTK model for a single dose of 1 mg/kg BW of Triclosan in a rat:
parameters["Funbound.plasma"] <- 0.001 out <- solve_pbtk(parameters = parameters, suppress.messages = TRUE)
Making a table
In the example below, setting model to "pbtk" in "get_cheminfo" removes the chemicals from the list with $f_{up}$ below the limit of detection which have been set to zero because the model uses partition coefficients that are calculated with $f_{up}$. However, we could include all chemicals that work with the models without partition coefficients by using the default option of "3compartmentss" or setting exclude.fup.zero to false, and $f_{up}$ would then automatically be set to 0.005.
First we make up a list of chemicals with both literature $C_{ss}$ values and HTTK data for making new $C_{ss}$ predictions:
chem.list <- intersect(get_cheminfo(model = "pbtk", suppress.messages = TRUE)[seq( 1, NUM.CHEMS, SKIP.CHEMS)], get_wetmore_cheminfo())
Then we initialize a NULL table and build it up one row at a time:
css.table <- NULL for (this.cas in chem.list) { ids <- get_chem_id(chem.cas=this.cas) this.row <- data.frame(Compound=ids$chem.name, DTXSID=ids$dtxsid, CAS=this.cas) this.row <- cbind(this.row, as.data.frame(calc_analytic_css(chem.cas = this.cas, model = "pbtk", output.units = "uM", suppress.messages=TRUE))) this.row <- cbind(this.row, as.data.frame(get_wetmore_css(chem.cas = this.cas, which.quantile = 0.50, output.units = "uM", suppress.messages=TRUE))) this.row <- cbind(this.row, as.data.frame(calc_mc_css(chem.cas = this.cas, which.quantile = 0.50, output.units = "uM", samples = NSAMP, suppress.messages=TRUE))) css.table <- rbind(css.table, this.row) } colnames(css.table) <- c("Compound","DTXSID","CAS", "PBTK", "Wetmore", "MC")
Now display the table and plot two columns against each other:
knitr::kable(css.table, caption = "Literature and HTTK Plasma Css", floating.environment="sidewaystable", row.names=FALSE, digits=3) litvshttkcss <- ggplot(css.table, aes(Wetmore, MC)) + geom_point() + geom_abline() + scale_x_log10() + scale_y_log10() + xlab(bquote("Literature"~C[ss]~"("*mu*"M)")) + ylab(bquote("HTTK"~C[ss]~"("*mu*"M)")) + theme(axis.text = element_text(size = 16), axis.title = element_text(size = 16)) print(litvshttkcss)
Plotting example
To see how $C_{ss}$ resulting from discrete dosing deviates from the average steady state concentration, we can make a plot with ggplot2 that includes a horizontal line through the $y$-axis at the predicted $C_{ss}$ for oral infusion dosing (Figure 2 in Pearce et al., 2017).
out <- solve_pbtk(chem.name = "Bisphenol A", days = 50, doses.per.day = 3, daily.dose=1, output.units = "uM") plot.data <- as.data.frame(out) css <- calc_analytic_css(chem.name = "Bisphenol A", output.units = "uM") c.vs.t <- ggplot(plot.data, aes(time, Cplasma)) + geom_line() + geom_hline(yintercept = css) + ylab(bquote("Plasma Concentration ("*mu*"M)")) + xlab("Day") + theme(axis.text = element_text(size = 16), axis.title = element_text(size = 16), plot.title = element_text(size = 17, hjust=0.5)) + ggtitle("Bisphenol A") print(c.vs.t)
Suppressing Messages
Note that since in vitro-in vivo extrapolation (IVIVE) is built upon many, many assumptions, httk* attempts to give many warning messages by default. These messages do not usually mean something is wrong, but are rather intended to make the user aware of the assumptions involved. However, they quickly grow annoying and can be turned off with the "suppress.messages=TRUE" argument. Proceed with caution...
out <- solve_pbtk(chem.name = "Bisphenol A", days = 50, doses.per.day = 3, daily.dose=1, output.units = "uM", suppress.messages = TRUE) css <- calc_analytic_css(chem.name = "Bisphenol A", output.units = "uM", suppress.messages = TRUE)
TK Study Summary Statistics
"calc_tk_stats" allows summary TK statistics to be calculated for a specific study design (including dose regiment, duration, and species). The following code calculates the peak plasma concentration for all chemicals in httk simulated for 10 days at 1 mg/kg BW/day with 3 doses per day. Note that the function "calc_stats" was renamed "calc_tk_stats" in a later release of httk.
all.peak.stats <- calc_stats(days = 10, doses.per.day = 3, stats = "peak")
The same function can be used for a single chemical. For example, the AUC, peak, and mean for a single 1 mg dose of Triclosan over 10 day:
triclosan.stats <- calc_stats(days = 10, chem.name = "triclosan")
Steady-state Plasma Concentration
Below are examples of two functions,comparing the medians of the Wetmore data in humans for 1 mg/kg BW/day of Bisphenol A with the "calc_mc_css" simulation with probability distributions containing a third of the standard deviation, half the limit of detection for $f_{up}$, and the same number of samples of the parameters used in Wetmore et al. (2012).
We use make use of the default Monte Carlo sampler by setting argument "httkpop=FALSE" to turn off httk-pop (Ring et al., 2017) and "invitrouv=FALSE" to turn off uncertainty/variability for the in vitro parameters (Wambaugh et al., 2019).
Note that the function "get_wetmore_css" was renamed "get_lit_css" in a later release of httk.
get_wetmore_css(chem.cas = "80-05-7", daily.dose = 1, which.quantile = 0.5, output.units = "uM") set.seed(654321) calc_mc_css(chem.cas = "80-05-7", daily.dose = 1, which.quantile = 0.5, censored.params = list( Funbound.plasma = list(cv = 0.1, lod = 0.005)), vary.params = list( BW = 0.15, Vliverc = 0.15, Qgfrc = 0.15, Qtotal.liverc = 0.15, million.cells.per.gliver = 0.15, Clint = 0.15), output.units = "uM", samples = NSAMP, httkpop=FALSE, invitrouv=FALSE, suppress.messages = TRUE)
Using more sophisticated Monte Carlo
httk uses Monte Carlo to simulate population variability and propagate parameter uncertainty. The algorithm for population variability, "httk-pop" (Ring et al., 2017) simulates population variability in TK by predicting distributions of physiological parameters based on distributions of demographic and biometric quantities from the National Health and Nutrition Examination Survey (NHANES), conducted by the U.S. Centers for Disease Control and Prevention (CDC). MEthods for propagating uncertainty in in vitro measurements were described by Wambaugh et al. (2019).
Both httk-pop and in vitro uncertainty/variability simulation, are on by default:
set.seed(654321) calc_mc_css(chem.cas = "80-05-7", daily.dose = 1, which.quantile = 0.5, output.units = "uM", samples = NSAMP, suppress.messages = TRUE)
Controlling the random number generator
Any of the Monte Carlo functions in httk, often indicated by the inclusion of "mc" in the function name, make use of random draws from distributions to simulate uncertainty and variability. The random number generator in any computer is actually a pseudo-random number generator that creates a sequence of nearly uncorrelated numbers, but that sequence can be recreated at any time if we set a random number generator "seed". In R we control the seed with the function "set.seed", which allows us to get the same Monte Carlo output again and again (and in many cases on different computers). The seed can take any value, and if you use the same seed followed by the same functions called in the same order with the same arguments, you will get the same answer again and again:
# Random number generator seed 1: set.seed(654321) calc_mc_css(chem.cas = "80-05-7", daily.dose = 1, which.quantile = 0.5, output.units = "uM", samples = NSAMP, suppress.messages = TRUE) # Continuing to draw random numbers without resetting the seed: calc_mc_css(chem.cas = "80-05-7", daily.dose = 1, which.quantile = 0.5, output.units = "uM", samples = NSAMP, suppress.messages = TRUE) # Random number generator seed 2: set.seed(123456) calc_mc_css(chem.cas = "80-05-7", daily.dose = 1, which.quantile = 0.5, output.units = "uM", samples = NSAMP, suppress.messages = TRUE) # Continuing to draw random numbers without resetting the seed: calc_mc_css(chem.cas = "80-05-7", daily.dose = 1, which.quantile = 0.5, output.units = "uM", samples = NSAMP, suppress.messages = TRUE) # Random number generator seed 2 gives the same answer as it did above: set.seed(123456) calc_mc_css(chem.cas = "80-05-7", daily.dose = 1, which.quantile = 0.5, output.units = "uM", samples = NSAMP, suppress.messages = TRUE) # Random number generator seed 1 gives the same answer as it did above: set.seed(654321) calc_mc_css(chem.cas = "80-05-7", daily.dose = 1, which.quantile = 0.5, output.units = "uM", samples = NSAMP, suppress.messages = TRUE)
IVIVE with HTTK
Simple "reverse dosimetry" in vitro-in vivo extrapolation (IVIVE) determines an administered equivalent dose (AED) by taking an in vitro concentration $C_{\text{in vitro}}$ (50 uM in the example below) and dividing it by the steady-state plasma concentration $C_{ss}$ produced by a dose rate of 1 mg/kg bw/day:
$$ AED = \frac{C_{\text{in vitro}}}{C_{ss}}$$
We can also calculate the AED using literature values or sampling with httk:
get_wetmore_oral_equiv(50, chem.cas = "80-05-7") set.seed(654321) calc_mc_oral_equiv(50, chem.cas = "80-05-7", samples = NSAMP)
Monte Carlo Simulation of $C_{ss}$
We can perform a Monte Carlo simulation on Zoxamide with the model pbtk with the same limit of detection and coefficients of variation (cv). Note, the function "monte_carlo" was replaced with a similar function "calc_mc_tk" for simulation concentration timecourses, while arguments were added to "calc_mc_css" that allowed the functionality seen in the 2017 paper. Separately, a new function "monte_carlo" was created to complement "httkpop_mc" and "invitro_mc" as part of "create_mc_samples". "monte_carlo" varies parameters according to a normal distribution with given mean and coefficient of variation or according to a censored distribution with an additional limit of detection parameter. Note that we again turn off httkpop and invitrouv to replicate the 2017 version of Monte Carlo.
First we create a list of parameters and then assign a coefficient of variation to each parameter we wish to vary:
vary.params <- NULL params <- parameterize_pbtk(chem.name = "Zoxamide") for (this.param in names(subset(params, names(params) != "Funbound.plasma"))) # Only want to vary numerical parameters: if (is.numeric(params[[this.param]])) vary.params[this.param] <- 0.2
We can draw $f_{up}$ from a censored distribution with a limit of dextion (LOD) of 0.01:
censored.params <- list(Funbound.plasma = list(cv = 0.2, lod = 0.01))
Solve the full TK time-course
set.seed(1) out <- calc_mc_tk(parameters=params, vary.params = vary.params, censored.params = censored.params, return.samples = TRUE, model = "pbtk", suppress.messages = TRUE, httkpop = FALSE, invitrouv = FALSE, samples = NSAMP, solvemodel.arg.list = list(times = seq(0,0.5,0.025)) )
Make a table of concentration vs. time with confidence intervals:
zoxtable <- cbind(out[["means"]][,"time"], out[["means"]][,"Cplasma"], out[["means"]][,"Cplasma"] - 1.96*out[["sds"]][,"Cplasma"], out[["means"]][,"Cplasma"] + 1.96*out[["sds"]][,"Cplasma"]) colnames(zoxtable) <- c("time","Cplasma","lcl","ucl") knitr::kable(zoxtable, caption = "Zoxamide plasma concentration vs. time", floating.environment="sidewaystable")
Plot Monte Carlo analysis of concentration vs. time:
zoxamide1 <- ggplot(as.data.frame(zoxtable), aes(x=time,y=Cplasma)) + geom_line(color = "dark blue",size=2) + geom_ribbon(aes(ymin=lcl, ymax=ucl), alpha = 0.3, fill = "light blue", color="black", linetype="dotted")+ ylab("Plasma concentration") + xlab("Time (days)") + theme(axis.text = element_text(size = 16), axis.title = element_text(size = 16)) print(zoxamide1)
Examine $C_{ss}$
out <- calc_mc_css(parameters=params, vary.params = vary.params, censored.params = censored.params, return.samples = TRUE, model = "pbtk", suppress.messages = TRUE, httkpop = FALSE, samples = NSAMP, invitrouv = FALSE) zoxamide2 <- ggplot(as.data.frame(out), aes(out)) + geom_histogram(fill = "blue", binwidth = 1/6) + scale_x_log10() + ylab("Number of Samples") + xlab(bquote(C[ss]~"("*mu*"M)")) + theme(axis.text = element_text(size = 16), axis.title = element_text(size = 16)) print(zoxamide2)
Adding a tissue
The httk package contains a data.frame called tissue.data that describes the composition of various tissues in terms of the Schmitt (2008) mechanistic model for deriving tissue:plasma partition coefficients. Once described, these tissues are available for use as compartments in new models or to be lumped into the rest of body in existing models (using function "lump_tissues"). We can add a new tissue (for example, mammary) to the tissue data by replicating the data from another tissue and adjusting as appropriate.
new.tissue <- subset(tissue.data,Tissue == "adipose" & Species =="Human") new.tissue[, "Tissue"] <- "mammary" new.tissue[new.tissue$variable=="Vol (L/kg)","value"] <- 320/1000/60 # Itsukage et al. (2017) PMID: 29308107 new.tissue[new.tissue$variable %in% c('Flow (mL/min/kg^(3/4))'),'value'] <- # We'll arbitrarily set flow to a tenth of total adipose: new.tissue[new.tissue$variable %in% c('Flow (mL/min/kg^(3/4))'),'value']/10 tissue.data <- rbind(tissue.data, new.tissue) knitr::kable(subset(tissue.data,Tissue=="mammary"), caption = "Approximate Mamary Tissue Parameters", floating.environment="sidewaystable", row.names=FALSE, digits=3)
If we thought this tissue had been included in the rest of body total previously we could consider removing it from those volumes and flows, but we won't do that here (Note eval=FALSE):
# If we thought this tissue was included in the rest of the bod tissue.data[tissue.data$Tissue == "rest", 'value'] <- tissue.data[tissue.data$Tissue == "rest", 'value'] - new.tissue[new.tissue$variable %in% c( 'Vol (L/kg)', 'Flow (mL/min/kg^(3/4))'), 'value']
To generate the parameters for a model with kidneys, thyroid, brain, breast, liver compartment combining the liver and gut, and a rest of body compartment:
compartments <- list(liver = c("liver", "gut"), kidney = "kidney", breast = "mammary", brain = "brain", thyroid = "thyroid") tissues.to.include <- unique(tissue.data$Tissue) tissues.to.include <- tissues.to.include[!(tissues.to.include=="placenta")] Kp <- predict_partitioning_schmitt( chem.name = "Nicotine", tissues = tissues.to.include, suppress.messages = TRUE) lumped.params <- lump_tissues(Kp, tissuelist=compartments) knitr::kable(as.data.frame(lumped.params), caption = "PCs, Volumes, and Flows for Lumped Tissues", floating.environment="sidewaystable", row.names=FALSE, digits=3)
Adding a species
The httk package contains a data.frame called physiology.data that describes the species-specific aspects of physiology necessary to parameterize a PBTK model. We can add a new species (for example, wolverines) to the physiology.data by replicating the data from another species and adjusting as appropriate.
new.species <- physiology.data[,"Rabbit"] names(new.species) <- physiology.data[,"Parameter"] rabbit.BW <- new.species["Average BW"] new.species["Average BW"] <- 31.2 # Rausch and Pearson (1972) https://doi.org/10.2307/3799057 new.species["Average Body Temperature"] <- 38.5 # Thiel et al. (2019) https://doi.org/10.1186/s12983-019-0319-8 physiology.data <- cbind(physiology.data, new.species) colnames(physiology.data)[length(colnames(physiology.data))] <- "Wolverine" knitr::kable(physiology.data[,c("Parameter","Units","Wolverine")], caption = "Approximate Wolverine Physiological Parameters", floating.environment="sidewaystable", row.names=FALSE, digits=3)
The tissue volumes and flows are stored separately in tissue.data
new.tissue.data <- subset(tissue.data,Species=="Rabbit") new.tissue.data$Species <- "Wolverine" tissue.data <- rbind(tissue.data,new.tissue.data)
Now we can make predictions for wolverines!
calc_mc_css(chem.cas="80-05-7",species="wolverine", parameterize.arg.list=list(default.to.human=TRUE), suppress.messages=TRUE, samples = NSAMP)
Export functions
Jarnac (Sauro and Fell 2000) and SBML (Hucka et al. 2003) are commonly used languages for systems biology models of cellular and physiological processes. In the event that a modeler wishes to couple such a model to a toxicokinetic model, we provide functions to export model equations and chemical-specific parameters to these languages. The two functions, "export_pbtk_sbml" and "export_pbtk_jarnac", have the same arguments and only differ in the file extension names (.xml and .jan) entered into the filename argument. Both use liters as the units for volume, but the amounts are unitless and to be determined by the user. If we suppose that we enter an initial amount of 1 mg in the gut lumen, then all the other compartments will contain amounts in mg.
Below is a call of an export function for a dose of 1 given to a rat:
export_pbtk_sbml(chem.name = "Bisphenol A", species = "Rat", initial.amounts = list(Agutlumen = 1), filename = "PBTKmodel.xml")
Days to steady state histogram
Creating histograms can allow us to visualize how a given value varies across all the chemicals contained within the package. To create a histogram using ggplot2 of the number of days to steady state, we must first set up a for loop with "get_cheminfo" and "calc_css" to generate a vector containing the data. Vectors containing the average and maximum concentrations at steady state are also generated in this example, avg and max. The data contained in the days vector are then plotted as a histogram (Pearce et al., (2017) Figure 3). We can just as easily create a histogram containing the average or maximum steady state concentrations by substituting avg or max for days.
css.data <- data.frame() chem.list <- get_cheminfo(model='pbtk', suppress.messages = TRUE)[seq( 1, NUM.CHEMS, SKIP.CHEMS)] for (this.cas in chem.list) { css.info <- calc_css(chem.cas = this.cas, doses.per.day = 1, suppress.messages = TRUE) css.data[this.cas,"days"] <- css.info[["the.day"]] css.data[this.cas,"avg"] <- css.info[["avg"]] css.data[this.cas,"max"] <- css.info[["max"]] } hist <- ggplot(css.data, aes(days+0.1)) + geom_histogram(fill = "blue", bins=5) + scale_x_log10() + ylab("Number of Chemicals") + xlab("Days") + theme(axis.text = element_text(size = 16), axis.title = element_text(size = 16)) print(hist)
Average vs. maximum concentration
We can compare the average and maximum concentrations at steady state using the average and maximum concentration at steady state vectors, avg and max, from the previous example. The vectors are bound into a data frame and plotted with a line through the origin with a slope of 1 (Pearce et al. (2017) Figure 4).
avg.vs.max <- ggplot(css.data, aes(avg, max)) + geom_point() + geom_abline() + scale_x_log10() + scale_y_log10() + xlab(bquote("Avg. Conc. at Steady State ("*mu*"M)")) + ylab(bquote("Max. Conc. at Steady State ("*mu*"M)")) + theme(axis.text = element_text(size = 16), axis.title = element_text(size = 16)) print(avg.vs.max)
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