---
title: "Pearce et al. (2017): Updated v79i04.R Examples"
author: "Robert G Pearce, R Woodrow Setzer, Cory L Strope, Nisha S Sipes, and John F Wambaugh"
date: "`r Sys.Date()`"
output: rmarkdown::html_vignette
vignette: >
  %\VignetteIndexEntry{a) Pearce (2017): HTTK Basics}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---
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](https://www.jstatsoft.org/index.php/jss/article/view/v079i04/3500) 
for the 
[2017 paper that introduced **httk**](https://doi.org/10.18637%2Fjss.v079.i04).

## HTTK Version

The 
[R replication code v79i04.R](https://www.jstatsoft.org/index.php/jss/article/view/v079i04/3500) 
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.
```{r configure_knitr, eval = TRUE}
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.
```{r clear_memory, eval = TRUE}
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.
```{r runchunks, eval = TRUE}
# 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.
```{r load_packages, eval = execute.vignette}
library(ggplot2)
library(httk)
```

Check what version of **httk** is installed:

```{r version_check, eval = execute.vignette}
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:
```{r chemical_thining, eval = execute.vignette}
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:
```{r MC_samples, eval = execute.vignette}
NSAMP <- 25
```

# Examples
To get a list of parameters for the pbtk model of Triclosan in a rat:
```{r rat_pbtk_parameters, eval = execute.vignette}
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":
```{r rat_pbtk_parameters2, eval = execute.vignette}
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:
```{r use)pbtk_parameters, eval = execute.vignette}
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:
```{r select_Chemicals, eval = execute.vignette}
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:
```{r make_Css_table, eval = execute.vignette}
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:
```{r display_Css_table, eval = execute.vignette}
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).
```{r plot_examples, eval = execute.vignette}
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...

```{r suppress_messages, eval = execute.vignette}
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**.
```{r stats_example1, eval = FALSE}
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:
```{r stats_example2, eval = execute.vignette}
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)](https://doi.org/10.1093/toxsci/kfr254). 

We use make use of the default
Monte Carlo sampler by setting argument "httkpop=FALSE" to turn off
httk-pop ([Ring et al., 2017](https://doi.org/10.1016/j.envint.2017.06.004)) and 
"invitrouv=FALSE" to turn off uncertainty/variability
for the *in vitro* parameters ([Wambaugh et al., 2019](https://doi.org/10.1093/toxsci/kfz205)). 

Note that the function "get_wetmore_css" was renamed "get_lit_css" in a later release
of **httk**.
```{r css_examples, eval = execute.vignette}
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)](https://doi.org/10.1016/j.envint.2017.06.004) 
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)](https://doi.org/10.1093/toxsci/kfz205).

Both httk-pop and *in vitro* uncertainty/variability simulation, are on by default:
```{r css_examples2, eval = execute.vignette}
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:
```{r set_seed_example, eval = execute.vignette}
# 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**:
```{r literature_oral_equivalent_example, eval = execute.vignette}
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:
```{r monte_carlo_css_example_1, eval = execute.vignette}
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:
```{r monte_carlo_css_example_2, eval = execute.vignette}
censored.params <- list(Funbound.plasma = list(cv = 0.2, lod = 0.01))
```
### Solve the full TK time-course
```{r monte_carlo_css_example_3, eval = execute.vignette}
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:
```{r monte_carlo_css_example_4, eval = execute.vignette}
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:
```{r monte_carlo_css_example_5, eval = execute.vignette}
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 $C_{ss}$
```{r monte_carlo_css_example_6, eval = execute.vignette}
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)](https://doi.org/10.1016/j.tiv.2007.09.010) 
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.
```{r add_a_tissue, eval = execute.vignette}
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$variable %in% c('Flow (mL/min/kg^(3/4))'),'value']/10
tissue.data <- rbind(tissue.data, new.tissue)
knitr::kable(subset(tissue.data,Tissue=="mammary"), 
             caption = "Approximate Mamary Tissue Parameters", 
             floating.environment="sidewaystable",
             row.names=FALSE,
             digits=3)
```
If we thought this tissue had been included in the rest of body total
previously we could consider removing it from those volumes and flows, but
we won't do that here (Note eval=FALSE):
```{r add_a_tissue2, eval = FALSE}
# If we thought this tissue was included in the rest of the bod
tissue.data[tissue.data$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:
```{r add_a_tissue3, eval = execute.vignette}
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.

```{r add_a_species1, eval = execute.vignette}
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
```{r add_a_species2, eval = execute.vignette}
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!
```{r add_a_species3, eval = execute.vignette}
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)](http://academic.sun.ac.za/natural/biochem/btk/book/Sauro.pdf) 
and SBML [(Hucka et al. 2003)](https://doi.org/10.1093/bioinformatics/btg015) 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:

```{r export, eval = FALSE}
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.

```{r figure3, eval = execute.vignette}
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).


```{r figure4, eval = execute.vignette}
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)
```
