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"))
#> Error in check_model(chem.cas = chem.cas, chem.name = chem.name, dtxsid = dtxsid, :
#> Chemical CAS: 3380-34-5, DTXSID: DTXSID5032498, named: triclosan has insufficient parameters for model pbtk. Try setting default.to.human=TRUE. See also help(get_cheminfo)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)
#> Warning in apply_clint_adjustment(Clint.point, Fu_hep = Fu_hep,
#> suppress.messages = suppress.messages): Clint adjusted for in vitro
#> partitioning (Kilford, 2008), see calc_hep_fu.
#> Warning in calc_ma(chem.cas = chem.cas, chem.name = chem.name, dtxsid = dtxsid,
#> : Membrane affintity (MA) predicted with method of Yun and Edginton (2013), see
#> calc_ma.
#> Warning in get_fup(dtxsid = dtxsid, chem.name = chem.name, chem.cas = chem.cas,
#> : Fraction unbound below limit of detection for rat replaced with human value.
#> Warning in get_fup(dtxsid = dtxsid, chem.name = chem.name, chem.cas = chem.cas,
#> : Fraction unbound is provided as a distribution.
#> Warning in apply_fup_adjustment(fup.point, fup.correction = fup.adjustment, :
#> Fup adjusted for in vivo lipid partitioning (Pearce, 2017), see
#> calc_fup_correction.
#> Warning in available_rblood2plasma(chem.cas = chem.cas, species = species, :
#> Human in vivo measured Rblood2plasma substituted.
#> Warning in get_caco2(chem.cas = chem.cas, chem.name = chem.name, dtxsid =
#> dtxsid, : Default value of 1.6 used for Caco2 permeability.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())
#> Warning in get_wetmore_cheminfo(): Function "get_wetmore_cheminfo" has been
#> renamed to "get_lit_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)
}
#> Warning in (function (chem.name = NULL, chem.cas = NULL, dtxsid = NULL, :
#> calc_analytic_css deprecated argument daily.dose replaced with new argument
#> dose, value given assigned to dose
#> Warning in (function (chem.name = NULL, chem.cas = NULL, dtxsid = NULL, :
#> calc_analytic_css deprecated argument daily.dose replaced with new argument
#> dose, value given assigned to dose
#> Warning in (function (chem.name = NULL, chem.cas = NULL, dtxsid = NULL, :
#> calc_analytic_css deprecated argument daily.dose replaced with new argument
#> dose, value given assigned to dose
#> Warning in (function (chem.name = NULL, chem.cas = NULL, dtxsid = NULL, :
#> calc_analytic_css deprecated argument daily.dose replaced with new argument
#> dose, value given assigned to dose
#> Warning in (function (chem.name = NULL, chem.cas = NULL, dtxsid = NULL, :
#> calc_analytic_css deprecated argument daily.dose replaced with new argument
#> dose, value given assigned to dose
#> Warning in (function (chem.name = NULL, chem.cas = NULL, dtxsid = NULL, :
#> calc_analytic_css deprecated argument daily.dose replaced with new argument
#> dose, value given assigned to dose
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)| Compound | DTXSID | CAS | PBTK | Wetmore | MC |
|---|---|---|---|---|---|
| 2,4-d | DTXSID0020442 | 94-75-7 | 40.550 | 43.320 | 56.530 |
| Diethyltoluamide | DTXSID2021995 | 134-62-3 | 0.958 | 0.847 | 2.445 |
| Isoxaben | DTXSID8024159 | 82558-50-7 | 0.962 | 24.460 | 1.234 |
| Rotenone | DTXSID6021248 | 83-79-4 | 2.232 | 1.833 | 3.170 |
| Genistein | DTXSID5022308 | 446-72-0 | 1.109 | 0.310 | 1.844 |
| Coumarin | DTXSID7020348 | 91-64-5 | 0.430 | 0.424 | 17.780 |
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")
#> Warning in get_clint(dtxsid = dtxsid, chem.name = chem.name, chem.cas =
#> chem.cas, : Clint is provided as a distribution.
#> Warning in apply_clint_adjustment(Clint.point, Fu_hep = Fu_hep,
#> suppress.messages = suppress.messages): Clint adjusted for in vitro
#> partitioning (Kilford, 2008), see calc_hep_fu.
#> Warning in get_fup(dtxsid = dtxsid, chem.name = chem.name, chem.cas = chem.cas,
#> : Fraction unbound is provided as a distribution.
#> Warning in apply_fup_adjustment(fup.point, fup.correction = fup.adjustment, :
#> Fup adjusted for in vivo lipid partitioning (Pearce, 2017), see
#> calc_fup_correction.
#> Warning in available_rblood2plasma(chem.cas = chem.cas, species = species, :
#> Human in vivo measured Rblood2plasma used.
#> Warning in get_caco2(chem.cas = chem.cas, chem.name = chem.name, dtxsid =
#> dtxsid, : Default value of 1.6 used for Caco2 permeability.
#> None of the monitored components undergo unit conversions (i.e. conversion factor of 1).
#>
#> AUC is area under the plasma concentration curve in uM*days units with Rblood2plasma = 0.795.
#> The model outputs are provided in the following units:
#> umol: Agutlumen, Atubules, Ametabolized
#> uM: Cgut, Cliver, Cven, Clung, Cart, Crest, Ckidney, Cplasma
#> uM*days: AUC
plot.data <- as.data.frame(out)
css <- calc_analytic_css(chem.name = "Bisphenol A",
output.units = "uM")
#> Warning in get_clint(dtxsid = dtxsid, chem.name = chem.name, chem.cas =
#> chem.cas, : Clint is provided as a distribution.
#> Warning in apply_clint_adjustment(Clint.point, Fu_hep = Fu_hep,
#> suppress.messages = suppress.messages): Clint adjusted for in vitro
#> partitioning (Kilford, 2008), see calc_hep_fu.
#> Warning in get_fup(dtxsid = dtxsid, chem.name = chem.name, chem.cas = chem.cas,
#> : Fraction unbound is provided as a distribution.
#> Warning in apply_fup_adjustment(fup.point, fup.correction = fup.adjustment, :
#> Fup adjusted for in vivo lipid partitioning (Pearce, 2017), see
#> calc_fup_correction.
#> Warning in available_rblood2plasma(chem.cas = chem.cas, species = species, :
#> Human in vivo measured Rblood2plasma used.
#> Warning in get_caco2(chem.cas = chem.cas, chem.name = chem.name, dtxsid =
#> dtxsid, : Default value of 1.6 used for Caco2 permeability.
#> Plasma concentration returned in uM units.
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")
#> Warning in calc_stats(days = 10, chem.name = "triclosan"): Function
#> "calc_stats" has been renamed to "calc_tkstats".
#> Human plasma concentrations returned in uM units.
#> AUC is area under plasma concentration curve in uM * days units with Rblood2plasma = 0.6436 .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")
#> Warning in get_wetmore_css(chem.cas = "80-05-7", daily.dose = 1, which.quantile
#> = 0.5, : Function "get_wetmore_css" has been renamed to "get_lit_cheminfo".
#> Human plasma concentrations returned in uM units.
#> Retrieving Css from literature based on 1 uM intrinsic clearance data for the 0.5 quantile in Human.
#> [1] 0.8569
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)
#> Warning in (function (chem.name = NULL, chem.cas = NULL, dtxsid = NULL, :
#> calc_analytic_css deprecated argument daily.dose replaced with new argument
#> dose, value given assigned to dose
#> 50%
#> 0.8689Using 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)
#> Warning in (function (chem.name = NULL, chem.cas = NULL, dtxsid = NULL, :
#> calc_analytic_css deprecated argument daily.dose replaced with new argument
#> dose, value given assigned to dose
#> 50%
#> 2.342Controlling 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)
#> Warning in (function (chem.name = NULL, chem.cas = NULL, dtxsid = NULL, :
#> calc_analytic_css deprecated argument daily.dose replaced with new argument
#> dose, value given assigned to dose
#> 50%
#> 2.342
# 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)
#> Warning in (function (chem.name = NULL, chem.cas = NULL, dtxsid = NULL, :
#> calc_analytic_css deprecated argument daily.dose replaced with new argument
#> dose, value given assigned to dose
#> 50%
#> 2.202
# 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)
#> Warning in (function (chem.name = NULL, chem.cas = NULL, dtxsid = NULL, :
#> calc_analytic_css deprecated argument daily.dose replaced with new argument
#> dose, value given assigned to dose
#> 50%
#> 2.108
# 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)
#> Warning in (function (chem.name = NULL, chem.cas = NULL, dtxsid = NULL, :
#> calc_analytic_css deprecated argument daily.dose replaced with new argument
#> dose, value given assigned to dose
#> 50%
#> 1.034
# 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)
#> Warning in (function (chem.name = NULL, chem.cas = NULL, dtxsid = NULL, :
#> calc_analytic_css deprecated argument daily.dose replaced with new argument
#> dose, value given assigned to dose
#> 50%
#> 2.108
# 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)
#> Warning in (function (chem.name = NULL, chem.cas = NULL, dtxsid = NULL, :
#> calc_analytic_css deprecated argument daily.dose replaced with new argument
#> dose, value given assigned to dose
#> 50%
#> 2.342IVIVE 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")
#> Warning in get_wetmore_oral_equiv(50, chem.cas = "80-05-7"): Function
#> "get_wetmore_oral_equiv" has been renamed to "get_lit_oral_equiv".
#> Retrieving Css from literature based on 10 uM intrinsic clearance data for the 0.95 quantile in Human.
#> Human uM concentration converted to mg/kg bw/day dose.
#> [1] 37.06
set.seed(654321)
calc_mc_oral_equiv(50, chem.cas = "80-05-7", samples = NSAMP)
#> Warning in get_clint(dtxsid = dtxsid, chem.name = chem.name, chem.cas =
#> chem.cas, : Clint is provided as a distribution.
#> Warning in get_fup(dtxsid = dtxsid, chem.name = chem.name, chem.cas = chem.cas,
#> : Fraction unbound is provided as a distribution.
#> Warning in get_caco2(chem.cas = chem.cas, chem.name = chem.name, dtxsid =
#> dtxsid, : Default value of 1.6 used for Caco2 permeability.
#> Warning in (function (chem.name = NULL, chem.cas = NULL, dtxsid = NULL, :
#> calc_analytic_css deprecated argument daily.dose replaced with new argument
#> dose, value given assigned to dose
#> Human plasma concentration returned in uM units for 0.95 quantile.
#> uM concentration converted to mgpkgpday dose for 0.95 quantile.
#> 95%
#> 9.713Monte 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")
#> Warning in apply_clint_adjustment(Clint.point, Fu_hep = Fu_hep,
#> suppress.messages = suppress.messages): Clint adjusted for in vitro
#> partitioning (Kilford, 2008), see calc_hep_fu.
#> Warning in calc_ma(chem.cas = chem.cas, chem.name = chem.name, dtxsid = dtxsid,
#> : Membrane affintity (MA) predicted with method of Yun and Edginton (2013), see
#> calc_ma.
#> Warning in apply_fup_adjustment(fup.point, fup.correction = fup.adjustment, :
#> Fup adjusted for in vivo lipid partitioning (Pearce, 2017), see
#> calc_fup_correction.
#> Warning in available_rblood2plasma(chem.cas = chem.cas, species = species, :
#> Human in vivo measured Rblood2plasma used.
#> Warning in get_caco2(chem.cas = chem.cas, chem.name = chem.name, dtxsid =
#> dtxsid, : Default value of 1.6 used for Caco2 permeability.
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] <- 0.2We 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")| time | Cplasma | lcl | ucl |
|---|---|---|---|
| 0.0000 | 0.0000000 | 0.0000000 | 0.0000000 |
| 0.0001 | 0.0000137 | 0.0000074 | 0.0000200 |
| 0.0250 | 0.4607000 | 0.3590348 | 0.5623652 |
| 0.0500 | 0.5514000 | 0.4394252 | 0.6633748 |
| 0.0750 | 0.5804000 | 0.4646228 | 0.6961772 |
| 0.1000 | 0.5972000 | 0.4789532 | 0.7154468 |
| 0.1250 | 0.6098000 | 0.4897108 | 0.7298892 |
| 0.1500 | 0.6198000 | 0.4982800 | 0.7413200 |
| 0.1750 | 0.6281000 | 0.5054040 | 0.7507960 |
| 0.2000 | 0.6350000 | 0.5111868 | 0.7588132 |
| 0.2250 | 0.6406000 | 0.5160028 | 0.7651972 |
| 0.2500 | 0.6453000 | 0.5199188 | 0.7706812 |
| 0.2750 | 0.6492000 | 0.5231720 | 0.7752280 |
| 0.3000 | 0.6525000 | 0.5258840 | 0.7791160 |
| 0.3250 | 0.6552000 | 0.5280548 | 0.7823452 |
| 0.3500 | 0.6573000 | 0.5298412 | 0.7847588 |
| 0.3750 | 0.6592000 | 0.5313492 | 0.7870508 |
| 0.4000 | 0.6607000 | 0.5325160 | 0.7888840 |
| 0.4250 | 0.6620000 | 0.5335612 | 0.7904388 |
| 0.4500 | 0.6630000 | 0.5343652 | 0.7916348 |
| 0.4750 | 0.6638000 | 0.5349692 | 0.7926308 |
| 0.5000 | 0.6645000 | 0.5355320 | 0.7934680 |
Plot Monte Carlo analysis of concentration vs. time:
zoxamide1 <- ggplot(as.data.frame(zoxtable), aes(x=time,y=Cplasma)) +
geom_line(color = "dark blue",linewidth=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)
#> Warning in (function (chem.name = NULL, chem.cas = NULL, dtxsid = NULL, :
#> calc_analytic_css deprecated argument daily.dose replaced with new argument
#> dose, value given assigned to dose
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$variable %in% c('Flow (mL/min/kg^(3/4))'),'value']/10
tissue.data <- rbind(tissue.data, new.tissue)
knitr::kable(subset(tissue.data,Tissue=="mammary"),
caption = "Approximate Mamary Tissue Parameters",
floating.environment="sidewaystable",
row.names=FALSE,
digits=3)| Tissue | Species | Reference | variable | value |
|---|---|---|---|---|
| mammary | Human | Schmitt 2008 | Fcell | 0.860 |
| mammary | Human | Schmitt 2008 | Fint | 0.140 |
| mammary | Human | Schmitt 2008 | FWc | 0.020 |
| mammary | Human | Schmitt 2008 | FLc | 0.934 |
| mammary | Human | Schmitt 2008 | FPc | 0.046 |
| mammary | Human | Schmitt 2008 | Fn_Lc | 0.936 |
| mammary | Human | Schmitt 2008 | Fn_PLc | 0.056 |
| mammary | Human | Schmitt 2008 | Fa_PLc | 0.008 |
| mammary | Human | Schmitt 2008 | pH | 7.100 |
| mammary | Human | EPA, Physiological Parameters Database for PBPK Modeling | Density (g/cm^3) | 0.916 |
| mammary | Human | ILSI-RSI 1994 | Vol (L/kg) | 0.005 |
| mammary | Human | Davies and Morris 1993 | Flow (mL/min/kg^(3/4)) | 1.074 |
If we thought this tissue had been included in the rest of body total previously we could consider removing it from those volumes and flows, but we won’t do that here (Note eval=FALSE):
# If we thought this tissue was included in the rest of the bod
tissue.data[tissue.data$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)| Krbc2pu | Kliver2pu | Kkidney2pu | Kbreast2pu | Kbrain2pu | Kthyroid2pu | Krest2pu | Vliverc | Vkidneyc | Vbreastc | Vbrainc | Vthyroidc | Vrestc | Qtotal.liverf | Qkidneyf | Qbreastf | Qbrainf | Qthyroidf | Qrestf | Qgutf |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0.802 | 4.749 | 5.149 | 11.61 | 1.451 | 1.448 | 1.916 | 0.04 | 0.004 | 0.005 | 0.019 | 0 | 0.764 | 0.464 | 0.221 | 0.005 | 0.125 | 0.016 | 0.376 | 0.205 |
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)| Parameter | Units | Wolverine |
|---|---|---|
| Total Body Water | ml/kg | 716.000 |
| Plasma Volume | ml/kg | 44.000 |
| Cardiac Output | ml/min/kg^(3/4) | 212.000 |
| Average BW | kg | 31.200 |
| Total Plasma Protein | g/ml | 0.057 |
| Plasma albumin | g/ml | 0.039 |
| Plasma a-1-AGP | g/ml | 0.001 |
| Hematocrit | fraction | 0.360 |
| Urine | ml/min/kg^(3/4) | 0.042 |
| Bile | ml/min/kg^(3/4) | 0.083 |
| GFR | ml/min/kg^(3/4) | 3.120 |
| Average Body Temperature | C | 38.500 |
| Plasma Effective Neutral Lipid Volume Fraction | unitless | 0.002 |
| Plasma Protein Volume Fraction | unitless | 0.057 |
| Pulmonary Ventilation Rate | l/h/kg^(3/4) | 24.750 |
| Alveolar Dead Space Fraction | unitless | 0.330 |
| Small Intestine Mean Residence Time | min | NA |
| Small Intestine Radius | cm | NA |
The tissue volumes and flows are stored separately in tissue.data. Physiological parameters are in the table physiology.data.
new.tissue.data <- subset(tissue.data,Species=="Rabbit")
new.tissue.data$Species <- "Wolverine"
tissue.data <- rbind(tissue.data,new.tissue.data)
new.physiology.data <- physiology.data[,"Rabbit"]
physiology.data <- rbind(physiology.data, new.physiology.data)
#> Warning in rbind(deparse.level, ...): number of columns of result, 9, is not a
#> multiple of vector length 18 of arg 2
colnames(physiology.data)[length(colnames(physiology.data))] <- "Wolverine"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)
#> Warning in (function (chem.cas = NULL, chem.name = NULL, dtxsid = NULL, : httkpop model only available for human and thus not used.
#>
#> Set species="Human" to run httkpop model.
#> Warning in (function (chem.name = NULL, chem.cas = NULL, dtxsid = NULL, :
#> calc_analytic_css deprecated argument daily.dose replaced with new argument
#> dose, value given assigned to dose
#> 95%
#> 0.5492Export 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,
model="pbtk",
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"]]
}
#> Warning in min(out[which(out[, target]/max(out[, target]) == 1), "time"]): no
#> non-missing arguments to min; returning Inf
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)
#> Warning: Removed 1 row containing non-finite outside the scale range
#> (`stat_bin()`).
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)
#> Warning in scale_x_log10(): log-10 transformation introduced infinite values.
#> Warning in scale_y_log10(): log-10 transformation introduced infinite values.