# Solve_PBTK This function solves for the amounts or concentrations in uM of a chemical in different tissues as functions of time based on the dose and dosing frequency. In this PBTK formulation. $C_{tissue}$ is the concentration in tissue at time t. Since the perfusion limited partition coefficients describe instantaneous equilibrium between the tissue and the free fraction in plasma, the whole plasma concentration is $C_{tissue,plasma} = \frac{1}{f_{up}*K_{tissue2fup}}*C_{tissue}$. Note that we use a single, constant value of $f_{up}$ across all tissues. Correspondingly the free plasma concentration is modeled as $C_{tissue,free plasma} = \frac{1}{K_{tissue2fup}}*C_tissue$. The amount of blood flowing from tissue x is $Q_{tissue}$ (L/h) at a concentration $C_{x,blood} = \frac{R_{b2p}}{f_{up}*K_{tissue2fup}}*C_{tissue}$, where we use a single $R_{b2p}$ value throughout the body. Metabolic clearance is modeled as being from the total plasma concentration here, though it is restricted to the free fraction in `calc_hep_clearance` by default. Renal clearance via glomerular filtration is from the free plasma concentration. The compartments used in this model are the gutlumen, gut, liver, kidneys, veins, arteries, lungs, and the rest of the body. The extra compartments include the amounts or concentrations metabolized by the liver and excreted by the kidneys through the tubules. AUC is the area under the curve of the plasma concentration. ```r solve_pbtk( chem.name = NULL, chem.cas = NULL, dtxsid = NULL, times = NULL, parameters = NULL, days = 10, tsteps = 4, daily.dose = NULL, dose = NULL, doses.per.day = NULL, initial.values = NULL, plots = FALSE, suppress.messages = FALSE, species = "Human", iv.dose = FALSE, input.units = "mg/kg", output.units = NULL, default.to.human = FALSE, class.exclude = TRUE, physchem.exclude = TRUE, recalc.blood2plasma = FALSE, recalc.clearance = FALSE, dosing.matrix = NULL, adjusted.Funbound.plasma = TRUE, regression = TRUE, restrictive.clearance = TRUE, minimum.Funbound.plasma = 1e-04, Caco2.options = list(), monitor.vars = NULL, ... ) ``` ## Arguments - `chem.name`: Either the chemical name, CAS number, or the parameters must be specified. - `chem.cas`: Either the chemical name, CAS number, or the parameters must be specified. - `dtxsid`: EPA's DSSTox Structure ID ([https://comptox.epa.gov/dashboard](https://comptox.epa.gov/dashboard)) the chemical must be identified by either CAS, name, or DTXSIDs - `times`: Optional time sequence for specified number of days. Dosing sequence begins at the beginning of times. - `parameters`: Chemical parameters from parameterize_pbtk function, overrides chem.name and chem.cas. - `days`: Length of the simulation. - `tsteps`: The number of time steps per hour. - `daily.dose`: Total daily dose, defaults to mg/kg BW. - `dose`: Amount of a single, initial oral dose in mg/kg BW. - `doses.per.day`: Number of doses per day. - `initial.values`: Vector containing the initial concentrations or amounts of the chemical in specified tissues with units corresponding to output.units. Defaults are zero. - `plots`: Plots all outputs if true. - `suppress.messages`: Whether or not the output message is suppressed. - `species`: Species desired (either "Rat", "Rabbit", "Dog", "Mouse", or default "Human"). - `iv.dose`: Simulates a single i.v. dose if true. - `input.units`: Input units of interest assigned to dosing, defaults to mg/kg BW - `output.units`: A named vector of output units expected for the model results. Default, NULL, returns model results in units specified in the 'modelinfo' file. See table below for details. - `default.to.human`: Substitutes missing animal values with human values if true (hepatic intrinsic clearance or fraction of unbound plasma). - `class.exclude`: Exclude chemical classes identified as outside of domain of applicability by relevant modelinfo_[MODEL] file (default TRUE). - `physchem.exclude`: Exclude chemicals on the basis of physico-chemical properties (currently only Henry's law constant) as specified by the relevant modelinfo_[MODEL] file (default TRUE). - `recalc.blood2plasma`: Recalculates the ratio of the amount of chemical in the blood to plasma using the input parameters, calculated with hematocrit, Funbound.plasma, and Krbc2pu. - `recalc.clearance`: Recalculates the the hepatic clearance (Clmetabolism) with new million.cells.per.gliver parameter. - `dosing.matrix`: Vector of dosing times or a matrix consisting of two columns or rows named "dose" and "time" containing the time and amount, in mg/kg BW, of each dose. - `adjusted.Funbound.plasma`: Uses adjusted Funbound.plasma when set to TRUE along with partition coefficients calculated with this value. - `regression`: Whether or not to use the regressions in calculating partition coefficients. - `restrictive.clearance`: Protein binding not taken into account (set to 1) in liver clearance if FALSE. - `minimum.Funbound.plasma`: Monte Carlo draws less than this value are set equal to this value (default is 0.0001 -- half the lowest measured Fup in our dataset). - `Caco2.options`: A list of options to use when working with Caco2 apical to basolateral data `Caco2.Pab`, default is Caco2.options = list(Caco2.Pab.default = 1.6, Caco2.Fabs = TRUE, Caco2.Fgut = TRUE, overwrite.invivo = FALSE, keepit100 = FALSE). Caco2.Pab.default sets the default value for Caco2.Pab if Caco2.Pab is unavailable. Caco2.Fabs = TRUE uses Caco2.Pab to calculate fabs.oral, otherwise fabs.oral = `Fabs`. Caco2.Fgut = TRUE uses Caco2.Pab to calculate fgut.oral, otherwise fgut.oral = `Fgut`. overwrite.invivo = TRUE overwrites Fabs and Fgut in vivo values from literature with Caco2 derived values if available. keepit100 = TRUE overwrites Fabs and Fgut with 1 (i.e. 100 percent) regardless of other settings. See `get_fbio` for further details. - `monitor.vars`: Which variables are returned as a function of time. The default value of NULL provides "Cgut", "Cliver", "Cven", "Clung", "Cart", "Crest", "Ckidney", "Cplasma", "Atubules", "Ametabolized", and "AUC" - `...`: Additional arguments passed to the integrator (`ode`). ## Returns A matrix of class deSolve with a column for time(in days), each compartment, the area under the curve, and plasma concentration and a row for each time point. ## Details Note that the model parameters have units of hours while the model output is in days. Default NULL value for doses.per.day solves for a single dose. Model Figure When species is specified as rabbit, dog, or mouse, the function uses the appropriate physiological data(volumes and flows) but substitutes human fraction unbound, partition coefficients, and intrinsic hepatic clearance. Because this model does not simulate exhalation, inhalation, and other processes relevant to volatile chemicals, this model is by default restricted to chemicals with a logHenry's Law Constant less than that of Acetone, a known volatile chemical. That is, chemicals with logHLC > -4.5 (Log10 atm-m3/mole) are excluded. Volatility is not purely determined by the Henry's Law Constant, therefore this chemical exclusion may be turned off with the argument "physchem.exclude = FALSE". Similarly, per- and polyfluoroalkyl substances (PFAS) are excluded by default because the transporters that often drive PFAS toxicokinetics are not included in this model. However, PFAS chemicals can be included with the argument "class.exclude = FALSE". ## Examples ```r # Multiple doses per day: head(solve_pbtk( chem.name='Bisphenol-A', daily.dose=.5, days=2.5, doses.per.day=2, tsteps=2)) # Starting with an initial concentration: out <- solve_pbtk( chem.name='bisphenola', dose=0, days=2.5, output.units="mg/L", initial.values=c(Agut=200)) # Working with parameters (rather than having solve_pbtk retrieve them): params <- parameterize_pbtk(chem.cas="80-05-7") head(solve_pbtk(parameters=params, days=2.5)) # We can change the parameters given to us by parameterize_pbtk: params <- parameterize_pbtk(dtxsid="DTXSID4020406", species = "rat") params["Funbound.plasma"] <- 0.1 out <- solve_pbtk(parameters=params, days=2.5) # A fifty day simulation: out <- solve_pbtk( chem.name = "Bisphenol A", days = 50, daily.dose=1, doses.per.day = 3) plot.data <- as.data.frame(out) css <- calc_analytic_css(chem.name = "Bisphenol A") library("ggplot2") c.vs.t <- ggplot(plot.data, aes(time, Cplasma)) + geom_line() + geom_hline(yintercept = css) + ylab("Plasma Concentration (uM)") + xlab("Day") + theme( axis.text = element_text(size = 16), axis.title = element_text(size = 16), plot.title = element_text(size = 17)) + ggtitle("Bisphenol A") print(c.vs.t) # The following will not work because Diquat dibromide monohydrate's # Henry's Law Constant (-3.912) is higher than that of Acetone (~-4.5): try(head(solve_pbtk(chem.cas = "6385-62-2"))) # However, we can turn off checking for phys-chem properties, since we know # that Diquat dibromide monohydrate is not too volatile: head(solve_pbtk(chem.cas = "6385-62-2", physchem.exclude = FALSE)) # Caco-2 absorption tests: p <- parameterize_pbtk(chem.name="Aminopterin") # calculate what initial dose of 1 mg/kg should be in uM in the gut: initial.dose <- signif(1/1e3*1e6/p[["MW"]]*p[["BW"]]*p[["Fabsgut"]], 4) # This should be the same as what solve_pbtk givesus: initial.dose == solve_pbtk(chem.cas="80-05-7",days=1)[1,"Agutlumen"] # By default we now include calculation of Fabs and Fgut (we explicitly model # first-pass hepatic metabolism in the model "pbtk") head(solve_pbtk(chem.cas="80-05-7",days=1)) # Therefore if we set Fabs = Fgut = 1 with keetit100=TRUE, we should get a # higher tissue concentrations: head(solve_pbtk(chem.cas="80-05-7",days=1, Caco2.options=list(keepit100=TRUE))) # Different ways to call the function: head(solve_pbtk(chem.cas="80-05-7",days=1)) head(solve_pbtk(parameters=parameterize_pbtk(chem.cas="80-05-7"),days=1)) ``` ## References \insertRef pearce2017httkhttk ## See Also `solve_model` `parameterize_gas_pbtk` `calc_analytic_css_pbtk` ## Author(s) John Wambaugh and Robert Pearce

solve_pbtk function