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Mab7E3 (Cao 2013)

Source: vignettes/articles/Cao_2013_mab7E3.Rmd
Cao_2013_mab7E3.Rmd

Model and source

  • Citation: Cao Y, Balthasar JP, Jusko WJ. Second-generation minimal physiologically-based pharmacokinetic model for monoclonal antibodies. J Pharmacokinet Pharmacodyn. 2013 Oct;40(5):597-607.
  • Article: https://doi.org/10.1007/s10928-013-9332-2
  • Source data: Garg A, Balthasar JP. J Pharmacokinet Pharmacodyn. 2007;34(5):687-709 (PMID 17636457).

This is the mab7E3 preclinical mouse entry from the 12-fit Cao 2013 mAb cohort. 7E3 is the parent murine anti-GPIIb/IIIa IgG1 mAb (the chimeric Fab fragment of which is approved as abciximab). The function name is mab7E3 because R identifiers cannot start with a digit; the antibody is referred to as 7E3 in the source publications.

Population

Cao et al. fit the mPBPK model to plasma profiles of 7E3 in mice from Garg & Balthasar (2007). The mouse system parameters Cao 2013 used for fitting are: V_p = 0.85 mL, ISF = 4.35 mL, total lymph flow = 0.12 mL/hr (= 2.88 mL/day), assumed body weight 20 g, K_p = 0.8 (native IgG1), sigma_L = 0.2. The dosing reported in Cao 2013 Figure 2 was a single 8 mg/kg IV bolus (= 0.16 mg in a 20 g mouse).

Source trace

Equation / parameter Value Source location
4-compartment mPBPK ODE system – Cao 2013 Eqs 1-4 (Model A)
sigma1 (vascular reflection coefficient, tight tissues) 0.95, fixed Cao 2013 Table 1 (7E3 Model A); footnote b “Assumed”
sigma2 (vascular reflection coefficient, leaky tissues) 0.421 Cao 2013 Table 1 (7E3 Model A; CV 10.4%)
CLp (plasma clearance) 0.499e-5 L/hr = 1.1976e-4 L/day Cao 2013 Table 1 (7E3 Model A; CV 14.1%)
Mouse Vplasma 0.85 mL = 0.00085 L Cao 2013 Table 1 footnote
Mouse total ISF volume 4.35 mL = 0.00435 L Cao 2013 Table 1 footnote
Mouse total lymph flow 0.12 mL/hr = 2.88 mL/day Cao 2013 Table 1 footnote

Virtual cohort

The packaged model has no IIV. We simulate the single 8 mg/kg IV dose reported in Cao 2013 Figure 2.

obs_times <- sort(unique(c(seq(0, 1/24, by = 1/240),
                            seq(1/24, 1, by = 1/24),
                            seq(1, 12, by = 0.25))))

ev <- rxode2::et(amt = 0.16, cmt = "plasma", id = 1L) |>
  rxode2::et(time = obs_times, id = 1L)
events <- as.data.frame(ev) |> dplyr::mutate(dose_mg_per_kg = 8)
stopifnot(!anyDuplicated(unique(events[, c("id", "time", "evid")])))

Simulation 

mod <- readModelDb("Cao_2013_mab7E3")
sim <- rxode2::rxSolve(rxode2::rxode2(mod), events = events,
                       keep = "dose_mg_per_kg") |>
  as.data.frame()
# rxSolve drops the id column when there is a single subject; add it back
# so PKNCA's `~ ... | id` formula has the column it expects.
if (!"id" %in% names(sim)) sim$id <- 1L

Replicate Figure 2 (7E3 in mice) 

sim |>
  dplyr::filter(time > 0) |>
  ggplot2::ggplot(ggplot2::aes(time, Cc)) +
  ggplot2::geom_line() +
  ggplot2::scale_y_log10() +
  ggplot2::labs(
    x = "Time (day)", y = "Plasma concentration (mg/L)",
    title = "Cao 2013 Figure 2A (7E3 plasma) -- typical-value reproduction",
    caption = "Replicates the plasma profile of 7E3 in mice (8 mg/kg IV, 20 g mouse) using the packaged Model A mPBPK fit."
  )

PKNCA validation 

sim_nca <- sim |>
  dplyr::filter(!is.na(Cc), Cc > 0) |>
  dplyr::transmute(id = id, time = time, conc = Cc,
                   dose_mg_per_kg = dose_mg_per_kg)
dose_df <- events |>
  dplyr::filter(evid == 1) |>
  dplyr::transmute(id = id, time = time, amt = amt,
                   dose_mg_per_kg = dose_mg_per_kg)
conc_obj <- PKNCA::PKNCAconc(sim_nca, conc ~ time | dose_mg_per_kg + id)
dose_obj <- PKNCA::PKNCAdose(dose_df, amt ~ time | dose_mg_per_kg + id)
intervals <- data.frame(start = 0, end = Inf,
                        cmax = TRUE, tmax = TRUE,
                        aucinf.obs = TRUE, half.life = TRUE)
nca <- PKNCA::pk.nca(PKNCA::PKNCAdata(conc_obj, dose_obj, intervals = intervals))
knitr::kable(summary(nca),
             caption = "Simulated NCA parameters for Cao 2013 mab7E3 (Model A typical-value fit; 8 mg/kg single IV in 20 g mouse).")
Simulated NCA parameters for Cao 2013 mab7E3 (Model A typical-value fit; 8 mg/kg single IV in 20 g mouse).
start end dose_mg_per_kg N cmax tmax half.life aucinf.obs
0 Inf 8 1 188 0.000 12.9 1310

Assumptions and deviations

  • Preclinical-only entry. Filed under inst/modeldb/pharmacokinetics/ rather than specificDrugs/ because nlmixr2lib’s specificDrugs tier is reserved for human drugs.
  • No IIV, no residual error. The packaged model is a structural typical-value mPBPK fit. Cao 2013’s variance model V_i = (intercept + slope * Y_hat)^2 (Eq 9) has its parameter values un-reported, and there is no biological-variability layer over a single mean profile.
  • Compartment names deviate from the canonical set (plasma, tight, leaky, lymph). The deviation is necessary because the four mPBPK compartments are mechanistically distinct; checkModelConventions() raises four warnings (one per compartment) and no errors.
  • sigma1 = 0.95 was fixed (assumed). Cao 2013 Table 1 footnote b states “Assumed” for sigma1; CV is reported as not applicable.
  • Concentration unit. The packaged model returns Cc in mg/L. Cao 2013 Figure 2A plots 7E3 plasma in mg/L; the simulated curve is in those units. Tissue compartments hold amounts in mg; concentrations would need to be divided by the corresponding ISF tissue volume (vtight, vleaky) to compare against Cao 2013 Figure 2B.
  • Mouse system parameters are hard-coded for a 20 g body weight (V_p = 0.85 mL, ISF = 4.35 mL, lymph flow = 2.88 mL/day). These are the values Cao 2013 used during fitting; rescaling for different mouse strains or weights requires recomputing all four physiological constants.