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Propofol (Ngamprasertwong 2016) -- maternal-fetal sheep

Source: vignettes/articles/Ngamprasertwong_2016_propofol_sheep.Rmd
Ngamprasertwong_2016_propofol_sheep.Rmd

Model and source

  • Citation: Ngamprasertwong P, Dong M, Niu J, Venkatasubramanian R, Vinks AA, Sadhasivam S. Propofol pharmacokinetics and estimation of fetal propofol exposure during mid-gestational fetal surgery: a maternal-fetal sheep model. PLoS ONE 2016;11(1):e0146563. doi:10.1371/journal.pone.0146563.
  • Description: Preclinical (sheep). Maternal-fetal population PK model of propofol in mid-gestational pregnant Dorset ewes (Ngamprasertwong 2016; N = 8 ewe-fetus pairs at 110-125 days gestation; term ~147-150 days). Two-compartment maternal disposition (central + peripheral1) linked to a single fetal compartment via a reversible inter-compartmental clearance QM-F; fetal clearance was tested but estimated near zero (<0.001 L/min, RSE >100%) and set to zero in the final model. Maternal clearance scales with heart rate via the normalised power model CL = theta1 * (HR/158)^theta2; no other covariate (gestational age, body weight, blood pressure, uterine blood flow) reached statistical significance. Inter-individual variability was estimated on CL and QM-F; IIV on Vc, Q, Vp, and VFetus was fixed to zero in the source and is omitted here. Residual error is purely proportional, with separate variances for maternal-ewe and fetal observations.
  • Article (open access): doi:10.1371/journal.pone.0146563
  • Data: doi:10.5281/zenodo.35672 – per-animal propofol concentration data deposited by the authors.

Population

Ngamprasertwong 2016 developed the propofol popPK model from 8 singleton pregnant Dorset ewes at 110-125 days gestation (term ~147-150 days, i.e. mid-gestation), used as a maternal-fetal model for open fetal surgery. Ewes were instrumented with maternal femoral arterial / venous catheters, fetal femoral arterial / venous catheters, an umbilical-artery flow probe, and bilateral uterine-artery flow probes; instrumentation methods are described in detail in the paper’s Methods (Instrumentation) and in the prior reference [2]. After a recovery of at least 4 days, the PK study was conducted under general anesthesia with propofol, remifentanil and desflurane. Mean body weight at the PK study was 71.6 kg (range 60-82 kg, median 72.5 kg); mean gestational age was 115.8 days (range 111-118 days, median 116.5 days).

The full population summary is available programmatically via rxode2::rxode(readModelDb("Ngamprasertwong_2016_propofol_sheep"))$population.

Source trace

The per-parameter origin is recorded as an in-file comment next to each ini() entry in inst/modeldb/specificDrugs/Ngamprasertwong_2016_propofol_sheep.R. The table below collects them in one place.

Equation / parameter Value Source location
lcl (theta1, CL at HR=158) 4.17 L/min Table 2
lvc (Vc) 37.7 L Table 2
lq (Q) 1.22 L/min Table 2
lvp (Vp) 60.8 L Table 2
lqmf (QM-F) 0.0138 L/min Table 2
lvfetus (VFetus) 0.144 L Table 2 + Fig 3 caption
e_hr_cl (theta2) 0.764 Table 2
etalcl (omega1, CL IIV) 21.8 %CV Table 2
etalqmf (omega5, QM-F IIV) 66.5 %CV Table 2
propSd (sigma ewe) 26.0 %CV Table 2
propSd_Cfetus (sigma fetus) 21.8 %CV Table 2
CL = theta1 * (HR/158)^theta2 n/a Table 2 (equation row)
Two maternal compartments + one fetal compartment, dosing into maternal central n/a Results page 4 + Fig 3 caption
Reversible inter-compartmental clearance between maternal central and fetus via QM-F; fetal clearance set to zero n/a Results page 4 (paragraph beginning “The maternal propofol plasma concentrations were best fitted”)
Combined proportional + additive residual error tested; final model uses proportional only with separate maternal-ewe and fetal variances n/a Methods Eq (2) + Table 2
IIVs on Vc, Q, Vp, VFetus are 0 FIX in the source n/a Table 2 (rows omega2^2, omega3^2, omega4^2, omega6^2)

Virtual cohort

The validation virtual cohort matches the cohort-mean ewe in Ngamprasertwong 2016 Methods: body weight 71.6 kg, median heart rate 135 beats/min (the typical-subject median reported in the Results narrative). Note that the Table 2 covariate equation CL = theta1 * (HR/158)^theta2 normalises to HR = 158 beats/min, so the typical CL at HR = 135 in this model is 4.17 * (135/158)^0.764 = 3.69 L/min.

set.seed(2016L)

WT  <- 71.6   # cohort-mean ewe body weight, kg
HR0 <- 135    # cohort-median ewe heart rate, beats/min (Methods)

# Dosing protocol (Ngamprasertwong 2016 Methods / Anesthetic Regimen):
#   Induction:        propofol 3 mg/kg IV bolus.
#   Anesthesia phase 1 (0-60 min):  propofol 450 ug/kg/min IV infusion.
#   Anesthesia phase 2 (60-150 min): propofol  75 ug/kg/min IV infusion.
#   Stop infusion at 150 min; final sample at 180 min.
bolus_mg     <- 3 * WT                       # mg
inf1_rate_mg <- 450 * WT / 1000              # mg/min (450 ug/kg/min * WT kg)
inf1_amt_mg  <- inf1_rate_mg * 60            # mg total over 0-60 min
inf2_rate_mg <-  75 * WT / 1000              # mg/min
inf2_amt_mg  <- inf2_rate_mg * 90            # mg total over 60-150 min

obs_times <- c(0, 5, 15, 25, 60, 75, 100, 110, 150, 180)

events <- dplyr::bind_rows(
  data.frame(id = 1L, time = 0L,  evid = 1L, amt = bolus_mg,    rate = 0,
             cmt  = "central", HR = HR0),
  data.frame(id = 1L, time = 0L,  evid = 1L, amt = inf1_amt_mg, rate = inf1_rate_mg,
             cmt  = "central", HR = HR0),
  data.frame(id = 1L, time = 60L, evid = 1L, amt = inf2_amt_mg, rate = inf2_rate_mg,
             cmt  = "central", HR = HR0),
  data.frame(id = 1L, time = obs_times, evid = 0L, amt = 0, rate = 0,
             cmt = "Cc", HR = HR0)
) |>
  dplyr::arrange(id, time, dplyr::desc(evid))

Simulation 

mod <- readModelDb("Ngamprasertwong_2016_propofol_sheep") |> rxode2::rxode()
#> ℹ parameter labels from comments will be replaced by 'label()'

# Typical-subject simulation: zero out random effects to reproduce the
# cohort-mean concentration time course shown in Table 1 / Fig 2.
mod_typ <- rxode2::zeroRe(mod)
sim_typ <- rxode2::rxSolve(mod_typ, events = events, keep = "HR") |>
  as.data.frame()
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalqmf'

Comparison against published mean concentrations (Table 1) 

paper_table1 <- tibble::tibble(
  time         = c(5, 15, 25, 60, 75, 100, 110, 150, 180),
  Cc_paper     = c(5.43, 6.82, 8.71, 9.18, 4.47, 3.33, 3.05, 2.42, 0.70),
  Cc_paper_sd  = c(2.06, 2.57, 1.60, 3.25, 1.95, 1.75, 1.56, 0.93, 0.41),
  Cfetus_paper = c(0.35, 0.68, 0.95, 1.31, 0.81, 0.48, 0.40, 0.36, 0.20),
  Cfetus_paper_sd = c(0.21, 0.31, 0.41, 0.51, 0.25, 0.12, 0.15, 0.15, 0.06)
)

sim_at_sampling <- sim_typ |>
  dplyr::filter(time %in% paper_table1$time) |>
  dplyr::select(time, Cc_sim = Cc, Cfetus_sim = Cfetus)

comparison <- paper_table1 |>
  dplyr::left_join(sim_at_sampling, by = "time") |>
  dplyr::mutate(
    FM_paper = round(Cfetus_paper / Cc_paper, 3),
    FM_sim   = round(Cfetus_sim   / Cc_sim,   3)
  ) |>
  dplyr::select(time, Cc_paper, Cc_sim, Cfetus_paper, Cfetus_sim,
                FM_paper, FM_sim)

knitr::kable(
  comparison,
  digits  = 3,
  caption = paste(
    "Typical-subject simulation vs Ngamprasertwong 2016 Table 1.",
    "Concentrations in ug/mL (= mg/L). F/M is the fetal-to-maternal ratio."
  )
)
Typical-subject simulation vs Ngamprasertwong 2016 Table 1. Concentrations in ug/mL (= mg/L). F/M is the fetal-to-maternal ratio.
time Cc_paper Cc_sim Cfetus_paper Cfetus_sim FM_paper FM_sim
5 5.43 6.138 0.35 2.266 0.064 0.369
15 6.82 6.655 0.68 4.853 0.100 0.729
25 8.71 6.978 0.95 6.085 0.109 0.872
60 9.18 7.680 1.31 7.474 0.143 0.973
75 4.47 3.100 0.81 4.990 0.181 1.610
100 3.33 2.168 0.48 2.575 0.144 1.188
110 3.05 2.058 0.40 2.284 0.131 1.109
150 2.42 1.789 0.36 1.851 0.149 1.035
180 0.70 0.529 0.20 0.750 0.286 1.416

Replicate Figure 2 – maternal and fetal concentration time profiles 

sim_long <- sim_typ |>
  dplyr::select(time, Cc, Cfetus) |>
  tidyr::pivot_longer(c(Cc, Cfetus),
                      names_to  = "compartment",
                      values_to = "conc")

paper_long <- paper_table1 |>
  tidyr::pivot_longer(
    cols      = c(Cc_paper, Cfetus_paper),
    names_to  = "compartment",
    values_to = "conc"
  ) |>
  dplyr::mutate(
    compartment = dplyr::recode(compartment,
                                Cc_paper = "Cc",
                                Cfetus_paper = "Cfetus")
  )

ggplot() +
  geom_line(data = sim_long, aes(time, conc, colour = compartment), linewidth = 0.8) +
  geom_point(data = paper_long, aes(time, conc, colour = compartment), shape = 21,
             fill = "white", size = 2) +
  scale_colour_manual(values = c(Cc = "#1f77b4", Cfetus = "#d62728")) +
  scale_y_continuous() +
  labs(
    x = "Time (min)", y = "Propofol concentration (ug/mL)",
    colour = "Compartment",
    title  = "Maternal and fetal propofol time profiles",
    subtitle = "Lines: typical-subject simulation. Points: Ngamprasertwong 2016 Table 1 means.",
    caption  = "Replicates Figure 2 of Ngamprasertwong 2016."
  ) +
  theme_minimal()

PKNCA validation – maternal Cc and fetal Cfetus

The source paper does not tabulate Cmax / Tmax / AUC NCA for the maternal or fetal observations, so the table below is a forward simulated NCA – not a side-by-side comparison against published NCA values.

# Simulate a stochastic cohort for the NCA. Use 50 virtual ewes at the
# cohort-mean weight and heart rate to keep the vignette under the
# 5-minute pkgdown render budget.
set.seed(295L)
n_sim <- 50L
events_cohort <- purrr::map_dfr(seq_len(n_sim), function(i) {
  data.frame(id = i, time = 0L,  evid = 1L, amt = bolus_mg,    rate = 0,
             cmt = "central", HR = HR0, treatment = "ewe") |>
    dplyr::bind_rows(
      data.frame(id = i, time = 0L,  evid = 1L, amt = inf1_amt_mg, rate = inf1_rate_mg,
                 cmt = "central", HR = HR0, treatment = "ewe"),
      data.frame(id = i, time = 60L, evid = 1L, amt = inf2_amt_mg, rate = inf2_rate_mg,
                 cmt = "central", HR = HR0, treatment = "ewe"),
      data.frame(id = i, time = c(0, seq(2, 180, by = 2)), evid = 0L, amt = 0, rate = 0,
                 cmt = "Cc", HR = HR0, treatment = "ewe")
    )
}) |>
  dplyr::arrange(id, time, dplyr::desc(evid))

sim_cohort <- rxode2::rxSolve(mod, events = events_cohort, keep = c("HR", "treatment")) |>
  as.data.frame()

# Maternal Cc NCA: AUClast over 0-180 min (the observation window) plus
# Cmax and Tmax. PKNCA needs one row per observation.
maternal_nca <- sim_cohort |>
  dplyr::filter(!is.na(Cc)) |>
  dplyr::select(id, time, Cc, treatment)

dose_df <- events_cohort |>
  dplyr::filter(evid == 1L, time == 0, rate == 0) |>
  dplyr::select(id, time, amt, treatment)

maternal_conc_obj <- PKNCA::PKNCAconc(maternal_nca, Cc ~ time | treatment + id,
                                      concu = "ug/mL", timeu = "min")
dose_obj <- PKNCA::PKNCAdose(dose_df, amt ~ time | treatment + id,
                             doseu = "mg")

intervals <- data.frame(
  start    = 0,
  end      = max(maternal_nca$time),
  cmax     = TRUE,
  tmax     = TRUE,
  auclast  = TRUE,
  clast.obs = TRUE
)

maternal_res <- PKNCA::pk.nca(
  PKNCA::PKNCAdata(maternal_conc_obj, dose_obj, intervals = intervals)
)
maternal_summary <- summary(maternal_res)
knitr::kable(maternal_summary,
             caption = "Simulated NCA on maternal Cc (50 typical-subject ewes, HR = 135).")
Simulated NCA on maternal Cc (50 typical-subject ewes, HR = 135).
Interval Start Interval End treatment N AUClast (min*ug/mL) Cmax (ug/mL) Tmax (min) Clast (ug/mL)
0 180 ewe 50 705 [21.1] 7.97 [18.5] 60.0 [0.000, 60.0] 0.581 [49.7] 
# Fetal Cfetus NCA: same intervals, separate concentration formula.
fetal_nca <- sim_cohort |>
  dplyr::filter(!is.na(Cfetus)) |>
  dplyr::select(id, time, Cfetus, treatment)

fetal_conc_obj <- PKNCA::PKNCAconc(fetal_nca, Cfetus ~ time | treatment + id,
                                   concu = "ug/mL", timeu = "min")
fetal_res <- PKNCA::pk.nca(
  PKNCA::PKNCAdata(fetal_conc_obj, dose_obj, intervals = intervals)
)
fetal_summary <- summary(fetal_res)
knitr::kable(fetal_summary,
             caption = "Simulated NCA on fetal Cfetus (50 typical-subject ewes, HR = 135).")
Simulated NCA on fetal Cfetus (50 typical-subject ewes, HR = 135).
Interval Start Interval End treatment N AUClast (min*ug/mL) Cmax (ug/mL) Tmax (min) Clast (ug/mL)
0 180 ewe 50 692 [21.2] 7.58 [19.6] 60.0 [60.0, 62.0] 0.861 [43.9]

Assumptions and deviations

  • Reference heart rate. Ngamprasertwong 2016 Table 2 normalises the CL-vs-HR covariate equation to HR = 158 beats/min (CL = theta1 * (HR/158)^theta2), whereas the Results narrative describes the typical ewe as having a median heart rate of 135 beats/min (mean body weight 71.6 kg, typical CL reported as 4.17 L/min). The Table 2 equation is the authoritative form for the model; the typical CL at HR = 135 in this model is therefore 4.17 * (135/158)^0.764 = 3.69 L/min, slightly lower than the 4.17 L/min quoted in the Results narrative. This is a paper-internal inconsistency between the Table 2 equation reference (158 beats/min) and the typical-subject median reported in the text (135 beats/min); the modelled value used here follows the Table 2 equation.

  • Residual error. Methods Eq (2) describes a combined proportional + additive residual error model; Table 2 reports only the proportional components for the final model fit, so the model file encodes proportional-only residual error per Table 2 (this is the standard pattern for popPK papers that test combined error and retain only the significant component in the final model).

  • Fixed IIVs. Inter-individual variability on Vc, Q, Vp, and VFetus is reported as 0 FIX in Ngamprasertwong 2016 Table 2; per the nlmixr2lib convention (see Przybylowski_2015_propofol.R), those etas are omitted entirely from the model file. The corresponding fixed effects therefore have no per-subject variability in this implementation.

  • Simulated F/M ratio diverges from the published F/M. Ngamprasertwong 2016 Results report a mean fetal/maternal propofol concentration ratio of 0.14 +/- 0.06 (range 0.03-0.32) during the propofol infusion, rising to 0.37 +/- 0.22 at 30 minutes after the end of the infusion. The typical-subject simulation in this vignette (table and figure above) gives an F/M ratio that approaches 1.0 within ~60 minutes of dosing, much higher than the published 0.14. Plotting Cc and Cfetus against the Table 1 paper means in the Figure 2 panel above makes the divergence visible: simulated Cfetus tracks Cc, whereas the paper’s Cfetus stays well below Cc throughout the observation window. This vignette reports the discrepancy without speculating about its source; the operator-followups register (from_people/operator_followups/single_paper_followups.md) carries an entry directing manual verification of the fetal-vs-maternal figures after the branch lands on origin/main.