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Meropenem in morbidly obese patients (Wittau 2015)

Source: vignettes/articles/Wittau_2015_meropenem.Rmd
Wittau_2015_meropenem.Rmd

Model and source

  • Citation: Wittau M, Scheele J, Kurlbaum M, Brockschmidt C, Wolf AM, Hemper E, Henne-Bruns D, Bulitta JB. Population pharmacokinetics and target attainment of meropenem in plasma and tissue of morbidly obese patients after laparoscopic intraperitoneal surgery. Antimicrob Agents Chemother. 2015;59(10):6241-6247. doi:10.1128/AAC.00259-15. PMID 26248373.
  • Description: Two-compartment intravenous population PK model for meropenem in morbidly obese adults (Wittau 2015). Allometric scaling on fat-free mass with a reference FFM of 53 kg. Unbound meropenem concentrations in subcutaneous tissue and peritoneal fluid are described as the plasma concentration multiplied by the site-to-plasma AUC ratios FSC and FPF (the final model assumed very rapid equilibration with plasma, so SC and PF are not carried as separate ODE states).
  • Article: https://doi.org/10.1128/AAC.00259-15
  • ClinicalTrials.gov: https://clinicaltrials.gov/ct2/show/NCT01407965

Population

Wittau et al. enrolled six morbidly obese adults (one excluded from analysis due to an incorrect retrodialysis recovery measurement, leaving n = 5) undergoing elective laparoscopic intra-abdominal surgery at the University of Ulm. Five patients had laparoscopic sleeve gastrectomies; one had a laparoscopic abdominal wall hernia repair. Two were male and three female. Mean (SD) age was 40.0 (7.87) years (range 31 - 49), total body weight 158 (33.5) kg (range 116 - 203), fat-free mass 72.5 (19.8) kg (range 52.3 - 94.0), height 170 (14.5) cm, and BMI 54.2 (7.02) kg/m^2 (range 47.6 - 62.3) (Table 1 of Wittau 2015). All patients had serum creatinine in the 64 - 80 umol/L range and albumin 41 - 45 g/L; severe renal insufficiency (CrCL <= 30 mL/min), severe hepatic disease, and concurrent valproic acid were exclusion criteria.

Each patient received 1 g meropenem (Meronem) intravenously every 8 h as a 15-min infusion, beginning on the day of surgery. The fourth dose, given on day 1 after surgery, was used for sample collection. Plasma was sampled at 0.5, 1, 2, 3, 5, and 8 h after the start of the fourth infusion; unbound subcutaneous tissue and unbound peritoneal fluid concentrations were sampled in parallel windows via microdialysis with retrodialysis recovery calibration. The same information is available programmatically via readModelDb("Wittau_2015_meropenem")$population.

Source trace

Per-parameter origin comments are recorded in inst/modeldb/specificDrugs/Wittau_2015_meropenem.R. The table below collects them in one place for review.

Equation / parameter Value Source location
lcl (CL at FFM = 53 kg) log(18.7 L/h) Table 2 row ‘Total clearance’ (population mean)
lvc (V1 at FFM = 53 kg) log(21.5 L) Table 2 row ‘Volume of distribution of central compartment’
lvp (V2 at FFM = 53 kg) log(6.16 L) Table 2 row ‘Volume of distribution of peripheral compartment’
lq (CLd at FFM = 53 kg) log(29.4 L/h) Table 2 row ‘Distribution clearance between central and peripheral compartments’
lfsc (FSC, SC:plasma AUC ratio) log(0.721) Table 2 row ‘Ratio of AUC values in subcutaneous tissue and plasma’
lfpf (FPF, PF:plasma AUC ratio) log(0.943) Table 2 row ‘Ratio of AUC values in peritoneal fluid and plasma’
e_ffm_cl_q (shared allometric exp on CL and CLd) fixed(0.75) Methods ‘Parameter variability model and covariate effects’; Discussion paragraph 4
e_ffm_vc_vp (shared allometric exp on V1 and V2) fixed(1.00) Methods ‘Parameter variability model and covariate effects’
etalcl (IIV variance on lcl) log(0.0386^2 + 1) = 0.001489 Table 2 BSV column (apparent CV per footnote c)
etalq (IIV variance on lq) log(1.79^2 + 1) = 1.43607 Table 2 BSV column
etalvc (IIV variance on lvc) log(0.104^2 + 1) = 0.010758 Table 2 BSV column
etalvp (IIV variance on lvp) log(0.0422^2 + 1) = 0.001779 Table 2 BSV column
etalfsc (IIV variance on lfsc) log(1.12^2 + 1) = 0.81277 Table 2 BSV column
etalfpf (IIV variance on lfpf) log(0.311^2 + 1) = 0.09229 Table 2 BSV column
propSd (plasma) 0.216 Table 2 footnote a
addSd (plasma) 0.0235 mg/L Table 2 footnote a
propSd_Csc (SC tissue) 0.0958 Table 2 footnote a
addSd_Csc (SC tissue) 1.26 mg/L Table 2 footnote a
propSd_Cpf (peritoneal fluid) 0.103 Table 2 footnote a
addSd_Cpf (peritoneal fluid) 0.617 mg/L Table 2 footnote a
Reference FFM 53 kg Table 2 footnote b (‘Estimates represent a patient with normal body size (i.e., 53 kg fat-free mass)’)
d/dt(central), d/dt(peripheral1) structural 2-compartment IV Materials and Methods ‘Structural model’ paragraph 1 (linear two-disposition-compartment model selected)
Csc = FSC * Cc, Cpf = FPF * Cc algebraic scaling Materials and Methods ‘Structural model’ paragraph 1 + Table 2 footnote d (very rapid SC/PF-plasma equilibration in the final model)

Virtual cohort

The original observed data are not publicly available. We simulate a virtual cohort matched to the paper’s Monte Carlo simulation covariates (Methods ‘Monte Carlo simulations’ paragraph): a log-normal distribution of FFM with geometric mean 70.3 kg and 27.4% CV. The dosing regimen follows the protocol: 1 g meropenem given as a 15-min IV infusion every 8 h for four doses; PK sampling is on the fourth-dose interval (24 - 32 h).

set.seed(2015L)
n_subj <- 200L

# Geometric mean 70.3 kg, 27.4% CV on FFM (log-normal); per Methods.
omega_ffm <- sqrt(log(0.274^2 + 1))
ffm_mean  <- 70.3

obs_grid <- c(24,
              24 + c(0.25, 0.5, 1, 2, 3, 5, 8))  # start of 4th dose + sampling times to 8 h

dose_times <- seq(0, by = 8, length.out = 4)     # four doses q8h
inf_dur    <- 0.25                                # 15-min infusion

make_cohort <- function(n, id_offset = 0L) {
  ids <- id_offset + seq_len(n)
  ffm <- rlnorm(n, log(ffm_mean) - 0.5 * omega_ffm^2, omega_ffm)

  # Dose rows: 1 g (= 1000 mg) given as 15-min infusion; encode via `dur`.
  dose_rows <- tidyr::expand_grid(id = ids, time = dose_times) |>
    dplyr::mutate(
      amt  = 1000,
      cmt  = "central",
      evid = 1L,
      dur  = inf_dur,
      rate = NA_real_
    )

  # Observation rows. This is a 3-endpoint model (Cc plasma, Csc subcutaneous,
  # Cpf peritoneal fluid); address each endpoint by its dvid (1 = Cc, 2 = Csc,
  # 3 = Cpf) rather than by the algebraic-observable name, so rxode2 maps each
  # observation to its endpoint under the default solver. rxSolve returns the
  # Cc/Csc/Cpf columns on every observation row regardless of dvid.
  obs_rows <- tidyr::expand_grid(id = ids, time = obs_grid,
                                 dvid = c(1L, 2L, 3L)) |>
    dplyr::mutate(
      amt  = NA_real_,
      evid = 0L,
      dur  = NA_real_,
      rate = NA_real_
    )

  # Merge dose- and observation-rows with the per-subject covariate FFM.
  cov_df <- tibble::tibble(id = ids, FFM = ffm)
  dplyr::bind_rows(dose_rows, obs_rows) |>
    dplyr::left_join(cov_df, by = "id") |>
    dplyr::arrange(id, time) |>
    dplyr::mutate(treatment = "1 g q8h IV (15-min infusion)")
}

events <- make_cohort(n_subj)
stopifnot(!anyDuplicated(unique(events[, c("id", "time", "evid")])))

Simulation

The model has three algebraic observables (Cc plasma, Csc subcutaneous, Cpf peritoneal fluid) backed by the two-compartment ODE state; observation rows are addressed by dvid endpoint id (1 = Cc, 2 = Csc, 3 = Cpf) so rxode2 maps each to its endpoint under the default solver (the multi-output pattern in references/known-vignette-failure-patterns.md Section 5b).

mod <- readModelDb("Wittau_2015_meropenem")

# Stochastic VPC simulation: keeps IIV, returns one trajectory per subject.
sim_stoch <- rxode2::rxSolve(
  mod, events = events,
  keep        = c("treatment", "FFM")
) |> as.data.frame()
#> ℹ parameter labels from comments will be replaced by 'label()'

# Typical-value simulation (no IIV) for replicating Figure 1's individual fits.
mod_typ <- mod |> rxode2::zeroRe()
#> ℹ parameter labels from comments will be replaced by 'label()'
events_typ <- make_cohort(1L) |>
  dplyr::mutate(FFM = ffm_mean)        # impose the cohort geometric mean exactly
sim_typ <- rxode2::rxSolve(
  mod_typ, events = events_typ,
  keep      = c("treatment", "FFM")
) |> as.data.frame()
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalq', 'etalvc', 'etalvp', 'etalfsc', 'etalfpf'

Replicate Figure 1: plasma, subcutaneous, and peritoneal-fluid profiles

Figure 1 of Wittau 2015 shows the individually-fitted meropenem concentrations in plasma, subcutaneous tissue, and peritoneal fluid across the 8-h fourth-dose interval. The typical-value profile below reproduces the same qualitative behaviour: plasma and peritoneal-fluid traces are nearly superimposable (FPF = 0.943), while subcutaneous-tissue concentrations are about 28% lower (FSC = 0.721), with the same terminal slope across all three sites (rapid equilibration assumption).

fig1 <- sim_typ |>
  dplyr::filter(time >= 24) |>
  dplyr::mutate(t_after_dose = time - 24) |>
  dplyr::select(t_after_dose, Plasma = Cc, Subcutaneous = Csc, `Peritoneal fluid` = Cpf) |>
  tidyr::pivot_longer(-t_after_dose, names_to = "Site", values_to = "C")

ggplot(fig1, aes(t_after_dose, C, colour = Site)) +
  geom_line(linewidth = 0.8) +
  scale_y_log10() +
  labs(x = "Time after start of fourth infusion (h)",
       y = "Meropenem concentration (mg/L)",
       title = "Figure 1 -- typical-value profile, 1 g q8h IV (15-min infusion)",
       caption = "Replicates Figure 1 of Wittau 2015 (typical FFM = 70.3 kg).")

Replicate Figure 1 VPC envelope (stochastic)

The stochastic simulation reproduces the between-subject spread in the same fourth-dose window, separately for each observation site.

vpc_df <- sim_stoch |>
  dplyr::filter(time >= 24) |>
  dplyr::mutate(t_after_dose = time - 24) |>
  dplyr::select(t_after_dose, Plasma = Cc, Subcutaneous = Csc, `Peritoneal fluid` = Cpf) |>
  tidyr::pivot_longer(c(Plasma, Subcutaneous, `Peritoneal fluid`),
                      names_to = "Site", values_to = "C") |>
  dplyr::group_by(Site, t_after_dose) |>
  dplyr::summarise(
    Q05 = quantile(C, 0.05, na.rm = TRUE),
    Q50 = quantile(C, 0.50, na.rm = TRUE),
    Q95 = quantile(C, 0.95, na.rm = TRUE),
    .groups = "drop"
  )

ggplot(vpc_df, aes(t_after_dose, Q50)) +
  geom_ribbon(aes(ymin = Q05, ymax = Q95), alpha = 0.25) +
  geom_line() +
  facet_wrap(~Site, scales = "free_y") +
  scale_y_log10() +
  labs(x = "Time after start of fourth infusion (h)",
       y = "Meropenem concentration (mg/L; 5/50/95th percentiles)",
       title = "Stochastic VPC envelope -- fourth-dose window",
       caption = "200 simulated subjects, FFM drawn from log-normal(geo. mean 70.3 kg, 27.4% CV).")

PKNCA validation

The paper’s NCA values were computed by Wittau et al. via the linear-up / log-down trapezoidal rule in WinNonlin Professional 5.3 on the actual five patients. Without their actual covariates we cannot reproduce subject-by-subject NCA; we instead compute PKNCA NCA parameters on the simulated cohort over the fourth-dose interval (24 - 32 h) and compare population summaries against the paper’s median and average.

We compute one NCA block per observation site (plasma, SC, PF). Time is re-zeroed at the start of the fourth dose so the AUC over the interval is directly comparable to AUC0-tau at steady state.

sim_nca_long <- sim_stoch |>
  dplyr::filter(time >= 24) |>
  dplyr::mutate(t_after_dose = time - 24) |>
  dplyr::select(id, treatment, t_after_dose, Cc, Csc, Cpf) |>
  tidyr::pivot_longer(c(Cc, Csc, Cpf),
                      names_to = "Site", values_to = "C")

# Guarantee a time=0 row per (id, treatment, Site); for IV infusion the
# pre-fourth-dose row is the trough Cc(24), but a defensive 0 is fine for
# PKNCA's AUC anchor and is the standard pattern.
sim_nca_long <- dplyr::bind_rows(
  sim_nca_long,
  sim_nca_long |>
    dplyr::distinct(id, treatment, Site) |>
    dplyr::mutate(t_after_dose = 0, C = 0)
) |>
  dplyr::distinct(id, treatment, Site, t_after_dose, .keep_all = TRUE) |>
  dplyr::arrange(id, treatment, Site, t_after_dose)
nca_one <- function(site_code, friendly_site) {
  conc_df <- sim_nca_long |>
    dplyr::filter(Site == site_code) |>
    dplyr::transmute(id, treatment, time = t_after_dose, Cc = C)
  dose_df <- events |>
    dplyr::filter(evid == 1L, time == 24) |>
    dplyr::distinct(id, treatment) |>
    dplyr::mutate(time = 0, amt = 1000)

  conc_obj <- PKNCA::PKNCAconc(
    conc_df, Cc ~ time | treatment + id,
    concu = "mg/L", timeu = "h"
  )
  dose_obj <- PKNCA::PKNCAdose(
    dose_df, amt ~ time | treatment + id,
    doseu = "mg"
  )
  intervals <- data.frame(
    start      = 0,
    end        = 8,
    cmax       = TRUE,
    tmax       = TRUE,
    auclast    = TRUE,
    half.life  = TRUE
  )
  res <- PKNCA::pk.nca(PKNCA::PKNCAdata(conc_obj, dose_obj, intervals = intervals))
  res_df <- as.data.frame(res$result)
  res_df$Site <- friendly_site
  res_df
}

nca_plasma <- nca_one("Cc",  "Plasma")
nca_sc     <- nca_one("Csc", "Subcutaneous tissue")
nca_pf     <- nca_one("Cpf", "Peritoneal fluid")
nca_all    <- dplyr::bind_rows(nca_plasma, nca_sc, nca_pf)
pknca_summary <- nca_all |>
  dplyr::filter(PPTESTCD %in% c("cmax", "auclast", "half.life")) |>
  dplyr::group_by(Site, PPTESTCD) |>
  dplyr::summarise(
    Median = median(PPORRES, na.rm = TRUE),
    Q25    = quantile(PPORRES, 0.25, na.rm = TRUE),
    Q75    = quantile(PPORRES, 0.75, na.rm = TRUE),
    .groups = "drop"
  ) |>
  dplyr::mutate(
    PPTESTCD = factor(PPTESTCD, levels = c("cmax", "auclast", "half.life")),
    Parameter = dplyr::recode(as.character(PPTESTCD),
                              cmax      = "Cmax (mg/L)",
                              auclast   = "AUC0-8 (mg*h/L)",
                              half.life = "t1/2 (h)")
  ) |>
  dplyr::arrange(Site, PPTESTCD) |>
  dplyr::select(Site, Parameter, Median, Q25, Q75)

knitr::kable(
  pknca_summary,
  digits  = 2,
  caption = "Simulated NCA over the fourth-dose interval (n = 200; FFM ~ log-normal)."
)
Simulated NCA over the fourth-dose interval (n = 200; FFM ~ log-normal).
Site Parameter Median Q25 Q75
Peritoneal fluid Cmax (mg/L) 27.52 21.29 39.10
Peritoneal fluid AUC0-8 (mg*h/L) 41.93 33.04 54.24
Peritoneal fluid t1/2 (h) 1.15 1.06 1.25
Plasma Cmax (mg/L) 30.19 25.45 34.95
Plasma AUC0-8 (mg*h/L) 44.77 39.57 51.20
Plasma t1/2 (h) 1.15 1.06 1.25
Subcutaneous tissue Cmax (mg/L) 22.95 11.30 46.46
Subcutaneous tissue AUC0-8 (mg*h/L) 33.09 17.31 69.00
Subcutaneous tissue t1/2 (h) 1.15 1.06 1.25

Comparison against published values

The paper reports peak concentrations 30 min after the start of the last infusion (mean +/- SD across the five patients) and terminal half-lives (median, range) from a non-compartmental analysis without body-size scaling. AUC ratios are reported as population means of the model-derived F_SC and F_PF.

# Compute simulated AUC ratios per subject from PKNCA auclast, then summarise.
auc_wide <- nca_all |>
  dplyr::filter(PPTESTCD == "auclast") |>
  dplyr::select(id, Site, AUC = PPORRES) |>
  tidyr::pivot_wider(names_from = Site, values_from = AUC) |>
  dplyr::mutate(
    ratio_sc_plasma = `Subcutaneous tissue` / Plasma,
    ratio_pf_plasma = `Peritoneal fluid`    / Plasma
  )

ratio_med <- c(
  sc = median(auc_wide$ratio_sc_plasma, na.rm = TRUE),
  pf = median(auc_wide$ratio_pf_plasma, na.rm = TRUE)
)

plasma_cmax_med <- pknca_summary |>
  dplyr::filter(Site == "Plasma", Parameter == "Cmax (mg/L)") |>
  dplyr::pull(Median)
sc_cmax_med <- pknca_summary |>
  dplyr::filter(Site == "Subcutaneous tissue", Parameter == "Cmax (mg/L)") |>
  dplyr::pull(Median)
pf_cmax_med <- pknca_summary |>
  dplyr::filter(Site == "Peritoneal fluid", Parameter == "Cmax (mg/L)") |>
  dplyr::pull(Median)

plasma_thalf_med <- pknca_summary |>
  dplyr::filter(Site == "Plasma", Parameter == "t1/2 (h)") |>
  dplyr::pull(Median)
sc_thalf_med <- pknca_summary |>
  dplyr::filter(Site == "Subcutaneous tissue", Parameter == "t1/2 (h)") |>
  dplyr::pull(Median)
pf_thalf_med <- pknca_summary |>
  dplyr::filter(Site == "Peritoneal fluid", Parameter == "t1/2 (h)") |>
  dplyr::pull(Median)

compare_df <- tibble::tribble(
  ~Metric,                                  ~Published,                ~Simulated,
  "Plasma Cmax (mg/L)",                     "24.6 +/- 10.1 (mean +/- SD)", sprintf("%.1f (median)", plasma_cmax_med),
  "SC Cmax (mg/L)",                         "24.1 +/- 22.1 (mean +/- SD)", sprintf("%.1f (median)", sc_cmax_med),
  "Peritoneal-fluid Cmax (mg/L)",           "23.2 +/- 10.8 (mean +/- SD)", sprintf("%.1f (median)", pf_cmax_med),
  "Plasma terminal t1/2 (h)",               "1.24 (1.04 - 1.41) (median, range)", sprintf("%.2f (median)", plasma_thalf_med),
  "SC terminal t1/2 (h)",                   "1.16 (0.833 - 2.45) (median, range)", sprintf("%.2f (median)", sc_thalf_med),
  "Peritoneal-fluid terminal t1/2 (h)",     "1.35 (0.978 - 1.95) (median, range)", sprintf("%.2f (median)", pf_thalf_med),
  "AUC_SC / AUC_plasma (FSC, mean)",        "0.721",                       sprintf("%.3f (median)", ratio_med["sc"]),
  "AUC_PF / AUC_plasma (FPF, mean)",        "0.943",                       sprintf("%.3f (median)", ratio_med["pf"])
)

knitr::kable(
  compare_df,
  caption = "Simulated vs. published Wittau 2015 NCA (plasma, SC, PF). Published values are population summaries across the n = 5 cohort."
)
Simulated vs. published Wittau 2015 NCA (plasma, SC, PF). Published values are population summaries across the n = 5 cohort.
Metric Published Simulated
Plasma Cmax (mg/L) 24.6 +/- 10.1 (mean +/- SD) 30.2 (median)
SC Cmax (mg/L) 24.1 +/- 22.1 (mean +/- SD) 23.0 (median)
Peritoneal-fluid Cmax (mg/L) 23.2 +/- 10.8 (mean +/- SD) 27.5 (median)
Plasma terminal t1/2 (h) 1.24 (1.04 - 1.41) (median, range) 1.15 (median)
SC terminal t1/2 (h) 1.16 (0.833 - 2.45) (median, range) 1.15 (median)
Peritoneal-fluid terminal t1/2 (h) 1.35 (0.978 - 1.95) (median, range) 1.15 (median)
AUC_SC / AUC_plasma (FSC, mean) 0.721 0.729 (median)
AUC_PF / AUC_plasma (FPF, mean) 0.943 0.946 (median)

The simulated AUC ratios (FSC and FPF) match the published values by construction because these are the typical-value population means encoded in ini(). The simulated Cmax and terminal t1/2 are population summaries from the n = 200 virtual cohort and are compared against the n = 5 observed population summaries; the dispersion bounds in the paper are wide because of the small sample size and the large between-subject variability on FSC (112% CV) and the distribution clearance (179% CV).

Assumptions and deviations

  • Cohort size. The paper enrolled n = 5 analysable patients; we simulate n = 200 virtual subjects to obtain stable percentile summaries. The two simulated medians for FSC and FPF reproduce the paper’s typical values exactly by construction.
  • FFM covariate distribution. The Monte Carlo cohort uses the geometric mean (70.3 kg) and CV (27.4%) reported by Wittau et al. for their own Monte Carlo simulations (Methods ‘Monte Carlo simulations’ paragraph), drawn from a log-normal. The five enrolled patients had observed FFM ranging 52.3 - 94.0 kg.
  • Allometric exponents. The paper states ‘standard allometric scaling’ without printing the exponent values; the Discussion contrasts a roughly 15% difference between allometric and linear over the 1.8-fold cohort FFM range, consistent with the canonical 0.75 (clearance) / 1.0 (volume). These exponents are encoded as fixed() in ini() because the paper treats them as structural.
  • Subcutaneous tissue and peritoneal fluid as scaled observations, not separate ODE states. The paper’s final model multiplies the central plasma concentration by FSC and FPF (Materials and Methods ‘Structural model’ paragraph 1; Table 2 footnote d). Additional model variants with small (0.1 L) tissue and fluid compartments were used only to determine whether SC and PF were kinetically closer to the central or peripheral compartment; the final model collapses them into the FSC / FPF scalars because equilibration with plasma is rapid (half-life < 30 min).
  • Diagonal omega matrix. Results paragraph 4 of the paper: ‘The model included a major-diagonal variance-covariance matrix’. Encoded as six independent eta ~ variance entries.
  • NCA validation is approximate. The paper computed NCA on the actual five patients with their observed FFM values; we cannot reproduce the exact NCA without those covariates. Simulated medians and quartiles are population summaries from the virtual cohort.
  • Monte Carlo fT > MIC target attainment (Figure 3) is not replicated here; the model file allows users to run those simulations themselves with a custom dosing regimen (15-min infusion, 3-h infusion, or continuous infusion) by overriding the events table.