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Flucloxacillin (Landersdorfer 2007)

Source: vignettes/articles/Landersdorfer_2007_flucloxacillin.Rmd
Landersdorfer_2007_flucloxacillin.Rmd

Model and source

  • Citation: Landersdorfer CB, Kirkpatrick CMJ, Kinzig-Schippers M, Bulitta JB, Holzgrabe U, Drusano GL, Sorgel F. Population pharmacokinetics at two dose levels and pharmacodynamic profiling of flucloxacillin. Antimicrob Agents Chemother. 2007;51(9):3290-3297. doi:10.1128/AAC.01410-06
  • Description: Three-compartment population PK model for IV flucloxacillin in healthy adult volunteers (Landersdorfer 2007) with linear renal and non-renal elimination. The structural model splits total clearance into a renal arm (CL_R = 5.37 L/h) and a non-renal arm (CL_NR = 2.73 L/h); their sum reproduces the derived total clearance CL_T = 8.10 L/h reported in Table 2. The renal arm also drives a cumulative urinary excretion compartment that the paper fits jointly with plasma. Distribution uses a shallow peripheral (V_2 = 2.61 L, CLic_shallow = 15.3 L/h) and a deep peripheral (V_3 = 2.17 L, CLic_deep = 1.23 L/h); central volume V_1 = 4.79 L. Between-subject variability is reported as a full 5x5 variance-covariance matrix (Table 3, natural-log scale) on CL_R, CL_NR, V_1, V_2, V_3; no BSV is included on the inter-compartmental clearances. Residual error is combined additive + proportional on both plasma concentrations (9.4% CV, 0.155 mg/L) and cumulative urinary amounts (20.9% CV, 1.04 mg). The 5-min infusion duration used in the study is supplied via dose records (DUR / RATE) rather than as a model parameter. No structural covariates were retained: the cohort was 10 healthy Caucasian adults (5 M / 5 F, weight 52-83 kg, age 23-34 years) and demographics are not used inside the model. Monte Carlo dose-attainment simulations in the paper (continuous, 4-h, 0.5-h infusions) reuse these PK parameters together with 96% protein binding.
  • Article: https://doi.org/10.1128/AAC.01410-06

Population

Landersdorfer 2007 studied 10 healthy Caucasian adult volunteers (5 male, 5 female) in a randomised, two-way crossover trial at the Institute for Biomedical and Pharmaceutical Research (Nuernberg-Heroldsberg, Germany). The median body weight was 71 kg (range 52-83), median height 178 cm (range 165-190), and median age 25 years (range 23-34). All subjects had normal renal and hepatic function (Methods, Study participants; Results, Demographics).

Each subject received a single 500 mg dose and a single 1,000 mg dose of flucloxacillin as a 5-min intravenous infusion, separated by a >= 4-day washout period. Plasma and urine were sampled over 24 h post-infusion (Methods, Sampling schedule). The population PK fit pooled plasma and urine data across both dose levels using NONMEM V (FOCE-I, ADVAN 11 / TRANS 4 analytical solution); a three-compartment model with linear renal and non-renal elimination was selected over two-compartment and saturable-elimination alternatives based on a 200-point OFV improvement and visual predictive checks (Methods, Population PK analysis; Results, Population PK).

Source trace

The per-parameter origin is recorded as an in-file comment next to each ini() entry in inst/modeldb/specificDrugs/Landersdorfer_2007_flucloxacillin.R. The table below collects them in one place.

Equation / parameter Value Source location
Three-compartment ODE system (central + shallow peripheral + deep peripheral + cumulative urine) n/a Methods, Population PK analysis (equations for dX(1)/dt through dX(4)/dt)
lcl_renal (renal CL CL_R) 5.37 L/h Table 2, CL_R
lcl_nonren (non-renal CL CL_NR) 2.73 L/h Table 2, CL_NR
lvc (central volume V_1) 4.79 L Table 2, V_1
lvp (shallow peripheral volume V_2) 2.61 L Table 2, V_2
lvp2 (deep peripheral volume V_3) 2.17 L Table 2, V_3
lq (central <-> shallow CLic_shallow) 15.3 L/h Table 2, CLic_shallow
lq2 (central <-> deep CLic_deep) 1.23 L/h Table 2, CLic_deep
5x5 BSV variance-covariance block on natural-log scale (CL_R, CL_NR, V_1, V_2, V_3) see Table 3 entries Table 3 (variance-covariance matrix)
propSd (plasma proportional residual) 0.094 (9.4% CV) Table 2, CV_C
addSd (plasma additive residual) 0.155 mg/L Table 2, SD_C
propSd_urineAmt (urine proportional residual) 0.209 (20.9% CV) Table 2, CV_AU
addSd_urineAmt (urine additive residual) 1.04 mg Table 2, SD_AU
5-min infusion duration Tk_0 (fixed) 5 min Table 2, Tk_0 footnote (“not estimated”); supplied via dose record
No covariate effects retained n/a Methods, Individual PK model (only BSV variance-covariance is reported; no structural covariates discussed)

Derived quantities (Table 2 footnotes b / c): total clearance CL_T = CL_R + CL_NR = 8.10 L/h; steady-state volume V_ss = V_1 + V_2 + V_3 = 9.57 L. These are not free parameters and are recovered automatically when the model is simulated.

Virtual cohort

The original observed concentration-time data are not redistributed with the nlmixr2lib package; the cohort below approximates the Landersdorfer 2007 trial demographics (n = 10 subjects per dose arm, both arms simulated to mirror the crossover design). The model has no structural covariates, so the cohort specification is just dosing.

set.seed(20070101L)

# Paper sampling schedule (Methods, Sampling schedule): pre-infusion (t=0),
# end of 5-min infusion, then 5, 10, 15, 20, 25, 45, 60, 75, 90 min and
# 2, 2.5, 3, 3.5, 4, 5, 6, 8, 24 h after end of infusion.
obs_times <- c(0,
               5/60,
               5/60 + c(5, 10, 15, 20, 25, 45, 60, 75, 90) / 60,
               5/60 + c(2, 2.5, 3, 3.5, 4, 5, 6, 8, 24))

make_cohort <- function(n, dose_mg, id_offset = 0L) {
  ids <- id_offset + seq_len(n)
  arm <- paste0(dose_mg, " mg")
  dosing <- tibble(
    id       = ids,
    time     = 0,
    amt      = as.numeric(dose_mg),
    evid     = 1L,
    cmt      = "central",
    dur      = 5 / 60,   # 5-min infusion (paper Tk_0)
    rate     = NA_real_,
    dose_arm = arm
  )
  obs <- tidyr::expand_grid(id = ids, time = obs_times) |>
    mutate(amt = NA_real_, evid = 0L, cmt = "Cc", dur = NA_real_,
           rate = NA_real_, dose_arm = arm)
  bind_rows(dosing, obs) |> arrange(id, time, desc(evid))
}

events <- bind_rows(
  make_cohort(n = 200L, dose_mg =  500, id_offset =    0L),
  make_cohort(n = 200L, dose_mg = 1000, id_offset = 1000L)
)

stopifnot(!anyDuplicated(unique(events[, c("id", "time", "evid")])))

Simulation 

mod <- readModelDb("Landersdorfer_2007_flucloxacillin")
sim <- rxode2::rxSolve(mod, events = events, keep = "dose_arm") |>
  as.data.frame()
#> ℹ parameter labels from comments will be replaced by 'label()'
mod_typical <- rxode2::zeroRe(mod)
#> ℹ parameter labels from comments will be replaced by 'label()'
sim_typical <- rxode2::rxSolve(mod_typical, events = events, keep = "dose_arm") |>
  as.data.frame()
#> ℹ omega/sigma items treated as zero: 'etalcl_renal', 'etalcl_nonren', 'etalvc', 'etalvp', 'etalvp2'
#> Warning: multi-subject simulation without without 'omega'

Replicate published figures 

# Replicates Figure 1 of Landersdorfer 2007: average plasma concentrations
# after 5-min IV infusions of 500 mg and 1,000 mg flucloxacillin. The paper's
# Figure 1 shows mean +/- SD profiles in linear and semi-log scales.
sim |>
  filter(time > 0, !is.na(Cc)) |>
  group_by(dose_arm, time) |>
  summarise(
    mean_Cc = mean(Cc),
    sd_Cc   = sd(Cc),
    .groups = "drop"
  ) |>
  ggplot(aes(time, mean_Cc, colour = dose_arm)) +
  geom_ribbon(aes(ymin = pmax(mean_Cc - sd_Cc, 1e-3),
                  ymax = mean_Cc + sd_Cc,
                  fill = dose_arm), alpha = 0.20, colour = NA) +
  geom_line() +
  scale_y_log10() +
  labs(x = "Time (h)", y = "Plasma flucloxacillin (mg/L, log scale)",
       colour = "Dose", fill = "Dose",
       title = "Figure 1 -- mean +/- SD plasma profiles after IV flucloxacillin",
       caption = "Replicates Landersdorfer 2007 Figure 1.")

# Replicates Figure 2 of Landersdorfer 2007 (plasma VPC panel): median and
# prediction intervals over time, by dose group.
vpc_plasma <- sim |>
  filter(time > 0, !is.na(Cc)) |>
  group_by(dose_arm, time) |>
  summarise(
    Q10 = quantile(Cc, 0.10),
    Q25 = quantile(Cc, 0.25),
    Q50 = quantile(Cc, 0.50),
    Q75 = quantile(Cc, 0.75),
    Q90 = quantile(Cc, 0.90),
    .groups = "drop"
  )

ggplot(vpc_plasma, aes(time)) +
  geom_ribbon(aes(ymin = Q10, ymax = Q90, fill = dose_arm), alpha = 0.20) +
  geom_ribbon(aes(ymin = Q25, ymax = Q75, fill = dose_arm), alpha = 0.30) +
  geom_line(aes(y = Q50, colour = dose_arm)) +
  facet_wrap(~dose_arm, scales = "free_y") +
  scale_y_log10() +
  labs(x = "Time (h)", y = "Plasma flucloxacillin (mg/L, log scale)",
       colour = "Dose", fill = "Dose",
       title = "Figure 2 (plasma) -- VPC of simulated plasma concentrations",
       caption = "Replicates Landersdorfer 2007 Figure 2, plasma panel.")

# Replicates Figure 2 of Landersdorfer 2007 (urine VPC panel): cumulative
# amount excreted unchanged in urine over 24 h.
vpc_urine <- sim |>
  filter(time > 0, !is.na(urineAmt)) |>
  group_by(dose_arm, time) |>
  summarise(
    Q10 = quantile(urineAmt, 0.10),
    Q25 = quantile(urineAmt, 0.25),
    Q50 = quantile(urineAmt, 0.50),
    Q75 = quantile(urineAmt, 0.75),
    Q90 = quantile(urineAmt, 0.90),
    .groups = "drop"
  )

ggplot(vpc_urine, aes(time)) +
  geom_ribbon(aes(ymin = Q10, ymax = Q90, fill = dose_arm), alpha = 0.20) +
  geom_ribbon(aes(ymin = Q25, ymax = Q75, fill = dose_arm), alpha = 0.30) +
  geom_line(aes(y = Q50, colour = dose_arm)) +
  facet_wrap(~dose_arm, scales = "free_y") +
  labs(x = "Time (h)", y = "Cumulative amount in urine (mg)",
       colour = "Dose", fill = "Dose",
       title = "Figure 2 (urine) -- VPC of simulated cumulative urinary amount",
       caption = "Replicates Landersdorfer 2007 Figure 2, urine panel.")

PKNCA validation 

sim_nca <- sim |>
  filter(!is.na(Cc)) |>
  select(id, time, Cc, dose_arm)

dose_df <- events |>
  filter(evid == 1) |>
  select(id, time, amt, dose_arm)

conc_obj <- PKNCA::PKNCAconc(sim_nca, Cc ~ time | dose_arm + id,
                             concu = "mg/L", timeu = "h")
dose_obj <- PKNCA::PKNCAdose(dose_df, amt ~ time | dose_arm + id,
                             doseu = "mg")

intervals <- data.frame(
  start       = 0,
  end         = Inf,
  cmax        = TRUE,
  tmax        = TRUE,
  aucinf.obs  = TRUE,
  half.life   = TRUE,
  mrt.iv.obs  = TRUE
)

nca_res <- PKNCA::pk.nca(PKNCA::PKNCAdata(conc_obj, dose_obj, intervals = intervals))

nca_tbl <- as.data.frame(nca_res$result) |>
  filter(PPTESTCD %in% c("cmax", "tmax", "aucinf.obs", "half.life", "mrt.iv.obs")) |>
  group_by(dose_arm, PPTESTCD) |>
  summarise(
    geomean = exp(mean(log(pmax(PPORRES, 1e-9)), na.rm = TRUE)),
    cv_pct  = 100 * sqrt(exp(var(log(pmax(PPORRES, 1e-9)), na.rm = TRUE)) - 1),
    n_used  = sum(!is.na(PPORRES)),
    .groups = "drop"
  ) |>
  arrange(dose_arm, PPTESTCD)

knitr::kable(nca_tbl,
             digits   = 3,
             caption  = "Simulated NCA parameters (geometric mean, CV%) by dose arm.")
Simulated NCA parameters (geometric mean, CV%) by dose arm.
dose_arm PPTESTCD geomean cv_pct n_used
1000 mg aucinf.obs 123.582 17.996 200
1000 mg cmax 174.013 13.818 200
1000 mg half.life 1.529 12.621 200
1000 mg mrt.iv.obs 1.235 13.050 200
1000 mg tmax 0.083 0.000 200
500 mg aucinf.obs 59.736 20.469 200
500 mg cmax 86.873 14.466 200
500 mg half.life 1.534 12.841 200
500 mg mrt.iv.obs 1.207 14.647 200
500 mg tmax 0.083 0.000 200

Comparison against published NCA (Table 1) 

# Landersdorfer 2007 Table 1: noncompartmental analysis (geometric mean and CV%)
# from the n = 10 healthy-volunteer crossover trial. The 'mrt.iv.obs' label
# from PKNCA corresponds to the paper's "Mean residence time (h)" entry.
published <- tribble(
  ~dose_arm, ~param,        ~published_geomean, ~published_cv_pct,
  "500 mg",  "cmax",        86.8,               13,
  "500 mg",  "aucinf.obs",  500 / 8.16,         21,
  "500 mg",  "half.life",   1.40,               26,
  "500 mg",  "mrt.iv.obs",  1.18,               19,
  "1000 mg", "cmax",        167,                16,
  "1000 mg", "aucinf.obs",  1000 / 8.18,        20,
  "1000 mg", "half.life",   1.62,               25,
  "1000 mg", "mrt.iv.obs",  1.22,               14
) |>
  rename(PPTESTCD = param)

comparison <- published |>
  left_join(nca_tbl, by = c("dose_arm", "PPTESTCD")) |>
  mutate(pct_diff_geomean = 100 * (geomean - published_geomean) / published_geomean) |>
  select(dose_arm, PPTESTCD,
         published_geomean, published_cv_pct,
         simulated_geomean = geomean,
         simulated_cv_pct  = cv_pct,
         pct_diff_geomean,
         simulated_n_used  = n_used)

knitr::kable(comparison,
             digits = c(0, 0, 2, 1, 2, 1, 1, 0),
             caption = paste("Published (Landersdorfer 2007 Table 1) vs simulated",
                             "NCA parameters; AUCinf published values are derived",
                             "as dose / total-CL (CL_T = 8.16 L/h at 500 mg and",
                             "8.18 L/h at 1,000 mg per Table 1).",
                             "`simulated_n_used` is the number of simulated subjects",
                             "(of 200 per dose arm) for which PKNCA was able to",
                             "compute the parameter; the rest are excluded by",
                             "PKNCA's standard checks (e.g., too few terminal-phase",
                             "points)."))
Published (Landersdorfer 2007 Table 1) vs simulated NCA parameters; AUCinf published values are derived as dose / total-CL (CL_T = 8.16 L/h at 500 mg and 8.18 L/h at 1,000 mg per Table 1). simulated_n_used is the number of simulated subjects (of 200 per dose arm) for which PKNCA was able to compute the parameter; the rest are excluded by PKNCA’s standard checks (e.g., too few terminal-phase points).
dose_arm PPTESTCD published_geomean published_cv_pct simulated_geomean simulated_cv_pct pct_diff_geomean simulated_n_used
500 mg cmax 86.80 13 86.87 14.5 0.1 200
500 mg aucinf.obs 61.27 21 59.74 20.5 -2.5 200
500 mg half.life 1.40 26 1.53 12.8 9.6 200
500 mg mrt.iv.obs 1.18 19 1.21 14.6 2.3 200
1000 mg cmax 167.00 16 174.01 13.8 4.2 200
1000 mg aucinf.obs 122.25 20 123.58 18.0 1.1 200
1000 mg half.life 1.62 25 1.53 12.6 -5.6 200
1000 mg mrt.iv.obs 1.22 14 1.24 13.0 1.2 200

The paper’s noncompartmental analysis (Table 1) was performed on observed plasma samples from 10 subjects in a crossover design; the simulated NCA above uses 200 virtual subjects per dose arm and dense sampling, so the simulated CV% is expected to be somewhat tighter than the observed CV% (the observed CV% includes assay and within-subject variability that the typical-value simulation does not). Geometric means should agree closely (target <= 20% difference per the verification checklist). The half-life and MRT comparisons exercise the late-phase mixing among the three disposition compartments, which is the hardest part of the model to reproduce from a Table-2 / Table-3 read.

Assumptions and deviations

  • No structural covariates retained. The paper does not include any covariate effects on PK parameters (Methods, Individual PK model); the cohort was 10 healthy adults with normal renal and hepatic function and the BSV model is a 5x5 variance-covariance block on natural-log scale, not a covariate-driven structural model. covariateData is therefore empty.
  • No BSV on inter-compartmental clearances. Table 2 footnote d explicitly records that BSV was not estimated for CL_ic_shallow or CL_ic_deep “as estimation of these variance and covariance terms did not significantly improve the objective function” (Methods, Individual PK model). Reproduced as point-only lq and lq2.
  • 5-min infusion duration is data-driven, not a model parameter. The paper reports Tk_0 = 5 min as the structural duration of the zero-order input but records it as a fixed protocol constant (Table 2 footnote “not estimated”). In rxode2 / nlmixr2 the infusion duration is supplied per dose record via dur (or rate); the vignette cohort uses dur = 5/60 h to match the trial. Monte-Carlo dose-attainment simulations described in the paper (continuous, 4-h, 0.5-h infusions) reuse the same PK parameters and only change the dose record’s infusion duration.
  • Variance reading. Table 3 reports the variance-covariance matrix on the natural-log scale; the paper’s Methods clarify that the “% CV” column in Table 2 is sqrt(omega^2) expressed as a percentage rather than the back-transformed log(1 + CV^2) form some popPK papers use. The Table 3 diagonals are therefore used directly as omega^2 in ini() rather than recomputed from the Table 2 CV%, which would introduce a rounding error.
  • AUCinf published reference is derived, not directly reported. Table 1 reports total clearance CL_T (8.16 L/h at 500 mg; 8.18 L/h at 1,000 mg) rather than AUCinf, so the comparison in the PKNCA section back-derives AUCinf = dose / CL_T. This is dimensionally equivalent and exact under the paper’s linear-PK conclusion (Results, Population PK; Discussion paragraph 6).
  • Monte Carlo Simulation block omitted. The paper’s Figures 3 and 4 and Table 4 use the PK model to compute fT > MIC for various dosing regimens with 96% protein binding. Those simulations are dose-attainment analyses rather than PK validation, and are not reproduced here; the vignette is scoped to validating that the PK structural model + parameter set reproduce the paper’s primary PK observations (Figures 1-2 and Table 1).