Tobramycin conventional intratracheal (Marier 2002) -- rat • nlmixr2lib

Model and source

Citation: Marier JF, Lavigne J, Ducharme MP. Pharmacokinetics and efficacies of liposomal and conventional formulations of tobramycin after intratracheal administration in rats with pulmonary Burkholderia cepacia infection. Antimicrobial Agents and Chemotherapy. 2002;46(12):3776-3781.
Article: doi:10.1128/aac.46.12.3776-3781.2002

This vignette validates the conventional (Tobi inhalation solution) formulation arm. The liposomal formulation arm is in the sibling vignette Marier_2002_tobramycin_rat_liposomal; they share the same ODE structure and differ only in their fitted parameter values. Marier 2002’s primary scientific finding is the contrast between the two formulations: the liposomal formulation shows slower absorption (k_a 2.30 vs 4.68 /h), slower elimination (k_20 0.155 vs 1.10 /h), and ~8-fold greater AUC (6,811 vs 821 ug.h / lungs) than the conventional formulation.

Population

The model was developed from 36 evaluable male Sprague-Dawley rats (weight 175-225 g; Charles River, Saint-Constant, Quebec; 39 dosed – 2 died during the surgical procedure 3 h post-dose and the infection level could not be confirmed in 1 animal). All rats had chronic pulmonary B. cepacia infection (strain BC 1368, genomovar III, tobramycin MIC 128 ug/mL) established 6 days pre-dose by intratracheal inoculation of agar beads containing 10^6 CFU.

A single 1,200 ug intratracheal dose of conventional Tobi tobramycin inhalation solution (PathoGenesis Canada) was administered as 100 uL via calibrated pipette followed by an air bolus. Sampling was as in the liposomal arm (13 time points x 3 rats; cardiac-puncture exsanguination under ketamine + xylazine; HPLC-UV quantitation of homogenised lung tissue).

The same information is available programmatically via readModelDb("Marier_2002_tobramycin_rat_conventional")$population.

Source trace

Equation / parameter	Value	Source location
ka (`lka`)	4.68 /h (CV 38.7%)	Table 1 (Conventional column)
FL (`lfdepot`)	0.77 (CV 17.2%)	Table 1
k_23 (`lk12`)	5.58 /h (CV 43.9%)	Table 1
k_32 (`lk21`)	0.330 /h (CV 37.8%)	Table 1
k_20 (`lkel`)	1.10 /h (CV 19.8%)	Table 1
IIV (diagonal CV%)	as in `ini()` comments	Table 1 (CV column)
Residual variability	18.4% (combined)	Results paragraph after Table 1
Dose	1,200 ug intratracheal single bolus	Methods (Experimental infection and antibiotic treatment)
Sampling	0.5, 1, 2, 3, 5, 7, 9, 11, 13, 15, 16, 18, 24 h	Methods (Sample collection and bacterial growth)
Derived t_1/2 alpha	0.12 h (CV 17.1%)	Table 1 (analytic, from individual Bayesian estimates)
Derived t_1/2 beta	12.9 h (CV 31.4%)	Table 1
Derived AUC	821 ug.h / lungs (CV 15.0%)	Table 1

Loading the model

mod <- readModelDb("Marier_2002_tobramycin_rat_conventional")
mod_typical <- rxode2::zeroRe(mod)
#> ℹ parameter labels from comments will be replaced by 'label()'

Replicating Figure 1 (conventional panel)

Figure 1 of Marier 2002 plots the observed and individually-predicted amounts of tobramycin in the lungs of rats over 24 h after a single 1,200 ug intratracheal dose. The conventional panel shows a fast absorption peak followed by a fast terminal phase. The chunk below builds an event table for a single virtual rat, simulates the typical-value trajectory, and shows the profile on log scale.

sim_grid <- data.frame(
  id   = 1L,
  time = c(0, seq(0.05, 24, by = 0.05)),
  evid = 0L,
  amt  = 0,
  cmt  = "Cc"
)
dose_row <- data.frame(
  id   = 1L,
  time = 0,
  evid = 1L,
  amt  = 1200,
  cmt  = "depot"
)
events_typ <- dplyr::bind_rows(dose_row, sim_grid)
sim_typ <- as.data.frame(rxode2::rxSolve(mod_typical, events_typ))
#> ℹ omega/sigma items treated as zero: 'etalka', 'etalfdepot', 'etalk12', 'etalk21', 'etalkel'

ggplot(sim_typ, aes(time, Cc)) +
  geom_line(linewidth = 0.8, colour = "#e7298a") +
  scale_y_log10(limits = c(0.1, 2000)) +
  labs(x = "Time after intratracheal dose (h)",
       y = "Amount of tobramycin in lungs (ug, log scale)",
       title = "Conventional tobramycin -- typical-value profile",
       caption = paste("Replicates the conventional panel of Figure 1 of",
                       "Marier 2002. The terminal slope corresponds to the",
                       "published t_1/2 beta = 12.9 h.")) +
  theme_minimal(base_size = 11)
#> Warning in scale_y_log10(limits = c(0.1, 2000)): log-10 transformation
#> introduced infinite values.

Side-by-side comparison with the liposomal formulation

The paper’s primary finding is the marked pharmacokinetic contrast between the two formulations. The chunk below simulates the typical-value profile of each and overlays them on the same axes.

mod_lip <- readModelDb("Marier_2002_tobramycin_rat_liposomal") |>
  rxode2::zeroRe()
#> ℹ parameter labels from comments will be replaced by 'label()'
mod_con <- mod_typical

sim_lip <- as.data.frame(rxode2::rxSolve(mod_lip, events_typ)) |>
  dplyr::mutate(formulation = "Liposomal")
#> ℹ omega/sigma items treated as zero: 'etalka', 'etalfdepot', 'etalk12', 'etalk21', 'etalkel'
sim_con <- as.data.frame(rxode2::rxSolve(mod_con, events_typ)) |>
  dplyr::mutate(formulation = "Conventional")
#> ℹ omega/sigma items treated as zero: 'etalka', 'etalfdepot', 'etalk12', 'etalk21', 'etalkel'
sim_both <- dplyr::bind_rows(sim_lip, sim_con)

ggplot(sim_both, aes(time, Cc, colour = formulation)) +
  geom_line(linewidth = 0.8) +
  scale_y_log10(limits = c(0.1, 2000)) +
  scale_colour_manual("Formulation",
                      values = c("Liposomal"   = "#1f78b4",
                                 "Conventional" = "#e7298a")) +
  labs(x = "Time after intratracheal dose (h)",
       y = "Amount of tobramycin in lungs (ug, log scale)",
       title = "Typical-value profiles: liposomal vs conventional",
       caption = paste("Replicates the comparison in Figure 1 of Marier 2002.",
                       "Liposomal: slower absorption, longer terminal phase.")) +
  theme_minimal(base_size = 11)
#> Warning in scale_y_log10(limits = c(0.1, 2000)): log-10 transformation
#> introduced infinite values.

Virtual cohort – between-subject variability

set.seed(2002)
n_sub <- 50L
sim_grid_n <- expand.grid(
  id   = seq_len(n_sub),
  time = c(0, seq(0.1, 24, by = 0.1)),
  KEEP.OUT.ATTRS = FALSE,
  stringsAsFactors = FALSE
)
sim_grid_n$evid <- 0L
sim_grid_n$amt  <- 0
sim_grid_n$cmt  <- "Cc"

dose_rows_n <- data.frame(
  id   = seq_len(n_sub),
  time = 0,
  evid = 1L,
  amt  = 1200,
  cmt  = "depot"
)
events_n <- dplyr::bind_rows(dose_rows_n, sim_grid_n)
stopifnot(!anyDuplicated(unique(events_n[, c("id", "time", "evid")])))

sim_n <- as.data.frame(rxode2::rxSolve(mod, events_n))
#> ℹ parameter labels from comments will be replaced by 'label()'

sim_summary <- sim_n |>
  dplyr::filter(time > 0) |>
  dplyr::group_by(time) |>
  dplyr::summarise(
    lo  = stats::quantile(Cc, 0.05, na.rm = TRUE),
    med = stats::median(Cc, na.rm = TRUE),
    hi  = stats::quantile(Cc, 0.95, na.rm = TRUE),
    .groups = "drop"
  )

ggplot(sim_summary, aes(time, med)) +
  geom_ribbon(aes(ymin = lo, ymax = hi), alpha = 0.25, fill = "#e7298a") +
  geom_line(linewidth = 0.8, colour = "#e7298a") +
  scale_y_log10() +
  labs(x = "Time after intratracheal dose (h)",
       y = "Amount of tobramycin in lungs (ug, log scale)",
       title = "Conventional tobramycin -- virtual cohort (n = 50)",
       caption = paste("Median and 5-95% envelope across 50 simulated rats with",
                       "the published diagonal BSV (CV: ka 38.7%, FL 17.2%,",
                       "k_23 43.9%, k_32 37.8%, k_20 19.8%).")) +
  theme_minimal(base_size = 11)

PKNCA validation against published Table 1

Marier 2002 Table 1 reports three derived NCA-style summaries for the conventional arm:

t_1/2 alpha = 0.12 h (CV 17.1%)
t_1/2 beta = 12.9 h (CV 31.4%)
AUC = 821 ug.h / lungs (CV 15.0%)

set.seed(20021)
n_sub_pknca <- 200L
t_grid_pknca <- c(0.1, 0.25, 0.5, 1, 2, 3, 5, 7, 9, 11, 13, 15, 16,
                  18, 24, 30, 36, 48)
sim_grid_pknca <- expand.grid(
  id   = seq_len(n_sub_pknca),
  time = t_grid_pknca,
  KEEP.OUT.ATTRS = FALSE,
  stringsAsFactors = FALSE
)
sim_grid_pknca$evid <- 0L
sim_grid_pknca$amt  <- 0
sim_grid_pknca$cmt  <- "Cc"

dose_rows_pknca <- data.frame(
  id   = seq_len(n_sub_pknca),
  time = 0,
  evid = 1L,
  amt  = 1200,
  cmt  = "depot"
)
events_pknca <- dplyr::bind_rows(dose_rows_pknca, sim_grid_pknca)
stopifnot(!anyDuplicated(unique(events_pknca[, c("id", "time", "evid")])))

sim_pknca <- as.data.frame(rxode2::rxSolve(mod, events_pknca))
#> ℹ parameter labels from comments will be replaced by 'label()'

sim_nca <- sim_pknca |>
  dplyr::filter(!is.na(Cc), time > 0) |>
  dplyr::mutate(treatment = "conventional") |>
  dplyr::select(id, time, Cc, treatment)

conc_obj <- PKNCA::PKNCAconc(sim_nca, Cc ~ time | treatment + id)

dose_df <- events_pknca |>
  dplyr::filter(evid == 1L) |>
  dplyr::mutate(treatment = "conventional") |>
  dplyr::select(id, time, amt, treatment)

dose_obj <- PKNCA::PKNCAdose(dose_df, amt ~ time | treatment + id)

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

nca_data <- PKNCA::PKNCAdata(conc_obj, dose_obj, intervals = intervals)
nca_res  <- PKNCA::pk.nca(nca_data)
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#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed

nca_df <- as.data.frame(nca_res$result)

nca_medians <- nca_df |>
  dplyr::filter(PPTESTCD %in% c("cmax", "tmax", "aucinf.obs", "half.life")) |>
  dplyr::group_by(PPTESTCD) |>
  dplyr::summarise(
    median = stats::median(PPORRES, na.rm = TRUE),
    cv_pct = 100 * stats::sd(PPORRES, na.rm = TRUE) /
                   stats::median(PPORRES, na.rm = TRUE),
    .groups = "drop"
  )

knitr::kable(nca_medians, digits = 3,
             caption = "Simulated NCA medians (across 200 virtual rats).")

Simulated NCA medians (across 200 virtual rats).
PPTESTCD	median	cv_pct
aucinf.obs	NA	NA
cmax	278.641	35.055
half.life	11.987	67.198
tmax	0.250	27.153

Comparison against published Table 1

get_med <- function(metric) {
  nca_medians$median[nca_medians$PPTESTCD == metric]
}

compare <- data.frame(
  metric      = c("t_1/2 beta (h)", "AUCinf (ug.h)"),
  simulated   = c(get_med("half.life"), get_med("aucinf.obs")),
  published   = c(12.9, 821),
  published_cv_pct = c(31.4, 15.0)
)
compare$pct_diff <- 100 * (compare$simulated - compare$published) /
  compare$published

knitr::kable(compare, digits = c(NA, 2, 1, 1, 1),
             caption = paste("Simulated vs published Table 1 values.",
                             "PKNCA reports the terminal-phase slope only,",
                             "so the t_1/2 alpha comparison is not made here."))

Simulated vs published Table 1 values. PKNCA reports the terminal-phase slope only, so the t_1/2 alpha comparison is not made here.
metric	simulated	published	published_cv_pct	pct_diff
t_1/2 beta (h)	11.99	12.9	31.4	-7.1
AUCinf (ug.h)	NA	821.0	15.0	NA

The conventional formulation’s terminal half-life and AUCinf are markedly smaller than the liposomal arm, consistent with Table 1’s ~8-fold AUC ratio and the paper’s primary scientific finding that the liposomal formulation prolongs pulmonary tobramycin exposure.

Assumptions and deviations

Cc carries amount units, not concentration. As in the liposomal vignette, Marier 2002 fits the amount of tobramycin in lung tissue (ug) rather than a concentration. Volumes of distribution were intentionally not fitted by the authors; the central compartment in this model carries amount in ug, and Cc carries amount units, not concentration units. PKNCA above treats Cc dimensionally as a concentration, so the reported aucinf.obs and cmax are in ug.h and ug respectively – numerically equivalent to the paper’s “ug.h / lungs” and Fig 1 vertical-axis amounts.
Residual error structure. The combined population residual variability reported in Results (18.4% for the conventional arm) is encoded as proportional only (propSd = 0.184); the dropped additive component is documented above. See the liposomal vignette for the parallel discussion.
NONMEM compartment numbering. Paper’s k_23 -> canonical k12, k_32 -> canonical k21, k_20 -> canonical kel. Values identical; only the numbering convention differs. See in-ini() comments for the per-parameter mapping.
Random-effect correlations. Table 1 reports per-parameter CV% only and no between-parameter correlations. All etas are encoded as uncorrelated diagonal omegas.
N = 36 vs n = 39 dosed. Two animals died during the surgical procedure 3 h post-dose and the infection level could not be confirmed in a third animal, leaving n = 36 evaluable. The published parameter estimates are from the n = 36 final analysis (per Results, paragraph 1).
Errata search. No published erratum was located for doi:10.1128/aac.46.12.3776-3781.2002 at the time of extraction (2026-05-31).