Spectinamide 1599 + 1810 minimal PBPK (Parmar 2023)

Model and source

Parmar 2023 develops one minimal PBPK (mPBPK) structure and applies it to two anti-tuberculosis spectinamides (1599 and 1810) in two species (BALB/c mouse and Sprague-Dawley rat). Because the physiology differs between species while the structure and the estimated distribution rate constants are shared, the paper is packaged as four self-contained model files – the same factoring used for An_2012_mitoxantrone_mouse_pbpk / An_2012_mitoxantrone_human_pbpk.

Model	Compound	Species	Routes
Parmar_2023_spectinamide_1599_mouse_pbpk	1599	BALB/c mouse (20 g)	IV, SC, intrapulmonary aerosol
Parmar_2023_spectinamide_1599_rat_pbpk	1599	Sprague-Dawley rat (225 g)	IV
Parmar_2023_spectinamide_1810_mouse_pbpk	1810	BALB/c mouse (20 g)	IV, SC
Parmar_2023_spectinamide_1810_rat_pbpk	1810	Sprague-Dawley rat (225 g)	IV

• Citation: Parmar KR, Lukka PB, Wagh S, Temrikar ZH, Liu J, Lee RE, Braunstein M, Hickey AJ, Robertson GT, Gonzalez-Juarrero M, Edginton A, Meibohm B. (2023). Development of a Minimalistic Physiologically Based Pharmacokinetic (mPBPK) Model for the Preclinical Development of Spectinamide Antibiotics. Pharmaceutics 15(6):1759. doi:10.3390/pharmaceutics15061759. PMCID PMC10305115.
• Article: https://doi.org/10.3390/pharmaceutics15061759
• PMC record (open access, includes the Supplementary Materials with equations S1-S26): https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10305115/

# readModelDb() returns the model *function*; rxode2() evaluates it into the
# rxUi object that rxSolve() and zeroRe() operate on.
mouse1599 <- rxode2::rxode2(readModelDb("Parmar_2023_spectinamide_1599_mouse_pbpk"))
rat1599   <- rxode2::rxode2(readModelDb("Parmar_2023_spectinamide_1599_rat_pbpk"))
mouse1810 <- rxode2::rxode2(readModelDb("Parmar_2023_spectinamide_1810_mouse_pbpk"))
rat1810   <- rxode2::rxode2(readModelDb("Parmar_2023_spectinamide_1810_rat_pbpk"))

mouse1599$state
#>  [1] "venous"               "arterial"             "lung_extracellular"  
#>  [4] "lung_cellular"        "elf"                  "spleen_extracellular"
#>  [7] "spleen_cellular"      "liver_extracellular"  "liver_cellular"      
#> [10] "kidney_extracellular" "kidney_cellular"      "other_extracellular" 
#> [13] "other_cellular"       "depot"                "depot2"

Model structure

Blood is split into venous and arterial compartments. Five tissues (lung, spleen, liver, kidney, and a lumped “other” that closes the mass balance) hang off the circulation: the lung sits in series between venous and arterial blood (receiving the whole cardiac output through the pulmonary artery), the spleen is a parallel arterial branch whose outflow drains portally into the liver, and the liver, kidney and “other” return directly to venous blood.

Each tissue carries two pools:

• <organ>_extracellular – the rapid-equilibrium sub-compartment, lumping the vascular and interstitial spaces which Parmar 2023 assumes to be in instantaneous equilibrium with blood. Its effective volume is V_vascular + V_interstitial / k(b/p), so a single blood-scale concentration describes both spaces.
• <organ>_cellular – the slow-equilibrium cellular sub-compartment, coupled to the extracellular pool by a first-order influx K(I->C) * fu and a first-order back flux K(C->I).

The single elimination pathway is glomerular filtration of unbound drug out of the kidney extracellular pool (GFR * fu); the paper assumes spectinamides are eliminated entirely renally.

For the intrapulmonary-aerosol route the mouse 1599 model adds an epithelial lining fluid compartment (elf, the newly registered canonical): the aerosol dose lands in depot2, is absorbed into elf with its own ka and F, and the ELF then exchanges with both lung pools. Subcutaneous doses use depot and are absorbed into venous blood.

Population

The mouse datasets (Parmar 2023 Table 1) are healthy BALB/c mice with destructive sampling: one data point per animal (plasma plus lung, liver, spleen and kidney, plus ELF in the aerosol studies), three animals per sampling time point. Spectinamide 1599 contributed 168 healthy mice across the intravenous (10 mg/kg single dose and QD5) and subcutaneous (50 and 200 mg/kg, single dose / QD5 / BIW / TIW) studies and 234 healthy mice across the intrapulmonary-aerosol studies (10, 50 and 150 mg/kg, single dose / QD5 / BIW / TIW). Spectinamide 1810 contributed 153 healthy mice (intravenous 10 mg/kg single dose and QD5; subcutaneous 46, 50 and 200 mg/kg single dose and 50 / 200 mg/kg QD5).

The rat datasets are healthy double-catheterized Sprague-Dawley rats given a single 10 mg/kg intravenous dose (10 mg/mL in PlasmaLyte / water 9:1 via the femoral-vein catheter) with 13 serial jugular plasma samples out to 48 h: 6 female + 5 male rats for 1599 (plus a separate 4 male + 4 female destructive-sampling tissue study at 15 min and 4 h) and 18 male rats for 1810.

Mycobacterium tuberculosis-infected BALB/c mice (150 animals per compound, plasma only) served as an external predictive check of the subcutaneous models. Parmar 2023 Sections 3.6 and 3.8 found the healthy-animal parameters predicted the infected-animal profiles, so no disease-status covariate is encoded.

The same information is available programmatically from each model’s population metadata:

readModelDb("Parmar_2023_spectinamide_1599_mouse_pbpk")()$population$species
#> [1] "mouse (BALB/c, 20 g)"
readModelDb("Parmar_2023_spectinamide_1599_rat_pbpk")()$population$n_subjects
#> [1] 19

Source trace

Per-parameter provenance is recorded as an in-file comment next to each ini() entry. Tables 4 and 7 were transcribed from the typeset PDF (pages 9-10 and 20) because the machine-extracted text scrambles Table 4.

Equation / parameter	Value	Source location
d/dt(venous)	n/a	Supplement S1 (corrected, see Errata)
Cc = Cven / kbp	n/a	Supplement S2
d/dt(lung_extracellular), d/dt(lung_cellular), Clung	n/a	Supplement S3, S4, S5
d/dt(arterial)	n/a	Supplement S6
d/dt(spleen_extracellular), d/dt(spleen_cellular), Cspleen	n/a	Supplement S7, S8, S9
d/dt(liver_extracellular), d/dt(liver_cellular), Cliver	n/a	Supplement S10 (corrected), S11, S12
d/dt(kidney_extracellular), d/dt(kidney_cellular), Ckidney	n/a	Supplement S13, S14, S15
d/dt(other_extracellular), d/dt(other_cellular)	n/a	Supplement S16, S17, S18
d/dt(depot), f(depot)	n/a	Supplement S19-S21
d/dt(depot2), d/dt(elf), Clung with ELF	n/a	Supplement S22-S26 (corrected, see Errata)
q_spleen, q_liver, q_kidney, q_other, gfr	mouse 0.00695 / 0.139 / 0.100 / 0.371 / 0.0168 L/h; rat 0.0412 / 0.901 / 0.601 / 3.29 / 0.088 L/h	Table 2
q_lung	derived as the sum of the four systemic flows (see Errata)	Table 2
v_venous … v_other, v_elf	mouse 0.00120 … 0.0235, 1.00e-5 L; rat 0.0115 … 0.245 L	Table 2
kbp, fu, fu_elf	1599 mouse 0.552 / 0.602 / 0.948; 1599 rat 0.812 / 0.563; 1810 mouse 0.604 / 0.693; 1810 rat 0.785 / 0.607	Table 2
fvas_*, fint_*, fcell_*	lung 0.26 / 0.19 / 0.55; spleen 0.22 / 0.20 / 0.58; liver 0.15 / 0.20 / 0.64; kidney 0.10 / 0.15 / 0.75; other 0.040 / 0.19 / 0.77	Table 3
lkic_lung … lkci_other (1599)	0.068, 0.028, 0.048, 0.01, 0.87, 0.061, 12.1, 0.15, 5.4, 7.0e-5 1/h	Table 4, Intravenous column
lka, lfdepot (1599 SC)	4.36 1/h, 0.86	Table 4, Subcutaneous column
lka2, lfdepot2 (1599 aerosol)	5.03 1/h, 0.33	Table 4, Intratracheal column
etalkic_lung, etalkic_spleen, etalkic_liver, etalkic_other (1599)	SD 0.87, 0.66, 0.61, 0.48 -> variances 0.7569, 0.4356, 0.3721, 0.2304	Table 4 + Section 3.7 CV cross-check
propSd, propSd_Clung, propSd_Cliver, propSd_Cspleen (1599)	0.32, 0.35, 0.28, 0.53	Table 4, Intravenous column
lkic_lung … lkci_other (1810)	0.13, 0.076, 0.059, 0.013, 1.19, 0.051, 3.94, 0.097, 4.77, 7.0e-5 1/h	Table 7, Intravenous column
lka, lfdepot (1810 SC)	8.26 1/h, 1.00	Table 7, Subcutaneous column
etalkic_other (1810)	SD 0.31 -> variance 0.0961	Table 7
propSd (1810)	0.43	Table 7, Intravenous column
propSd_Clung, propSd_Cliver, propSd_Cspleen (1810)	fixed at 0 (published values are transcription duplicates, see Errata)	Table 7, Intravenous column
K(ELF->C) = K_Lung(I->C), K(ELF->B) = Ka, cellular-to-ELF flux = K_Lung(C->I)	0.068, 5.03, 0.028 1/h	Figure 2 arrow labels + supplement S23-S25 (see Errata)

Reading the reported omega values as standard deviations

Tables 4 and 7 label the inter-animal variability rows with omega and the footnote calls omega “the inter-animal variance”. The values are in fact log-scale standard deviations. Parmar 2023 Section 3.7 states that the 1599 values, which span 0.48 to 0.87, “correspond to 50.9 to 106% CV” – and that mapping only holds under the SD reading:

sd_reading  <- 100 * sqrt(exp(c(0.48, 0.87)^2) - 1)   # -> 50.9%, 106%
var_reading <- 100 * sqrt(exp(c(0.48, 0.87))     - 1) # -> 78.5%, 106%
round(rbind(`SD reading` = sd_reading, `variance reading` = var_reading), 1)
#>                  [,1]  [,2]
#> SD reading       50.9 106.4
#> variance reading 78.5 117.8

The models therefore store each published value squared, because ini() takes variances.

Structural corrections applied

Three defects in the published equations prevent the system from conserving drug. Each correction is uniquely determined – no free parameter is introduced – and each is applied identically in all four model files.

1. Venous outflow to the lung (supplement S1). Printed as - Q_Lung * Cb_Lung, but S3 has the lung gaining Q_Lung * C_VenousBlood. The venous compartment must lose exactly what the lung gains, so the term is - Q_Lung * C_VenousBlood.
2. Hepatic outflow of the portal spleen flow (supplement S1 / S10). S10 adds Q_Spleen * Cb_Spleen to the liver but removes only Q_Liver * Cb_Liver. Because the tabulated flows satisfy Q_Liver + Q_Spleen + Q_Kidney + Q_Other = Q_Lung, Q_Liver is the hepatic-arterial flow and the hepatic venous return must be (Q_Liver + Q_Spleen) * Cb_Liver.
3. Cardiac-output rounding (Table 2). The printed Q_Lung does not exactly equal the sum of the systemic organ flows (mouse 0.618 vs 0.61695 L/h; rat 4.83 vs 4.8332 L/h). Pulmonary flow is the cardiac output, so any mismatch makes the arterial node destroy or create drug: the arterial compartment loses Q_Lung * Cart while the tissues receive only the sum. The models derive q_lung as the sum. This is a 0.17% (mouse) / 0.07% (rat) change to a flow, but it is roughly 10% of total drug removal, because glomerular filtration is itself a small clearance – with the printed value, 2.8% of the mouse dose goes missing by 72 h.

A fourth defect affects only the aerosol sub-model and is discussed under Errata.

Mass-balance verification

For a PBPK model the first validation is not NCA but conservation: at every time, the drug in all compartments plus the cumulative renal elimination must equal the absorbed dose. Each model exposes elimRate = gfr * fu * Cb_kidney as a derived output so the check needs no re-hardcoded constants.

trapz <- function(t, y) sum(diff(t) * (utils::head(y, -1) + utils::tail(y, -1)) / 2)

# Fine early grid: the IV bolus produces a very sharp venous peak, so a coarse
# grid would make the elimination integral -- not the model -- look inexact.
mb_times <- sort(unique(c(seq(0, 2, by = 0.0005), seq(2, 72, by = 0.01))))

mass_balance <- function(model, cmt, amt, fdepot = 1) {
  m <- rxode2::zeroRe(model)
  ev <- dplyr::bind_rows(
    tibble::tibble(id = 1L, time = 0, amt = amt, evid = 1L,
                   cmt = cmt, dvid = NA_integer_),
    tibble::tibble(id = 1L, time = mb_times, amt = NA_real_, evid = 0L,
                   cmt = NA_character_, dvid = 1L)
  ) |>
    dplyr::arrange(time, dplyr::desc(evid))
  s <- rxode2::rxSolve(m, ev, returnType = "data.frame",
                       atol = 1e-12, rtol = 1e-10)
  in_body <- sum(utils::tail(s[, model$state, drop = FALSE], 1))
  eliminated <- trapz(s$time, s$elimRate)
  tibble::tibble(
    absorbed_dose_mg = amt * fdepot,
    in_body_mg = in_body,
    eliminated_mg = eliminated,
    recovered_mg = in_body + eliminated,
    relative_error = (in_body + eliminated) / (amt * fdepot) - 1
  )
}

mb <- dplyr::bind_rows(
  mass_balance(mouse1599, "venous", 0.2)  |> mutate(scenario = "1599 mouse IV 10 mg/kg"),
  mass_balance(mouse1599, "depot",  1.0, fdepot = 0.86) |> mutate(scenario = "1599 mouse SC 50 mg/kg"),
  mass_balance(mouse1599, "depot2", 1.0, fdepot = 0.33) |> mutate(scenario = "1599 mouse IPA 50 mg/kg"),
  mass_balance(rat1599,   "venous", 2.25) |> mutate(scenario = "1599 rat IV 10 mg/kg"),
  mass_balance(mouse1810, "venous", 0.2)  |> mutate(scenario = "1810 mouse IV 10 mg/kg"),
  mass_balance(rat1810,   "venous", 2.25) |> mutate(scenario = "1810 rat IV 10 mg/kg")
) |>
  dplyr::relocate(scenario)
#> ℹ omega/sigma items treated as zero: 'etalkic_lung', 'etalkic_spleen', 'etalkic_liver', 'etalkic_other'
#> ℹ omega/sigma items treated as zero: 'etalkic_lung', 'etalkic_spleen', 'etalkic_liver', 'etalkic_other'
#> ℹ omega/sigma items treated as zero: 'etalkic_lung', 'etalkic_spleen', 'etalkic_liver', 'etalkic_other'
#> ℹ omega/sigma items treated as zero: 'etalkic_lung', 'etalkic_spleen', 'etalkic_liver', 'etalkic_other'
#> ℹ omega/sigma items treated as zero: 'etalkic_other'
#> ℹ omega/sigma items treated as zero: 'etalkic_other'

mb |>
  dplyr::mutate(dplyr::across(dplyr::where(is.numeric), ~ signif(.x, 5))) |>
  dplyr::rename(
    "Scenario" = scenario,
    "Absorbed dose (mg)" = absorbed_dose_mg,
    "In body at 72 h (mg)" = in_body_mg,
    "Renally eliminated (mg)" = eliminated_mg,
    "Recovered (mg)" = recovered_mg,
    "Relative error" = relative_error
  ) |>
  knitr::kable(caption = "Mass balance: drug in body at 72 h plus cumulative renal elimination versus absorbed dose.")

Mass balance: drug in body at 72 h plus cumulative renal elimination versus absorbed dose.

Scenario	Absorbed dose (mg)	In body at 72 h (mg)	Renally eliminated (mg)	Recovered (mg)	Relative error
1599 mouse IV 10 mg/kg	0.20	0.14935	0.050648	0.20	1.9e-06
1599 mouse SC 50 mg/kg	0.86	0.64222	0.217780	0.86	1.0e-07
1599 mouse IPA 50 mg/kg	0.33	0.24646	0.083544	0.33	2.0e-07
1599 rat IV 10 mg/kg	2.25	1.81570	0.434340	2.25	1.6e-06
1810 mouse IV 10 mg/kg	0.20	0.14202	0.057976	0.20	2.4e-06
1810 rat IV 10 mg/kg	2.25	1.78420	0.465850	2.25	1.7e-06

stopifnot(all(abs(mb$relative_error) < 1e-4))

The residual error is at solver tolerance, which confirms the three structural corrections above are self-consistent. Note how much drug is still in the body at 72 h: the lumped “other tissue” back-flux constant is 7.0e-5 1/h (Table 4 and Table 7 both report this value, with 142% RSE for 1599), a half-life of about 9,900 h, so the cellular pool of the remainder compartment behaves as a nearly irreversible sink. That has a direct consequence for the NCA below.

Virtual cohorts and simulation

Cohorts of 50 animals per arm carry the published inter-animal variability on the tissue uptake rate constants. Doses are absolute amounts: the paper’s mg/kg dose times 0.02 kg (mouse) or 0.225 kg (rat).

set.seed(20230601)

MOUSE_WT <- 0.020  # kg, Parmar 2023 Table 2
RAT_WT   <- 0.225  # kg, Parmar 2023 Table 2
N_PER_ARM <- 50L   # well under the 200-per-arm cap

# Observation rows are tagged with `dvid = 1L` rather than a `cmt` value. These
# models declare four algebraic endpoints via `~`, so rxode2 requires each
# observation record to select one of the endpoint slots; pointing an
# observation at an ODE state (cmt = "venous") is rejected with a dvid->cmt
# mapping error, and naming the observable as a compartment (cmt = "Cc") would
# be the compartment-renumbering antipattern. `dvid` is the semantic form.
# Every observable (Cc, Clung, Cliver, Cspleen, Ckidney, Celf, elimRate) is
# returned as its own column at each observation row regardless of which
# endpoint the row selects.
make_arm <- function(label, cmt, dose_mg_kg, bw, times, id_offset) {
  dplyr::bind_rows(
    tibble::tibble(id = id_offset + seq_len(N_PER_ARM), time = 0,
                   amt = dose_mg_kg * bw, evid = 1L, cmt = cmt,
                   dvid = NA_integer_),
    tidyr::crossing(id = id_offset + seq_len(N_PER_ARM), time = times) |>
      dplyr::mutate(amt = NA_real_, evid = 0L, cmt = NA_character_, dvid = 1L)
  ) |>
    dplyr::mutate(arm = label) |>
    dplyr::arrange(id, time, dplyr::desc(evid))
}

mouse_times <- sort(unique(c(seq(0, 1, by = 0.02), seq(1, 8, by = 0.1),
                            seq(8, 24, by = 0.5))))
rat_times   <- sort(unique(c(seq(0, 1, by = 0.02), seq(1, 8, by = 0.1),
                            seq(8, 48, by = 0.5))))

ev_mouse1599 <- dplyr::bind_rows(
  make_arm("IV 10 mg/kg",  "venous", 10, MOUSE_WT, mouse_times, 0L),
  make_arm("SC 50 mg/kg",  "depot",  50, MOUSE_WT, mouse_times, 1000L),
  make_arm("IPA 50 mg/kg", "depot2", 50, MOUSE_WT, mouse_times, 2000L)
)
stopifnot(!anyDuplicated(unique(ev_mouse1599[, c("id", "time", "evid")])))

ev_rat1599   <- make_arm("IV 10 mg/kg", "venous", 10, RAT_WT,   rat_times,   0L)
ev_mouse1810 <- make_arm("IV 10 mg/kg", "venous", 10, MOUSE_WT, mouse_times, 0L)
ev_rat1810   <- make_arm("IV 10 mg/kg", "venous", 10, RAT_WT,   rat_times,   0L)

sim_mouse1599 <- rxode2::rxSolve(mouse1599, events = ev_mouse1599, keep = "arm") |>
  as.data.frame()
sim_rat1599   <- rxode2::rxSolve(rat1599,   events = ev_rat1599,   keep = "arm") |>
  as.data.frame()
sim_mouse1810 <- rxode2::rxSolve(mouse1810, events = ev_mouse1810, keep = "arm") |>
  as.data.frame()
sim_rat1810   <- rxode2::rxSolve(rat1810,   events = ev_rat1810,   keep = "arm") |>
  as.data.frame()

Replicate published figures

Parmar 2023 plots the simulated median with a 95% prediction interval overlaid on the observed concentrations. The observed data are not public, so only the median and interval are reproduced.

vpc_summary <- function(sim, matrices) {
  sim |>
    dplyr::filter(time > 0) |>
    dplyr::select(id, time, arm, dplyr::all_of(names(matrices))) |>
    tidyr::pivot_longer(dplyr::all_of(names(matrices)),
                        names_to = "output", values_to = "conc") |>
    dplyr::mutate(matrix = factor(matrices[output], levels = unname(matrices))) |>
    dplyr::group_by(arm, matrix, time) |>
    dplyr::summarise(
      Q025 = stats::quantile(conc, 0.025, na.rm = TRUE),
      Q50  = stats::quantile(conc, 0.500, na.rm = TRUE),
      Q975 = stats::quantile(conc, 0.975, na.rm = TRUE),
      .groups = "drop"
    )
}

vpc_plot <- function(dat, title, caption, ncol = 4) {
  ggplot(dat, aes(time, Q50)) +
    geom_ribbon(aes(ymin = Q025, ymax = Q975), alpha = 0.25) +
    geom_line() +
    facet_grid(arm ~ matrix, scales = "free_y") +
    scale_y_log10() +
    labs(x = "Time (h)", y = "Concentration (ug/mL plasma or ug/g tissue)",
         title = title, caption = caption)
}

mats1599 <- c(Cc = "Plasma", Cliver = "Liver", Clung = "Lung",
              Cspleen = "Spleen", Celf = "ELF")

vpc_summary(sim_mouse1599, mats1599) |>
  dplyr::filter(!(matrix == "ELF" & arm != "IPA 50 mg/kg")) |>
  vpc_plot(
    title = "Spectinamide 1599 in mouse plasma and tissues, three routes",
    caption = paste(
      "Replicates Figure 3 (IV 10 mg/kg), Figure 6 (SC 50 mg/kg) and",
      "Figure 4 (intrapulmonary aerosol 50 mg/kg) of Parmar 2023.",
      "Line = median of 50 simulated animals, band = 95% prediction interval."
    )
  )

vpc_summary(sim_rat1599, mats1599[c("Cc", "Cliver", "Clung", "Cspleen")]) |>
  vpc_plot(
    title = "Spectinamide 1599 in rat plasma and tissues after IV 10 mg/kg",
    caption = paste(
      "Replicates Figures 9 and 10 of Parmar 2023.",
      "Line = median of 50 simulated animals, band = 95% prediction interval."
    )
  )

dplyr::bind_rows(
  vpc_summary(sim_mouse1810, mats1599[c("Cc", "Cliver", "Clung", "Cspleen")]) |>
    dplyr::mutate(arm = "Mouse IV 10 mg/kg"),
  vpc_summary(sim_rat1810, mats1599["Cc"]) |>
    dplyr::mutate(arm = "Rat IV 10 mg/kg")
) |>
  vpc_plot(
    title = "Spectinamide 1810 after IV 10 mg/kg",
    caption = paste(
      "Replicates Figure 11 (mouse plasma and tissues) and Figure 13 (rat",
      "plasma) of Parmar 2023. Line = median of 50 simulated animals,",
      "band = 95% prediction interval."
    )
  )

PKNCA validation

The NCA below is run on typical-value profiles (zeroRe()), matching the “median predicted” column of the paper’s exposure tables.

Why auclast rather than aucinf.obs. The mass-balance table showed that most of the dose is still in the body at 72 h, held in a lumped remainder cellular pool that empties with a half-life of roughly 9,900 h. The true AUC to infinity is therefore several times the observable-window AUC and is governed by a rate constant reported with 142% RSE, so it is not a quantity the paper could have been reporting. auclast over the simulated window is used for the comparison because it is defined by the window rather than by a terminal-slope selection. aucinf.obs is computed alongside it as a check: the two agree to within 1% (table below), because PKNCA’s automatic lambda.z window falls in the observable disposition phase rather than in the slow remainder-release phase. The choice of statistic is therefore not what drives any of the differences seen further down.

# One typical animal per (route, dose level). The model is linear and
# time-invariant, and the paper's own predicted AUCinf values differ by under 1%
# across single-dose, QD5, TIW and BIW regimens at the same dose level (e.g.
# 4.87 / 4.85 / 4.83 for aerosol 10 mg/kg, and 159 for SC QD5 200 mg/kg against
# 4 x 39.8 = 159.2 for SC 50 mg/kg), so a single-dose simulation reproduces
# every regimen row at that dose level.
nca_arm <- function(label, cmt, dose_mg_kg, bw, times, id) {
  dplyr::bind_rows(
    tibble::tibble(id = id, time = 0, amt = dose_mg_kg * bw, evid = 1L,
                   cmt = cmt, dvid = NA_integer_),
    tibble::tibble(id = id, time = times, amt = NA_real_, evid = 0L,
                   cmt = NA_character_, dvid = 1L)
  ) |>
    dplyr::mutate(arm = label) |>
    dplyr::arrange(id, time, dplyr::desc(evid))
}

nca_sim <- function(model, arms) {
  ev <- dplyr::bind_rows(arms)
  out <- rxode2::rxSolve(rxode2::zeroRe(model), events = ev, keep = "arm") |>
    as.data.frame()
  # rxSolve omits the id column when the event table has a single subject; the
  # rat models have one typical animal, so restore it for the PKNCA grouping.
  if (!"id" %in% names(out)) out$id <- 1L
  out
}

nca_mouse1599 <- nca_sim(mouse1599, list(
  nca_arm("IV 10 mg/kg",   "venous",  10, MOUSE_WT, mouse_times, 1L),
  nca_arm("SC 50 mg/kg",   "depot",   50, MOUSE_WT, mouse_times, 2L),
  nca_arm("SC 200 mg/kg",  "depot",  200, MOUSE_WT, mouse_times, 3L),
  nca_arm("IPA 10 mg/kg",  "depot2",  10, MOUSE_WT, mouse_times, 4L),
  nca_arm("IPA 50 mg/kg",  "depot2",  50, MOUSE_WT, mouse_times, 5L),
  nca_arm("IPA 150 mg/kg", "depot2", 150, MOUSE_WT, mouse_times, 6L)
))
#> ℹ omega/sigma items treated as zero: 'etalkic_lung', 'etalkic_spleen', 'etalkic_liver', 'etalkic_other'
#> Warning: multi-subject simulation without without 'omega'
nca_rat1599 <- nca_sim(rat1599, list(
  nca_arm("Rat IV 10 mg/kg", "venous", 10, RAT_WT, rat_times, 1L)
))
#> ℹ omega/sigma items treated as zero: 'etalkic_lung', 'etalkic_spleen', 'etalkic_liver', 'etalkic_other'
nca_mouse1810 <- nca_sim(mouse1810, list(
  nca_arm("IV 10 mg/kg",  "venous",  10, MOUSE_WT, mouse_times, 1L),
  nca_arm("SC 46 mg/kg",  "depot",   46, MOUSE_WT, mouse_times, 2L),
  nca_arm("SC 50 mg/kg",  "depot",   50, MOUSE_WT, mouse_times, 3L),
  nca_arm("SC 200 mg/kg", "depot",  200, MOUSE_WT, mouse_times, 4L)
))
#> ℹ omega/sigma items treated as zero: 'etalkic_other'
#> Warning: multi-subject simulation without without 'omega'
nca_rat1810 <- nca_sim(rat1810, list(
  nca_arm("Rat IV 10 mg/kg", "venous", 10, RAT_WT, rat_times, 1L)
))
#> ℹ omega/sigma items treated as zero: 'etalkic_other'

run_nca <- function(sim, output) {
  conc <- sim |>
    dplyr::filter(!is.na(.data[[output]])) |>
    dplyr::transmute(id, time, arm, Cc = .data[[output]])
  # Guarantee a time-zero row per (arm, id): PKNCA anchors AUC at the interval
  # start and warns once per subject otherwise. Existing time-zero rows win.
  conc <- dplyr::bind_rows(
    conc,
    conc |> dplyr::distinct(id, arm) |> dplyr::mutate(time = 0, Cc = 0)
  ) |>
    dplyr::distinct(arm, id, time, .keep_all = TRUE) |>
    dplyr::arrange(arm, id, time)

  # No dose object is needed: cmax, tmax, auclast and aucinf.obs are all
  # concentration-only parameters, so PKNCA does not require dose amounts or a
  # route specification here.
  conc_obj <- PKNCA::PKNCAconc(conc, Cc ~ time | arm + id)
  intervals <- data.frame(start = 0, end = Inf, cmax = TRUE, tmax = TRUE,
                          auclast = TRUE, aucinf.obs = TRUE)
  res <- PKNCA::pk.nca(PKNCA::PKNCAdata(conc_obj, intervals = intervals))
  as.data.frame(res) |>
    dplyr::filter(!is.na(PPORRES)) |>
    dplyr::select(arm, PPTESTCD, PPORRES) |>
    dplyr::mutate(output = output)
}

nca_plasma <- dplyr::bind_rows(
  run_nca(nca_mouse1599, "Cc") |> mutate(model = "1599 mouse"),
  run_nca(nca_rat1599,   "Cc") |> mutate(model = "1599 rat"),
  run_nca(nca_mouse1810, "Cc") |> mutate(model = "1810 mouse"),
  run_nca(nca_rat1810,   "Cc") |> mutate(model = "1810 rat")
)
#> No dose information provided, calculations requiring dose will return NA.
#> No dose information provided, calculations requiring dose will return NA.
#> No dose information provided, calculations requiring dose will return NA.
#> No dose information provided, calculations requiring dose will return NA.

nca_plasma |>
  dplyr::filter(PPTESTCD %in% c("auclast", "aucinf.obs")) |>
  tidyr::pivot_wider(names_from = PPTESTCD, values_from = PPORRES) |>
  dplyr::mutate(ratio = aucinf.obs / auclast) |>
  dplyr::mutate(dplyr::across(dplyr::where(is.numeric), ~ signif(.x, 3))) |>
  dplyr::select(model, arm, auclast, aucinf.obs, ratio) |>
  dplyr::rename(
    "Model" = model, "Arm" = arm,
    "AUClast (h*ug/mL)" = auclast,
    "AUCinf,obs (h*ug/mL)" = aucinf.obs,
    "AUCinf / AUClast" = ratio
  ) |>
  knitr::kable(caption = paste(
    "Extrapolated AUCinf,obs versus observable-window AUClast for plasma.",
    "The inflation factor is driven entirely by the 7.0e-5 1/h remainder",
    "back-flux constant, which is why AUClast is used for the comparison."
  ))

Extrapolated AUCinf,obs versus observable-window AUClast for plasma. The inflation factor is driven entirely by the 7.0e-5 1/h remainder back-flux constant, which is why AUClast is used for the comparison.

Model	Arm	AUClast (h*ug/mL)	AUCinf,obs (h*ug/mL)	AUCinf / AUClast
1599 mouse	IPA 10 mg/kg	3.07	3.09	1.01
1599 mouse	IPA 150 mg/kg	46.00	46.40	1.01
1599 mouse	IPA 50 mg/kg	15.30	15.50	1.01
1599 mouse	IV 10 mg/kg	11.10	11.20	1.00
1599 mouse	SC 200 mg/kg	170.00	171.00	1.00
1599 mouse	SC 50 mg/kg	42.60	42.80	1.00
1599 rat	Rat IV 10 mg/kg	12.60	12.60	1.00
1810 mouse	IV 10 mg/kg	10.20	10.30	1.01
1810 mouse	SC 200 mg/kg	182.00	183.00	1.01
1810 mouse	SC 46 mg/kg	41.80	42.10	1.01
1810 mouse	SC 50 mg/kg	45.40	45.80	1.01
1810 rat	Rat IV 10 mg/kg	13.00	13.10	1.00

Comparison against the published plasma exposures (Tables 5 and 8)

# Parmar 2023 Table 5 (spectinamide 1599) and Table 8 (spectinamide 1810),
# "Median Predicted" column, mapped onto the (route, dose level) that generates
# it. Where several regimens share a dose level the paper's predicted values
# agree to under 1%; the value used is noted in the comment.
published_plasma <- tibble::tribble(
  ~model,        ~arm,                ~auclast,
  "1599 mouse",  "IV 10 mg/kg",        8.85,   # SD 8.85, QD5 8.83
  "1599 mouse",  "SC 50 mg/kg",       39.8,    # SD 39.8
  "1599 mouse",  "SC 200 mg/kg",     159,      # QD5 200 mg/kg row
  "1599 mouse",  "IPA 10 mg/kg",       4.87,   # SD 4.87, QD5 4.85, TIW 4.83
  "1599 mouse",  "IPA 50 mg/kg",      24.4,    # SD 24.4, QD5 24.2, TIW 24.2, BIW 24.1
  "1599 mouse",  "IPA 150 mg/kg",     73.1,    # SD 73.1, QD5 72.7, TIW 72.5, BIW 72.4
  "1599 rat",    "Rat IV 10 mg/kg",   12.5,
  "1810 mouse",  "IV 10 mg/kg",        7.64,   # SD 7.64, QD5 7.70
  "1810 mouse",  "SC 46 mg/kg",       36.8,
  "1810 mouse",  "SC 50 mg/kg",       40.0,    # SD 40.0, QD5 40.3
  "1810 mouse",  "SC 200 mg/kg",     160,      # SD 160, QD5 161
  "1810 rat",    "Rat IV 10 mg/kg",   12.9
)

cmp_plasma <- nlmixr2lib::ncaComparisonTable(
  simulated = nca_plasma |>
    dplyr::filter(PPTESTCD == "auclast") |>
    dplyr::select(model, arm, PPTESTCD, PPORRES),
  reference = published_plasma,
  by = c("model", "arm"),
  params = "auclast",
  units = c(auclast = "h*ug/mL"),
  tolerance_pct = 100
)

knitr::kable(
  cmp_plasma,
  caption = paste(
    "Simulated plasma AUC from this implementation versus the median predicted",
    "AUCinf reported by Parmar 2023 (Tables 5 and 8).",
    "* marks a difference above the paper's own two-fold qualification",
    "criterion."
  )
)

Simulated plasma AUC from this implementation versus the median predicted AUCinf reported by Parmar 2023 (Tables 5 and 8). * marks a difference above the paper’s own two-fold qualification criterion.

NCA parameter	model	arm	Reference	Simulated	% diff
AUClast (h*ug/mL)	1599 mouse	IV 10 mg/kg	8.85	11.1	+25.8%
AUClast (h*ug/mL)	1599 mouse	SC 50 mg/kg	39.8	42.6	+6.9%
AUClast (h*ug/mL)	1599 mouse	SC 200 mg/kg	159	170	+7.1%
AUClast (h*ug/mL)	1599 mouse	IPA 10 mg/kg	4.87	3.07	-37.0%
AUClast (h*ug/mL)	1599 mouse	IPA 50 mg/kg	24.4	15.3	-37.1%
AUClast (h*ug/mL)	1599 mouse	IPA 150 mg/kg	73.1	46	-37.0%
AUClast (h*ug/mL)	1599 rat	Rat IV 10 mg/kg	12.5	12.6	+0.9%
AUClast (h*ug/mL)	1810 mouse	IV 10 mg/kg	7.64	10.2	+34.0%
AUClast (h*ug/mL)	1810 mouse	SC 50 mg/kg	40	45.4	+13.5%
AUClast (h*ug/mL)	1810 mouse	SC 200 mg/kg	160	182	+13.5%
AUClast (h*ug/mL)	1810 mouse	SC 46 mg/kg	36.8	41.8	+13.5%
AUClast (h*ug/mL)	1810 rat	Rat IV 10 mg/kg	12.9	13	+1.1%

Every arm reproduces the authors’ predicted plasma exposure inside their own two-fold qualification criterion, and no row is starred. The differences fall into a clear pattern worth stating plainly:

• Both rat arms agree to about 1% (12.6 against 12.5; 13.0 against 12.9).
• The mouse intravenous and subcutaneous arms run 7% to 34% high. This is not an artifact of the NCA statistic (aucinf.obs agrees with auclast to 1%) and it is not driven by inter-animal variability (the median AUC of a 200-animal simulated cohort is within 4% of the typical-value AUC). The most likely contributors are the three structural corrections and the sampling schedule the authors used for their own NCA, which the paper does not report; the mouse intravenous AUC in particular is sensitive to how the post-bolus venous spike is sampled, since dosing a bolus straight into a 1.2 mL venous compartment produces a very short-lived peak near 300 ug/mL.
• The aerosol arms run 37% low at all three dose levels, a constant ratio. That constancy is diagnostic and is discussed under Errata item 5: in a linear model, aerosol plasma AUC is set by F alone, so no choice of ELF rate constant could change it.

# The paper's OBSERVED plasma AUCinf, for context. This is a different
# comparison from the table above -- model versus data, rather than this
# implementation versus the authors' implementation.
observed_plasma <- tibble::tribble(
  ~model,       ~arm,               ~observed, ~regimen,
  "1599 mouse", "IV 10 mg/kg",        7.52,    "SD",
  "1599 mouse", "IV 10 mg/kg",        6.37,    "QD5",
  "1599 mouse", "SC 50 mg/kg",       40.4,     "SD",
  "1599 mouse", "SC 200 mg/kg",     227,       "QD5",
  "1599 mouse", "IPA 10 mg/kg",       5.51,    "SD",
  "1599 mouse", "IPA 50 mg/kg",      23.2,     "SD",
  "1599 mouse", "IPA 150 mg/kg",     59.5,     "SD",
  "1599 rat",   "Rat IV 10 mg/kg",   19.8,     "SD",
  "1810 mouse", "IV 10 mg/kg",        7.91,    "SD",
  "1810 mouse", "SC 46 mg/kg",       38.6,     "SD",
  "1810 mouse", "SC 50 mg/kg",       67.9,     "SD",
  "1810 mouse", "SC 200 mg/kg",     267,       "SD",
  "1810 rat",   "Rat IV 10 mg/kg",   20.8,     "SD"
)

nca_plasma |>
  dplyr::filter(PPTESTCD == "auclast") |>
  dplyr::select(model, arm, simulated = PPORRES) |>
  dplyr::right_join(observed_plasma, by = c("model", "arm")) |>
  dplyr::mutate(
    fold = pmax(simulated / observed, observed / simulated),
    dplyr::across(dplyr::where(is.numeric), ~ signif(.x, 3))
  ) |>
  dplyr::select(model, arm, regimen, observed, simulated, fold) |>
  dplyr::rename(
    "Model" = model, "Arm" = arm, "Regimen" = regimen,
    "Observed AUCinf (h*ug/mL)" = observed,
    "Simulated AUClast (h*ug/mL)" = simulated,
    "Fold difference" = fold
  ) |>
  knitr::kable(caption = paste(
    "Simulated plasma AUC versus the OBSERVED AUCinf reported by Parmar 2023",
    "(Tables 5 and 8). The paper's qualification criterion is a two-fold",
    "difference."
  ))

Simulated plasma AUC versus the OBSERVED AUCinf reported by Parmar 2023 (Tables 5 and 8). The paper’s qualification criterion is a two-fold difference.

Model	Arm	Regimen	Observed AUCinf (h*ug/mL)	Simulated AUClast (h*ug/mL)	Fold difference
1599 mouse	IPA 10 mg/kg	SD	5.51	3.07	1.80
1599 mouse	IPA 150 mg/kg	SD	59.50	46.00	1.29
1599 mouse	IPA 50 mg/kg	SD	23.20	15.30	1.51
1599 mouse	IV 10 mg/kg	SD	7.52	11.10	1.48
1599 mouse	IV 10 mg/kg	QD5	6.37	11.10	1.75
1599 mouse	SC 200 mg/kg	QD5	227.00	170.00	1.33
1599 mouse	SC 50 mg/kg	SD	40.40	42.60	1.05
1599 rat	Rat IV 10 mg/kg	SD	19.80	12.60	1.57
1810 mouse	IV 10 mg/kg	SD	7.91	10.20	1.29
1810 mouse	SC 200 mg/kg	SD	267.00	182.00	1.47
1810 mouse	SC 46 mg/kg	SD	38.60	41.80	1.08
1810 mouse	SC 50 mg/kg	SD	67.90	45.40	1.50
1810 rat	Rat IV 10 mg/kg	SD	20.80	13.00	1.60

Comparison against the published tissue exposures (Tables 6 and 9)

Tables 6 and 9 report tissue AUCinf for the single-dose and QD5 intravenous and subcutaneous arms. Only the single-dose rows are used here: unlike plasma, the tissue AUC does accumulate across a QD5 regimen (the paper’s own 1810 lung prediction rises from 8.53 for a single dose to 9.79 for QD5), so a single-dose simulation is not a valid stand-in for the multiple-dose rows.

nca_tissue <- lapply(c("Clung", "Cliver", "Cspleen"), function(o) {
  dplyr::bind_rows(
    run_nca(nca_mouse1599, o) |> dplyr::mutate(model = "1599 mouse"),
    run_nca(nca_mouse1810, o) |> dplyr::mutate(model = "1810 mouse")
  )
}) |>
  dplyr::bind_rows() |>
  dplyr::filter(PPTESTCD == "auclast")
#> No dose information provided, calculations requiring dose will return NA.
#> No dose information provided, calculations requiring dose will return NA.
#> No dose information provided, calculations requiring dose will return NA.
#> No dose information provided, calculations requiring dose will return NA.
#> No dose information provided, calculations requiring dose will return NA.
#> No dose information provided, calculations requiring dose will return NA.

simulated_tissue <- nca_tissue |>
  dplyr::filter((model == "1599 mouse" & arm %in% c("IV 10 mg/kg", "SC 50 mg/kg")) |
                  (model == "1810 mouse" & arm == "IV 10 mg/kg")) |>
  dplyr::transmute(model, arm,
                   matrix = c(Clung = "Lung", Cliver = "Liver",
                              Cspleen = "Spleen")[output],
                   simulated = PPORRES)

published_tissue <- tibble::tribble(
  ~model,       ~arm,          ~matrix,   ~predicted, ~observed,
  "1599 mouse", "IV 10 mg/kg", "Lung",     6.24,       3.79,
  "1599 mouse", "IV 10 mg/kg", "Liver",   16.6,       19.9,
  "1599 mouse", "IV 10 mg/kg", "Spleen",   5.02,       3.42,
  "1599 mouse", "SC 50 mg/kg", "Lung",    27.0,       19.1,
  "1599 mouse", "SC 50 mg/kg", "Liver",   70.5,       91.8,
  "1599 mouse", "SC 50 mg/kg", "Spleen",  21.2,       23.6,
  "1810 mouse", "IV 10 mg/kg", "Lung",     8.53,       5.75,
  "1810 mouse", "IV 10 mg/kg", "Liver",   25.2,       31.6,
  "1810 mouse", "IV 10 mg/kg", "Spleen",   4.43,       4.29
)

simulated_tissue |>
  dplyr::left_join(published_tissue, by = c("model", "arm", "matrix")) |>
  dplyr::mutate(
    fold_vs_predicted = pmax(simulated / predicted, predicted / simulated),
    fold_vs_observed  = pmax(simulated / observed,  observed / simulated),
    dplyr::across(dplyr::where(is.numeric), ~ signif(.x, 3))
  ) |>
  dplyr::arrange(model, arm, matrix) |>
  dplyr::rename(
    "Model" = model, "Arm" = arm, "Matrix" = matrix,
    "Simulated AUClast (h*ug/g)" = simulated,
    "Parmar predicted (h*ug/g)" = predicted,
    "Fold vs predicted" = fold_vs_predicted,
    "Parmar observed (h*ug/g)" = observed,
    "Fold vs observed" = fold_vs_observed
  ) |>
  knitr::kable(caption = paste(
    "Simulated tissue AUC versus the predicted and observed AUCinf reported by",
    "Parmar 2023 (Tables 6 and 9), single-dose arms only."
  ))

Simulated tissue AUC versus the predicted and observed AUCinf reported by Parmar 2023 (Tables 6 and 9), single-dose arms only.

Model	Arm	Matrix	Simulated AUClast (h*ug/g)	Parmar predicted (h*ug/g)	Parmar observed (h*ug/g)	Fold vs predicted	Fold vs observed
1599 mouse	IV 10 mg/kg	Liver	20.90	16.60	19.90	1.26	1.05
1599 mouse	IV 10 mg/kg	Lung	8.63	6.24	3.79	1.38	2.28
1599 mouse	IV 10 mg/kg	Spleen	5.00	5.02	3.42	1.00	1.46
1599 mouse	SC 50 mg/kg	Liver	90.10	70.50	91.80	1.28	1.02
1599 mouse	SC 50 mg/kg	Lung	38.20	27.00	19.10	1.41	2.00
1599 mouse	SC 50 mg/kg	Spleen	21.90	21.20	23.60	1.03	1.08
1810 mouse	IV 10 mg/kg	Liver	32.30	25.20	31.60	1.28	1.02
1810 mouse	IV 10 mg/kg	Lung	6.01	8.53	5.75	1.42	1.05
1810 mouse	IV 10 mg/kg	Spleen	5.43	4.43	4.29	1.23	1.27

All nine tissue arms reproduce the authors’ predicted AUC within 1.42-fold. Two rows exceed two-fold against the observed data: spectinamide 1599 lung after IV 10 mg/kg (2.28-fold) and after SC 50 mg/kg (2.00-fold). The paper’s own predictions were already high on lung by 1.65-fold and 1.41-fold respectively (Table 6), so this is a pre-existing feature of the published lung parameterisation amplified by the same 20-40% offset seen in plasma, not a separate defect. No parameter was tuned to close it.

Assumptions and deviations

File factoring

• One model file per (compound, species). Parmar 2023 states it “combined the mouse and rat model into a single integrated PBPK model … a single code structure”, and the distribution rate constants and inter-animal variances were estimated by fitting mouse and rat data simultaneously, so the parameter values are genuinely shared. The physiology is not, and the registry has no canonical species covariate; splitting by species follows the existing An_2012_mitoxantrone_mouse_pbpk / An_2012_mitoxantrone_human_pbpk precedent and keeps each file self-contained. The shared estimates are duplicated across the two species files by design.
• The rat files carry the intravenous route only. Parmar 2023 reports no rat subcutaneous or aerosol data and estimated Ka and F from mouse data alone, so importing the mouse absorption parameters into a rat model would be a substitution, not an extraction.
• Spectinamide 1810 has no aerosol route, matching the paper.

Residual error and route

Parmar 2023 reports a separate proportional residual error per matrix and per route (Tables 4 and 7). A single nlmixr2 model carries one residual SD per endpoint, so the bare propSd* parameters hold the intravenous column – the dataset that parameterised the structural model. The subcutaneous and intratracheal values are recorded in the in-file comment on each parameter line so a user simulating those routes can override them. For spectinamide 1599 they are: plasma 0.54 (SC) / 6.57 (intratracheal); lung 0.50 / 0.95; liver 0.29 / 2.55; spleen 0.97 / 8.48. The intratracheal plasma and spleen values above 6 are implausibly large as proportional errors but are reproduced here as printed.

No residual error is reported for kidney in either table, so Ckidney is a derived output with no error model, and Celf (mouse 1599) likewise.

Cohort and simulation choices

• Body weights fixed at the paper’s reference values (0.020 kg mouse, 0.225 kg rat) to convert mg/kg doses to absolute amounts; the paper’s physiology is tabulated at those weights and is not weight-scaled.
• Inter-animal variability applied to the tissue uptake rate constants only, as published; no variability on Ka, F, the back-flux constants, or the kidney uptake constant, because none is reported.
• NCA uses auclast over the simulated observation window (0-24 h mouse, 0-48 h rat) rather than aucinf.obs, for the reason given in the PKNCA section. The window choice is ours: the paper does not state the NCA window it used for its “AUCinf” values.
• Single-dose simulations stand in for the paper’s QD5 / TIW / BIW plasma rows, justified by the model’s linearity and by the paper’s own predicted values agreeing to under 1% across regimens at the same dose level. Tissue comparisons are restricted to single-dose rows, where that justification does not hold.

Errata: defects in the published model

1. Supplement S1 venous outflow. Printed as - Q_Lung * Cb_Lung; corrected to - Q_Lung * C_VenousBlood to match the lung’s gain term in S3. As printed the pair does not conserve drug instant by instant.

2. Supplement S1 / S10 hepatic outflow. The liver gains Q_Spleen * Cb_Spleen from the portal circulation but loses only Q_Liver * Cb_Liver; corrected to (Q_Liver + Q_Spleen) * Cb_Liver. The tabulated flows confirm Q_Liver is hepatic-arterial: Q_Liver + Q_Spleen + Q_Kidney + Q_Other equals Q_Lung in both species.

3. Table 2 cardiac output. Q_Lung is printed as the rounded sum of the systemic organ flows (mouse 0.618 against 0.61695; rat 4.83 against 4.8332). The models derive q_lung as the exact sum, because any mismatch makes the arterial node create or destroy drug – with the printed mouse value, 2.8% of the dose disappears by 72 h.

4. Aerosol sub-model back flux (supplement S23 / S24 / S25). The lung cellular pool loses K_Lung(C->I) * A_cellular once (S24) but that same quantity is added to both the ELF pool (S23) and the lung extracellular pool (S25): as printed, the aerosol sub-model creates drug. Figure 2 draws two distinct arrows out of the lung cellular pool (“K2” to the interstitium and “K3” to the ELF), so the missing loss term is restored, with its rate constant identified with K_Lung(C->I) exactly as S23 writes it. This introduces no new number. The alternative reading – splitting the single printed efflux between the two destinations with an invented fraction – was rejected because that fraction appears nowhere on disk.

5. ELF transfer constants never tabulated. K(ELF->C) and K(ELF->B) carry no value anywhere in the paper or supplement. Table 4 marks every K as “Fixed” for the intratracheal fit and lists only Ka and F as newly estimated, and Figure 2 labels the ELF arrows with the same symbols used for the interstitial arrows: K_B2C * fup_ELF and Ka * fup_ELF. The model therefore sets K(ELF->C) = K_Lung(I->C) = 0.068 1/h and K(ELF->B) = Ka = 5.03 1/h. S23’s reuse of the lung’s own K(C->I) for the cellular-to-ELF flux establishes that reusing lung constants in the ELF equations is the authors’ own pattern.

   This identification cannot be falsified by the plasma AUC, and it is important to say so plainly: in a linear model with no elimination in the lung, the plasma AUC after an aerosol dose is fixed by F alone, whatever the ELF rate constants are. The simulated aerosol plasma AUC is 37% below the authors’ predicted value at all three dose levels (3.07 against 4.87, 15.3 against 24.4, 46.0 against 73.1), a constant ratio, which means the authors’ implementation delivers roughly 55% of the aerosol dose to the systemic circulation despite F = 0.33. The most likely cause is the drug-creating back flux of item 4 above, which was present in their code. The discrepancy is within the paper’s own two-fold qualification criterion, so the aerosol route is shipped; a user who needs the authors’ exact aerosol exposures should scale lfdepot2 accordingly and document it.

6. Table 7 intravenous tissue residual errors (spectinamide 1810). Printed as eps_Lung 0.13 (16.0), eps_Liver 0.076 (17.6) and eps_Spleen 1.19 (12.0) – verbatim duplicates, value and %RSE, of the K_Lung(I->C), K_Lung(C->I) and K_Liver(I->C) rows immediately above them. Confirmed against the typeset PDF (page 20), so this is a publisher transcription error rather than a conversion artifact, and a 119% proportional error on spleen alongside a 43% plasma error is not credible. The three values are treated as unreported and fixed at zero rather than invented. The clean subcutaneous-column values (0.30 lung, 0.31 liver, 0.43 spleen) are recorded in the in-file comments for users who need stochastic tissue simulations.

7. Table 2 tissue volumes exceed body volume. The mouse volumes sum to 27.8 mL for a 20 g animal and the rat volumes to 284 mL for a 225 g animal, in both cases driven by V_Other (23.5 mL and 245 mL). The values are reproduced as published because they are load-bearing for the fitted rate constants, but a user rescaling the model to a different body weight should be aware that V_Other is not a literal remainder-tissue volume.

8. Omega values labelled as variances. Tables 4 and 7 and their footnote call the inter-animal variability values variances; the paper’s own CV mapping in Section 3.7 shows they are log-scale standard deviations. See the source-trace section above for the arithmetic.

Out of scope

Section 3.9 of the paper explores relative drug exposure in granulomatous lesion substructures using a human Simcyp whole-lung and granuloma model, with the drug-specific inputs in supplement Table S1 (fu 0.436, k(b/p) 0.693, CL_R 3.27 L/h – human values, not the rodent values in Table 2). That analysis depends on a proprietary platform whole-body model whose equations are not on disk, and it is not part of the mPBPK model extracted here.