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Enrofloxacin oral + intravenous popPK in largemouth bass (Xu 2025)

Source: vignettes/articles/Xu_2025_enrofloxacin_largemouthBass.Rmd
Xu_2025_enrofloxacin_largemouthBass.Rmd

Model and source

Xu 2025 fitted the oral and the intravenous data separately, with different structural models, so the paper contributes two model files:

  • Xu_2025_enrofloxacin_largemouthBass_oral — one-compartment, first-order absorption, 20 mg/kg oral gavage.
  • Xu_2025_enrofloxacin_largemouthBass_iv — two-compartment, 10 mg/kg intravenous bolus into the caudal vein.
#> ℹ parameter labels from comments will be replaced by 'label()'

  • Citation: Xu N, Zhou S, Dong J, Li J, Ding Y, Ai X. (2025). Population Pharmacokinetics of Enrofloxacin in Micropterus salmoides Based on a Nonlinear Mixed Effect Model After Intravenous and Oral Administration. Animals 15(10):1362. doi:10.3390/ani15101362.

  • Article: Animals 2025;15(10):1362 (open access, CC BY 4.0; PMC12108383)

  • Supplement: none. The article has no supplementary material and the Data Availability Statement states that the individual data were not deposited and are “available upon request”.

#> ℹ parameter labels from comments will be replaced by 'label()'

Xu_2025_enrofloxacin_largemouthBass_oral — Veterinary (largemouth bass, Micropterus salmoides). One-compartment population PK model with first-order absorption and no absorption lag for enrofloxacin after a single 20 mg/kg body-weight oral (gavage) dose in largemouth bass held at 25.0 +/- 0.5 degC. Xu 2025 fitted 24 sparsely sampled fish (four plasma samples each, drawn from a 16-point 0.083-120 h grid) in Phoenix NLME 8.0 by first-order conditional estimation, extended least squares. Dose, clearance and volume are all body-weight normalised in the source (dose in mg/kg, tvV in L/kg, tvCL in L/h/kg), so the model is driven with amt in mg/kg and returns Cc directly in ug/mL. Final model, Table 4 ‘Without importing covariate of wt’ block: tvKa 0.98 1/h, tvV 6.82 L/kg, tvCL 0.098 L/h/kg, with a Phoenix multiplicative residual error, stdev0 = 0.30, encoded as prop(propSd). V and CL are APPARENT (per bioavailability); the companion intravenous model Xu_2025_enrofloxacin_largemouthBass_iv gives the absolute values, and the two together imply an oral bioavailability of 12.24%. Body weight was screened on Ka, V and CL and rejected (Table 3), so no covariate enters the model. Exponential between-fish variability was fitted on all three structural parameters but its magnitude is never published, so the three etas are carried at fixed(0); see the vignette.

#> ℹ parameter labels from comments will be replaced by 'label()'

Xu_2025_enrofloxacin_largemouthBass_iv — Veterinary (largemouth bass, Micropterus salmoides). Two-compartment population PK model for enrofloxacin after a single 10 mg/kg body-weight intravenous (caudal vein) dose in largemouth bass held at 25.0 +/- 0.5 degC. Xu 2025 fitted 24 sparsely sampled fish (four plasma samples each, drawn from a 16-point 0.083-120 h grid) in Phoenix NLME 8.0 by first-order conditional estimation, extended least squares. Dose, clearances and volumes are all body-weight normalised in the source (dose in mg/kg, tvV1 and tvV2 in L/kg, tvCL and tvCL2 in L/h/kg), so the model is driven with amt in mg/kg and returns Cc directly in ug/mL. Final model, Table 6 ‘Without importing covariate of wt’ block: tvV1 0.57 L/kg, tvV2 1.28 L/kg, tvCL 0.012 L/h/kg, tvCL2 1.00 L/h/kg, with a Phoenix multiplicative residual error, stdev0 = 0.14, encoded as prop(propSd). These are absolute (not apparent) values; paired with the companion oral model Xu_2025_enrofloxacin_largemouthBass_oral they imply an oral bioavailability of 12.24%. Body weight was screened on V1, V2, CL and CL2 and rejected (Table 5), so no covariate enters the model. Exponential between-fish variability was fitted on all four structural parameters but its magnitude is never published, so the four etas are carried at fixed(0); see the vignette.

Population

Both cohorts are healthy juvenile largemouth bass (Micropterus salmoides) sourced from Huazhong Agricultural University and held at the Yangtze River Fisheries Research Institute, Wuhan. The purchase lot of 60 fish weighed 243.11 +/- 54.86 g (Section 2.2); no per-fish weights are published. Fish acclimated for 14 days on antibiotic-free feed in 480 L tanks at 26 L/min, with water temperature held at 25.0 +/- 0.5 degC by air conditioning and dissolved oxygen, total ammonia nitrogen, nitrite nitrogen and pH checked daily.

Each route used 24 fish randomised to four groups of six (Sections 2.3.1 and 2.3.2). Oral fish received a single 20 mg/kg gavage of a 20 mg/mL enrofloxacin solution by plastic tube into the stomach; a fish that regurgitated was removed and replaced. Intravenous fish received a single 10 mg/kg injection of the same solution into the caudal vein; a fish that bled heavily or in which the needle translocated was removed and replaced.

Sampling is sparse — the design that motivates the whole paper. Fish have too little blood for a full serial profile, so each fish contributes only four samples, and the four groups interleave to cover 16 nominal times between 5 min and 120 h:

Group Sampling times
1 5 min, 1 h, 8 h, 48 h
2 10 min, 2 h, 12 h, 72 h
3 15 min, 4 h, 16 h, 96 h
4 0.5 h, 6 h, 24 h, 120 h

Plasma enrofloxacin was measured by HPLC with fluorescence detection (LOQ 0.01 ug/mL; recovery 83.3-103.1%; Table 1). Only the parent was assayed — the metabolite ciprofloxacin was not measured in this study.

The same information is available programmatically via each model’s population metadata, e.g. readModelDb("Xu_2025_enrofloxacin_largemouthBass_iv")()$population.

Source trace

Every ini() entry carries an in-file comment naming its source. They are collected here for review. Both final models come from the “Without importing covariate of wt” block of their table — not the “Importing covariate of wt” block and not the bootstrap block.

Oral model (..._oral)

Equation / parameter Value Source location
lka (Ka) 0.98 1/h Table 4, “Without importing covariate of wt”; restated Sections 3.3, 4, 5
lvc (V/F) 6.82 L/kg Table 4, same block; restated Sections 3.3, 4, 5
lcl (CL/F) 0.098 L/h/kg Table 4, same block; restated Sections 3.3, 4, 5
etalka, etalvc, etalcl fixed(0) Section 2.6 declares exponential IIV; magnitudes never published (see Errata)
propSd (stdev0) 0.30 Table 4, same block
d/dt(depot), d/dt(central) n/a Section 2.6 (“one-compartment model with extravascular administration”); Section 4 confirms first-order absorption
Residual form prop() n/a Section 2.6: OBSV = IPCN x (1 + eps)
IIV form exp(eta) n/a Section 2.6: P_i = tvP x exp(eta_Pi)

Intravenous model (..._iv)

Equation / parameter Value Source location
lvc (V1) 0.57 L/kg Table 6, “Without importing covariate of wt”; restated Sections 3.3, 5
lvp (V2) 1.28 L/kg Table 6, same block; restated Sections 3.3, 5
lcl (CL) 0.012 L/h/kg Table 6, same block; restated Sections 3.3, 4, 5
lq (CL2) 1.00 L/h/kg Table 6, same block; restated Sections 3.3, 5
etalvc, etalvp, etalcl, etalq fixed(0) Section 2.6 (IV “parameterizations were consistent with the above”); magnitudes never published
propSd (stdev0) 0.14 Table 6, same block
k12 = q/vc, k21 = q/vp n/a Section 2.6: K12 = tvCL2/V1, K21 = tvCL2/V2
d/dt(central), d/dt(peripheral1) n/a Section 2.6 (“two-compartment model with intravenous administration”); Section 4 confirms no absorption

Secondary quantities used as validation targets

These are not parameters — they are quantities Xu 2025 derived from the parameters above, and they are what the gates in this vignette reproduce.

Quantity Published value Source location
Ke (oral) 0.014 1/h Section 3.3, 5; Ke = tvCL/tvV (Section 2.6)
T1/2Ke (oral) 49.50 h Section 3.3, 5
AUC0-inf (oral, 20 mg/kg) 204.08 ug.h/mL Section 3.3, 5; AUC = Dose/tvCL (Section 2.6)
Kbeta (IV) 0.0065 1/h Section 3.3, 5; Kbeta = tvCL/(tvV1 + tvV2) (Section 2.6)
T1/2beta (IV) 106.62 h Section 3.3, 5
AUC0-inf (IV, 10 mg/kg) 833.33 ug.h/mL Section 3.3, 5
Vss (IV) 1.85 L/kg Section 4 (“the values of V … 1.85 L/kg”)
Bioavailability F 12.24% Abstract, Section 4
AUC/MIC 12755.0 / 816.32 / 408.16 Section 4

Assembling the two models 

mod_oral <- readModelDb("Xu_2025_enrofloxacin_largemouthBass_oral")
mod_iv   <- readModelDb("Xu_2025_enrofloxacin_largemouthBass_iv")

dose_oral <- 20 # mg/kg, Section 2.3.1
dose_iv   <- 10 # mg/kg, Section 2.3.2

Both models are body-weight normalised throughout: the dose is mg/kg, volumes are L/kg and clearances are L/h/kg, so Cc = central/vc is mg/L == ug/mL with no weight column anywhere. That is why body weight is recorded in covariatesDataExcluded rather than covariateData — see Errata.

The ODE system is live, not silently replaced

rxode2 will auto-solve a model whose parameters happen to be named cl/vc (and q/vp), discarding the explicit d/dt() block. If that happened here the published K12/K21 micro-constants would be bypassed. The cheap gate is to collapse the peripheral arm and confirm the profile actually moves: it can only move if the d/dt(peripheral1) equation is being integrated.

grid_iv <- seq(0, 480, by = 0.25)
ev_iv <- rxode2::et(amt = dose_iv, cmt = "central") |> rxode2::et(grid_iv)

sim_iv_typ <- rxode2::rxSolve(mod_iv, ev_iv, returnType = "data.frame")
#> ℹ parameter labels from comments will be replaced by 'label()'
#> ℹ omega/sigma items treated as zero: 'etalvc', 'etalvp', 'etalcl', 'etalq'
sim_iv_noq <- rxode2::rxSolve(mod_iv, ev_iv, params = c(lq = log(1e-6)),
                              returnType = "data.frame")
#> ℹ omega/sigma items treated as zero: 'etalvc', 'etalvp', 'etalcl', 'etalq'

c24_base <- sim_iv_typ$Cc[sim_iv_typ$time == 24]
c24_noq  <- sim_iv_noq$Cc[sim_iv_noq$time == 24]

# Killing intercompartmental clearance must change the 24 h concentration by a
# large margin. Observed here: 4.58 vs 10.58 ug/mL, a factor of 2.3.
stopifnot(c24_noq / c24_base > 1.5)

# The peripheral compartment must also be a genuine state in the solve output.
stopifnot(all(c("central", "peripheral1") %in% names(sim_iv_typ)))

Deterministic typical-value profiles

Xu 2025 published no between-fish variances (Errata), so the etas are held at zero and the typical-value solve is the population prediction. Every published secondary parameter below is a typical-value quantity, so this is the right object to validate against — no cohort averaging is involved.

grid_oral <- seq(0, 480, by = 0.25)
ev_oral <- rxode2::et(amt = dose_oral, cmt = "depot") |> rxode2::et(grid_oral)

sim_oral_typ <- rxode2::rxSolve(mod_oral, ev_oral, returnType = "data.frame")
#> ℹ parameter labels from comments will be replaced by 'label()'
#> ℹ omega/sigma items treated as zero: 'etalka', 'etalvc', 'etalcl'

typical <- dplyr::bind_rows(
  sim_oral_typ |> dplyr::transmute(arm = "Oral 20 mg/kg", time, Cc),
  sim_iv_typ   |> dplyr::transmute(arm = "IV 10 mg/kg",   time, Cc)
)
# Not a replication of a published figure -- Xu 2025 publishes only diagnostic
# plots (Figures 1 and 2 are CWRES-vs-TAD and DV-vs-(I)PRED), and the
# individual concentration data behind them are not available. This is the
# typical-value profile implied by the two published parameter sets.
typical |>
  dplyr::filter(Cc > 1e-4) |>
  ggplot(aes(time, Cc, colour = arm)) +
  geom_line(linewidth = 0.8) +
  scale_y_log10() +
  labs(x = "Time after dose (h)", y = "Plasma enrofloxacin (ug/mL)",
       colour = NULL,
       title = "Typical-value profiles from the two published parameter sets",
       caption = "Xu 2025 Tables 4 and 6, covariate-free final models.")

Closed-form validation gates

The published secondary parameters are algebraic functions of the estimates, so they can be reproduced exactly rather than approximately. These gates would break on any transcription error in the model files.

pars_oral <- sim_oral_typ[1, c("ka", "vc", "cl", "kel")]
pars_iv   <- sim_iv_typ[1, c("cl", "vc", "q", "vp", "kel", "k12", "k21")]

# `Rounding limited` marks the rows where the paper prints too few significant
# figures for the identity to close exactly: the two elimination rate constants
# are given to two significant figures (0.014, 0.0065), and both half-lives
# were then computed from those ROUNDED constants rather than from the
# unrounded ratio. See Errata item 3. The remaining rows are printed to enough
# digits that the identity is exact.
closed_form <- tibble::tribble(
  ~Quantity,                        ~Model,     ~Published, ~Reproduced,                                          ~`Rounding limited`,
  "Ke = CL/V (1/h)",                "oral",     0.014,      pars_oral$kel,                                        TRUE,
  "T1/2Ke = ln2/Ke (h)",            "oral",     49.50,      log(2) / pars_oral$kel,                               TRUE,
  "AUC0-inf = Dose/CL (ug.h/mL)",   "oral",     204.08,     dose_oral / pars_oral$cl,                             FALSE,
  "Vss = V1 + V2 (L/kg)",           "IV",       1.85,       pars_iv$vc + pars_iv$vp,                              FALSE,
  "Kbeta = CL/Vss (1/h)",           "IV",       0.0065,     pars_iv$cl / (pars_iv$vc + pars_iv$vp),               TRUE,
  "T1/2beta = ln2/Kbeta (h)",       "IV",       106.62,     log(2) / (pars_iv$cl / (pars_iv$vc + pars_iv$vp)),    TRUE,
  "K12 = CL2/V1 (1/h)",             "IV",       1.7544,     pars_iv$k12,                                          FALSE,
  "K21 = CL2/V2 (1/h)",             "IV",       0.7812,     pars_iv$k21,                                          FALSE,
  "AUC0-inf = Dose/CL (ug.h/mL)",   "IV",       833.33,     dose_iv / pars_iv$cl,                                 FALSE
) |>
  dplyr::mutate(`% diff` = 100 * (Reproduced - Published) / Published)

closed_form |>
  knitr::kable(digits = 4, caption = "Published secondary parameters vs. the packaged models.")
Published secondary parameters vs. the packaged models.
Quantity Model Published Reproduced Rounding limited % diff
Ke = CL/V (1/h) oral 0.0140 0.0144 TRUE 2.6393
T1/2Ke = ln2/Ke (h) oral 49.5000 48.2374 TRUE -2.5507
AUC0-inf = Dose/CL (ug.h/mL) oral 204.0800 204.0816 FALSE 0.0008
Vss = V1 + V2 (L/kg) IV 1.8500 1.8500 FALSE 0.0000
Kbeta = CL/Vss (1/h) IV 0.0065 0.0065 TRUE -0.2079
T1/2beta = ln2/Kbeta (h) IV 106.6200 106.8602 TRUE 0.2253
K12 = CL2/V1 (1/h) IV 1.7544 1.7544 FALSE -0.0008
K21 = CL2/V2 (1/h) IV 0.7812 0.7812 FALSE 0.0064
AUC0-inf = Dose/CL (ug.h/mL) IV 833.3300 833.3333 FALSE 0.0004 
# Every row above is an algebraic identity in the fitted parameters, so the
# only slack is the paper's own rounding, and both tiers are deterministic --
# there is no cohort here, so these bounds do not vary between machines.
#
# Observed: the five exactly-printed rows agree to <= 0.007% (worst: K21,
# 0.0064%), and the four rounding-limited rows to <= 2.64% (worst: Ke, where
# the paper's 0.014 stands for 0.014370). The bounds below sit outside those
# ranges without being unfalsifiable: a single-digit transcription error in any
# theta moves the affected rows by tens of percent.
exact_rows <- !closed_form$`Rounding limited`
stopifnot(
  max(abs(closed_form$`% diff`[exact_rows])) < 0.05,
  max(abs(closed_form$`% diff`[!exact_rows])) < 5
)

Bioavailability — the cross-model gate

F = 12.24% is the one published number that both models must agree on: it is computed from the oral AUC and the intravenous AUC together, so it cannot be reproduced by either file alone and it catches a transcription error in either.

auc_oral <- dose_oral / pars_oral$cl
auc_iv   <- dose_iv   / pars_iv$cl

F_pct <- 100 * (auc_oral / dose_oral) / (auc_iv / dose_iv)

# Equivalently F = CL_iv / (CL/F)_oral, since both AUCs are Dose/CL.
stopifnot(abs(F_pct - 100 * pars_iv$cl / pars_oral$cl) < 1e-8)

# Xu 2025 Abstract and Section 4 report 12.24%. Reproduced: 12.2449%.
stopifnot(abs(F_pct - 12.24) < 0.05)
sprintf("Bioavailability: reproduced %.4f%%, published 12.24%%", F_pct)
#> [1] "Bioavailability: reproduced 12.2449%, published 12.24%"

The terminal slope actually produced by the two-compartment system

Xu 2025 defines Kbeta = tvCL/(tvV1 + tvV2), which is the steady-state-volume approximation to the terminal eigenvalue, not the eigenvalue itself. The two coincide only when distribution is fast relative to elimination, so it is worth checking that the approximation is benign for these estimates — with a slower peripheral compartment it would not be, and the published T1/2beta would then not be reproducible from the ODE system at all.

tail_iv <- sim_iv_typ |> dplyr::filter(time >= 300, Cc > 0)
beta_true <- -stats::coef(stats::lm(log(Cc) ~ time, data = tail_iv))[["time"]]
beta_paper <- pars_iv$cl / (pars_iv$vc + pars_iv$vp)

# True eigenvalue 0.006449 1/h vs the paper's Vss approximation 0.006486 1/h.
# They differ by 0.57% -- far inside the 6.1% RSE the paper reports for tvCL,
# so the approximation costs nothing here, but they are NOT identical: rounded
# to four decimals the eigenvalue is 0.0064 and the Vss form is 0.0065.
# Both give a terminal half-life within 1% of the published 106.62 h.
stopifnot(
  abs(beta_true - beta_paper) / beta_paper < 0.02,
  abs(log(2) / beta_true - 106.62) / 106.62 < 0.02,
  # The distribution phase must be fast relative to elimination for the Vss
  # form to be benign; k21 / beta is ~120 here. A slow-peripheral model would
  # break this, which is why the check exists.
  pars_iv$k21 / beta_true > 20
)
sprintf("terminal beta: eigenvalue %.6f vs CL/Vss %.6f (t1/2 %.2f vs %.2f h, published 106.62 h)",
        beta_true, beta_paper, log(2) / beta_true, log(2) / beta_paper)
#> [1] "terminal beta: eigenvalue 0.006449 vs CL/Vss 0.006486 (t1/2 107.48 vs 106.86 h, published 106.62 h)"

PKNCA validation

The closed-form gates above test the algebra. This section tests the solved profiles independently, by running non-compartmental analysis over them with PKNCA and comparing against the published AUC and half-life.

# Dense grid to 2000 h so aucinf.obs extrapolates a small tail. Cc is the
# individual prediction (no residual error), which is what a typical-value
# NCA should consume.
grid_nca <- seq(0, 2000, by = 0.5)

nca_input <- dplyr::bind_rows(
  rxode2::rxSolve(mod_oral,
                  rxode2::et(amt = dose_oral, cmt = "depot") |> rxode2::et(grid_nca),
                  returnType = "data.frame") |>
    dplyr::transmute(id = 1L, arm = "Oral 20 mg/kg", time, Cc),
  rxode2::rxSolve(mod_iv,
                  rxode2::et(amt = dose_iv, cmt = "central") |> rxode2::et(grid_nca),
                  returnType = "data.frame") |>
    dplyr::transmute(id = 2L, arm = "IV 10 mg/kg", time, Cc)
) |>
  dplyr::filter(!is.na(Cc))
#> ℹ omega/sigma items treated as zero: 'etalka', 'etalvc', 'etalcl'
#> ℹ omega/sigma items treated as zero: 'etalvc', 'etalvp', 'etalcl', 'etalq'

# Guarantee a time = 0 record per (id, arm). The oral solve already carries
# Cc = 0 at t = 0 and the IV solve carries the bolus C0, so this is defensive
# only -- but PKNCA warns per subject if it is ever missing.
nca_input <- dplyr::bind_rows(
  nca_input,
  nca_input |> dplyr::distinct(id, arm) |> dplyr::mutate(time = 0, Cc = 0)
) |>
  dplyr::distinct(id, arm, time, .keep_all = TRUE) |>
  dplyr::arrange(id, arm, time)

stopifnot(sum(nca_input$time == 0) == 2L)
# The grouping column is named `arm`, NOT `route`: PKNCA reserves `route` for
# its own dose-route column and a user column of that name collides with it.
conc_obj <- PKNCA::PKNCAconc(nca_input, Cc ~ time | arm + id)

dose_df <- tibble::tibble(
  id   = c(1L, 2L),
  arm  = c("Oral 20 mg/kg", "IV 10 mg/kg"),
  time = 0,
  amt  = c(dose_oral, dose_iv)
)
dose_obj <- PKNCA::PKNCAdose(dose_df, amt ~ time | arm + id)

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

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

Comparison against published values 

# Xu 2025 publishes AUC0-inf and a terminal half-life per route (Sections 3.3
# and 5) but reports NO Cmax or Tmax for either route, so those two rows have
# no reference value and are omitted from the comparison.
published <- tibble::tribble(
  ~arm,             ~aucinf.obs, ~half.life,
  "Oral 20 mg/kg",  204.08,      49.50,
  "IV 10 mg/kg",    833.33,      106.62
)

cmp <- nlmixr2lib::ncaComparisonTable(
  simulated     = nca_res,
  reference     = published,
  by            = "arm",
  params        = c("aucinf.obs", "half.life"),
  units         = c(aucinf.obs = "ug*h/mL", half.life = "h"),
  tolerance_pct = 20
)

cmp |>
  knitr::kable(caption = "Simulated (PKNCA) vs. published NCA. * differs from reference by >20%.")
Simulated (PKNCA) vs. published NCA. * differs from reference by >20%.
NCA parameter arm Reference Simulated % diff
AUC0-∞ (obs) (ug*h/mL) Oral 20 mg/kg 204 204 -0.0%
AUC0-∞ (obs) (ug*h/mL) IV 10 mg/kg 833 834 +0.0%
t½ (h) Oral 20 mg/kg 49.5 48.2 -2.6%
t½ (h) IV 10 mg/kg 107 107 +0.8% 
# Assert on the numbers, not on the formatted `% diff` column that
# ncaComparisonTable() returns as character.
nca_wide <- as.data.frame(nca_res) |>
  dplyr::select(arm, PPTESTCD, PPORRES) |>
  tidyr::pivot_wider(names_from = PPTESTCD, values_from = PPORRES)

chk <- published |>
  dplyr::left_join(nca_wide, by = "arm", suffix = c("_ref", "_sim"))

# AUC0-inf is an identity (Dose/CL) that NCA must recover to within the
# trapezoidal error of the grid. Observed: < 0.02% on both arms.
stopifnot(max(abs(100 * (chk$aucinf.obs_sim - chk$aucinf.obs_ref) / chk$aucinf.obs_ref)) < 1)

# The half-lives are the loosest comparison in the vignette because the
# published values were computed from rounded rate constants (Errata).
# Observed: -2.5% (oral) and +0.8% (IV).
stopifnot(max(abs(100 * (chk$half.life_sim - chk$half.life_ref) / chk$half.life_ref)) < 5)

PK/PD: AUC/MIC against fish pathogens

Section 4 converts the oral AUC0-inf into AUC/MIC ratios against three fish pathogens, using MIC50 values quoted in the same paragraph, and compares them against the conventional fluoroquinolone efficacy breakpoint of 125.

pathogens <- tibble::tribble(
  ~Pathogen,                  ~`MIC50 (ug/mL)`, ~`Published AUC/MIC`,
  "Flavobacterium columnare", 0.016,            12755.0,
  "Aeromonas hydrophila",     0.25,             816.32,
  "Aeromonas sobria",         0.5,              408.16
) |>
  dplyr::mutate(`Reproduced AUC/MIC` = auc_oral / `MIC50 (ug/mL)`)

pathogens |>
  # Per-column digits: the F. columnare MIC50 is 0.016 ug/mL and would render
  # as "0.02" under a scalar digits = 2.
  knitr::kable(digits = c(0, 3, 2, 2),
               caption = "Oral 20 mg/kg AUC0-inf / MIC50 vs. the values in Xu 2025 Section 4.")
Oral 20 mg/kg AUC0-inf / MIC50 vs. the values in Xu 2025 Section 4.
Pathogen MIC50 (ug/mL) Published AUC/MIC Reproduced AUC/MIC
Flavobacterium columnare 0.016 12755.00 12755.10
Aeromonas hydrophila 0.250 816.32 816.33
Aeromonas sobria 0.500 408.16 408.16 
# Each ratio is AUC0-inf / MIC50 exactly; the only slack is the paper's
# rounding of 12755.06 to 12755.0. Observed: max |% diff| = 0.0005%.
stopifnot(
  max(abs(100 * (pathogens$`Reproduced AUC/MIC` - pathogens$`Published AUC/MIC`) /
            pathogens$`Published AUC/MIC`)) < 0.1,
  # All three exceed the AUC/MIC >= 125 breakpoint the paper cites.
  all(pathogens$`Reproduced AUC/MIC` >= 125)
)

This arithmetic also settles a labelling error in the paper — see Errata.

Study-design simulation

For orientation, the figure below overlays the paper’s actual sparse-sampling design on the typical-value profiles, with residual error applied at the observed times. It is not a VPC: with no published between-fish variances the only stochastic element is the residual error, so the spread below understates the real between-fish spread that Figures 1 and 2 of the paper show.

# rxSetSeed() fixes rxode2's stream per solver thread, not across thread
# counts, so this cohort is not byte-identical across machines. Nothing below
# asserts on it.
rxode2::rxSetSeed(20250508)
set.seed(20250508)

sched <- list(
  c(5 / 60, 1, 8, 48),
  c(10 / 60, 2, 12, 72),
  c(15 / 60, 4, 16, 96),
  c(0.5, 6, 24, 120)
)

# 24 fish per arm, matching Sections 2.3.1 / 2.3.2 and well under the
# 200-per-arm cap.
make_arm <- function(cmt, amt, label, id_offset) {
  purrr_free <- lapply(seq_len(24), function(i) {
    times <- sched[[((i - 1L) %% 4L) + 1L]]
    dplyr::bind_rows(
      tibble::tibble(id = id_offset + i, time = 0, amt = amt, evid = 1,
                     cmt = cmt, arm = label),
      tibble::tibble(id = id_offset + i, time = times, amt = NA_real_, evid = 0,
                     cmt = if (cmt == "depot") "central" else cmt, arm = label)
    )
  })
  dplyr::bind_rows(purrr_free)
}

events <- dplyr::bind_rows(
  make_arm("depot",   dose_oral, "Oral 20 mg/kg", id_offset =  0L),
  make_arm("central", dose_iv,   "IV 10 mg/kg",   id_offset = 100L)
)
stopifnot(!anyDuplicated(unique(events[, c("id", "time", "evid")])))
sim_design <- dplyr::bind_rows(
  rxode2::rxSolve(mod_oral,
                  events |> dplyr::filter(arm == "Oral 20 mg/kg"),
                  keep = "arm", returnType = "data.frame"),
  rxode2::rxSolve(mod_iv,
                  events |> dplyr::filter(arm == "IV 10 mg/kg"),
                  keep = "arm", returnType = "data.frame")
)
#> ℹ omega/sigma items treated as zero: 'etalka', 'etalvc', 'etalcl'
#> Warning: multi-subject simulation without without 'omega'
#> ℹ omega/sigma items treated as zero: 'etalvc', 'etalvp', 'etalcl', 'etalq'
#> Warning: multi-subject simulation without without 'omega'

# `Cc` is the individual prediction; `sim` carries the residual error, which is
# what an observed sample would look like.
sim_design |>
  dplyr::filter(time > 0, sim > 0) |>
  ggplot(aes(time, sim)) +
  geom_point(aes(colour = arm), alpha = 0.5, size = 1.4) +
  geom_line(data = dplyr::filter(typical, Cc > 1e-3, time <= 120),
            aes(y = Cc, colour = arm), linewidth = 0.8) +
  scale_y_log10() +
  labs(x = "Time after dose (h)", y = "Plasma enrofloxacin (ug/mL)",
       colour = NULL,
       title = "Sparse-sampling design (4 samples/fish, 24 fish/arm)",
       caption = "Points: simulated observations with residual error. Lines: typical-value prediction.")

# Nothing here depends on which cohort was drawn: the residual error is
# proportional with SD 0.30 (oral) and 0.14 (IV), so simulated observations
# must stay positive and finite and must bracket the typical prediction.
stopifnot(
  all(is.finite(sim_design$sim)),
  nrow(sim_design |> dplyr::filter(time > 0)) == 2 * 24 * 4
)

Assumptions and deviations

  • Between-fish variability is fixed at zero in both models. Xu 2025 Section 2.6 states that exponential IIV, P_i = tvP x exp(eta_Pi) with eta ~ N(0, omega^2), was estimated on the PK parameters, and defines CV(%) = 100 x sqrt(exp(omega^2) - 1). The omega values are never printed anywhere in the paper. That etas were estimated — three in the oral model, four in the IV model — is recoverable from the parameter counts in Tables 3 and 5 (the covariate-free oral model has 7 parameters = 3 thetas + 1 stdev0 + 3 omegas; the covariate-free IV model has 9 = 4 + 1 + 4, and each “-wt” scenario adds exactly one). Per the standing policy for unreported variability with structural values present, the etas are carried as ~ fixed(0) rather than invented. Consequence: simulating from either model gives the typical-value profile, not a population. A user who wants a stochastic cohort must supply their own omega.
  • The “Coefficient of Variation (%)” columns of Tables 4 and 6 are relative standard errors, not inter-animal CVs, and are not the CV(%) defined in Section 2.6. 0.50/6.82 = 7.3% reproduces the printed 7.34 for tvV, and 0.12/1.00 = 12.0% reproduces the printed 12.47 for tvCL2. Reading them as IIV would have produced two models with plausible-looking but entirely fabricated variances.
  • Body weight is in covariatesDataExcluded, not covariateData. It was screened on every structural parameter of both models, selected on -2LL/AIC (V-wt orally, V2-wt intravenously), fitted, and then rejected in Section 3.3. Note also that weight scaling is already built into the units — the dose is mg/kg and every volume and clearance is per kg — so the rejected test was for a departure from exponent-1 proportionality, not for the presence of any weight effect. No per-fish weights are published, so the centring value for dVdwt/dV2dwt is unrecoverable and the covariate models could not be reproduced even if wanted.
  • Two files, not one. The two routes were fitted separately, to different structural models (one-compartment oral, two-compartment IV), on disjoint fish. They are not two arms of one fit and are not encoded as one model with a route flag. The oral file’s V and CL are apparent (per F); the IV file’s are absolute.
  • The IV bolus is instantaneous. Section 2.3.2 reports a caudal-vein injection from a 1 mL microinjector with no stated duration, so no infusion duration is modelled.
  • Only the parent drug is modelled. The metabolite ciprofloxacin, which Xu’s own earlier work in other species does measure, was not assayed here.
  • Every parameter value in both files comes from the paper’s own tables. No value was digitised from a figure, obtained by correspondence, or carried from an upstream model.

Errata

Four discrepancies in the published article. None changes a parameter value; all are recorded so a reader comparing this vignette against the PDF is not surprised.

  1. Table 6’s caption says “after oral administration”; it is the intravenous model. The caption is a copy-paste of Table 4’s. Its own Note, its parameter names (tvV1, tvV2, tvCL2), the Section 3.3 text that introduces it, and the Table 5 scenario list that precedes it all identify it as intravenous.

  2. Section 4 misorders the three pathogens against their AUC/MIC values. The text reads “the AUC/MIC values were estimated to be 12755.0, 816.32, and 408.16 for A. hydrophila, A. sobria, and F. columnare”. Dividing the published oral AUC0-inf of 204.08 by the MIC50 values quoted two sentences earlier gives 204.08/0.016 = 12755.06 for F. columnare, 204.08/0.25 = 816.32 for A. hydrophila and 204.08/0.5 = 408.16 for A. sobria — so the pathogen list is in the reverse of the order the numbers require. The auc-mic chunk above reproduces all three ratios exactly, which is what identifies the pairing. The numbers are right; only the labels are swapped, and the paper’s conclusion (all three far exceed the breakpoint of 125) is unaffected.

  3. The elimination rate constants are printed to two significant figures, and both half-lives were then computed from those rounded values. The oral Ke is printed as 0.014 1/h where the identity CL/V = 0.098/6.82 gives 0.014370 1/h (2.6% higher), and T1/2Ke = ln2/0.014 = 49.51 h matches the printed 49.50 h whereas the unrounded constant gives 48.24 h. Likewise the IV Kbeta is printed as 0.0065 1/h against an unrounded 0.012/1.85 = 0.006486 1/h, and the printed T1/2beta of 106.62 h corresponds to ln2/0.0065 rather than to the unrounded 106.86 h. These four rows are flagged Rounding limited in the closed-form table and gated at 5%; the five rows the paper prints at full precision are gated at 0.05% and agree to better than 0.007%.

  4. Table 2’s Units column is scrambled (initial naive-pooled estimates, not used by either model). It assigns “h” to V and V1, “/h” to V2 and CL, and “L/h/kg” to CL2. The correct units are clear from Table 4 and Table 6: volumes are L/kg and clearances are L/h/kg. No value in either model file is taken from Table 2.

Additionally, the paper’s Section 2.6 states that both inter-individual and inter-occasion variability were modelled, but every fish receives only a single dose, so there is no occasion structure to estimate; no IOV term is reported and none is encoded here.