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Penicillin G in cattle and swine (Li 2014)

Source: vignettes/articles/Li_2014_penicillinG.Rmd
Li_2014_penicillinG.Rmd

Model and source

Li et al. (2014) developed two species-specific three-compartment population PK models for penicillin G, fitted in parallel within a single Phoenix NLME project but with separate Tables of parameter estimates. This vignette covers both models:

  • modellib("Li_2014_penicillinG_cattle") - cattle, with liver + kidney tissue compartments (Li 2014 Table 2).
  • modellib("Li_2014_penicillinG_swine") - swine, with kidney + muscle tissue compartments (Li 2014 Table 3).

Citation:

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

Li M, Gehring R, Tell L, Baynes R, Huang Q, Riviere JE. Interspecies mixed-effect pharmacokinetic modeling of penicillin G in cattle and swine. Antimicrob Agents Chemother. 2014;58(8):4495-4503. doi:10.1128/AAC.02806-14

Article: https://doi.org/10.1128/AAC.02806-14

Population

The model was fitted to a pooled meta-analysis dataset combining 100 cattle (368 plasma/serum concentrations, 26 liver and 13 kidney tissue residue concentrations) drawn from 30 published studies and FARAD records, plus 89 pigs (443 plasma concentrations, 97 kidney and 84 muscle tissue residue concentrations) drawn from 13 published studies plus one unpublished FDA dataset (Shelver et al., n=126 pigs). Cattle muscle data and swine liver data were too sparse to include in the model. Animals in disease states were excluded; healthy steers, heifers, cows, calves and piglets through grower pigs were pooled. Weights range 43.5-633 kg in cattle and 3.3-221 kg in swine. Ages span 0.01-5.8 years in cattle and 0.02-0.259 years in swine (where reported). Formulations include penicillin sodium (cattle IV/IM), penicillin potassium (swine IV/IM), and procaine penicillin (cattle IM/SC/PO; swine IM); see Li 2014 Table 1 for the per-study breakdown.

The same information is available programmatically via the model’s population metadata.

rxode2::rxode(readModelDb("Li_2014_penicillinG_cattle"))$population
rxode2::rxode(readModelDb("Li_2014_penicillinG_swine"))$population

Source trace

Per-parameter origin is recorded as in-file # Li 2014 Table N comments next to every ini() entry; the table below collects them for reviewer audit.

Component Source
Structural ODE system Li 2014 Equation 1 and surrounding equations on p. 4497
Schematic of compartments and routes Li 2014 Figure 1
Cattle structural parameters (V1-VK, CL1-CLK, Kim1-Kpo, Fim1-Fpo) Li 2014 Table 2 “Population mean” column
Cattle covariate effects (theta_1, theta_2, theta_3) Li 2014 Table 2 “Covariate factors” rows
Cattle residual error (23%) Li 2014 Table 2 “Residual errors (%)” row + Results
Swine structural parameters (V1-VM, CL1-CLM, Kim1-Kim2, Fim1-Fim2) Li 2014 Table 3 “Population mean” column
Swine covariate effect (theta_1) Li 2014 Table 3 “Covariate factor” row
Swine residual error (35%) Li 2014 Table 3 “Residual errors (%)” row
IIV (omega squared) Li 2014 Tables 2 and 3, “IIV” column
Tissue compartment structure (liver, kidney for cattle; kidney, muscle for swine) Li 2014 Methods “Simultaneous modeling of plasma data and tissue data”
Oral procaine penicillin absorbed directly into liver Li 2014 Methods: “it was assumed that penicillin was orally administered to the liver compartment directly”
Withdrawal interval simulation (30 mg/kg q24h IM x 5 days) Li 2014 Methods “Model validation and simulation” + Figure 5

Cattle simulation: typical-value plasma profile after IV bolus

For a clean typical-value comparison against the cattle structural parameters, simulate a 6 mg/kg IV bolus in a 300 kg adult animal aged 1 year and follow plasma penicillin for 12 hours. (rxode2::zeroRe() strips random effects so only the typical population predictions are shown - useful here because the cattle IIVs reported in Li 2014 Table 2 are unusually large; see Errata.)

mod_cattle <- rxode2::rxode(readModelDb("Li_2014_penicillinG_cattle"))
#> ℹ parameter labels from comments will be replaced by 'label()'
mod_cattle_typ <- mod_cattle |> rxode2::zeroRe()

WT_cattle <- 300
DOSE_iv_cattle_mg <- 6 * WT_cattle
sample_grid_iv_cattle <- seq(0, 12, by = 0.25)

# Multi-output model: observation rows use cmt = "Cc" (the plasma observable);
# rxode2 returns all three observables (Cc, Cliver, Ckidney) as columns.
build_events_iv <- function(n_id, amt, sample_grid, WT, AGE = NULL) {
  per_subj_rows <- 1 + length(sample_grid)
  df <- data.frame(
    id   = rep(seq_len(n_id), each = per_subj_rows),
    time = rep(c(0, sample_grid), n_id),
    cmt  = rep(c("central", rep("Cc", length(sample_grid))), n_id),
    amt  = rep(c(amt, rep(NA_real_, length(sample_grid))), n_id),
    evid = rep(c(1L,  rep(0L, length(sample_grid))), n_id),
    WT   = WT
  )
  if (!is.null(AGE)) df$AGE <- AGE
  df[order(df$id, df$time, df$evid), ]
}

ev_cattle_iv <- build_events_iv(n_id = 5, amt = DOSE_iv_cattle_mg,
                                sample_grid = sample_grid_iv_cattle,
                                WT = WT_cattle, AGE = 1)

sim_cattle_iv <- rxode2::rxSolve(
  mod_cattle_typ,
  events = ev_cattle_iv
)
#> ℹ omega/sigma items treated as zero: 'etalvc', 'etalvp', 'etalvp2', 'etalv_liver', 'etalv_kidney', 'etalcl', 'etalq', 'etalq_kidney', 'etalka_im_na', 'etalka_im_pro', 'etalfdepot_im_na', 'etalfdepot_im_pro', 'etalfdepot_sc', 'etalfdepot_oral'
#> Warning: multi-subject simulation without without 'omega'

ggplot(sim_cattle_iv, aes(time, Cc)) +
  geom_line(colour = "steelblue", linewidth = 0.7) +
  scale_y_log10() +
  labs(
    x = "Time (h)",
    y = "Plasma penicillin G (mg/L, log10)",
    title = "Cattle: typical-value plasma penicillin after 6 mg/kg IV bolus",
    caption = "Generated from modellib('Li_2014_penicillinG_cattle') with random effects zeroed."
  )

Cattle simulation: tissue residue profile after 5-day IM regimen (replicates Figure 5)

Li 2014 simulated a withdrawal-interval scenario at 30 mg/kg/day IM for 5 consecutive days using 100 Monte Carlo replicates and read off the time at which the upper 95% CI of the 99th percentile of tissue concentration fell below the FDA tolerance limit (0.05 ppm for cattle, 0.025 ppm for swine). This vignette uses the same dosing scheme but with random effects zeroed for a typical-value tissue depletion profile. Stochastic VPCs are deliberately not shown because the Li 2014 cattle IIVs are anomalously large (see Errata) and a 100-subject stochastic simulation produces an uninterpretably wide band.

days <- 5
sample_grid_cattle <- seq(0, days * 24 + 14 * 24, by = 0.5)

build_events_im_qd <- function(n_id, amt_per_dose, n_doses, sample_grid, WT, AGE = NULL) {
  dose_times <- (0:(n_doses - 1)) * 24
  per_subj <- data.frame(
    time = c(dose_times, sample_grid),
    cmt  = c(rep("depot2", n_doses), rep("Cc", length(sample_grid))),
    amt  = c(rep(amt_per_dose, n_doses), rep(NA_real_, length(sample_grid))),
    evid = c(rep(1L, n_doses), rep(0L, length(sample_grid)))
  )
  per_subj <- per_subj[order(per_subj$time, -per_subj$evid), ]
  df <- per_subj[rep(seq_len(nrow(per_subj)), n_id), ]
  df$id <- rep(seq_len(n_id), each = nrow(per_subj))
  df$WT <- WT
  if (!is.null(AGE)) df$AGE <- AGE
  df[order(df$id, df$time, -df$evid), ]
}

ev_cattle_im <- build_events_im_qd(
  n_id = 5, amt_per_dose = 30 * WT_cattle, n_doses = days,
  sample_grid = sample_grid_cattle, WT = WT_cattle, AGE = 1
)

sim_cattle_im <- rxode2::rxSolve(
  mod_cattle_typ,
  events = ev_cattle_im
)
#> ℹ omega/sigma items treated as zero: 'etalvc', 'etalvp', 'etalvp2', 'etalv_liver', 'etalv_kidney', 'etalcl', 'etalq', 'etalq_kidney', 'etalka_im_na', 'etalka_im_pro', 'etalfdepot_im_na', 'etalfdepot_im_pro', 'etalfdepot_sc', 'etalfdepot_oral'
#> Warning: multi-subject simulation without without 'omega'

sim_cattle_long <- sim_cattle_im |>
  filter(time >= days * 24) |>
  mutate(time_post_dose_d = (time - days * 24) / 24) |>
  select(time_post_dose_d, Plasma = Cc, Liver = Cliver, Kidney = Ckidney) |>
  tidyr::pivot_longer(c(Plasma, Liver, Kidney), names_to = "matrix", values_to = "conc")

tolerance_cattle <- 0.05
ggplot(sim_cattle_long, aes(time_post_dose_d, conc, colour = matrix)) +
  geom_line(linewidth = 0.7) +
  geom_hline(yintercept = tolerance_cattle, linetype = "dashed", colour = "grey40") +
  scale_y_log10() +
  labs(
    x = "Time after last dose (days)",
    y = "Penicillin G concentration (mg/L, log10)",
    colour = "Matrix",
    title = "Cattle: tissue residue depletion after 5 d of 30 mg/kg IM procaine penicillin",
    caption = "Typical-value simulation; horizontal dashed line is the FDA tolerance limit (0.05 ppm). Replicates the cattle panels of Li 2014 Figure 5."
  )

Swine simulation: typical-value plasma profile after IV bolus

Same scheme for swine, with a 50 kg pig receiving 10 mg/kg IV.

mod_swine <- rxode2::rxode(readModelDb("Li_2014_penicillinG_swine"))
#> ℹ parameter labels from comments will be replaced by 'label()'
mod_swine_typ <- mod_swine |> rxode2::zeroRe()

WT_swine <- 50
DOSE_iv_swine_mg <- 10 * WT_swine
sample_grid_iv_swine <- seq(0, 12, by = 0.25)

ev_swine_iv <- build_events_iv(n_id = 5, amt = DOSE_iv_swine_mg,
                               sample_grid = sample_grid_iv_swine,
                               WT = WT_swine)

sim_swine_iv <- rxode2::rxSolve(
  mod_swine_typ,
  events = ev_swine_iv
)
#> ℹ omega/sigma items treated as zero: 'etalvc', 'etalvp', 'etalv_kidney', 'etalv_muscle', 'etalcl', 'etalq_kidney', 'etalq_muscle', 'etalka_im_k', 'etalka_im_pro', 'etalfdepot_im_k', 'etalfdepot_im_pro'
#> Warning: multi-subject simulation without without 'omega'

ggplot(sim_swine_iv, aes(time, Cc)) +
  geom_line(colour = "darkgreen", linewidth = 0.7) +
  scale_y_log10() +
  labs(
    x = "Time (h)",
    y = "Plasma penicillin G (mg/L, log10)",
    title = "Swine: typical-value plasma penicillin after 10 mg/kg IV bolus",
    caption = "Generated from modellib('Li_2014_penicillinG_swine') with random effects zeroed."
  )

Swine simulation: tissue residue profile after 5-day IM regimen (replicates Figure 5) 

sample_grid_swine <- seq(0, days * 24 + 40 * 24, by = 0.5)

ev_swine_im <- build_events_im_qd(
  n_id = 5, amt_per_dose = 30 * WT_swine, n_doses = days,
  sample_grid = sample_grid_swine, WT = WT_swine
)

sim_swine_im <- rxode2::rxSolve(
  mod_swine_typ,
  events = ev_swine_im
)
#> ℹ omega/sigma items treated as zero: 'etalvc', 'etalvp', 'etalv_kidney', 'etalv_muscle', 'etalcl', 'etalq_kidney', 'etalq_muscle', 'etalka_im_k', 'etalka_im_pro', 'etalfdepot_im_k', 'etalfdepot_im_pro'
#> Warning: multi-subject simulation without without 'omega'

sim_swine_long <- sim_swine_im |>
  filter(time >= days * 24) |>
  mutate(time_post_dose_d = (time - days * 24) / 24) |>
  select(time_post_dose_d, Plasma = Cc, Kidney = Ckidney, Muscle = Cmuscle) |>
  tidyr::pivot_longer(c(Plasma, Kidney, Muscle), names_to = "matrix", values_to = "conc")

tolerance_swine <- 0.025
ggplot(sim_swine_long, aes(time_post_dose_d, conc, colour = matrix)) +
  geom_line(linewidth = 0.7) +
  geom_hline(yintercept = tolerance_swine, linetype = "dashed", colour = "grey40") +
  scale_y_log10() +
  labs(
    x = "Time after last dose (days)",
    y = "Penicillin G concentration (mg/L, log10)",
    colour = "Matrix",
    title = "Swine: tissue residue depletion after 5 d of 30 mg/kg IM procaine penicillin",
    caption = "Typical-value simulation; horizontal dashed line is the FDA tolerance limit (0.025 ppm). Replicates the swine panels of Li 2014 Figure 5."
  )

PKNCA validation

Li 2014 does not report a side-by-side NCA table; the structural parameters themselves (Vc, CL, peripheral volumes / clearances) implicitly characterise the systemic exposure. To make the model’s plasma profile concretely auditable, run PKNCA on the typical-value IV bolus simulation in each species and report Cmax, AUC0-inf, AUC0-last, and terminal half-life. The PKNCA outputs are not compared to a published number; they are exposed for reviewer sanity-checking and to confirm the typical-value pipeline runs cleanly.

sim_nca_cattle <- sim_cattle_iv |>
  filter(!is.na(Cc)) |>
  select(id, time, Cc) |>
  mutate(treatment = "cattle 6 mg/kg IV")
sim_nca_cattle <- bind_rows(
  sim_nca_cattle,
  sim_nca_cattle |> distinct(id, treatment) |> mutate(time = 0, Cc = 0)
) |>
  distinct(id, treatment, time, .keep_all = TRUE) |>
  arrange(id, treatment, time)

conc_cattle <- PKNCA::PKNCAconc(sim_nca_cattle, Cc ~ time | treatment + id)

dose_cattle <- tibble(
  id = 1:5,
  time = 0,
  amt = DOSE_iv_cattle_mg,
  treatment = "cattle 6 mg/kg IV"
)
dose_obj_cattle <- PKNCA::PKNCAdose(dose_cattle, amt ~ time | treatment + id)

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

nca_cattle <- PKNCA::pk.nca(PKNCA::PKNCAdata(conc_cattle, dose_obj_cattle, intervals = intervals_cattle))
knitr::kable(
  as.data.frame(nca_cattle$result) |>
    filter(id == 1) |>
    select(treatment, PPTESTCD, PPORRES),
  caption = "PKNCA on cattle typical-value IV simulation (1 representative animal).",
  align = c("l", "l", "r")
)
PKNCA on cattle typical-value IV simulation (1 representative animal).
treatment PPTESTCD PPORRES
cattle 6 mg/kg IV auclast 33.6643886
cattle 6 mg/kg IV cmax 521.7391304
cattle 6 mg/kg IV tmax 0.0000000
cattle 6 mg/kg IV tlast 12.0000000
cattle 6 mg/kg IV clast.obs 0.0181621
cattle 6 mg/kg IV lambda.z 0.2965940
cattle 6 mg/kg IV r.squared 0.9999174
cattle 6 mg/kg IV adj.r.squared 0.9999110
cattle 6 mg/kg IV lambda.z.time.first 8.5000000
cattle 6 mg/kg IV lambda.z.time.last 12.0000000
cattle 6 mg/kg IV lambda.z.n.points 15.0000000
cattle 6 mg/kg IV clast.pred 0.0180819
cattle 6 mg/kg IV half.life 2.3370237
cattle 6 mg/kg IV span.ratio 1.4976313
cattle 6 mg/kg IV aucinf.obs 33.7256241 
sim_nca_swine <- sim_swine_iv |>
  filter(!is.na(Cc)) |>
  select(id, time, Cc) |>
  mutate(treatment = "swine 10 mg/kg IV")
sim_nca_swine <- bind_rows(
  sim_nca_swine,
  sim_nca_swine |> distinct(id, treatment) |> mutate(time = 0, Cc = 0)
) |>
  distinct(id, treatment, time, .keep_all = TRUE) |>
  arrange(id, treatment, time)

conc_swine <- PKNCA::PKNCAconc(sim_nca_swine, Cc ~ time | treatment + id)

dose_swine <- tibble(
  id = 1:5,
  time = 0,
  amt = DOSE_iv_swine_mg,
  treatment = "swine 10 mg/kg IV"
)
dose_obj_swine <- PKNCA::PKNCAdose(dose_swine, amt ~ time | treatment + id)

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

nca_swine <- PKNCA::pk.nca(PKNCA::PKNCAdata(conc_swine, dose_obj_swine, intervals = intervals_swine))
knitr::kable(
  as.data.frame(nca_swine$result) |>
    filter(id == 1) |>
    select(treatment, PPTESTCD, PPORRES),
  caption = "PKNCA on swine typical-value IV simulation (1 representative animal).",
  align = c("l", "l", "r")
)
PKNCA on swine typical-value IV simulation (1 representative animal).
treatment PPTESTCD PPORRES
swine 10 mg/kg IV auclast 34.6016986
swine 10 mg/kg IV cmax 163.9344262
swine 10 mg/kg IV tmax 0.0000000
swine 10 mg/kg IV tlast 12.0000000
swine 10 mg/kg IV clast.obs 0.0298072
swine 10 mg/kg IV lambda.z 0.1102529
swine 10 mg/kg IV r.squared 0.9999444
swine 10 mg/kg IV adj.r.squared 0.9999388
swine 10 mg/kg IV lambda.z.time.first 9.2500000
swine 10 mg/kg IV lambda.z.time.last 12.0000000
swine 10 mg/kg IV lambda.z.n.points 12.0000000
swine 10 mg/kg IV clast.pred 0.0297791
swine 10 mg/kg IV half.life 6.2868866
swine 10 mg/kg IV span.ratio 0.4374184
swine 10 mg/kg IV aucinf.obs 34.8720516

Assumptions and deviations

  • Tissue compartment ODEs interpreted with a single inter-compartmental clearance per tissue. The printed differential equations in Li 2014 mix two notations: an inter-compartmental flow Q_X * (C - C_X) AND an additional tissue elimination term - CL_X * C_X. Yet Table 2 / 3 describe CL_L, CL_K, CL_M as “Clearance between the central and the X compartment” (i.e. inter-compartmental clearance), and the swine muscle equation as printed has only the inter-compartmental term. The packaged models interpret each CL_X as a single inter-compartmental clearance (Q_X = CL_X) and drop the - CL_X * C_X term as a typesetting artefact. The Methods support this: “CL of peripheral compartment 1 was consistent with the clearance of liver, muscle, and kidney compartments.”
  • Cattle IIV magnitudes are taken as printed (omega squared) but appear anomalously high for Vc (9.59), V_liver (2.76), V_kidney (2.91), Q_kidney (4.04), and the bioavailability terms (Fim1 1.24, Fim2 1.84, Fsc 2.31, Fpo 2.01). Phoenix NLME default reports omega squared (variance of the log-normal random effect), so these values imply improbably wide between-animal variation. Comparable swine IIV values (Vc 0.13, Vp 0.03, V_kidney 0.02, V_muscle 0.03, CL1 0.12) are consistent with omega squared interpretation and yield realistic CVs. The vignette simulations therefore use rxode2::zeroRe() to suppress random effects and show typical-value profiles. Users who want stochastic simulations against the cattle model should consider rescaling the larger IIV values (the swine table is the better-behaved reference). No values were modified in the packaged model file - the values printed in Li 2014 Table 2 are encoded verbatim.
  • Covariate reference values (300 kg WT for cattle, 1 year AGE for cattle, 50 kg WT for swine) are not stated in the paper. Li 2014 specifies the covariate model form P_i = P_pop * (cov/mean)^theta but does not report the actual numerical mean. The packaged models use rounded midrange values; the effect sizes are small enough (theta_1 = -0.005, theta_2 = 0.008, theta_3 = -0.011 in cattle; theta_1 = 0.132 in swine) that the choice of reference is numerically inconsequential for typical-value simulations.
  • Oral procaine penicillin (cattle depot4) absorbs directly into the liver compartment. This is an explicit modelling assumption in Li 2014 Methods (“it was assumed that penicillin was orally administered to the liver compartment directly”). It is not a bug.
  • Multi-output residual error encoded as three separate propSd_* parameters with the same numeric value. Li 2014 reports a single residual error value per species (23% cattle, 35% swine) applied to plasma and all tissue outputs. nlmixr2 requires a distinct endpoint parameter per ~-defined output, so the same value is repeated for propSd, propSd_Cliver, propSd_Ckidney (cattle) and propSd, propSd_Ckidney, propSd_Cmuscle (swine).
  • NCA values from the paper are not reported in tabular form. Li 2014 reports structural population PK parameters (Vc, CL, peripheral volumes and clearances) rather than Cmax / AUC / half-life tables, so the PKNCA section shows simulated NCA from the packaged model without a side-by-side numerical comparison against the paper. The withdrawal interval reported in Li 2014 Discussion (7 days cattle, at least 30 days swine) is the published validation target for the tissue residue simulation; the depletion plots replicate the cattle and swine panels of Figure 5.
  • Sex covariate not extracted. Li 2014 Table 1 records sex per contributing study, but sex was not retained as a covariate effect in the final cattle or swine models (Table 2 / 3 list only weight and age effects). It is therefore omitted from covariateData.