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Imipenem + aminoglycoside MBM vs. resistant Pseudomonas aeruginosa (Yadav 2017)

Source: vignettes/articles/Yadav_2017_imipenem_aminoglycoside_pseudomonas.Rmd
Yadav_2017_imipenem_aminoglycoside_pseudomonas.Rmd

Model and source

  • Article: https://doi.org/10.1128/AAC.01011-16
  • Citation: Yadav R, Bulitta JB, Nation RL, Landersdorfer CB. Optimization of synergistic combination regimens against carbapenem- and aminoglycoside-resistant clinical Pseudomonas aeruginosa isolates via mechanism-based pharmacokinetic/pharmacodynamic modeling. Antimicrob Agents Chemother 2017;61(1):e01011-16.

This is not a population PK model. It is a mechanism-based PK/PD model (MBM) of bacterial killing and resistance, fit with S-ADAPT to total viable counts from 48-h static-concentration time-kill (SCTK) assays in cation-adjusted Mueller-Hinton II broth. The paper studied three carbapenem-resistant clinical isolates of P. aeruginosa (FADDI-PA088, FADDI-PA001, FADDI-PA022) with monotherapies and combinations of imipenem (IPM) with the aminoglycosides tobramycin (TOB) and amikacin (AMK). Amikacin combinations against FADDI-PA022 were not studied.

The MBM (Table 3 of Yadav 2017) is contributed to nlmixr2lib as five model files, one per studied (strain, aminoglycoside) combination, all sharing the same structural model and differing only in the strain- and AGS-specific parameter values:

yadav_models <- c(
  "Yadav_2017_imipenem_tobramycin_PA088",
  "Yadav_2017_imipenem_amikacin_PA088",
  "Yadav_2017_imipenem_tobramycin_PA001",
  "Yadav_2017_imipenem_amikacin_PA001",
  "Yadav_2017_imipenem_tobramycin_PA022"
)
yadav_models
#> [1] "Yadav_2017_imipenem_tobramycin_PA088"
#> [2] "Yadav_2017_imipenem_amikacin_PA088"  
#> [3] "Yadav_2017_imipenem_tobramycin_PA001"
#> [4] "Yadav_2017_imipenem_amikacin_PA001"  
#> [5] "Yadav_2017_imipenem_tobramycin_PA022"

The antibiotic exposures cipm (imipenem) and cags (aminoglycoside) are state variables that the user doses. In the original SCTK assays they were essentially constant in time (with imipenem supplemented at 6 and 30 h to offset thermal degradation), so the model defaults to d/dt(cipm) = 0, d/dt(cags) = 0; the user can attach elimination terms or external popPK to simulate clinical regimens.

Because there is no absorption-distribution-elimination profile to integrate, PKNCA / NCA is not an appropriate validation. The checks below are the mechanistic equivalents: antibiotic-free carrying-capacity hold, the mechanistic-synergy curve (Figure 4), and replication of representative kill / regrowth combinations from Figure 2.

Population (biological context)

Three carbapenem-resistant P. aeruginosa clinical isolates from the Monash University collection (Yadav 2017 Table 1):

Isolate MIC IPM MIC TOB MIC AMK Notes
FADDI-PA088 16 mg/L 32 mg/L 4 mg/L Double-resistant for IPM/TOB; AMK-susceptible. Both IPM and TOB MICs at the 98th percentile of EUCAST distributions.
FADDI-PA001 32 mg/L 4 mg/L 32 mg/L Carbapenem- and amikacin-resistant; tobramycin breakpoint-susceptible. Harboured a preexisting IPM-resistant subpopulation (3.1 log10 CFU/mL at 0 h).
FADDI-PA022 16 mg/L 8 mg/L > 32 mg/L (NS) Carbapenem- and tobramycin-resistant; amikacin combinations not studied.

All susceptibility testing and SCTK experiments used cation-adjusted Mueller-Hinton II broth (CAMHB) at a clinically relevant high initial inoculum of ~10^7.5 CFU/mL. Bacteria were sampled at 0, 1, 3, 6, 24, 29 and 48 h. The model was fit jointly per strain across all IPM monotherapies, AGS monotherapies, and IPM + AGS combinations. The same metadata are available programmatically via readModelDb("<modelname>")$population.

Source trace

Per-parameter origins are recorded as in-file comments next to every ini() entry in inst/modeldb/specificDrugs/Yadav_2017_imipenem_*.R. All values are the population-mean estimates from Yadav 2017 Table 3 (“Population mean value (SE [%]) for strain, treatment”); footnote a tags tobramycin-specific estimates and footnote b tags amikacin-specific estimates. The structural model is from the Methods sub-sections “Life cycle growth model”, “Model for combinations of imipenem and an aminoglycoside” (Eqs 1-4), and “Mechanism-based modeling of synergy” (Eq 5).

Equation / parameter Source location
Total viable count CFUall = sum of 6 bacterial states Eq 1 (Methods)
Signal-molecule growth inhibition Inh_k12 = Imax,sig12 * Csig / (Csig + IC50,sig) Eq 2 (Methods); explicit Csig ODE not given in main text
State-1 ODE (Eq 3): replication + transition + killing Eq 3 (Methods, p. 14)
State-2 ODE (Eq 4) Eq 4 (Methods, p. 14)
Plateau factor PLAT = 1 - CFUall / (CFUall + CFUmax) Eq 3 footnote (Methods)
Outer-membrane synergy OM_effect = 1 - Imax,OM,AGS * C_AGS / (C_AGS + IC50,OM,AGS) Eq 5 (Methods)
Per-strain parameter columns (Log CFU0, CFUmax, k21, MGTs, Log MUT, Kmax/KC50/Hill for IPM and AGS, MTT_sig, Imax,sig12, Log10 IC50,sig, Imax,OM, IC50,OM, SD_CFU) Table 3
Tobramycin (a) vs. amikacin (b) AGS-specific values Table 3 footnotes a/b
3.11/1.15/2.53-fold KC50,IPM decrease at saturating AGS Table 3 footnote c (also = 1/(1-Imax,OM))
Initial conditions: total inoculum CFU0, RI seeded by 10^Log MUT,IPM, IR seeded by 10^Log MUT,AGS Methods, “Initial conditions”

Per-isolate parameter snapshot 

snap <- lapply(yadav_models, function(m) {
  th <- rxode2::rxode(readModelDb(m))$theta
  data.frame(model = m, parameter = names(th), value = unname(th))
}) |>
  do.call(rbind, args = _) |>
  tidyr::pivot_wider(names_from = model, values_from = value)
knitr::kable(snap, digits = 4,
             caption = "Population-mean parameter values per (strain, AGS) combination, as loaded from the five model files.")
Population-mean parameter values per (strain, AGS) combination, as loaded from the five model files.
parameter Yadav_2017_imipenem_tobramycin_PA088 Yadav_2017_imipenem_amikacin_PA088 Yadav_2017_imipenem_tobramycin_PA001 Yadav_2017_imipenem_amikacin_PA001 Yadav_2017_imipenem_tobramycin_PA022
log10cfu0 7.540 7.460 7.920 7.780 6.990
log10cfumax 9.560 9.560 9.230 9.230 9.540
lk21 3.912 3.912 3.912 3.912 3.912
mgt_ss 26.900 26.900 45.300 45.300 63.800
mgt_ri 873.000 873.000 481.000 481.000 565.000
mgt_ir 26.900 26.900 45.300 45.300 63.800
log10mf_ipm -4.730 -4.730 -4.990 -4.990 -3.900
log10mf_ags -7.000 -6.680 -7.330 -6.660 -7.550
kmax_ipm 3.340 3.340 3.210 3.210 2.230
kc50_ss_ipm 0.992 0.992 33.200 33.200 15.200
kc50_ri_ipm 264.000 264.000 118.000 118.000 67.300
kc50_ir_ipm 23.500 23.500 61.800 61.800 52.700
hill_ipm 3.000 3.000 3.090 3.090 3.080
kmax_ss_ags 11.800 11.800 2.840 2.840 2.930
kmax_ri_ags 3.280 3.280 3.140 3.140 2.800
kmax_ir_ags 11.800 11.800 2.840 2.840 2.930
kc50_ss_ags 18.600 4.880 16.600 153.000 54.900
kc50_ri_ags 849.000 280.000 228.000 738.000 568.000
kc50_ir_ags 615.000 329.000 46.700 170.000 159.000
hill_ags 1.110 1.110 2.040 2.040 0.998
mtt_sig 1.000 1.000 1.000 1.000 0.087
imax_sig12 0.997 0.997 0.996 0.996 0.881
log10ic50sig 10.200 10.200 9.630 9.630 8.950
imax_om 0.678 0.678 0.130 0.130 0.604
ic50_om 5.550 1.130 1.540 4.800 4.290
addSd 0.378 0.378 0.290 0.290 0.475

Units (dimensional analysis)

Symbol Meaning Units
bact_susceptible_susceptible{1,2}, bact_resistant_intermediate{1,2}, bact_intermediate_resistant{1,2} Bulitta life-cycle bacterial states CFU/mL
cipm, cags, csig imipenem / aminoglycoside / signal-molecule concentrations mg/L (IPM, AGS); CFU/mL (csig)
lk21, k12*, kmax_*, kill_*, kout_sig rate constants 1 / h
kc50_*, ic50_om, ic50sig half-effect concentrations mg/L (IPM, AGS); CFU/mL (sig)
mgt_*, mtt_sig mean generation / turnover times min (mgt_*); h (mtt_sig)
cfumax, cfu0 population scale / inoculum CFU/mL
hill_ipm, hill_ags, plat, inh_k12, om_effect, imax_sig12, imax_om dimensionless –
log10* parameters (log10cfu0, log10cfumax, log10mf_*, log10ic50sig) base-10 log of the linear value log10 of the corresponding unit

Every growth/kill ODE term reduces to (1/h) x (CFU/mL) = (CFU/mL)/h, matching d/dt(bact_*); k12 = 60/MGT carries 60 in (min/h), converting the mean generation time (min) to a rate (1/h); kout_sig = 1/MTT_sig converts the turnover time (h) to a rate (1/h).

mod <- rxode2::rxode(readModelDb("Yadav_2017_imipenem_tobramycin_PA088"))
mod$state
#> [1] "bact_susceptible_susceptible1" "bact_susceptible_susceptible2"
#> [3] "bact_resistant_intermediate1"  "bact_resistant_intermediate2" 
#> [5] "bact_intermediate_resistant1"  "bact_intermediate_resistant2" 
#> [7] "csig"                          "cipm"                         
#> [9] "cags"

Carrying-capacity (growth control) check

With no antibiotic, the population grows from the inoculum toward CFUmax. For the Yadav 2017 plateau factor PLAT = 1 - CFUall / (CFUall + CFUmax), the steady state is PLAT = 0.5 at CFUall = CFUmax, so the simulated plateau equals CFUmax (unlike the Rees 2018 plateau form which settles at half the carrying capacity). The signal-molecule inhibition adds a smaller secondary brake on growth and shifts the plateau only slightly.

gc_one <- function(mname) {
  m <- rxode2::rxode(readModelDb(mname))
  ev <- et(seq(0, 48, by = 0.5))
  s <- rxode2::rxSolve(m, ev, method = "lsoda",
                       atol = 1e-10, rtol = 1e-10, maxsteps = 1e6,
                       returnType = "data.frame")
  data.frame(model = mname, time = s$time, Cc = s$Cc, CFUall = s$CFUall)
}
gc <- do.call(rbind, lapply(yadav_models, gc_one))

gc_tab <- gc |>
  group_by(model) |>
  summarise(
    log10cfu0_sim     = round(first(Cc), 2),
    log10cfumax_sim   = round(max(Cc), 2),
    .groups = "drop"
  )
knitr::kable(gc_tab,
             caption = "Growth-control hold: each model starts at its log10cfu0 and reaches log10cfumax by 48 h.")
Growth-control hold: each model starts at its log10cfu0 and reaches log10cfumax by 48 h.
model log10cfu0_sim log10cfumax_sim
Yadav_2017_imipenem_amikacin_PA001 7.78 9.23
Yadav_2017_imipenem_amikacin_PA088 7.46 9.56
Yadav_2017_imipenem_tobramycin_PA001 7.92 9.23
Yadav_2017_imipenem_tobramycin_PA022 6.99 9.54
Yadav_2017_imipenem_tobramycin_PA088 7.54 9.56 

ggplot(gc, aes(time, Cc, colour = model)) +
  geom_line(linewidth = 0.8) +
  labs(x = "Time (h)", y = expression(log[10]~CFU/mL),
       title = "Antibiotic-free growth from inoculum to carrying capacity",
       colour = NULL) +
  theme(legend.position = "bottom", legend.text = element_text(size = 7)) +
  guides(colour = guide_legend(ncol = 1))

Mechanistic-synergy check (replicate Figure 4)

The outer-membrane effect OM_effect = 1 - Imax,OM * C_AGS / (C_AGS + IC50,OM) scales the effective imipenem KC50 (Eq 5). At saturating AGS the effective KC50,IPM is reduced to (1 - Imax,OM) * KC50,IPM, which gives the fold-decrease quoted in Table 3 footnote c: 3.11-fold for FADDI-PA088, 1.15-fold for FADDI-PA001, and 2.53-fold for FADDI-PA022.

om_effect <- function(cags, imax_om, ic50_om) 1 - imax_om * cags / (cags + ic50_om)

strain_params <- tibble::tribble(
  ~panel,                    ~ags,         ~imax_om, ~ic50_om, ~kc50_ss_ipm, ~kc50_ri_ipm, ~kc50_ir_ipm,
  "A: FADDI-PA088 + TOB",    "tobramycin", 0.678,    5.55,     0.992,        264,          23.5,
  "A: FADDI-PA088 + AMK",    "amikacin",   0.678,    1.13,     0.992,        264,          23.5,
  "B: FADDI-PA001 + TOB",    "tobramycin", 0.130,    1.54,     33.2,         118,          61.8,
  "B: FADDI-PA001 + AMK",    "amikacin",   0.130,    4.80,     33.2,         118,          61.8,
  "C: FADDI-PA022 + TOB",    "tobramycin", 0.604,    4.29,     15.2,         67.3,         52.7
)

fig4 <- strain_params |>
  tidyr::crossing(cags = seq(0, 32, by = 0.5)) |>
  mutate(
    om     = om_effect(cags, imax_om, ic50_om),
    KC50_SS_IPM_eff = om * kc50_ss_ipm,
    KC50_RI_IPM_eff = om * kc50_ri_ipm,
    KC50_IR_IPM_eff = om * kc50_ir_ipm
  ) |>
  tidyr::pivot_longer(c(KC50_SS_IPM_eff, KC50_RI_IPM_eff, KC50_IR_IPM_eff),
                      names_to = "subpop", values_to = "kc50_eff_mgL") |>
  mutate(subpop = recode(subpop,
                         KC50_SS_IPM_eff = "KC50,SS,IPM",
                         KC50_RI_IPM_eff = "KC50,RI,IPM",
                         KC50_IR_IPM_eff = "KC50,IR,IPM"))

ggplot(fig4, aes(cags, kc50_eff_mgL, colour = subpop, linetype = ags)) +
  geom_line(linewidth = 0.8) +
  facet_wrap(~panel, scales = "free_y") +
  labs(x = "Aminoglycoside (mg/L)", y = "Effective KC50,IPM (mg/L)",
       title = "Replicates Figure 4 of Yadav 2017",
       caption = "OM_effect lowers the effective KC50,IPM for two or three subpopulations.",
       colour = NULL, linetype = NULL) +
  theme(legend.position = "bottom")

strain_params |>
  mutate(
    fold_at_saturation_AGS = round(1 / (1 - imax_om), 2)
  ) |>
  select(panel, ags, imax_om, ic50_om, fold_at_saturation_AGS) |>
  knitr::kable(caption = "Maximum fold-decrease in KC50,IPM at saturating AGS (1/(1-imax_om)). Matches Table 3 footnote c.")
Maximum fold-decrease in KC50,IPM at saturating AGS (1/(1-imax_om)). Matches Table 3 footnote c.
panel ags imax_om ic50_om fold_at_saturation_AGS
A: FADDI-PA088 + TOB tobramycin 0.678 5.55 3.11
A: FADDI-PA088 + AMK amikacin 0.678 1.13 3.11
B: FADDI-PA001 + TOB tobramycin 0.130 1.54 1.15
B: FADDI-PA001 + AMK amikacin 0.130 4.80 1.15
C: FADDI-PA022 + TOB tobramycin 0.604 4.29 2.53

Replicate Figure 2 (selected time-kill panels)

Figure 2 of Yadav 2017 shows observed (markers) and individual fitted (lines) total viable counts for combinations of imipenem with tobramycin or amikacin against all three isolates. The published lines are the MBM fits we are reproducing. We pick representative cells that illustrate the qualitative patterns the authors emphasise in the Results: (i) regrowth under IPM monotherapy and at low AGS, (ii) prevention of regrowth at adequate AGS even below the AGS MIC for FADDI-PA088, and (iii) the near-monotherapy-like behaviour of low-IPM combinations against FADDI-PA001 (whose KC50,SS,IPM is much higher).

combo_sim <- function(mname, cipm_dose, cags_dose, tmax = 48) {
  m <- rxode2::rxode(readModelDb(mname)) |> rxode2::zeroRe()
  ev <- et(amt = cipm_dose, cmt = "cipm", time = 0) |>
    et(amt = cags_dose, cmt = "cags", time = 0) |>
    et(seq(0, tmax, by = 0.5))
  rxode2::rxSolve(m, ev, method = "lsoda", atol = 1e-10, rtol = 1e-10,
                  maxsteps = 1e6, returnType = "data.frame") |>
    transmute(time, log10CFU = log10(pmax(CFUall, 1)))
}

# Panels: A1 (PA088 + TOB), A2 (PA088 + AMK), B1 (PA001 + TOB), C (PA022 + TOB)
panels <- tibble::tribble(
  ~panel, ~model,                                        ~cipm_dose, ~cags_dose,
  "A1 PA088 + TOB", "Yadav_2017_imipenem_tobramycin_PA088",  0,   0,
  "A1 PA088 + TOB", "Yadav_2017_imipenem_tobramycin_PA088", 24,   0,
  "A1 PA088 + TOB", "Yadav_2017_imipenem_tobramycin_PA088", 24,   1,
  "A1 PA088 + TOB", "Yadav_2017_imipenem_tobramycin_PA088", 24,  16,
  "A2 PA088 + AMK", "Yadav_2017_imipenem_amikacin_PA088",   24,   0,
  "A2 PA088 + AMK", "Yadav_2017_imipenem_amikacin_PA088",   24,   1,
  "A2 PA088 + AMK", "Yadav_2017_imipenem_amikacin_PA088",   24,  16,
  "B1 PA001 + TOB", "Yadav_2017_imipenem_tobramycin_PA001",  0,   0,
  "B1 PA001 + TOB", "Yadav_2017_imipenem_tobramycin_PA001", 36,   0,
  "B1 PA001 + TOB", "Yadav_2017_imipenem_tobramycin_PA001", 36,  16,
  "C  PA022 + TOB", "Yadav_2017_imipenem_tobramycin_PA022",  0,   0,
  "C  PA022 + TOB", "Yadav_2017_imipenem_tobramycin_PA022", 24,   0,
  "C  PA022 + TOB", "Yadav_2017_imipenem_tobramycin_PA022", 24,  16
)

fig2 <- panels |>
  rowwise() |>
  mutate(sim = list(combo_sim(model, cipm_dose, cags_dose))) |>
  tidyr::unnest(sim) |>
  mutate(label = sprintf("IPM=%g + AGS=%g", cipm_dose, cags_dose))
#> Warning: There were 13 warnings in `mutate()`.
#> The first warning was:
#> ℹ In argument: `sim = list(combo_sim(model, cipm_dose, cags_dose))`.
#> ℹ In row 1.
#> Caused by warning:
#> ! No omega parameters in the model
#> ℹ Run `dplyr::last_dplyr_warnings()` to see the 12 remaining warnings.

ggplot(fig2, aes(time, log10CFU, colour = label)) +
  geom_line(linewidth = 0.8) +
  facet_wrap(~panel) +
  scale_x_continuous(breaks = seq(0, 48, by = 12)) +
  ylim(0, 11) +
  labs(x = "Time (h)", y = expression(log[10]~CFU/mL),
       title = "Replicates selected panels of Figure 2 of Yadav 2017",
       caption = "Growth control regrows to ~CFUmax; IPM monotherapies kill and regrow; effective IPM+AGS combinations suppress regrowth.",
       colour = "Regimen (mg/L)") +
  theme(legend.position = "bottom")

fig2 |>
  group_by(panel, label) |>
  summarise(
    log10CFU_t0   = round(first(log10CFU), 2),
    log10CFU_t6   = round(log10CFU[time == 6], 2),
    log10CFU_t24  = round(log10CFU[time == 24], 2),
    log10CFU_t48  = round(log10CFU[time == 48], 2),
    .groups = "drop"
  ) |>
  knitr::kable(caption = "Simulated log10 viable counts at sampling time-points used by Yadav 2017 (0, 6, 24, 48 h).")
Simulated log10 viable counts at sampling time-points used by Yadav 2017 (0, 6, 24, 48 h).
panel label log10CFU_t0 log10CFU_t6 log10CFU_t24 log10CFU_t48
A1 PA088 + TOB IPM=0 + AGS=0 7.54 9.55 9.56 9.56
A1 PA088 + TOB IPM=24 + AGS=0 7.54 4.19 4.09 7.38
A1 PA088 + TOB IPM=24 + AGS=1 7.54 3.29 3.47 4.13
A1 PA088 + TOB IPM=24 + AGS=16 7.54 2.83 2.90 2.99
A2 PA088 + AMK IPM=24 + AGS=0 7.46 4.11 4.27 7.60
A2 PA088 + AMK IPM=24 + AGS=1 7.46 2.87 3.30 3.86
A2 PA088 + AMK IPM=24 + AGS=16 7.46 2.44 1.55 0.38
B1 PA001 + TOB IPM=0 + AGS=0 7.92 9.17 9.23 9.23
B1 PA001 + TOB IPM=36 + AGS=0 7.92 6.39 8.15 8.80
B1 PA001 + TOB IPM=36 + AGS=16 7.92 2.98 3.51 6.25
C PA022 + TOB IPM=0 + AGS=0 6.99 8.84 9.51 9.54
C PA022 + TOB IPM=24 + AGS=0 6.99 4.68 6.98 9.14
C PA022 + TOB IPM=24 + AGS=16 6.99 2.21 0.00 0.00

Assumptions and deviations

  • Model class / species. This is an in-vitro mechanism-based PK/PD model, not a popPK model; population$species records the P. aeruginosa isolate. No PKNCA validation is performed (there is no drug NCA to compute); the mechanistic checks above replace it, per the endogenous/mechanistic validation strategy.
  • File naming. The dispatch metadata listed the drug as “Antimicrobial Agents and Chemo”, which is the journal name (Antimicrobial Agents and Chemotherapy), not a drug. The paper unambiguously models imipenem combined with tobramycin or amikacin, so the five model files use the corresponding drug + isolate suffix.
  • Five files, one paper. Per the replicate-author-structure policy, one vignette walks the paper as a whole and loads each of the five modellib() entries at the appropriate point. The authors did a single per-strain joint fit covering all IPM, AGS, and IPM + AGS data within that strain; we expose five fully-specified files because most parameters that differ between TOB and AMK within a strain (KC50,AGS, IC50,OM,AGS, Log MUT,AGS, Log CFU0) are drug-specific while the structural shared subset is duplicated. The parameter snapshot table makes the shared / drug-specific split explicit.
  • Signal-molecule ODE form. Methods Eq 2 defines the inhibition term Inh_k12 = Imax,sig12 * Csig / (Csig + IC50,sig) but the main paper does not give the Csig ODE; it cites Bulitta 2010 (ref 61), which is not on disk. The standard form d/dt(csig) = (1/MTT_sig) * (CFU_all - csig) with csig(0) = cfu0 is used, giving csig = CFU_all at steady state. This is the canonical Bulitta life-cycle formulation and the only internally-consistent reading of the reported MTT_sig and Log10 IC50,sig values (the latter is on a log10 CFU/mL scale, matching CFU_all at carrying capacity). See “Source trace” for the equation locations.
  • Plateau factor. PLAT = 1 - CFUall/(CFUall + CFUmax) (Methods Eq 3 footnote). At CFUall = CFUmax, PLAT = 0.5, which combined with the state-2 doubling factor of 2 produces steady-state growth balance at CFUmax. The simulated plateau therefore equals CFUmax, not 0.5 * CFUmax as in the Rees 2018 plateau form.
  • OM_effect placement. The aminoglycoside reduces the effective imipenem KC50 through (OM_effect * KC50,IPM)^Hill,IPM in the IPM killing denominator (Methods Eq 3). Footnote c of Table 3 reports a 3.11-fold decrease for FADDI-PA088 at saturating AGS, matching 1/(1 - 0.678) = 3.106 – the structural placement above. The AGS killing term uses its own KC50,AGS and is not affected by OM_effect.
  • Initial state partitioning. The total inoculum (CFU0) is placed in the SS subpopulation state 1; the RI and IR subpopulations are seeded at CFU0 * 10^Log MUT,IPM and CFU0 * 10^Log MUT,AGS respectively, also in state 1. Methods, “Initial conditions” specifies the seeds but not the state-1 / state-2 split; the balanced state-2 fraction is small (a few percent for the fast-MGT SS/IR populations) and equilibrates within ~1 / k21 (a few minutes). csig starts at cfu0 (steady state with the inoculum).
  • Antibiotic disposition. d/dt(cipm) = 0, d/dt(cags) = 0 is the SCTK assumption (constant bath concentrations, with the imipenem thermal-degradation supplementation at 6 and 30 h absorbed into the effective constant). Users simulating clinical PK should attach elimination terms or couple to an external popPK model (e.g. Hennig_2008_tobramycin, Delattre_2010_amikacin) by overriding d/dt(cipm) and d/dt(cags). The paper’s Monte Carlo simulations used previously reported critically-ill popPK models for imipenem (ref 37 Conil et al.) and tobramycin (ref 36 Aarons et al.); those popPK models are not extracted in this addition.
  • Csig observation floor. csig is bounded below by 0 by the ODE structure but never falls to zero in practice (it tracks CFUall which is bounded below by the unkilled subpopulations). No explicit flooring is required.
  • Solver. The default liblsoda solver was observed to return NaN for these models when the bacterial states approach the stationary plateau; method = "lsoda" is used throughout this vignette. maxsteps = 1e6 with tight tolerances (atol = rtol = 1e-10) is used because the rapid kill at high IPM near MIC makes the system stiff during the kill transient.
  • Erratum check. Web access for an erratum / corrigendum search is not available in this offline build. No erratum is referenced in the lead PDF. Any later correction in PubMed or the AAC journal page should be checked before deploying the model in a regulatory context.
  • Convention check. nlmixr2lib::checkModelConventions() returns clean (no warnings, no errors) for all five model files. The bacterial-state compartments (bact_susceptible_susceptible{1,2} etc.) match the existing bacterialSubpopRegex for two-drug Bulitta life-cycle models. The drug and signal-molecule concentration states (cipm, cags, csig) are declared via paper_specific_compartments.