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Meropenem + ciprofloxacin (Rees 2018)

Source: vignettes/articles/Rees_2018_meropenem_ciprofloxacin.Rmd
Rees_2018_meropenem_ciprofloxacin.Rmd

Model and source

  • Citation: Rees VE, Yadav R, Rogers KE, Bulitta JB, Wirth V, Oliver A, Boyce JD, Peleg AY, Nation RL, Landersdorfer CB. Meropenem combined with ciprofloxacin combats hypermutable Pseudomonas aeruginosa from respiratory infections of cystic fibrosis patients. Antimicrob Agents Chemother. 2018 Oct 24;62(11):e01150-18. doi:10.1128/AAC.01150-18. Model differential equations (Eqs 1-4) and static-time-kill parameters (Table S1) are in the supplemental material.
  • Description: In vitro (hollow-fiber infection model). Mechanism-based PK/PD (life-cycle growth) model of bacterial killing and resistance for meropenem plus ciprofloxacin against hypermutable Pseudomonas aeruginosa CW44, with three pre-existing subpopulations and subpopulation plus mechanistic synergy
  • Article: https://doi.org/10.1128/AAC.01150-18
  • Supplement (model equations Eqs 1-4, Table S1): https://doi.org/10.1128/AAC.01150-18

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 and resistant viable counts for the double-susceptible hypermutable Pseudomonas aeruginosa isolate CW44 in a dynamic hollow-fiber infection model (HFIM). The antibiotic exposures (meropenem and ciprofloxacin epithelial-lining-fluid concentrations) are model inputs that were simulated to reflect cystic-fibrosis patient pharmacokinetics; here they are reproduced as two concentration states (cmem, ccip) that the user doses and that decline with the published half-lives. Because there is no absorption-distribution-elimination profile of a drug to integrate for an NCA, NCA / PKNCA is not an appropriate validation; the checks below are the mechanistic equivalents (carrying-capacity hold, synergy quantification, and replication of the published kill / regrowth behaviour).

Population (biological context)

The model describes P. aeruginosa CW44, a hypermutable clinical isolate from a cystic fibrosis patient with chronic respiratory infection, susceptible to both meropenem (Etest MIC 0.5 mg/L) and ciprofloxacin (MIC 0.19 mg/L) (Rees 2018 Table 1). It was grown in cation-adjusted Mueller-Hinton broth at an initial inoculum of ~10^7.4 CFU/mL and treated over 8 days in the HFIM with meropenem (1 or 2 g q8h as 3-h infusions, or 3 g/day as a continuous infusion) and ciprofloxacin (400 mg q8h as 1-h infusions), alone and combined, with simulated ELF concentration-time profiles (Rees 2018 Table 3, Methods). Four other strains (PAO1, PAO-delta-mutS, CW8, CW35) were studied only in static time-kill assays and are not described by this HFIM model.

The same information is available programmatically via readModelDb("Rees_2018_meropenem_ciprofloxacin")$population.

Source trace

Per-parameter origins are recorded as in-file comments next to each ini() entry in inst/modeldb/specificDrugs/Rees_2018_meropenem_ciprofloxacin.R. All parameter values are the HFIM population-mean estimates from Rees 2018 Table 2; the static-time-kill (SCTK) counterparts are in supplement Table S1. The model structure is from supplement Equations 1-4 and Figure 3.

Equation / parameter Value Source location
log10cfu0 (initial inoculum) 7.37 Table 2
log10cfumax (max population size) 8.80 Table 2
lk21 (replication rate, fixed) 50.0 /h Table 2 (fixed)
mgt_ss, mgt_ri, mgt_ir (mean generation times) 181, 86.3, 121 min Table 2 (the “k12” rows; k12 = 60/MGT)
log10mf_mem, log10mf_cip (mutation frequencies) -7.70, -4.31 Table 2
kmax_mem, kmax_cip 0.975, 5.28 /h Table 2
kc50_{ss,ri,ir}_mem 2.08, 24.5, 5.48 mg/L Table 2
kc50_{ss,ri,ir}_cip 1.67, 14.5, 45.8 mg/L Table 2
hill_mem 1.60 Table 2
imax_syn (fixed), ic50_syn 1, 0.914 mg/L Table 2
addSd (residual SD, log10 scale) 0.370 Table 2 (SDCFU)
thalf_mem, thalf_cip (fixed inputs) 0.8, 2.9 h Methods (clinical PK refs 48, 49, 56)
Life-cycle growth ODEs (2 states/subpop) n/a Supplement Eqs 2-3
Killing term (Hill MEM + Emax CIP) n/a Supplement Eq 2
Mechanistic synergy syn = 1 - Imax*Ccip/(Ccip+IC50syn) n/a Supplement Eq 4
Total viable count CFUall = sum of 6 states n/a Supplement Eq 1

Units (dimensional analysis)

Symbol Meaning Units
bact_susceptible_susceptible1, bact_susceptible_susceptible2, bact_resistant_intermediate1, bact_resistant_intermediate2, bact_intermediate_resistant1, bact_intermediate_resistant2 bacterial states CFU/mL
cmem, ccip antibiotic concentrations mg/L
lk21, k12*, kel_*, kill_*, kmax_* rate constants 1/h
kc50_*, ic50_syn half-effect concentrations mg/L
hill_mem, plat, syn, imax_syn dimensionless –
cfumax, cfu0 population scale / inoculum CFU/mL

Every growth/kill ODE term has the form (1/h) x (CFU/mL) = (CFU/mL)/h, matching d/dt(state); the drug ODEs have (1/h) x (mg/L) = (mg/L)/h. k12 = 60/MGT carries 60 in (min/h), converting the mean generation time (min) to a rate (1/h).

mod <- rxode2::rxode(readModelDb("Rees_2018_meropenem_ciprofloxacin"))
mod$state
#> [1] "bact_susceptible_susceptible1" "bact_susceptible_susceptible2"
#> [3] "bact_resistant_intermediate1"  "bact_resistant_intermediate2" 
#> [5] "bact_intermediate_resistant1"  "bact_intermediate_resistant2" 
#> [7] "cmem"                          "ccip"

Parameter table (paper vs. file) 

params <- mod$theta
knitr::kable(
  data.frame(parameter = names(params), file_value = unname(params)),
  caption = "Fixed/typical parameter values as loaded from the model file (Rees 2018 Table 2)."
)
Fixed/typical parameter values as loaded from the model file (Rees 2018 Table 2).
parameter file_value
log10cfu0 7.370000
log10cfumax 8.800000
lk21 3.912023
mgt_ss 181.000000
mgt_ri 86.300000
mgt_ir 121.000000
log10mf_mem -7.700000
log10mf_cip -4.310000
kmax_mem 0.975000
kc50_ss_mem 2.080000
kc50_ri_mem 24.500000
kc50_ir_mem 5.480000
hill_mem 1.600000
kmax_cip 5.280000
kc50_ss_cip 1.670000
kc50_ri_cip 14.500000
kc50_ir_cip 45.800000
imax_syn 1.000000
ic50_syn 0.914000
addSd 0.370000
thalf_mem 0.800000
thalf_cip 2.900000

Carrying-capacity (growth control) check

With no antibiotic, the population grows from the inoculum (10^7.37) toward a stationary plateau. A notable structural property of this two-state life-cycle growth model: at steady state the plateau factor plat = 1 - CFUall/CFUmax settles at 0.5 (each surviving division replaces one cell), so the realized stationary population is 0.5 * CFUmax, i.e. log10(0.5 * 10^8.80) = 8.50 – not 8.80. This matches the regrowth plateau of “>= 8.5 log10 CFU/mL” reported by Rees 2018, and is the correct behaviour of the published equations rather than a transcription error.

ev_gc <- et(seq(0, 192, by = 1))
gc <- rxode2::rxSolve(mod, ev_gc, returnType = "data.frame", maxsteps = 1e5)

cat(sprintf("Inoculum log10CFU(0)  = %.3f  (Table 2 Log10CFU0 = 7.37)\n", gc$Cc[1]))
#> Inoculum log10CFU(0)  = 7.370  (Table 2 Log10CFU0 = 7.37)
cat(sprintf("Plateau  log10CFU(192)= %.3f  (expected 0.5*CFUmax = %.3f)\n",
            tail(gc$Cc, 1), log10(0.5) + 8.80))
#> Plateau  log10CFU(192)= 8.499  (expected 0.5*CFUmax = 8.499)

ggplot(gc, aes(time, Cc)) +
  geom_line(linewidth = 1) +
  geom_hline(yintercept = log10(0.5) + 8.80, linetype = 2, colour = "grey50") +
  labs(x = "Time (h)", y = expression(log[10]~CFU/mL),
       title = "Antibiotic-free growth control",
       caption = "Dashed line: stationary population 0.5 x CFUmax = 8.50 log10 CFU/mL.")

Mechanistic synergy check

Ciprofloxacin lowers the effective meropenem KC50 through the synergy factor syn = 1 - Imax_SYN * Ccip / (Ccip + IC50_SYN); the meropenem killing term uses (syn * KC50,MEM)^Hill in its denominator, so the effective KC50,MEM is syn * KC50,MEM and the fold-decrease in KC50,MEM is 1 / syn. Rees 2018 report an “~4.3-fold decrease in KC50,MEM in the presence of 3 mg/L ciprofloxacin”; the model reproduces this exactly.

imax_syn <- 1; ic50_syn <- 0.914
syn <- function(ccip) 1 - imax_syn * ccip / (ccip + ic50_syn)
data.frame(
  Ccip_mgL = c(0, ic50_syn, 3),
  syn = syn(c(0, ic50_syn, 3)),
  KC50_MEM_fold_decrease = 1 / syn(c(0, ic50_syn, 3))
) |>
  knitr::kable(digits = 3,
               caption = "Mechanistic synergy: fold-decrease in meropenem KC50 (1/syn). At 3 mg/L ciprofloxacin the model gives ~4.3-fold, matching Rees 2018.")
Mechanistic synergy: fold-decrease in meropenem KC50 (1/syn). At 3 mg/L ciprofloxacin the model gives ~4.3-fold, matching Rees 2018.
Ccip_mgL syn KC50_MEM_fold_decrease
0.000 1.000 1.000
0.914 0.500 2.000
3.000 0.234 4.282

Replicate Figure 2 (HFIM kill / regrowth)

Figure 2 of Rees 2018 shows total and resistant population time courses over 8 days for meropenem and ciprofloxacin in mono- and combination therapy. We reproduce the qualitative behaviour: monotherapies achieve initial killing followed by regrowth of the corresponding resistant subpopulation, whereas the 6 g/day meropenem (2 g q8h) plus ciprofloxacin combination produces sustained killing and resistance suppression.

Each regimen is dosed with a loading dose plus q8h infusions whose rates were chosen to reproduce the Table 3 epithelial-lining-fluid Cmax/Cmin. Simulations are deterministic typical-value trajectories (the model has no between-subject random effects). Counts below the limit of counting are floored at the published values (1.0 log10 CFU/mL total, 0.7 log10 CFU/mL resistant), as in the paper.

kel_mem <- log(2) / 0.8
kel_cip <- log(2) / 2.9

# Steady-state infusion rate (into a unit-volume concentration state) that
# reaches target Cmax for a tau-h interval with a T-h infusion.
rate_for <- function(Cmax, kel, tau, Tinf) {
  Cmax * kel * (1 - exp(-kel * tau)) / (1 - exp(-kel * Tinf))
}

# One regimen as a dosing data.frame; id_offset keeps subject IDs disjoint.
mem_inf <- function(Cmax, id) {
  R <- rate_for(Cmax, kel_mem, 8, 3)
  as.data.frame(et(id = id, amt = R * 3, rate = R, ii = 8, cmt = "cmem", until = 192))
}
cip_inf <- function(id) {
  R <- rate_for(2.8, kel_cip, 8, 1)
  bind_rows(
    as.data.frame(et(id = id, amt = 0.53, cmt = "ccip", time = 0)),                  # loading
    as.data.frame(et(id = id, amt = R * 1, rate = R, ii = 8, cmt = "ccip", until = 192))
  )
}

regimens <- list(
  "Growth control"            = function(id) as.data.frame(et(id = id, amt = 0, cmt = "cmem", time = 0)),
  "MEM 1 g q8h"               = function(id) mem_inf(6,  id),
  "MEM 2 g q8h (6 g/day)"     = function(id) mem_inf(12, id),
  "CIP 400 mg q8h"            = function(id) cip_inf(id),
  "MEM 2 g q8h + CIP"         = function(id) bind_rows(mem_inf(12, id), cip_inf(id)),
  "MEM 2 g q8h 60% ELF + CIP" = function(id) bind_rows(mem_inf(24, id), cip_inf(id))
)

obs <- function(id) as.data.frame(et(id = id, time = seq(0, 192, by = 1)))

events <- bind_rows(lapply(seq_along(regimens), function(i) {
  bind_rows(regimens[[i]](i), obs(i)) |>
    mutate(regimen = names(regimens)[i])
}))
stopifnot(!anyDuplicated(unique(events[, c("id", "time", "evid")])))

sim <- rxode2::rxSolve(mod, events, keep = "regimen",
                       returnType = "data.frame", maxsteps = 1e5) |>
  as.data.frame()
#> Warning: multi-subject simulation without without 'omega'
loc_total <- 1.0
loc_res   <- 0.7

plot_df <- sim |>
  transmute(
    time, regimen,
    Total              = pmax(log10(CFUall),  loc_total),
    `MEM-resistant`    = pmax(log10(CFUrmem), loc_res),
    `CIP-resistant`    = pmax(log10(CFUrcip), loc_res)
  ) |>
  pivot_longer(c(Total, `MEM-resistant`, `CIP-resistant`),
               names_to = "population", values_to = "log10CFU") |>
  mutate(regimen = factor(regimen, levels = names(regimens)))
#> Warning: There were 3 warnings in `transmute()`.
#> The first warning was:
#> ℹ In argument: `Total = pmax(log10(CFUall), loc_total)`.
#> Caused by warning in `pmax()`:
#> ! NaNs produced
#> ℹ Run `dplyr::last_dplyr_warnings()` to see the 2 remaining warnings.

ggplot(plot_df, aes(time, log10CFU, colour = population)) +
  geom_line(linewidth = 0.8) +
  facet_wrap(~regimen) +
  scale_x_continuous(breaks = seq(0, 192, by = 48)) +
  labs(x = "Time (h)", y = expression(log[10]~CFU/mL), colour = NULL,
       title = "Replicates Figure 2 of Rees 2018",
       caption = paste("Monotherapies regrow with resistance; the 6 g/day meropenem +",
                       "ciprofloxacin combination suppresses regrowth and resistance.")) +
  theme(legend.position = "bottom")
#> Warning: Removed 4 rows containing missing values or values outside the scale range
#> (`geom_line()`).

sim |>
  group_by(regimen) |>
  summarise(
    nadir_total_log10 = round(min(log10(pmax(CFUall, 1e-3))), 2),
    end_total_log10   = round(log10(pmax(tail(CFUall, 1), 1e-3)), 2),
    end_MEMres_log10  = round(log10(pmax(tail(CFUrmem, 1), 1e-3)), 2),
    end_CIPres_log10  = round(log10(pmax(tail(CFUrcip, 1), 1e-3)), 2),
    .groups = "drop"
  ) |>
  mutate(regimen = factor(regimen, levels = names(regimens))) |>
  arrange(regimen) |>
  knitr::kable(caption = "Simulated nadir and day-8 (191 h) populations by regimen. Monotherapies regrow to the ~8.5 log10 plateau with the matching resistant subpopulation; combinations drive the total below the limit of counting.")
Simulated nadir and day-8 (191 h) populations by regimen. Monotherapies regrow to the ~8.5 log10 plateau with the matching resistant subpopulation; combinations drive the total below the limit of counting.
regimen nadir_total_log10 end_total_log10 end_MEMres_log10 end_CIPres_log10
Growth control 7.37 8.50 2.01 4.74
MEM 1 g q8h 6.14 8.50 8.50 -3.00
MEM 2 g q8h (6 g/day) 5.08 8.49 8.49 -3.00
CIP 400 mg q8h 3.66 8.39 -3.00 8.39
MEM 2 g q8h + CIP -3.00 -3.00 -3.00 -3.00
MEM 2 g q8h 60% ELF + CIP -3.00 -3.00 -3.00 -3.00

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 CW44 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 meropenem plus ciprofloxacin, so the model file and this vignette use Rees_2018_meropenem_ciprofloxacin.
  • HFIM final model. Parameters are the HFIM estimates (Rees 2018 Table 2). The static-concentration time-kill (SCTK) MBM (supplement Table S1) shares the same structure but different estimates and was the precursor that “was adapted for the HFIM data”; it is not separately packaged.
  • Mean generation time. Table 2 labels the growth rows “k12 (min-1)” but the reported values (181, 86.3, 121) are the mean generation times in minutes; the supplement defines the rate constant as k12 = 60/MGT (1/h). The file stores the MGTs and derives k12 in model().
  • Synergy term placement. The supplement equation renders the meropenem killing denominator ambiguously; the effective KC50,MEM is taken as (syn * KC50,MEM)^Hill because that reproduces the paper’s stated ~4.3-fold KC50,MEM decrease at 3 mg/L ciprofloxacin (1/syn = 4.28), whereas syn * KC50,MEM^Hill would give only ~2.5-fold.
  • Stationary population is 0.5 x CFUmax. A structural property of the published two-state model (steady state at plat = 0.5), consistent with the observed plateau of “>= 8.5 log10 CFU/mL”; not adjusted to reach 8.80.
  • Antibiotic disposition. The antibiotic half-lives (0.8 h meropenem, 2.9 h ciprofloxacin) are fixed inputs taken from the clinical PK literature cited in Methods, not MBM estimates; they parameterize the cmem/ccip elimination so the model is self-contained. ELF penetration (30%/60% meropenem, 85% ciprofloxacin) was already absorbed into the Table 3 target concentrations and is therefore reflected in the dosing rates chosen here, not in the model parameters. Infusion rates in the Figure 2 chunk were derived analytically to hit the Table 3 Cmax/Cmin and are not fitted to the bacterial data.
  • Initial state partitioning. The inoculum and the two pre-existing resistant subpopulations (seeded by the meropenem and ciprofloxacin mutation frequencies) are placed entirely in life-cycle state 1; the paper specifies the inoculum and mutation frequencies but not the state-1/state-2 split. The balanced-growth state-2 fraction is < 1% of the population, so this introduces only a brief start-up transient.
  • Below limit of counting. Displayed counts are floored at the published limits of counting (1.0 log10 CFU/mL total, 0.7 log10 CFU/mL resistant), as in Rees 2018 Figures 1-2; the underlying states are not floored.
  • Solver. maxsteps = 1e5 is passed to rxSolve because the rapid kill of the combination regimens makes the system briefly stiff. Steady-state (ss=1) dosing must not be used: it would reinitialize the bacterial states to their grown steady state and destroy the inoculum.
  • Convention deviations (checkModelConventions() warnings, no errors). All are expected for an in-vitro mechanism-based model: (a) the bacterial-state compartments (bact_susceptible_susceptible1, bact_susceptible_susceptible2, bact_resistant_intermediate1, bact_resistant_intermediate2, bact_intermediate_resistant1, bact_intermediate_resistant2) and antibiotic- concentration states (cmem, ccip) are mechanism-specific; (b) lk21 is a fixed mechanistic rate constant that is log-transformed for parameterisation consistency; (c) the single observation Cc carries a non-PK output (log10 viable count, not a drug concentration); (d) the dosing/concentration units are both mg/L because the antibiotic input is a concentration in the in-vitro system.