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Cisplatin (Urien 2004)

Source: vignettes/articles/Urien_2004_cisplatin.Rmd
Urien_2004_cisplatin.Rmd

Model and source

The model describes the joint disposition of unbound (ultrafilterable) and total plasma platinum following 30-min intravenous infusions of cisplatin in adult cancer patients. The structure (Urien 2004 Figure 1) is a two-compartment open model for unbound platinum (central + peripheral1) coupled to a third “metabolite” compartment that captures the irreversibly protein-bound platinum formed at rate fm * CL from the central unbound compartment. The bound species has a much slower elimination rate constant CLm0 / Vm, and the apparent metabolite volume Vm is structurally not identifiable: only the composite parameters fm/Vm (1/L) and CLm0/Vm (1/h) are estimated from the joint analysis of 396 unbound and 477 total platinum measurements. The bound state is therefore carried in concentration units directly, with Vm folded into the two composite parameters.

Population

The model was fit to 873 plasma platinum measurements from 43 adult cancer patients (25 male, 18 female) enrolled in two phase I trials at Centre Rene Huguenin, Saint-Cloud, France. Cisplatin was combined with either irofulven (0.4 mg/kg as a 30-min infusion, 18 patients) or 5-fluorouracil (1 g/m^2/day as a 120-h continuous infusion, 25 patients); concomitant chemotherapy was tested as a covariate and not retained. Doses ranged 15-80 mg per 30-min infusion (median 34.4 mg; median 25 mg/m^2), given as 5 consecutive daily infusions or twice-monthly schedules; 1-5 consecutive daily infusions per patient contributed to the PK evaluation.

Baseline demographics from Table 1: age 21-76 years (median 58), body weight 40-102 kg (median 64), height 150-181 cm (median 168), body surface area 1.38-2.10 m^2 (median 1.62), serum protein 47-80 g/L (median 70), serum creatinine 43-120 umol/L (median 76), and Cockcroft-Gault creatinine clearance 44-155 mL/min (median 81). The same information is available programmatically via readModelDb("Urien_2004_cisplatin")$population.

Source trace

The per-parameter origin is recorded as an in-file comment next to each ini() entry in inst/modeldb/specificDrugs/Urien_2004_cisplatin.R. The table below collects them in one place.

Equation / parameter Value Source location
lvc log(23.4 L) Urien 2004 Table 4 row V1
lcl log(35.5 L/h) Urien 2004 Table 4 row CL
lq log(8.64 L/h) Urien 2004 Table 4 row Q
lvp log(12.0 L) Urien 2004 Table 4 row V2
e_bsa_vc +1.60 Urien 2004 Table 4 row V1, theta_BSA
e_bsa_cl +0.83 Urien 2004 Table 4 row CL, theta_BSA
e_crcl_cl +0.36 Urien 2004 Table 4 row CL, theta_CLCr
lfmVm log(0.017 1/L) Urien 2004 Table 5 row fm/Vm
lclm0Vm log(0.014 1/h) Urien 2004 Table 5 row CLm0/Vm
e_dose_fmVm -0.48 Urien 2004 Table 5 row fm/Vm, theta_DOSEm-2
e_tpro_fmVm +1.33 Urien 2004 Table 5 row fm/Vm, theta_PROT
e_bsa_fmVm -0.83 FIXED Urien 2004 Table 5 row fm/Vm, theta_BSA (fixed)
e_crcl_fmVm -0.36 FIXED Urien 2004 Table 5 row fm/Vm, theta_CLCr (fixed)
etalvc omega^2 = log(1+0.234^2) Urien 2004 Table 4 row ISV(V1) = 23.4% CV
etalcl omega^2 = log(1+0.149^2) Urien 2004 Table 4 row ISV(CL) = 14.9% CV
etalfmVm omega^2 = log(1+0.214^2) Urien 2004 Table 5 row ISV(fm/Vm) = 21.4% CV
etalclm0Vm omega^2 = log(1+0.318^2) Urien 2004 Table 5 row ISV(CLm/Vm) = 31.8% CV
addSd 0.116 ug/mL Urien 2004 Table 4 Res. Error = 116 ug/L (unbound)
addSd_Cc_total 0.103 ug/mL Urien 2004 Table 5 Res. Error = 103 ug/L (total)
ODE central n/a Urien 2004 Figure 1 (unbound compartment 1)
ODE peripheral1 n/a Urien 2004 Figure 1 (unbound compartment 2)
ODE bound n/a Urien 2004 Figure 1 (metabolite compartment m)

The bound-formation flux (fm/Vm) * CL * Cc deserves a closer look. The paper estimates the BSA and creatinine-clearance exponents on fm/Vm as the negatives of the corresponding exponents on CL (e_bsa_fmVm = -e_bsa_cl, e_crcl_fmVm = -e_crcl_cl) so that the product (fm/Vm) * CL is net BSA- and CLCr-neutral. Only the dose-per-area and total-protein exponents contribute substantively to the bound-formation flux.

Virtual cohort

Original observed data are not publicly available. The figures below use a virtual cohort matched to the published median covariates and dose range.

set.seed(2026L)

# Reference covariates correspond to the cohort medians (Urien 2004 Table 1).
ref_bsa  <- 1.62
ref_crcl <- 81
ref_tpro <- 70

# Build a single typical-value subject receiving one 40 mg cisplatin infusion
# over 30 minutes. amt is in mg; concentrations are reported in ug/mL = mg/L.
dose_amt    <- 40
infusion_dt <- 0.5
obs_times   <- sort(unique(c(seq(0, 6, by = 0.05), seq(6, 24, by = 0.25))))

build_events <- function(amt, bsa = ref_bsa, crcl = ref_crcl,
                         tpro = ref_tpro, id = 1L, treatment = "median") {
  doses <- data.frame(
    id = id, time = 0, amt = amt, dur = infusion_dt,
    evid = 1L, cmt = "central"
  )
  obs_cc <- data.frame(
    id = id, time = obs_times, amt = NA_real_, dur = NA_real_,
    evid = 0L, cmt = "Cc"
  )
  obs_total <- data.frame(
    id = id, time = obs_times, amt = NA_real_, dur = NA_real_,
    evid = 0L, cmt = "Cc_total"
  )
  events <- rbind(doses, obs_cc, obs_total)
  events$BSA       <- bsa
  events$CRCL      <- crcl
  events$TPRO      <- tpro
  events$DOSE      <- amt
  events$treatment <- treatment
  events
}

events <- build_events(dose_amt)

Simulation 

mod <- readModelDb("Urien_2004_cisplatin")

# Typical-value simulation (zero between-subject variability) for reproducing
# the population-prediction curves of Urien 2004 Figures 3 and 4.
mod_typical <- rxode2::zeroRe(mod)
#> ℹ parameter labels from comments will be replaced by 'label()'
sim_typical <- rxode2::rxSolve(
  mod_typical, events,
  keep = c("treatment"),
  returnType = "data.frame"
)
#> ℹ omega/sigma items treated as zero: 'etalvc', 'etalcl', 'etalfmVm', 'etalclm0Vm'
# rxSolve omits the id column for single-subject simulations; restore it so
# downstream PKNCA grouping has the subject key it needs.
if (!"id" %in% colnames(sim_typical)) sim_typical$id <- 1L
# Multi-output observations duplicate rows per time (one per `cmt`); both
# Cc and Cc_total are populated on every row, so deduplicating by time loses
# nothing and yields the single-row-per-time form PKNCA expects.
sim_typical <- sim_typical |>
  dplyr::distinct(id, time, .keep_all = TRUE)

Replicate published figures

Figure 4 of Urien 2004 – unbound platinum concentration-time profile 

# Replicates Figure 4 of Urien 2004 (predicted unbound platinum after a single
# 30-min infusion at the cohort-median covariates). The paper Figure shows
# the population prediction and the individual observed data; we plot the
# typical-value prediction.
sim_typical |>
  dplyr::filter(time <= 6, !is.na(Cc), Cc > 0) |>
  ggplot(aes(x = time, y = Cc)) +
  geom_line(linewidth = 0.8) +
  scale_y_log10() +
  labs(x = "Time after start of infusion (h)",
       y = "Unbound plasma platinum (ug/mL)",
       title = "Figure 4 -- unbound platinum vs. time",
       caption = "Replicates the population-prediction curve of Urien 2004 Figure 4.")

Figure 3 of Urien 2004 – total platinum concentration-time profile 

# Replicates Figure 3 of Urien 2004 (predicted total platinum, dominated by
# the slow protein-bound platinum elimination at late times).
sim_typical |>
  dplyr::filter(!is.na(Cc_total), Cc_total > 0) |>
  ggplot(aes(x = time, y = Cc_total)) +
  geom_line(linewidth = 0.8) +
  scale_y_log10() +
  labs(x = "Time after start of infusion (h)",
       y = "Total plasma platinum (ug/mL)",
       title = "Figure 3 -- total platinum vs. time",
       caption = "Replicates the population-prediction curve of Urien 2004 Figure 3.")

Figure 5 of Urien 2004 – joint unbound and total profile 

# Replicates Figure 5 of Urien 2004 (joint profile of unbound (+) and total
# (open circles) platinum for a representative patient). We plot the typical-
# value unbound and total curves overlaid on a log10 y-axis. The unbound
# rapidly declines (half-life ~1.3 h) while total platinum approaches the
# slow protein-bound terminal phase (half-life ~50 h).
sim_typical |>
  dplyr::filter(!is.na(Cc_total)) |>
  dplyr::transmute(
    time,
    Unbound = ifelse(Cc > 0, Cc, NA_real_),
    Total   = Cc_total
  ) |>
  tidyr::pivot_longer(-time, names_to = "species", values_to = "conc") |>
  dplyr::filter(!is.na(conc), conc > 0) |>
  ggplot(aes(x = time, y = conc, colour = species, linetype = species)) +
  geom_line(linewidth = 0.8) +
  scale_y_log10() +
  labs(x = "Time after start of infusion (h)",
       y = "Plasma platinum (ug/mL)",
       title = "Figure 5 -- joint unbound and total platinum profiles",
       caption = paste0("Replicates the joint-profile illustration of ",
                        "Urien 2004 Figure 5."),
       colour = "Species", linetype = "Species")

PKNCA validation

We validate the simulated unbound platinum against the paper’s reported distribution half-life (0.34 h) and elimination half-life (1.32 h) from Table 4, and the simulated total platinum against the paper’s reported elimination half-life (66.8 h, Table 3 derived parameter; and 50 h, Table 5 derived parameter, the latter being the integrated-model estimate for the bound species’ terminal phase).

sim_nca_unbound <- sim_typical |>
  dplyr::filter(!is.na(Cc), Cc > 0) |>
  dplyr::select(id, time, Cc, treatment)

dose_df <- events |>
  dplyr::filter(evid == 1L) |>
  dplyr::select(id, time, amt, treatment)

conc_obj_unb <- PKNCA::PKNCAconc(sim_nca_unbound,
                                 Cc ~ time | treatment + id,
                                 concu = "ug/mL", timeu = "h")
dose_obj <- PKNCA::PKNCAdose(dose_df, amt ~ time | treatment + id,
                             doseu = "mg")

intervals_unb <- data.frame(
  start       = 0,
  end         = 24,
  cmax        = TRUE,
  tmax        = TRUE,
  aucinf.obs  = TRUE,
  half.life   = TRUE
)

nca_data_unb <- PKNCA::PKNCAdata(conc_obj_unb, dose_obj,
                                 intervals = intervals_unb)
nca_unb <- PKNCA::pk.nca(nca_data_unb)
#> Warning: Requesting an AUC range starting (0) before the first measurement
#> (0.05) is not allowed
knitr::kable(
  summary(nca_unb),
  caption = "Simulated unbound platinum NCA (typical-value 40 mg infusion)."
)
Simulated unbound platinum NCA (typical-value 40 mg infusion).
Interval Start Interval End treatment N Cmax (ug/mL) Tmax (h) Half-life (h) AUCinf,obs (h*ug/mL)
0 24 median 1 1.12 0.500 1.31 NC 
sim_nca_total <- sim_typical |>
  dplyr::filter(!is.na(Cc_total), Cc_total > 0) |>
  dplyr::rename(Cc_obs = Cc_total) |>
  dplyr::select(id, time, Cc_obs, treatment)

conc_obj_tot <- PKNCA::PKNCAconc(sim_nca_total,
                                 Cc_obs ~ time | treatment + id,
                                 concu = "ug/mL", timeu = "h")

# Use a long observation window for total platinum so the slow bound-driven
# terminal phase is captured. Simulate out to 240 h for the NCA.
events_long <- events
extra_times <- seq(24, 240, by = 4)
extra_cc <- data.frame(
  id = 1L, time = extra_times, amt = NA_real_, dur = NA_real_,
  evid = 0L, cmt = "Cc_total",
  BSA = ref_bsa, CRCL = ref_crcl, TPRO = ref_tpro, DOSE = dose_amt,
  treatment = "median"
)
events_long <- rbind(events_long, extra_cc)
sim_long <- rxode2::rxSolve(mod_typical, events_long,
                            keep = c("treatment"),
                            returnType = "data.frame")
#> ℹ omega/sigma items treated as zero: 'etalvc', 'etalcl', 'etalfmVm', 'etalclm0Vm'
if (!"id" %in% colnames(sim_long)) sim_long$id <- 1L
sim_long <- sim_long |>
  dplyr::distinct(id, time, .keep_all = TRUE)
sim_nca_total_long <- sim_long |>
  dplyr::filter(!is.na(Cc_total), Cc_total > 0) |>
  dplyr::rename(Cc_obs = Cc_total) |>
  dplyr::select(id, time, Cc_obs, treatment)
conc_obj_tot_long <- PKNCA::PKNCAconc(sim_nca_total_long,
                                      Cc_obs ~ time | treatment + id,
                                      concu = "ug/mL", timeu = "h")
intervals_tot <- data.frame(
  start       = 0,
  end         = 240,
  cmax        = TRUE,
  tmax        = TRUE,
  aucinf.obs  = TRUE,
  half.life   = TRUE
)
nca_data_tot <- PKNCA::PKNCAdata(conc_obj_tot_long, dose_obj,
                                 intervals = intervals_tot)
nca_tot <- PKNCA::pk.nca(nca_data_tot)
#> Warning: Requesting an AUC range starting (0) before the first measurement
#> (0.05) is not allowed
knitr::kable(
  summary(nca_tot),
  caption = "Simulated total platinum NCA (typical-value 40 mg infusion, 0-240 h)."
)
Simulated total platinum NCA (typical-value 40 mg infusion, 0-240 h).
Interval Start Interval End treatment N Cmax (ug/mL) Tmax (h) Half-life (h) AUCinf,obs (h*ug/mL)
0 240 median 1 1.31 0.500 49.5 NC

Comparison against published half-lives 

extract_half_life <- function(nca_obj) {
  res <- as.data.frame(nca_obj$result)
  hl_row <- res[res$PPTESTCD == "half.life", , drop = FALSE]
  if (nrow(hl_row) == 0L) return(NA_real_)
  val <- suppressWarnings(as.numeric(hl_row$PPORRES))
  val[is.finite(val)][1]
}

simulated_t12_unb <- extract_half_life(nca_unb)
simulated_t12_tot <- extract_half_life(nca_tot)

format_t12 <- function(x, digits) {
  if (is.na(x) || !is.finite(x)) "NA" else formatC(round(x, digits), digits = digits, format = "f")
}

comparison <- data.frame(
  Analyte = c("Unbound platinum (terminal)", "Total platinum (terminal)"),
  `Published half-life (h)` = c("1.32", "50"),
  `Simulated half-life (h)` = c(format_t12(simulated_t12_unb, 2),
                                format_t12(simulated_t12_tot, 1)),
  `Source` = c("Table 4 derived", "Table 5 derived"),
  check.names = FALSE
)
knitr::kable(comparison, caption = "Simulated vs. published terminal half-lives.")
Simulated vs. published terminal half-lives.
Analyte Published half-life (h) Simulated half-life (h) Source
Unbound platinum (terminal) 1.32 1.31 Table 4 derived
Total platinum (terminal) 50 49.5 Table 5 derived

A discrepancy of more than 20% would warrant investigation rather than parameter tuning – but for this model the simulated half-life of unbound platinum (driven by CL / Vss = 35.5 / (23.4 + 12.0) ~= 1.0 1/h, so ln(2)/0.6 ~= 1.2 h after the bi-exponential mixing) matches the paper’s elimination half-life of 1.32 h, and the simulated total half-life is set by CLm0/Vm = 0.014 1/h which gives ln(2)/0.014 ~= 49.5 h, matching the paper’s 50 h.

Assumptions and deviations

  • Dose-per-BSA covariate carried via DOSE and BSA columns. The paper estimates the bound-formation parameter fm/Vm as a power function of dose-per-body-surface-area (DOSEm-2). For simulation, the user supplies DOSE (mg per record) and BSA (m^2) as covariate columns, and the model computes dose_per_bsa = DOSE / BSA internally. The DOSE column should be carried forward from the most recent infusion onto each subsequent observation record (LOCF) so the bound-formation kinetics use the correct per-infusion dose. The simulation snippet above uses a single fixed dose to make the LOCF requirement implicit; multi-infusion simulations must explicitly populate DOSE per observation record.

  • Vm is structurally not identifiable. The paper’s three-step sequential analysis estimates the composite parameters fm/Vm (1/L) and CLm0/Vm (1/h); the apparent metabolite volume Vm is not separately estimable. The bound state in d/dt(bound) is therefore carried in concentration units (ug/mL) directly – multiplying through by Vm recovers the amount form, but the resulting state would be ambiguous up to the unknown Vm. The total-platinum observation is computed as Cc + bound, both in ug/mL.

  • Unbound parameters are point estimates carried forward from Step 2 of the sequential fit. Per the paper’s methodology (page 760), the unbound-only fit in Step 2 estimated the unbound layer and its covariate effects; Step 3 held those parameters fixed and estimated the bound parameters in a joint fit. Provenance-wise the unbound values are estimated point estimates; the model file records them without fixed() to match the rest of the popPK library’s conventions for published final-model estimates. A downstream re-fitting workflow that reproduces the paper’s sequential approach would freeze the unbound layer at Step 3.

  • Q and V2 IIVs were fixed to zero in the source. The paper’s Results section (paragraph beneath Table 4) reports that “the data did not allow reliable estimations of intersubject variabilities for Q and V2 and fixing these parameters to zero did not increase the OFV”. No etalq or etalvp is declared in ini() accordingly.

  • No inter-occasion variability. The paper does not report IOV. Each patient contributed 1-5 consecutive daily infusions; treating the joint ISV as encapsulating intra-subject between-infusion variability is consistent with the source.

  • Concomitant-chemotherapy effect not modelled. The paper tested concomitant irofulven and 5-fluorouracil as covariates and did not retain them in the final model; this file follows the published final model and does not include a concomitant-drug covariate.