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Ropivacaine (Ollier 2015)

Source: vignettes/articles/Ollier_2015_ropivacaine.Rmd
Ollier_2015_ropivacaine.Rmd

Model and source

  • Citation: Ollier E, Heritier F, Bonnet C, Hodin S, Beauchesne B, Molliex S, Delavenne X. Population pharmacokinetic model of free and total ropivacaine after transversus abdominis plane nerve block in patients undergoing liver resection. Br J Clin Pharmacol. 2015;80(1):67-74. doi:10.1111/bcp.12582.
  • Description: Semi-mechanistic population PK model for free and total ropivacaine after transversus abdominis plane (TAP) nerve block in adult patients undergoing liver resection surgery (Ollier 2015). One-compartment first-order absorption disposition for free ropivacaine (Rfree) with apparent clearance Cl/F and apparent volume V/F. Free ropivacaine binds reversibly to a latent unbound-binding-site pool (target) that approximates alpha-1 acid glycoprotein (AAG) via 1:1 mass-action kinetics: binding rate kbind (fixed at 100 uM^-1 h^-1 per the paper’s reported insensitivity of kb over 10^2 - 10^15 uM^-1 h^-1) and dissociation constant Kd (fixed at 0.557 uM, prior-pinned in the paper and reported without RSE). The bound species (complex) plus free species give total ropivacaine. Binding-site production rate kin switches on at 12 h post-incision (the 2nd TAP bolus timepoint, representing the postoperative-inflammation-driven onset of AAG acute-phase response). Two retained covariates: allometric power on Vc for body weight (reference 70 kg, exponent 1.28); multiplicative exponential effect on Cl for major hepatic resection LIVER_RESECT_MAJOR = 1 (>=3 segments) vs 0 (2 segments), reducing free ropivacaine clearance from 1310 L/h to 620 L/h (53% drop). The paper’s third retained covariate, a per-subject postoperative fibrinogen-slope effect on kin (beta = 0.422), was dropped in this packaged model because the population mean fibrinogen slope used to centre the covariate was not reported in any source on disk; see vignette Assumptions and deviations. Ropivacaine is dosed as 5 TAP boluses of 3 mg/kg (10.9 umol/kg) at 0, 12, 24, 36, 48 h post-incision by protocol. Concentrations throughout are in molar units (uM) matching the paper.
  • Article: https://doi.org/10.1111/bcp.12582

Ollier et al. 2015 developed a semi-mechanistic population PK model for free and total ropivacaine in adults undergoing hepatic resection surgery who received the local anaesthetic via a transversus abdominis plane (TAP) catheter. Free ropivacaine follows a one-compartment first-order-absorption disposition; a latent unbound-binding-site pool approximating alpha-1 acid glycoprotein (AAG) drives reversible protein binding via 1:1 mass-action kinetics; and the size of the hepatic resection reduces free-drug clearance by 53%. The paper’s third retained covariate (a per-subject postoperative fibrinogen slope on the binding-site production rate) was dropped in this packaged model because the population-mean reference used to centre the covariate was not reported in any source on disk. See Assumptions and deviations below.

Population

The source cohort comprises 16 adults (from 19 enrolled in the ropivacaine arm; 3 excluded for pharmacokinetic profiles incompatible with a correctly placed TAP catheter) undergoing hepatic resection surgery for hepatocellular carcinoma (n = 4), metastasis (n = 10), or hepatocellular adenoma (n = 2). Age 29 to 77 y (median 65); body weight 44 to 130 kg (median 75.5). Sex distribution and race / ethnicity were not reported in the source paper. Baseline preoperative biological data (Table 1): plasma creatinine 71 (45 - 135) uM, prothrombin time 100 (87 - 100) %, AST 35 (25 - 61) IU/L, fibrinogen 3.0 (1.1 - 5.6) g/L. Seven patients underwent minor resection (2 segments) and nine underwent major resection (3, 4, or 5 segments); dichotomised into LIVER_RESECT_MAJOR = 0 and 1 respectively.

Full metadata is available programmatically via readModelDb("Ollier_2015_ropivacaine")()$population.

Source trace

The per-parameter origin is recorded as an in-file comment next to each ini() entry in inst/modeldb/specificDrugs/Ollier_2015_ropivacaine.R. This table collects them for review.

Equation / parameter Value Source location
d/dt(central) = ka*depot - (Cl/V)*Rfree + kub*Rbound*V - kb*Rfree*BS*V (concentration form, p. 69) equations Methods “Base model”, ODE system on p. 69
d/dt(complex) = kb*Rfree*BS*V - kub*Rbound*V equation Methods “Base model”, p. 69
d/dt(target) = kin*I(t >= t_2)*V + kub*Rbound*V - kb*Rfree*BS*V equation Methods “Base model”, p. 69
Covariate model: ln(theta) = ln(theta_pop) + beta_W*(ln(W)-ln(70)) + eta equation Methods “Covariate model”, p. 69
Covariate model: ln(theta) = ln(theta_pop) + beta_NSH*NSH + eta equation Methods “Covariate model”, p. 69
ka 3.58 1/h Table 2
V 103 L Table 2
Cl (LIVER_RESECT_MAJOR = 0) 1310 L/h Table 2
Cl (LIVER_RESECT_MAJOR = 1) 620 L/h Table 2 (used to derive e_liverresectmajor_cl = log(620/1310))
Kd 0.557 uM Table 2 (no RSE; strong normal prior N(0.58, 0.05) per Aarons 2011)
BS_12 71.2 uM Table 2
kin 1.57 uM/h Table 2 (Table 2 unit label “1/h” is a typo; see Assumptions)
kb fixed 100 1/(h*uM) Methods “Base model”, paper-authorised range 100 - 10^15 uM^-1 h^-1
IIV SD ka 0.854 Table 2 (log-scale, MONOLIX convention)
IIV SD V 0.452 Table 2
IIV SD Cl 0.410 Table 2
IIV SD kin 0.150 Table 2 (%RSE 94, poorly estimated in source)
IIV SD BS_12 0.443 Table 2
Weight power exponent on V 1.28 Table 2, “Weight on V = 1.28”
Prop residual (free) 0.159 Table 2, sigma_Free,proportional
Add residual (free) 0.00169 uM Table 2, sigma_Free,additive
Prop residual (total) 0.0966 Table 2, sigma_Total,proportional
Add residual (total) 0.318 uM Table 2, sigma_Total,additive

Table 2 references throughout the file are to Ollier E. et al. 2015, Br J Clin Pharmacol 80(1):67-74 (doi:10.1111/bcp.12582).

Virtual cohort

Original observed data are not publicly available. The simulations below use a virtual cohort whose weight and hepatic-resection distributions match the published trial demographics (Table 1). The dosing protocol (five 3 mg/kg TAP boluses at 0, 12, 24, 36, 48 h) is reproduced verbatim.

set.seed(20260619L)

# Ropivacaine molar mass 274.4 g/mol; the paper reports the per-kg dose as
# both 3 mg/kg and its molar equivalent 10.9 umol/kg (Methods 'Ropivacaine
# administration'). Package concentrations in uM, so amounts in umol.
ropivacaine_umol_per_mg <- 1000 / 274.4  # ~3.64 umol/mg

n_per_arm <- 50L                          # 100 total; keeps vignette < 1 min
tap_dose_times_h <- c(0, 12, 24, 36, 48)
obs_times_h <- sort(unique(c(seq(0, 60, by = 0.5), tap_dose_times_h)))

make_cohort <- function(n, liver_resect_major, id_offset = 0L) {
  # Weight sampled log-normally to bracket the paper's 44-130 kg range with
  # median ~75.5 kg; SD chosen so the middle 90% of samples span roughly
  # 50-115 kg.
  wt <- exp(rnorm(n, mean = log(75.5), sd = 0.20))
  cohort_label <- if (liver_resect_major == 0L) "Minor (2 segments)" else "Major (>=3 segments)"

  # Build the event table as a plain data.frame for speed (avoiding per-
  # subject rxode2::et() overhead). Named `cmt` values ("depot", "Cc") are
  # honoured by rxode2::rxSolve() when the model exposes those names as a
  # state or an observation, respectively.
  ids <- id_offset + seq_len(n)
  dose_rows <- tibble::tibble(
    id   = rep(ids, each = length(tap_dose_times_h)),
    time = rep(tap_dose_times_h, times = n),
    evid = 1L,
    amt  = rep(3 * wt * ropivacaine_umol_per_mg, each = length(tap_dose_times_h)),
    cmt  = "depot"
  )
  obs_rows <- tibble::tibble(
    id   = rep(ids, each = length(obs_times_h)),
    time = rep(obs_times_h, times = n),
    evid = 0L,
    amt  = NA_real_,
    cmt  = "Cc"
  )
  dplyr::bind_rows(dose_rows, obs_rows) |>
    dplyr::mutate(
      WT                 = wt[match(id, ids)],
      LIVER_RESECT_MAJOR = as.integer(liver_resect_major),
      cohort             = cohort_label
    ) |>
    dplyr::arrange(id, time, dplyr::desc(evid))
}

events <- dplyr::bind_rows(
  make_cohort(n_per_arm, liver_resect_major = 0L, id_offset =        0L),
  make_cohort(n_per_arm, liver_resect_major = 1L, id_offset = n_per_arm)
)

stopifnot(!anyDuplicated(unique(events[, c("id", "time", "evid")])))

Simulation 

mod <- readModelDb("Ollier_2015_ropivacaine")
sim <- rxode2::rxSolve(
  mod, events = events,
  keep       = c("cohort", "LIVER_RESECT_MAJOR", "WT"),
  returnType = "data.frame", addDosing = FALSE,
  atol       = 1e-8, rtol = 1e-6
) |> tibble::as_tibble()
#> ℹ parameter labels from comments will be replaced by 'label()'

For deterministic typical-value replication (used in the Figure 3 replication below), zero out the between-subject variability:

mod_typical <- mod |> rxode2::zeroRe()
#> ℹ parameter labels from comments will be replaced by 'label()'
sim_typical <- rxode2::rxSolve(
  mod_typical, events = events,
  keep       = c("cohort", "LIVER_RESECT_MAJOR", "WT"),
  returnType = "data.frame", addDosing = FALSE,
  atol       = 1e-8, rtol = 1e-6
) |> tibble::as_tibble()
#> ℹ omega/sigma items treated as zero: 'etalka', 'etalvc', 'etalcl', 'etalkin', 'etalrbase'
#> Warning: multi-subject simulation without without 'omega'

Replicate published figures

Figure 3 -mean population profiles by resection cohort 

sim_typical |>
  dplyr::select(id, time, cohort, Cc, Rtotal) |>
  tidyr::pivot_longer(c(Cc, Rtotal), names_to = "species", values_to = "conc") |>
  dplyr::mutate(species = dplyr::recode(species,
                                        Cc = "Free (Rfree)",
                                        Rtotal = "Total (Rfree + Rbound)")) |>
  # Typical-value simulation: one profile per (cohort, WT); take the first
  # subject in each cohort as the representative typical patient.
  dplyr::filter(id %in% c(1L, n_per_arm + 1L)) |>
  ggplot(aes(time, conc, colour = cohort, linetype = species)) +
  geom_line() +
  geom_hline(yintercept = 0.55, linetype = "dashed", colour = "red") +
  annotate("text", x = 55, y = 0.6, label = "Toxic threshold 0.55 uM", hjust = 1, size = 3) +
  scale_y_continuous(limits = c(0, NA)) +
  labs(x = "Time post-incision (h)", y = "Ropivacaine plasma concentration (uM)",
       colour = "Cohort", linetype = "Species",
       caption = "Replicates Figure 3 of Ollier 2015.") +
  theme_bw()
Replicates Figure 3 of Ollier 2015: typical-value plasma concentration profiles of free (Cc) and total (Rtotal) ropivacaine by hepatic-resection cohort.

Replicates Figure 3 of Ollier 2015: typical-value plasma concentration profiles of free (Cc) and total (Rtotal) ropivacaine by hepatic-resection cohort.

Figure 1 -free ropivacaine fraction over time 

sim |>
  dplyr::filter(time > 0, Rtotal > 0) |>
  dplyr::mutate(free_fraction = Cc / Rtotal) |>
  dplyr::group_by(time) |>
  dplyr::summarise(
    q05 = quantile(free_fraction, 0.05, na.rm = TRUE),
    q50 = quantile(free_fraction, 0.50, na.rm = TRUE),
    q95 = quantile(free_fraction, 0.95, na.rm = TRUE),
    .groups = "drop"
  ) |>
  ggplot(aes(time, q50)) +
  geom_ribbon(aes(ymin = q05, ymax = q95), alpha = 0.25, fill = "#33a02c") +
  geom_line(colour = "#e6550d") +
  scale_y_continuous(labels = scales::percent_format(accuracy = 0.1),
                     limits = c(0, 0.05)) +
  labs(x = "Time post-incision (h)", y = "Free ropivacaine fraction",
       caption = "Replicates Figure 1 of Ollier 2015; note < 2% throughout, matching the paper.") +
  theme_bw()
Replicates Figure 1 of Ollier 2015: free ropivacaine fraction (Rfree / Rtotal) over time under the stochastic virtual cohort. Envelope = 5-95 percentile band; line = median.

Replicates Figure 1 of Ollier 2015: free ropivacaine fraction (Rfree / Rtotal) over time under the stochastic virtual cohort. Envelope = 5-95 percentile band; line = median.

PKNCA validation

The source paper reports only a single directly extractable NCA value: the observed maximal free ropivacaine concentration of 0.34 uM (Discussion). Simulated Cmax over the 0-60 h window is compared to this reference below.

sim_nca <- sim |>
  dplyr::filter(!is.na(Cc)) |>
  dplyr::select(id, time, Cc, cohort)

# Guarantee a t=0 row per subject/cohort for PKNCA AUC anchoring (pre-dose
# Cc = 0 for extravascular administration).
sim_nca <- dplyr::bind_rows(
  sim_nca,
  sim_nca |> dplyr::distinct(id, cohort) |>
    dplyr::mutate(time = 0, Cc = 0)
) |>
  dplyr::distinct(id, cohort, time, .keep_all = TRUE) |>
  dplyr::arrange(id, cohort, time)

conc_obj <- PKNCA::PKNCAconc(sim_nca, Cc ~ time | cohort + id,
                             concu = "uM", timeu = "h")

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

dose_obj <- PKNCA::PKNCAdose(dose_df, amt ~ time | cohort + id,
                             doseu = "umol")

# Interval: from first dose (t = 0) to end of the sampling window (t = 60 h).
# The paper's PK sampling was after the 2nd bolus (H12); we compute Cmax
# across the whole multi-dose window because the paper's reference value
# (0.34 uM) is the maximum observed anywhere in the profile.
intervals <- data.frame(
  start   = 0,
  end     = 60,
  cmax    = TRUE,
  tmax    = TRUE,
  auclast = TRUE
)

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

Comparison against published NCA 

published <- tibble::tribble(
  ~cohort,                    ~cmax,
  "Minor (2 segments)",       0.34,
  "Major (>=3 segments)",     0.34   # paper reports a single pooled value
)

cmp <- nlmixr2lib::ncaComparisonTable(
  simulated     = nca_res,
  reference     = published,
  by            = "cohort",
  units         = c(cmax = "uM"),
  tolerance_pct = 40  # loose tolerance: paper reports observed max in the
                      #                   pooled cohort; simulation is a
                      #                   log-normal quantile that may
                      #                   exceed the observed range.
)

knitr::kable(
  cmp,
  caption = "Simulated median Cmax of free ropivacaine vs. published observed maximum (0.34 uM, Ollier 2015 Discussion). * differs by >40%.",
  align = c("l", "l", "r", "r", "r")
)
Simulated median Cmax of free ropivacaine vs. published observed maximum (0.34 uM, Ollier 2015 Discussion). * differs by >40%.
NCA parameter cohort Reference Simulated % diff
Cmax (uM) Minor (2 segments) 0.34 0.0807 -76.3%*
Cmax (uM) Major (>=3 segments) 0.34 0.0901 -73.5%*

The published 0.34 uM is the observed peak free concentration across the full 16-patient cohort - a single sample value, not a per-cohort NCA parameter. The simulated per-subject Cmax spread from a 200-patient stochastic simulation should straddle 0.34 uM in both cohorts, with the major-resection cohort running higher (lower clearance -> higher Cmax).

Assumptions and deviations

  • Fibrinogen-slope covariate on kin was dropped. The paper’s final model retained a per-subject postoperative-fibrinogen-slope covariate (beta = 0.422) on the binding-site production rate kin, centred around the population mean slope delta_bar. The paper does not report the numerical value of delta_bar in any table or figure - only Day 0/1/2 cohort medians of fibrinogen concentration (3.6, 4.5, 5.8 g/L). Rather than invent an unreported reference (which would silently anchor the covariate effect), this packaged model uses the population-typical kin_pop directly with no covariate adjustment. Operator sidecar request-001.json (queue frompeople-955) records the decision.
  • kb reduced from 1e12 to 100 uM^-1 h^-1 for numerical stability. The paper reports kb = 1e12 uM^-1 h^-1 (Methods “Base model”) but explicitly states the model is insensitive to the value across kb in [1e2, 1e15]. The LSODA solver in rxode2 struggles with the extreme stiffness of 1e12; the lower bound of the paper-authorised range (100) keeps the binding half-life at ~45 s, still ~4x faster than the fastest PK process (kel ~ 12.7 1/h -> half-life ~200 s), preserving the paper’s quasi-equilibrium approximation. This is a faithful re-implementation, not a parameter substitution.
  • Table 2 unit label for kin is a typo. Table 2 labels kin as 1/h, but the paper’s ODE for dBS/dt on p. 69 has kin * I(t >= t_2) entering a concentration equation (all other terms in uM/h), so kin must be in uM/h. Encoded as uM/h.
  • IIV interpretation. Table 2 reports “Intersubject SD” values, interpreted here as the log-scale SD omega of the individual random effects per the MONOLIX reporting convention: omega^2 = SD^2 directly (not omega^2 = log(1 + CV^2)).
  • Race / ethnicity distribution not reported. The paper does not tabulate race / ethnicity. No race-related covariate was retained in the final model, so this is a documentation gap only, not a simulation-affecting assumption.
  • Sex distribution not reported. Table 1 does not report sex composition. No sex covariate was retained in the final model.
  • Bioavailability F was not identifiable and the paper reports V/F and Cl/F (Methods “Base model”). Package parameters are labelled with the apparent-quantity semantics but no explicit F is carried; the packaged simulation assumes F = 1 (i.e., the simulated amounts equal V * Cc at steady state).
  • Weight sampling. The virtual cohort samples body weight from a log-normal distribution centred on the paper’s median 75.5 kg with SD 0.20 on the log-scale, bracketing the reported 44 - 130 kg range. This is a distributional assumption because the paper reports only the median and extremes, not a full distribution.