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Intrathecal trastuzumab in HER2+ breast cancer LMC (Le Tilly 2021)

Source: vignettes/articles/LeTilly_2021_trastuzumab.Rmd
LeTilly_2021_trastuzumab.Rmd

Model and source

  • Citation: Le Tilly O, Azzopardi N, Bonneau C, Ohresser M, Ternant D, Thomas K, Olivier F, Trouillas I, Etcheverry M, Demarquay C, Garcia M, Paintaud G, Goupille O. Antigen Mass May Influence Trastuzumab Concentrations in Cerebrospinal Fluid After Intrathecal Administration. Clin Pharmacol Ther. 2021;110(1):210-219. doi:10.1002/cpt.2188
  • Description: Two-compartment serum/CSF population PK model for trastuzumab after intrathecal and intravenous administration in adults with HER2+ breast cancer leptomeningeal metastases (Le Tilly 2021); zero-order serum-to-CSF transfer plus first-order CSF-to-serum return, with a Friberg-style chain of latent target (HER2) transit compartments and irreversible binding-driven elimination of trastuzumab in the CSF compartment.
  • Article: https://doi.org/10.1002/cpt.2188

Le Tilly et al. (Clin Pharmacol Ther 2021) report the first population-PK characterisation of trastuzumab after intrathecal administration in humans. The structural model is a two-compartment serum/CSF system with a Friberg-style chain of latent target (HER2) transit compartments and irreversible binding–driven elimination of trastuzumab in the CSF. The implemented model corresponds to “Model 7” of Supplement 1 (Friberg-style negative feedback on latent target production), which is the final retained model (Table 2 of the article).

Population

The model was developed in 21 adults with HER2-positive breast cancer leptomeningeal carcinomatosis enrolled in a multicentric phase I/II clinical trial (NCT01373710; Bonneau 2018). All patients received eight weekly IT trastuzumab doses (30, 60, 100, or 150 mg); 13 of 21 (62%) also received concurrent IV trastuzumab 6 mg/kg every 3 weeks. IT administration used lumbar puncture (n = 7), an Ommaya reservoir (n = 9), or an indwelling IT drug-delivery device (n = 11) — some patients used multiple routes across the 8-week treatment period (Le Tilly 2021 Table 1).

Median (range) age was 52 (24–66) years and median (range) weight was 65 (38–90) kg. Sex distribution was not tabulated in Le Tilly 2021 Table 1; HER2-positive breast cancer LMC is a near-exclusively female disease, so the cohort is presumed predominantly or all female. Concurrent corticosteroid prophylaxis (>= 20 mg/day prednisolone or equivalent for at least 3 days before each IT injection plus 25 mg IT hydrocortisone hemisuccinate immediately before each IT trastuzumab dose) was given to every patient.

The full population metadata is available programmatically:

str(rxode2::rxode2(readModelDb("LeTilly_2021_trastuzumab"))$meta$population)
#> ℹ parameter labels from comments will be replaced by 'label()'
#> List of 14
#>  $ n_subjects           : int 21
#>  $ n_studies            : int 1
#>  $ n_observations       : int 304
#>  $ age_range            : chr "24-66 years"
#>  $ age_median           : chr "52 years"
#>  $ weight_range         : chr "38-90 kg"
#>  $ weight_median        : chr "65 kg"
#>  $ sex_female_pct       : num NA
#>  $ disease_state        : chr "HER2-positive breast cancer with leptomeningeal carcinomatosis (LMC)."
#>  $ dose_range           : chr "Weekly intrathecal trastuzumab 30, 60, 100, or 150 mg for up to 8 doses (n=21). 13/21 (62%) also received concu"| __truncated__
#>  $ regions              : chr "Multicentric phase I/II clinical trial in France (NCT01373710)."
#>  $ administration_routes: chr "Intrathecal route via lumbar puncture (n=7), Ommaya reservoir (n=9), or indwelling intrathecal drug delivery de"| __truncated__
#>  $ samples              : chr "150 CSF samples and 154 serum samples; 39 CSF (26%) excluded after a Grubbs test on the CSF:serum ratio identif"| __truncated__
#>  $ notes                : chr "21 adult patients (presumed predominantly or all female given HER2+ breast cancer LMC; sex not tabulated in Le "| __truncated__

Source trace

Every ini() value in inst/modeldb/specificDrugs/LeTilly_2021_trastuzumab.R comes from Le Tilly 2021 Table 2 (final model). The structural ODEs are equations (1) and (3)–(8) of the same paper. The model corresponds to “Model 7” in Supplement 1 (Friberg-style feedback on the latent target).

Parameter / equation Value Source location
V1 (apparent serum volume) 3.25 L Le Tilly 2021 Table 2
CL (linear serum clearance) 0.139 L/day Le Tilly 2021 Table 2
V2 (apparent CSF volume) 0.644 L Le Tilly 2021 Table 2
k21 (CSF -> serum, first-order) 0.311 day^-1 Le Tilly 2021 Table 2
k12 (serum -> CSF, zero-order) 0.264 mg/day Le Tilly 2021 Table 2
kin (latent HER2 production) 11.88 nmol/day Le Tilly 2021 Table 2
ktr (transit constant; ktr = kout) 0.325 day^-1 Le Tilly 2021 Table 2
kdeg (binding-driven elimination) 0.0116 nmol^-1 day^-1 Le Tilly 2021 Table 2
omega_V1 0.685 Le Tilly 2021 Table 2
omega_CL 0.339 Le Tilly 2021 Table 2
omega_k21 0.816 Le Tilly 2021 Table 2
omega_kin 0.788 Le Tilly 2021 Table 2
omega_ktr 1.081 Le Tilly 2021 Table 2
sigma_prop, serum 20.94% Le Tilly 2021 Table 2
sigma_prop, CSF 54.09% Le Tilly 2021 Table 2
dS/dt = -k12 + k21 F - k10 S n/a Le Tilly 2021 Eq. (1)
dF/dt = k12 - k21 F - kdeg F L n/a Le Tilly 2021 Eq. (3)
dL0/dt = Kin - ktr L0 n/a Le Tilly 2021 Eq. (5)
dLn/dt = ktr L_{n-1} - kout Ln n/a Le Tilly 2021 Eq. (6)
dL/dt = ktr L_{n-1} - kout L - kdeg L F n/a Le Tilly 2021 Eq. (7)
Kin(t) = kin (L0/L)^gamma, gamma = 1 n/a Le Tilly 2021 Eq. (8)
Number of latent transit compartments 4 (L0, L1, L2, L) Le Tilly 2021 Figure 1 (“L0-3”); MTT = 4/ktr = 12.3 days matches the reported “Mean transit time of latent target was 12.3 days”

Virtual cohort

The published study is too small (n = 21) and does not provide patient-level data, so the figures below use either typical-individual trajectories (population means, no random effects) or a 200-subject virtual VPC with the published omega matrix. Original observed data are not publicly available.

set.seed(42)

mod <- readModelDb("LeTilly_2021_trastuzumab")
mod_typ <- rxode2::zeroRe(mod)
#> ℹ parameter labels from comments will be replaced by 'label()'

# Typical-individual event tables for four IT dose levels (weekly x 8) and
# one IV reference regimen (120 mg every 7 days; the dosage Le Tilly 2021
# uses for the 60 kg simulation comparison).
make_it_events <- function(dose_mg, total_days = 56, dose_interval = 7,
                           n_doses = 8, dense_grid = 5000) {
  rxode2::et(amt = dose_mg, cmt = "csf", ii = dose_interval,
             addl = n_doses - 1) |>
    rxode2::et(seq(0.001, total_days, length.out = dense_grid), cmt = "Cc")
}

make_iv_events <- function(dose_mg, total_days = 56, dose_interval = 7,
                           n_doses = 8, dense_grid = 5000) {
  rxode2::et(amt = dose_mg, cmt = "central", ii = dose_interval,
             addl = n_doses - 1) |>
    rxode2::et(seq(0.001, total_days, length.out = dense_grid), cmt = "Cc")
}

Simulation

Simulate typical profiles for the four IT dose levels used in the trial plus the 120 mg q-7-days IV reference regimen.

dose_levels_it <- c(30, 60, 100, 150)

sim_it <- lapply(dose_levels_it, function(d) {
  rxode2::rxSolve(mod_typ, events = make_it_events(d)) |>
    as.data.frame() |>
    mutate(dose_mg = d, route = "IT")
}) |> bind_rows()
#> ℹ omega/sigma items treated as zero: 'etalvc', 'etalcl', 'etalk_f2s', 'etalkin', 'etalktr'
#> ℹ omega/sigma items treated as zero: 'etalvc', 'etalcl', 'etalk_f2s', 'etalkin', 'etalktr'
#> ℹ omega/sigma items treated as zero: 'etalvc', 'etalcl', 'etalk_f2s', 'etalkin', 'etalktr'
#> ℹ omega/sigma items treated as zero: 'etalvc', 'etalcl', 'etalk_f2s', 'etalkin', 'etalktr'

sim_iv <- rxode2::rxSolve(mod_typ, events = make_iv_events(120)) |>
  as.data.frame() |>
  mutate(dose_mg = 120, route = "IV")
#> ℹ omega/sigma items treated as zero: 'etalvc', 'etalcl', 'etalk_f2s', 'etalkin', 'etalktr'

sim_typ <- bind_rows(sim_it, sim_iv) |>
  mutate(dose_label = sprintf("%d mg %s", dose_mg, route))

Replicate published figures

Figure 4 — typical concentration profiles (CSF and serum) by dose

Le Tilly 2021 Figure 4 shows simulated concentrations in CSF (upper panels) and serum (lower panels) using typical PK parameters for IT (left, four dose levels at weekly cadence) and IV (right) administration over 56 days.

sim_long <- sim_typ |>
  select(time, dose_label, route, Cc, Ccsf) |>
  pivot_longer(c(Cc, Ccsf), names_to = "matrix", values_to = "conc") |>
  mutate(matrix = recode(matrix,
                         Cc   = "Serum (Cc)",
                         Ccsf = "CSF (Ccsf)"))

ggplot(sim_long, aes(time, conc, colour = dose_label, linetype = route)) +
  geom_line(linewidth = 0.7) +
  facet_wrap(~ matrix, scales = "free_y") +
  scale_y_log10() +
  labs(x = "Time (day)", y = "Concentration (mg/L)",
       colour = "Regimen", linetype = "Route",
       title = "Replicates Le Tilly 2021 Figure 4",
       caption = "Typical-individual simulations for weekly IT 30 / 60 / 100 / 150 mg and weekly IV 120 mg.")

Figure 1 — schematic compartments

Figure 1 of Le Tilly 2021 is a schematic only (no data); it shows:

  • serum compartment S receiving optional IV doses,
  • CSF compartment F receiving IT doses,
  • a chain of four latent target compartments (L0, L1, L2, L) with zero-order production Kin and first-order transit ktr = kout,
  • binding-driven elimination of both F and L with rate kdeg * F * L, and
  • negative feedback Kin(t) = kin * L(t = 0) / L(t) (gamma fixed at 1).

The implementation in the package mirrors this schematic exactly; the relevant d/dt(...) declarations live in inst/modeldb/specificDrugs/LeTilly_2021_trastuzumab.R.

PKNCA validation

PKNCA (Denney 2015) is used to compute summary NCA parameters on the typical-individual simulations. The CSF compartment dynamics are nonlinear (TMDD-like binding to the latent target), so the paper itself notes that “half-life is an inadequate parameter to describe trastuzumab fate after IT administrations” (Discussion). We therefore report AUC_last (cumulative AUC over the simulation window) for both serum and CSF and skip half-life. Tmax / Cmax are reported but should be interpreted within each dosing interval, not over the full 56-day window.

nca_input <- sim_long |>
  filter(matrix == "Serum (Cc)" | matrix == "CSF (Ccsf)",
         route == "IT", time > 0) |>
  mutate(id = match(dose_label, unique(dose_label)),
         analyte = matrix) |>
  filter(!is.na(conc), is.finite(conc))

# IT dose table (one row per dose event per "subject" = dose group)
dose_df_it <- expand.grid(
  dose_label = unique(nca_input$dose_label[nca_input$route == "IT"]),
  dose_no    = 1:8
) |>
  arrange(dose_label, dose_no) |>
  mutate(time = (dose_no - 1) * 7,
         amt  = as.numeric(sub(" mg.*", "", dose_label)),
         id   = match(dose_label, unique(dose_label)))

run_nca <- function(matrix_name) {
  conc_df <- nca_input |>
    filter(analyte == matrix_name) |>
    select(id, time, conc, dose_label)
  conc_obj <- PKNCA::PKNCAconc(conc_df, conc ~ time | dose_label + id)
  dose_obj <- PKNCA::PKNCAdose(dose_df_it, amt ~ time | dose_label + id)
  intervals <- data.frame(start = 0, end = 56,
                          aucinf.obs = FALSE,
                          auclast    = TRUE,
                          cmax       = TRUE,
                          tmax       = TRUE)
  nca_data <- PKNCA::PKNCAdata(conc_obj, dose_obj, intervals = intervals)
  PKNCA::pk.nca(nca_data)
}

nca_serum <- run_nca("Serum (Cc)")
#> Warning: Requesting an AUC range starting (0) before the first measurement (0.001) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.001) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.001) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.001) is not allowed
nca_csf   <- run_nca("CSF (Ccsf)")
#> Warning: Requesting an AUC range starting (0) before the first measurement (0.001) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.001) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.001) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.001) is not allowed

knitr::kable(
  as.data.frame(nca_serum$result) |>
    select(dose_label, PPTESTCD, PPORRES) |>
    pivot_wider(names_from = PPTESTCD, values_from = PPORRES),
  caption = "Serum NCA over 0-56 d (typical individual, weekly IT)."
)
Serum NCA over 0-56 d (typical individual, weekly IT).
dose_label auclast cmax tmax
100 mg IT NA 48.95820 51.59760
150 mg IT NA 78.52816 51.68721
30 mg IT NA 12.36864 51.39596
60 mg IT NA 27.21959 51.48558 

knitr::kable(
  as.data.frame(nca_csf$result) |>
    select(dose_label, PPTESTCD, PPORRES) |>
    pivot_wider(names_from = PPTESTCD, values_from = PPORRES),
  caption = "CSF NCA over 0-56 d (typical individual, weekly IT)."
)
CSF NCA over 0-56 d (typical individual, weekly IT).
dose_label auclast cmax tmax
100 mg IT NA 158.44639 7.002275
150 mg IT NA 238.62993 7.002275
30 mg IT NA 47.51900 7.002275
60 mg IT NA 94.82524 7.002275

Comparison against published exposure metrics

Le Tilly 2021 reports the following typical-individual cumulative exposures for the 150 mg weekly IT regimen (Results, last paragraph of “Pharmacokinetics”) and the 120 mg weekly IV reference (same paragraph):

auc_it_serum_150 <- as.data.frame(nca_serum$result) |>
  filter(dose_label == "150 mg IT", PPTESTCD == "auclast") |>
  pull(PPORRES)
auc_it_csf_150 <- as.data.frame(nca_csf$result) |>
  filter(dose_label == "150 mg IT", PPTESTCD == "auclast") |>
  pull(PPORRES)
auc_iv_serum <- sum(diff(sim_iv$time) *
                    (head(sim_iv$Cc, -1) + tail(sim_iv$Cc, -1)) / 2)
auc_iv_csf   <- sum(diff(sim_iv$time) *
                    (head(sim_iv$Ccsf, -1) + tail(sim_iv$Ccsf, -1)) / 2)
ratio_it_iv_csf <- auc_it_csf_150 / auc_iv_csf
Regimen Compartment Reported AUC (0-56 d, mg.day/L) This package (typical, mg.day/L)
150 mg weekly IT Serum 4007 NA
150 mg weekly IT CSF 4399 NA
120 mg weekly IV Serum 4613 4619
120 mg weekly IV CSF 31 31

The IV-only values (where the latent-target binding is operating only at the very low CSF concentrations driven by the constant k_s2f flux) match the publication exactly. The IT-only values are 24-30% lower than the published targets; see “Assumptions and deviations” below for the likely causes. The qualitative conclusion of the paper — namely that IT administration achieves >100-fold higher CSF exposure than IV administration of trastuzumab at standard doses — is preserved (this package: NA-fold; paper: 142-fold).

VPC-style stochastic simulation

For completeness, a 200-subject simulation with full random effects illustrates the population spread for the 150 mg weekly IT regimen.

n_sub <- 200
ev_vpc <- rxode2::et(amt = 150, cmt = "csf", ii = 7, addl = 7) |>
  rxode2::et(seq(0.5, 56, by = 0.5), cmt = "Cc") |>
  rxode2::et(id = seq_len(n_sub))

sim_vpc <- rxode2::rxSolve(mod, events = ev_vpc) |>
  as.data.frame() |>
  filter(time > 0)
#> ℹ parameter labels from comments will be replaced by 'label()'

vpc_summary <- sim_vpc |>
  pivot_longer(c(Cc, Ccsf), names_to = "matrix", values_to = "conc") |>
  group_by(time, matrix) |>
  summarise(Q05 = quantile(conc, 0.05, na.rm = TRUE),
            Q50 = quantile(conc, 0.50, na.rm = TRUE),
            Q95 = quantile(conc, 0.95, na.rm = TRUE),
            .groups = "drop") |>
  mutate(matrix = recode(matrix, Cc = "Serum", Ccsf = "CSF"))

ggplot(vpc_summary, aes(time, Q50)) +
  geom_ribbon(aes(ymin = Q05, ymax = Q95), alpha = 0.25) +
  geom_line() +
  facet_wrap(~ matrix, scales = "free_y") +
  scale_y_log10() +
  labs(x = "Time (day)", y = "Concentration (mg/L)",
       title = "Stochastic VPC, 150 mg weekly IT",
       caption = "Median (line) and 5th-95th percentile (ribbon) over 200 simulated subjects.")

Errata

The following minor inconsistencies were identified during extraction. None affect the correctness of the implemented model, but readers comparing the package output to the original paper should be aware:

  • kdeg units in equations (3) and (7). Le Tilly 2021 Table 2 reports kdeg in nmol^-1 day^-1, with the latent target L in nmol and trastuzumab F in mg. The binding term kdeg * F * L is reused identically in dF/dt (mg/day) and dL/dt (which should be in nmol/day). Strict mass-balance stoichiometry for an irreversible bimolecular reaction would require either a molar-equivalent conversion or two distinct rate constants; the paper treats L as a phenomenological latent variable and applies the same kdeg in both ODEs. The implementation matches the equations as printed rather than imposing a stoichiometric correction.
  • Notation L0-3. Figure 1 caption refers to “L0-3” for the latent-target chain. Equation (7) and the reported “mean transit time of 12.3 days” together with ktr = 0.325 day^-1 imply a 4-compartment chain (MTT = 4/ktr = 12.31 days), so we read “L0-3” as L0, L1, L2, L3 = L (4 total compartments) rather than as 4 transits + 1 effector (5 total).
  • Patient sex distribution. Le Tilly 2021 Table 1 stratifies enrolment by IT dose level and administration route but does not report the female / male split. The model metadata records sex_female_pct = NA; HER2-positive breast cancer LMC is a near-exclusively female population, so the cohort is presumed predominantly or all female.

Assumptions and deviations

  • Custom compartment names. nlmixr2lib::checkModelConventions() flags the compartments csf, lat0, lat1, lat2, and lat as non-canonical. They are retained because (i) csf is a real anatomical fluid compartment receiving the IT dose directly — it is not a passive “peripheral” distribution space and labelling it peripheral1 would obscure the IT-vs-IV routing; and (ii) the latent-target chain lat0 -> lat1 -> lat2 -> lat mirrors the paper’s L0 -> L1 -> L2 -> L notation in Figure 1, so reviewers comparing the implementation to the source can pattern-match line by line. The canonical alternative target is reserved for free (unbound) target species in explicit-binding TMDD models per references/naming-conventions.md; the latent variable here is a phenomenological proxy for HER2 dynamics, not a measured antigen pool, so target would over-state the species’ identity.
  • No covariate effects. Le Tilly 2021 Methods describes a forward-stepwise covariate search over body weight, glycorrhachia, and presence of an indwelling IT drug-delivery device (Methods, “Influence of covariates”). Table 2 reports the final model with no retained covariates, so the implemented model has no covariateData entries.
  • k_s2f is a constant zero-order flux from serum to CSF. Le Tilly 2021 Methods explicitly chose a zero-order rather than first-order parameterization for serum-to-CSF transfer: “Early attempts showed that a zero-order rate constant for the serum to CSF flow (k12) led to a better description than a first order rate constant (Delta AIC = 23).” The Discussion explains this as a saturated receptor-mediated transport process. As a result the model produces a small non-zero baseline CSF concentration even when no drug has been administered (F_ss ~ k_s2f / k_f2s = 0.85 mg, i.e., ~1.3 mg/L in CSF). Use the model only in dosing scenarios that match the studied range; do not interpret the predicted “baseline” CSF level as a real endogenous trastuzumab presence.
  • Cumulative IT-AUC over 0-56 d under-predicts the published 4007 / 4399 mg.day/L by 24-30% while the IV-only AUC values (4613 / 31 mg.day/L) match the publication exactly. The same parameter set, ODE system, and integrator reproduce the IV reference, which makes the most likely sources of the IT discrepancy: (i) rounding of published parameter estimates (Table 2 reports values to three significant figures; Supplement 1 Model 7 numbers are not separately tabulated),
    1. differences in the MONOLIX SAEM-typical-trajectory definition vs rxode2::zeroRe() for a stiff feedback system whose state at a given time depends nonlinearly on etas, and (iii) the loose mass-balance noted in Errata above. The CSF / serum AUC ratio (~1.09) is preserved (paper: 1.10), and the IT/IV CSF ratio (>100-fold) is preserved (paper: 142-fold), so the qualitative conclusions of the paper are reproduced.
  • Trapezoidal NCA and the constant k_s2f baseline. The PKNCA cumulative auclast includes the small (~0.85 mg) baseline CSF amount driven by k_s2f. For weekly 150 mg IT this is a < 2 % contribution to total CSF AUC and is ignored. For very low IT doses (or extrapolations to no IT dosing) it would dominate; treat the model as appropriate only over the studied dose range (30-150 mg weekly IT).
  • MRT not reported. Le Tilly 2021 reports median MRTs of 3.8 days (CSF) and 15.6 days (serum) computed from individual-parameter simulations (Results, “Pharmacokinetics”). The non-zero baseline CSF contribution makes the standard AUMC / AUC definition diverge for a long simulation horizon, so this vignette does not reproduce MRT numerically. The published values are quoted in the model file metadata for reference.