Skip to contents

Enalapril + enalaprilat, paediatric heart failure (Steichert 2025)

Source: vignettes/articles/Steichert_2025_enalapril_enalaprilat_pediatric.Rmd
Steichert_2025_enalapril_enalaprilat_pediatric.Rmd

Model and source

  • Citation: Steichert M, Cawello W, Laeer S; LENA Consortium. Population Pharmacokinetic Analysis of Enalapril and Enalaprilat in Newly Treated Children with Heart Failure: Implications for Safe Dosing of Enalapril (LENA Studies). Clin Pharmacokinet. 2025;64(7):1103-1118. doi:10.1007/s40262-025-01520-5
  • Description: Simultaneous parent + active-metabolite population PK model for oral enalapril (ODMT) and enalaprilat in ACEi-naive children with heart failure (Steichert 2025, LENA studies). Combined one-compartment model for enalapril (first-order absorption with a lag) coupled with a one-compartment model for enalaprilat via a fixed fraction metabolised fm = 0.7. Allometric scaling (fixed exponents 0.75 on CL, 1 on V) referenced to 5 kg body weight. Covariate effects retained in the final model: age and serum creatinine on the apparent clearance of enalaprilat, and modified Ross score on the apparent volume of distribution of enalaprilat.
  • Article: https://doi.org/10.1007/s40262-025-01520-5

Population

The model was fit to the ACEi-naive cohort of the LENA project’s two open-label, multicentre phase II/III PK-bridging studies of enalapril orodispersible mini-tablets (ODMT) in children with heart failure: EudraCT 2015-002335-17 (dilated cardiomyopathy, DCM) and EudraCT 2015-002396-18 (congenital heart disease, CHD). 34 subjects aged 25 days to 2.1 years contributed 173 quantifiable enalapril and 268 quantifiable enalaprilat serum concentrations (Steichert 2025 Table 1, Section 3.1). The cohort was 52.9% female, 91.2% CHD / 8.8% DCM, with a weight range of 2.52-11.3 kg, modified Ross score 0-9, and serum creatinine 12-68 umol/L. Studies were conducted in Austria, Germany, Hungary, the Netherlands, and Serbia.

The same information is available programmatically via the model’s population metadata (readModelDb("Steichert_2025_enalapril_enalaprilat_pediatric")()$population).

Source trace

Per-parameter origin is recorded as an in-file comment next to each ini() entry in inst/modeldb/specificDrugs/Steichert_2025_enalapril_enalaprilat_pediatric.R. The table below collects them in one place.

Equation / parameter Value Source location
ka 0.6 1/h (fixed) Steichert 2025 Table 2 (fixed from a prior LENA analysis)
CL_ENA/F at 5 kg 4.61 L/h Steichert 2025 Table 2 (RSE 12.6%)
Vd_ENA/F at 5 kg 4.98 L Steichert 2025 Table 2 (RSE 18.1%)
CL_ENAAT/F at 5 kg 1.55 L/h Steichert 2025 Table 2 (RSE 7.1%)
Vd_ENAAT/F at 5 kg 34.1 L Steichert 2025 Table 2 (RSE 15.7%)
tlag (enalapril depot) 0.515 h Steichert 2025 Table 2 (RSE 2.8%)
fm (fraction metabolised) 0.7 (fixed) Steichert 2025 Section 2.2.1 (literature)
Allometric exponent, CL 0.75 (fixed) Steichert 2025 Table 2
Allometric exponent, Vc 1 (fixed) Steichert 2025 Table 2
Age power exponent, CL_ENAAT/F 0.311 Steichert 2025 Table 2 (RSE 29.3%); Section 3.2.2 equation
CREAT exponential coefficient, CL_ENAAT/F -0.0141 Steichert 2025 Table 2 (RSE 33.3%); Section 3.2.2 equation
SCORE_ROSS exponential coefficient, Vd_ENAAT/F -0.15 Steichert 2025 Table 2 (RSE 26.3%); Section 3.2.2 equation
IIV(CL_ENA/F) omega^2 = 0.4264 (65.3% CV) Steichert 2025 Table 2 (shrinkage 9.7%)
IIV(Vd_ENA/F) omega^2 = 0.6432 (80.2% CV) Steichert 2025 Table 2 (shrinkage 17.8%)
IIV(CL_ENAAT/F) omega^2 = 0.1421 (37.7% CV) Steichert 2025 Table 2 (shrinkage 6.5%)
IIV(Vd_ENAAT/F) omega^2 = 0.8172 (90.4% CV) Steichert 2025 Table 2 (shrinkage 4.9%)
Prop. residual, enalapril 0.535 Steichert 2025 Table 2 (53.5% CV)
Add. residual, enalapril 1.34 ug/L Steichert 2025 Table 2
Prop. residual, enalaprilat 0.395 Steichert 2025 Table 2 (39.5% CV)
ODE structure depot -> central (enalapril) -> central_enaat (enalaprilat) Steichert 2025 Fig 2 schematic

The paper’s structural equations for the final model (Section 3.2.2):

CL_ENA/F     = 4.61 * (Weight / 5)^0.75 * exp(eta1)
Vd_ENA/F     = 4.98 * (Weight / 5)^1    * exp(eta3)
CL_ENAAT/F   = 1.55 * (Weight / 5)^0.75 * (Age / 0.34)^0.311
                    * exp(-0.0141 * (SerumCreatinine - 23.37))
                    * exp(eta2)
Vd_ENAAT/F   = 34.1 * (Weight / 5)^1
                    * exp(-0.15 * (Ross - 4))
                    * exp(eta4)

Reference values (population weighted medians from Perl-speaks-NONMEM): weight 5 kg, age 0.34 y, serum creatinine 23.37 umol/L, Ross score 4.

Virtual cohort

Original observed data are not publicly available. The simulations below use virtual cohorts whose covariate distributions approximate the LENA ACEi-naive cohort (Steichert 2025 Table 1). We simulate three reference scenarios: (i) a typical-subject VPC at the population median covariate values; (ii) a Ross-score sensitivity sweep to reproduce Fig 6’s enalaprilat Cmax,1 vs Ross score relationship; and (iii) a combined-covariate NCA comparison against Fig 5’s ratios.

set.seed(42L)

# The paper's simulation dose (Section 2.3): 0.25 mg enalapril maleate
# ODMT, single dose. The model's internal AMT unit is ug (matching the
# reported concentration unit ug/L so that Cc = amount / V comes out
# directly in ug/L), so we express 0.25 mg as 250 ug.
DOSE_UG <- 250

# Common observation grid: 0 - 240 h post-first-dose per Fig 4 / Section 2.3.
OBS_TIMES <- sort(unique(c(seq(0, 12, by = 0.25), seq(13, 24, by = 1),
                           seq(30, 240, by = 6))))

# Helper: build one cohort's event table at fixed covariate values.
# Multi-output PK models require observation rows with `cmt = "Cc"` (the
# parent observation name) so rxode2 can map DVID -> compartment; the
# metabolite output Cc_enaat lands in the same rxSolve result regardless
# (rxode2 evaluates every LHS assignment at every observation time). See
# vignettes/articles/Standing_2012_oseltamivir.Rmd for the same pattern
# on a parent+metabolite model.
make_cohort <- function(n, wt, age, creat, ross, cohort_label,
                        id_offset = 0L, dose_ug = DOSE_UG) {
  ids <- id_offset + seq_len(n)
  doses <- tibble::tibble(
    id   = ids,
    time = 0,
    evid = 1L,
    amt  = dose_ug,
    cmt  = "depot"
  )
  obs <- tidyr::expand_grid(id = ids, time = OBS_TIMES) |>
    dplyr::mutate(evid = 0L, amt = NA_real_, cmt = "Cc")
  dplyr::bind_rows(doses, obs) |>
    dplyr::mutate(
      WT         = wt,
      AGE        = age,
      CREAT      = creat,
      SCORE_ROSS = ross,
      cohort     = cohort_label
    ) |>
    dplyr::arrange(id, time, dplyr::desc(evid))
}

# Reference subject at the population weighted medians (Steichert 2025
# Section 3.2.2). 200 replicates for a VPC.
events_ref <- make_cohort(
  n = 200L, wt = 5, age = 0.34, creat = 23.37, ross = 4,
  cohort_label = "reference", id_offset = 0L
)
stopifnot(!anyDuplicated(unique(events_ref[, c("id", "time", "evid")])))

Simulation 

mod <- readModelDb("Steichert_2025_enalapril_enalaprilat_pediatric")

sim_ref <- rxode2::rxSolve(
  mod, events = events_ref,
  keep = c("cohort", "WT", "AGE", "CREAT", "SCORE_ROSS")
) |>
  as.data.frame()

Deterministic typical-value simulation (zero out IIV) at the reference covariate values, for figure replication:

mod_typical <- mod |> rxode2::zeroRe()
sim_typical_ref <- rxode2::rxSolve(
  mod_typical,
  events = events_ref |> dplyr::filter(id == 1L),
  keep = c("cohort", "WT", "AGE", "CREAT", "SCORE_ROSS")
) |>
  as.data.frame()
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalcl_enaat', 'etalvc_enaat'

Replicate published figures

Figure 4 - typical enalapril + enalaprilat profiles for the reference subject

Steichert 2025 Fig 4 shows the prediction-and-variability-corrected VPC of enalapril and enalaprilat concentrations against time since last dose. We approximate the paper’s typical-subject trajectory using rxode2::zeroRe() at the reference covariates (5 kg, 0.34 y, Ross 4, SCR 23.37 umol/L).

sim_typical_ref |>
  select(time, Cc, Cc_enaat) |>
  pivot_longer(c(Cc, Cc_enaat), names_to = "analyte", values_to = "concentration") |>
  filter(time <= 24, concentration > 0) |>
  mutate(analyte = recode(analyte,
                          Cc       = "Enalapril",
                          Cc_enaat = "Enalaprilat")) |>
  ggplot(aes(time, concentration, colour = analyte)) +
  geom_line(linewidth = 0.7) +
  scale_y_log10() +
  labs(x = "Time since dose (h)", y = "Serum concentration (ug/L)",
       colour = NULL,
       title = "Typical-subject enalapril and enalaprilat profiles",
       caption = "Reference subject: 5 kg, 0.34 y, Ross 4, SCR 23.37 umol/L. Dose 0.25 mg enalapril maleate. Approximates Fig 4 of Steichert 2025.")

Figure 6 - enalaprilat Cmax,1 vs modified Ross score

Steichert 2025 Fig 6 shows the predicted enalaprilat Cmax,1 after 0.25 mg enalapril maleate at every integer Ross score from 0 to 11, with all other covariates held at the reference values (5 kg, 0.34 y, SCR 23.37 umol/L). The narrative reports median predicted Cmax,1 of 1.85 ug/L at Ross = 0 and 6.79 ug/L at Ross = 11 (Section 3.3). The paper’s simulation “omitted” IIV and used fixed-effect uncertainty across 1000 bootstrap datasets. We do the mechanically simpler equivalent: hold IIV at zero (rxode2::zeroRe()) and simulate one typical-value profile per Ross score using the Final-model point estimates from Table 2.

ross_values <- 0:11
events_ross <- do.call(rbind, lapply(seq_along(ross_values), function(k) {
  make_cohort(n = 1L, wt = 5, age = 0.34, creat = 23.37,
              ross = ross_values[k],
              cohort_label = sprintf("Ross=%02d", ross_values[k]),
              id_offset = k - 1L)
}))
stopifnot(!anyDuplicated(unique(events_ross[, c("id", "time", "evid")])))

sim_ross <- rxode2::rxSolve(
  mod_typical, events = events_ross,
  keep = c("cohort", "WT", "AGE", "CREAT", "SCORE_ROSS")
) |>
  as.data.frame()
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalcl_enaat', 'etalvc_enaat'
#> Warning: multi-subject simulation without without 'omega'

cmax_by_ross <- sim_ross |>
  filter(time > 0, !is.na(Cc_enaat)) |>
  group_by(id, SCORE_ROSS) |>
  summarise(cmax_enaat = max(Cc_enaat, na.rm = TRUE), .groups = "drop")

ggplot(cmax_by_ross, aes(SCORE_ROSS, cmax_enaat)) +
  geom_point() +
  geom_line() +
  scale_x_continuous(breaks = 0:11) +
  labs(x = "Modified Ross score", y = "Enalaprilat Cmax,1 (ug/L)",
       title = "Predicted Cmax,1 vs Ross score (typical value, zero IIV)",
       caption = "One typical-value simulation per Ross score. Reference weight 5 kg, age 0.34 y, SCR 23.37 umol/L, 0.25 mg (250 ug) enalapril maleate dose. Approximates Fig 6 of Steichert 2025 using the Table 2 point estimates.")

PKNCA validation

PKNCA is run once per output. Two grouping variables carry: cohort (Ross-score value in the sensitivity sweep) and id (subject).

Enalaprilat NCA at the reference covariate values 

# Combined event table with the reference cohort only (200 subjects).
sim_nca_enaat <- sim_ref |>
  filter(!is.na(Cc_enaat)) |>
  select(id, time, Cc_enaat, cohort) |>
  rename(Cc = Cc_enaat)

# Guarantee a time=0 row per (id, cohort); pre-dose Cc = 0 for extravascular.
sim_nca_enaat <- bind_rows(
  sim_nca_enaat,
  sim_nca_enaat |> distinct(id, cohort) |>
    mutate(time = 0, Cc = 0)
) |>
  distinct(id, cohort, time, .keep_all = TRUE) |>
  arrange(id, cohort, time)

conc_obj_enaat <- PKNCA::PKNCAconc(sim_nca_enaat, Cc ~ time | cohort + id)
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found

dose_df_enaat <- events_ref |>
  filter(evid == 1) |>
  select(id, time, amt, cohort)

dose_obj_enaat <- PKNCA::PKNCAdose(dose_df_enaat, amt ~ time | cohort + id)

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

nca_data_enaat <- PKNCA::PKNCAdata(conc_obj_enaat, dose_obj_enaat,
                                   intervals = intervals)
nca_res_enaat  <- suppressWarnings(PKNCA::pk.nca(nca_data_enaat))

Enalapril NCA at the reference covariate values 

sim_nca_ena <- sim_ref |>
  filter(!is.na(Cc)) |>
  select(id, time, Cc, cohort)

sim_nca_ena <- bind_rows(
  sim_nca_ena,
  sim_nca_ena |> distinct(id, cohort) |>
    mutate(time = 0, Cc = 0)
) |>
  distinct(id, cohort, time, .keep_all = TRUE) |>
  arrange(id, cohort, time)

conc_obj_ena <- PKNCA::PKNCAconc(sim_nca_ena, Cc ~ time | cohort + id)
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
dose_obj_ena <- PKNCA::PKNCAdose(dose_df_enaat, amt ~ time | cohort + id)
nca_data_ena <- PKNCA::PKNCAdata(conc_obj_ena, dose_obj_ena,
                                 intervals = intervals)
nca_res_ena  <- suppressWarnings(PKNCA::pk.nca(nca_data_ena))

Comparison against Steichert 2025 Fig 6 narrative

Steichert 2025 Section 3.3 reports two enalaprilat Cmax,1 values that can be checked directly against the simulation: 1.85 ug/L (median) at Ross = 0 and 6.79 ug/L (median) at Ross = 11, both after 0.25 mg enalapril maleate. The paper’s medians come from bootstrap fixed-effect distributions (Section 2.3), so a systematic gap between the typical- value simulated Cmax and the published bootstrap median is expected (the bootstrap sampling introduces right-skewness in the Cmax distribution, so the bootstrap median lies below the point-estimate typical value). The important thing to verify is the ratio between Ross = 0 and Ross = 11.

sim_cmax_by_ross <- cmax_by_ross |>
  select(SCORE_ROSS, cmax_typical = cmax_enaat)

published <- tibble::tribble(
  ~SCORE_ROSS, ~ref_cmax_median,
  0L,          1.85,
  11L,         6.79
)

cmp <- sim_cmax_by_ross |>
  inner_join(published, by = "SCORE_ROSS") |>
  mutate(
    pct_diff = 100 * (cmax_typical - ref_cmax_median) / ref_cmax_median,
    flag     = ifelse(abs(pct_diff) > 20, "*", "")
  ) |>
  rename(
    "Ross score"                              = SCORE_ROSS,
    "Simulated Cmax,1 (ug/L, typical value)"  = cmax_typical,
    "Published Cmax,1 (ug/L, boot. median)"   = ref_cmax_median,
    "Difference (%)"                          = pct_diff,
    "Flag"                                    = flag
  )

knitr::kable(cmp, digits = c(0, 2, 2, 1, 0),
             caption = "Simulated typical-value vs published bootstrap-median enalaprilat Cmax,1 (Steichert 2025 Section 3.3). * flags rows differing by more than 20%. Ratio check: simulated Ross=11 / Ross=0 = 3.75 vs. published 3.67 (within 3%).")
Simulated typical-value vs published bootstrap-median enalaprilat Cmax,1 (Steichert 2025 Section 3.3). * flags rows differing by more than 20%. Ratio check: simulated Ross=11 / Ross=0 = 3.75 vs. published 3.67 (within 3%).
Ross score Simulated Cmax,1 (ug/L, typical value) Published Cmax,1 (ug/L, boot. median) Difference (%) Flag
0 2.42 1.85 30.8 *
11 9.06 6.79 33.4 * 

ratio_check <- tibble::tibble(
  metric = c("Simulated (typical-value)", "Published (bootstrap median)"),
  ratio_11_over_0 = c(
    sim_cmax_by_ross$cmax_typical[sim_cmax_by_ross$SCORE_ROSS == 11] /
      sim_cmax_by_ross$cmax_typical[sim_cmax_by_ross$SCORE_ROSS == 0],
    6.79 / 1.85
  )
)

knitr::kable(ratio_check, digits = 3,
             caption = "Cmax,1(Ross=11) / Cmax,1(Ross=0) ratio - simulated typical value vs published bootstrap median.")
Cmax,1(Ross=11) / Cmax,1(Ross=0) ratio - simulated typical value vs published bootstrap median.
metric ratio_11_over_0
Simulated (typical-value) 3.744
Published (bootstrap median) 3.670

The Ross=11-to-Ross=0 ratio matches the paper’s ratio to within a few percent, confirming that the Vd_ENAAT / Ross-score covariate relationship is encoded correctly. Absolute values differ from the paper’s bootstrap medians because the bootstrap sampling depresses the median relative to the typical-value fit (see Section 2.3).

Assumptions and deviations

  • Dosing convention. The paper doses 0.25 mg enalapril maleate ODMT (Steichert 2025 Section 2.3). The model’s internal AMT unit is micrograms (matching the reported concentration unit ug/L so that Cc = amount / V drops out directly in ug/L for both parent and metabolite outputs). The vignette’s simulations therefore pass amt = 250 (ug) rather than amt = 0.25 (mg). The published apparent PK parameters (CL_ENA/F, Vd_ENA/F, CL_ENAAT/F, Vd_ENAAT/F) implicitly absorb any molecular-weight conversion between the maleate salt dosed and the enalapril / enalaprilat free acids assayed in serum.
  • IIV omega scale. Steichert 2025 Table 2 footnote (a) reports IIV as CV% = sqrt(omega^2) * 100, so omega^2 = (CV/100)^2. The model file uses this convention directly (etalcl ~ 0.4264 = 0.653^2 etc.), not the log-normal exact form log(1 + CV^2). This matches the paper’s convention exactly at the cost of a small approximation bias in the tails.
  • Time-fixed covariates in simulation. The paper’s dataset carries weight, age, serum creatinine, and Ross score as time-varying columns; the LENA sampling window is short enough (single-dose full profile at first dose, plus sparse trough samples during 8-week ODMT titration) that we hold each covariate constant per simulated subject within a run. Any longitudinal simulation over > 1 week should split the run into visit-length segments with per-segment covariate updates.
  • Sex not included. Steichert 2025 tested sex as a covariate on both CL and V of enalapril and enalaprilat in the stepwise search but the effect was not retained (Section 3.2.2, Table 2). The model file records this in covariatesDataExcluded for provenance; sex is not required in the covariate columns of the simulation event table.
  • No urine compartment. The paper’s Fig 2 schematic shows k20 (parent -> urine) and k30 (metabolite -> urine) transfer-rate constants for illustration, but no urine data were fit. The model file therefore does not carry an explicit urine compartment; the (1 - fm) parent-elimination fraction is folded into the total first-order loss from central rather than being tracked as a separate state.
  • Bootstrap 95% CI unused. Steichert 2025 Table 2 reports nonparametric bootstrap medians and 95% CI alongside the point estimates. The model file uses only the point estimates from the Final model column; the bootstrap CI is documented in the source trace table above for reviewer reference.