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Simvastatin and simvastatin acid (Jin 2014)

Source: vignettes/articles/Jin_2014_simvastatin.Rmd
Jin_2014_simvastatin.Rmd

Model and source

  • Citation: Jin SJ, Bae KS, Cho SH, Jung JA, Kim U, Choe S, Ghim JL, Noh YH, Park HJ, Kim Hs, Lim HS. Population Pharmacokinetic Analysis of Simvastatin and its Active Metabolite with the Characterization of Atypical Complex Absorption Kinetics. Pharm Res. 2014;31(7):1801-1812. doi:10.1007/s11095-013-1284-0
  • Article: https://doi.org/10.1007/s11095-013-1284-0

The packaged model is Jin_2014_simvastatin, a joint two-compartment population PK model for orally administered simvastatin (lactone parent) and its active metabolite simvastatin acid. The lactone uses three parallel mixed zero-and-first-order absorption processes (Model III of Jin 2014) – three depot compartments are dosed with fractional bioavailabilities F1, F2, F3 (sum = 1), each described by a zero-order infusion of duration D1, D2, D3 followed by first-order absorption with rate constants Ka1, Ka2, Ka3 and lag times ALAG1 = 0, ALAG2, ALAG3. The lactone disposes via a 2-compartment system with apparent clearance CL and inter-compartmental clearance Q. A fraction FM of the parent clearance is converted to simvastatin acid (acid central volume V6 fixed at 1 L for identifiability), and a reverse clearance Q64 returns acid to the parent central compartment, capturing the non-equilibrium interconversion between the two species.

Population

The popPK dataset comprised 2,182 simvastatin and 2,130 simvastatin acid plasma concentrations from 133 healthy adult Korean male volunteers across four single-dose oral simvastatin studies (Jin 2014 Table I):

  • Study I (PK, n = 20) – two-sequence two-period crossover with two doses randomly drawn from 10, 20, 30, 40 or 80 mg simvastatin separated by a 3-day washout. Dense PK sampling at pre-dose and 10, 20, 30, 40, 50 min and 1, 1.25, 1.5, 1.75, 2, 3, 4, 6, 8, 10, 12, 24 h post-dose.
  • Studies II, III, IV (bioequivalence, n = 30 + 30 + 53 = 113) – 2x2 crossover at 60 mg simvastatin reference (Zocor) vs test formulation with a 7-day washout. Only the reference-formulation data were used for this analysis. Sampling at pre-dose and 15, 30, 45 min and 1, 1.5, 2, 3, 4, 6, 8, 10, 12 h post-dose.

Subjects were 25.0 +/- 2.6 years (mean +/- SD), 69.8 +/- 6.7 kg, 174.8 +/- 5.4 cm, BMI 22.8 +/- 1.7 kg/m^2. All subjects were healthy adult Korean males; no females were enrolled. Age, body weight, and height were tested as covariates on both parent and metabolite parameters and none reached the criterion for inclusion (Results, parent and metabolite sections). The final model carries no covariate effects.

The same metadata is available programmatically:

nlmixr2lib::readModelDb("Jin_2014_simvastatin")$population

Source trace

Per-parameter origin is recorded inline next to each ini() entry in inst/modeldb/specificDrugs/Jin_2014_simvastatin.R. The table below collects the same provenance for review.

Equation / parameter Value Source location
lcl (simvastatin CL/F) log(571 L/h) Jin 2014 Table III
lvc (simvastatin V4/F) log(199 L) Jin 2014 Table III
lvp (simvastatin V5/F) log(2710 L) Jin 2014 Table III
lq (simvastatin Q/F) log(199 L/h) Jin 2014 Table III
lka1, lka2, lka3 log(0.00126, 0.964, 0.179 1/h) Jin 2014 Table III
lba1, lba2 log(0.636, 0.662) Jin 2014 Table III (see Errata)
llag2, llag3d log(0.142, 0.787 h) Jin 2014 Table III
ldur1, ldur2, ldur3 log(0.102, 0.502, 1.38 h) Jin 2014 Table III
logitfm (acid metabolic fraction FM) qlogis(0.236) Jin 2014 Table III
lq64 (acid -> parent reverse clearance) log(112 L/h) Jin 2014 Table III
lk67 (acid central -> acid peripheral) log(252 1/h) Jin 2014 Table III
lk76 (acid peripheral -> acid central) log(2.30 1/h) Jin 2014 Table III
lcl_acid (acid apparent clearance) log(0.035 L/h) Jin 2014 Table III
V6 (acid central) fixed at 1 L n/a Jin 2014 Methods, metabolite modelling
IIV %CV V_central / CL / Q 79.0 / 66.5 / 93.6 (correlated block) Jin 2014 Table III
Correlation r (V_central, CL) 0.62 Jin 2014 Table III footnote a
Correlation r (V_central, Q) -0.17 Jin 2014 Table III footnote a
Correlation r (CL, Q) -0.38 Jin 2014 Table III footnote a
IIV %CV Ka1, Ka2, Ka3 47.1, 43.9, 50.0 Jin 2014 Table III
IIV %CV BA1, BA2 47.6, 45.4 Jin 2014 Table III
IIV %CV ALAG2, ALAG3-ALAG2 46.4, 45.2 Jin 2014 Table III
IIV %CV D1, D2, D3 47.1, 46.3, 46.1 Jin 2014 Table III
IIV %CV K67, K76 (correlated block) 88.6, 130.2 (r = -0.90) Jin 2014 Table III
IIV %CV Q64, CLm 96.5, 41.0 Jin 2014 Table III
Residual error (parent additive / proportional) 0.118 nmol/L / 0.236 Jin 2014 Table III
Residual error (acid additive / proportional) 0.27 nmol/L / 0.43 Jin 2014 Table III
ODE structure (3 parallel depots, 2-cmt parent, 2-cmt acid, reversible) n/a Jin 2014 Figure 2
Bioavailability mapping F1 = 1/(1+BA1+BA2), F2 = BA1/(1+BA1+BA2), F3 = BA2/(1+BA1+BA2) n/a Jin 2014 Results, parent model

Virtual cohort

The original observed data are not publicly available. The figures below use a virtual cohort whose covariate distribution is degenerate (no covariates in the final model). Three dose levels are simulated to illustrate dose-proportional behaviour: 20, 40, and 80 mg single oral doses. Simvastatin molecular weight 418.57 g/mol is used to convert the mg dose to nmol – the model accepts molar dose amounts because Jin 2014 fit the data in molar units (Methods, Modeling Strategy).

set.seed(20260517)

mw_simva <- 418.57
mw_acid  <- 436.59

mg_to_nmol <- function(dose_mg) dose_mg * 1e6 / mw_simva

dose_levels_mg <- c(20, 40, 80)
n_per_dose <- 40L

# Each subject receives a single oral simvastatin dose. Because the
# three-parallel-absorption model represents three depots filled
# simultaneously from a single oral dose, each subject's dose record
# expands to three rows (cmt = depot1, depot2, depot3) with the same
# total dose amount; the per-depot bioavailability f(depotk) = Fk
# (set inside model()) splits the dose into F1, F2, F3.
cohort <- tibble::tibble(
  id_within = rep(seq_len(n_per_dose), times = length(dose_levels_mg)),
  dose_mg   = rep(dose_levels_mg,      each  = n_per_dose),
  id_offset = rep(c(0, n_per_dose, 2 * n_per_dose),
                  each = n_per_dose)
) |>
  dplyr::mutate(
    id        = id_offset + id_within,
    treatment = paste0(dose_mg, " mg"),
    dose_nmol = mg_to_nmol(dose_mg)
  ) |>
  dplyr::select(id, dose_mg, dose_nmol, treatment)

# Build dose rows: three depot dose events per subject at time 0,
# each row carries the same amt (the per-depot bioavailability
# multipliers F1/F2/F3 are applied inside model()).
dose_rows <- cohort |>
  dplyr::rowwise() |>
  dplyr::do(tibble::tibble(
    id = .$id,
    time = 0,
    evid = 1L,
    amt  = .$dose_nmol,
    cmt  = c("depot1", "depot2", "depot3"),
    treatment = .$treatment
  )) |>
  dplyr::ungroup()

# Observation grid -- dense early to capture the multiple-peak
# absorption phase, then thinning out to 24 h.
obs_times <- sort(unique(c(
  seq(0, 2, by = 0.05),
  seq(2.1, 6, by = 0.1),
  seq(6.5, 12, by = 0.5),
  seq(13, 24, by = 1)
)))

obs_rows <- tidyr::expand_grid(id = cohort$id, time = obs_times) |>
  dplyr::left_join(cohort |> dplyr::select(id, treatment), by = "id") |>
  dplyr::mutate(evid = 0L, amt = 0, cmt = "Cc")

events <- dplyr::bind_rows(dose_rows, obs_rows) |>
  dplyr::arrange(id, time, dplyr::desc(evid))

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

Simulation 

mod <- nlmixr2lib::readModelDb("Jin_2014_simvastatin")

# Typical-value replication (no IIV) for the figure comparisons.
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("treatment"))
#> ℹ omega/sigma items treated as zero: 'etalvc', 'etalcl', 'etalq', 'etalka1', 'etalka2', 'etalka3', 'etalba1', 'etalba2', 'etallag2', 'etallag3d', 'etaldur1', 'etaldur2', 'etaldur3', 'etalq64', 'etalk67', 'etalk76', 'etalcl_acid'
#> Warning: multi-subject simulation without without 'omega'

# Stochastic prediction across the cohort (drives the PKNCA block).
sim <- rxode2::rxSolve(mod, events = events, keep = c("treatment"))
#> ℹ parameter labels from comments will be replaced by 'label()'

Replicate published concentration-time profile

Jin 2014 Figure 1 shows individual concentration-time profiles for six representative subjects at 30, 40, 60 (three panels), and 80 mg single oral doses. The figure highlights the irregular multiple-peak absorption pattern that motivates the three-parallel-absorption model. Below, the simulated typical-value trajectories for one subject per dose level reproduce the qualitative shape: a rapid first-peak driven by depot 1 zero-order release (D1 = 0.102 h, Ka1 = 0.00126/h dominant during the infusion), a second peak around ALAG2 = 0.14 h driven by the depot-2 process (Ka2 = 0.964/h), and a broader late peak around ALAG3 = 0.93 h from depot 3 (Ka3 = 0.179/h).

sim_typical |>
  dplyr::filter(id %in% c(1, n_per_dose + 1, 2 * n_per_dose + 1)) |>
  dplyr::filter(time <= 12) |>
  tidyr::pivot_longer(c(Cc, Cc_acid),
                      names_to = "analyte", values_to = "conc_nM") |>
  dplyr::mutate(analyte = dplyr::recode(analyte,
                                        Cc      = "simvastatin",
                                        Cc_acid = "simvastatin acid")) |>
  ggplot(aes(time, conc_nM, colour = analyte)) +
  geom_line(linewidth = 0.7) +
  facet_wrap(~treatment, scales = "free_y") +
  scale_colour_manual(values = c(simvastatin = "black",
                                 `simvastatin acid` = "red")) +
  labs(x = "Time after dose (h)",
       y = "Plasma concentration (nmol/L)",
       colour = NULL,
       caption = "Typical-value (zero-RE) trajectories for one subject per dose. Reproduces the multiple-peak absorption pattern of Jin 2014 Figure 1.")

PKNCA validation

The paper itself does not report a tabulated NCA summary against which the simulation can be benchmarked directly. The block below nevertheless computes Cmax, Tmax, AUC(0-12 h), and (where the terminal-phase slope is well defined) the half-life for the parent and metabolite, broken out by dose group. The dose-proportional behaviour of the simulated Cmax and AUC values is a sanity check on the model implementation; the predicted parent AUC is expected to track dose / CL (= 60 mg * 1e6 / (418.57 g/mol) / 571 L/h ~ 251 nmol*h/L per 60 mg of simvastatin) up to the integration window.

ev_dose <- events |>
  dplyr::filter(evid == 1) |>
  dplyr::distinct(id, treatment, time, amt) |>
  dplyr::group_by(id, treatment, time) |>
  dplyr::summarise(amt = sum(amt), .groups = "drop")

intervals <- data.frame(
  start      = 0,
  end        = 12,
  cmax       = TRUE,
  tmax       = TRUE,
  auclast    = TRUE,
  cmin       = FALSE
)

# Parent (simvastatin lactone) NCA.
sim_parent <- sim |>
  dplyr::filter(!is.na(Cc)) |>
  dplyr::transmute(id, time, conc = Cc, treatment)
conc_parent <- PKNCA::PKNCAconc(sim_parent, conc ~ time | treatment + id,
                                concu = "nmol/L", timeu = "h")
dose_obj <- PKNCA::PKNCAdose(ev_dose, amt ~ time | treatment + id,
                             doseu = "nmol")
nca_parent <- PKNCA::pk.nca(PKNCA::PKNCAdata(conc_parent, dose_obj,
                                             intervals = intervals))

# Metabolite (simvastatin acid) NCA.
sim_acid <- sim |>
  dplyr::filter(!is.na(Cc_acid)) |>
  dplyr::transmute(id, time, conc = Cc_acid, treatment)
conc_acid <- PKNCA::PKNCAconc(sim_acid, conc ~ time | treatment + id,
                              concu = "nmol/L", timeu = "h")
nca_acid <- PKNCA::pk.nca(PKNCA::PKNCAdata(conc_acid, dose_obj,
                                           intervals = intervals))

knitr::kable(as.data.frame(summary(nca_parent)),
             caption = "Simulated single-dose NCA -- simvastatin parent (nmol/L, h).")
Simulated single-dose NCA – simvastatin parent (nmol/L, h).
Interval Start Interval End treatment N AUClast (h*nmol/L) Cmax (nmol/L) Tmax (h)
0 12 20 mg 40 41.1 [50.4] 9.86 [49.4] 0.875 [0.350, 2.00]
0 12 40 mg 40 95.2 [53.5] 23.7 [69.3] 0.750 [0.250, 2.00]
0 12 80 mg 40 160 [60.7] 44.0 [78.4] 0.750 [0.350, 1.85] 
knitr::kable(as.data.frame(summary(nca_acid)),
             caption = "Simulated single-dose NCA -- simvastatin acid (nmol/L, h).")
Simulated single-dose NCA – simvastatin acid (nmol/L, h).
Interval Start Interval End treatment N AUClast (h*nmol/L) Cmax (nmol/L) Tmax (h)
0 12 20 mg 40 41.7 [95.3] 6.86 [120] 1.68 [0.500, 12.0]
0 12 40 mg 40 94.9 [102] 14.1 [104] 2.03 [0.350, 8.00]
0 12 80 mg 40 213 [80.2] 34.2 [95.9] 1.75 [0.350, 12.0]

Comparison against published structural parameters

Jin 2014 Discussion paragraph 3 compares the present typical PK estimates to those reported in a previous simvastatin popPK study:

Parameter Previous report (Jin 2014 Discussion) Present study (Jin 2014 Table III) Packaged model
Central V/F n/a 199 L 199 L
Peripheral V/F n/a 2,710 L 2,710 L
V_central + V_peripheral 8,980 L 2,909 L 2,909 L
Apparent CL 1,740 L/h 571 L/h 571 L/h

The packaged model exactly reproduces the Table III point estimates; the substantial difference in absolute V and CL between the present analysis and the previous-report comparison is attributed by the authors to the choice of absorption model (Discussion, paragraph 3).

Assumptions and deviations

  • BA1/BA2 numerical discrepancy in source. Jin 2014 Results paragraph “Parent Model” reports BA1 = 0.16 and BA2 = 0.70 in the narrative (giving F1, F2, F3 = 53.8%, 8.6%, 37.6%), but Table III – the paper’s tabulated Final Pharmacokinetic Model Parameter Estimates – lists BA1 = 0.636 (RSE 49.4%, 95% CI 0.02-1.25) and BA2 = 0.662 (RSE 13.2%, 95% CI 0.54-0.86). The Table III point estimates and their reported confidence intervals are internally consistent (RSE 49.4% on a value of 0.636 reproduces the 0.02-1.25 CI; the same RSE on a value of 0.16 would not), so Table III is treated as authoritative. The narrative percentages 53.8 / 8.6 / 37.6 do not match the model; with Table III values the simulated F1, F2, F3 are 43.5 / 27.7 / 28.8 percent. The discrepancy is recorded here so that any future erratum can be reconciled against the packaged model. No erratum was located in May 2026.
  • Inter-occasion variability not encoded. Jin 2014 reports IOV estimates for BA1, BA2, D1, D2, and D3 (Table III, IOV %CV column). IOV is a within-subject across-occasion variance component that models residual differences between successive doses to the same subject; the packaged single-dose model treats every subject’s absorption process as a single occasion, so the encoded IIV alone represents the total between-occasion plus between-subject variability in this simulator. Users simulating multi-dose scenarios where intra-individual absorption variability matters can manually re-sample the absorption etas across doses.
  • No IIV reported for FM, V_peripheral. Jin 2014 Table III does not list an IIV %CV column for the metabolic-fraction parameter FM or for the peripheral simvastatin volume V5. The packaged model treats these as without IIV (etas omitted), matching the published parameterisation.
  • Acid central volume fixed at 1 L. Jin 2014 Methods paragraph 2 fixes V6 (the central distribution volume of simvastatin acid) at 1 L because, in the absence of intravenous simvastatin acid data, FM, V6, and CLm are confounded. This is a structural assumption carried into the packaged model. Simulated acid concentrations scale inversely with V6; users substituting a different V6 reference (e.g., the apparent V derived from a separately fit metabolite dataset) should rescale FM and CLm correspondingly.
  • K67 magnitude. Table III reports K67 = 252 1/h (RSE 6.0%) – a rate constant corresponding to a transfer half-time of about 10 seconds between the acid central and acid peripheral compartments. This value reflects the rapid equilibrium between the two acid compartments under the V6 = 1 L identifiability constraint; the effective distribution clearance Q67 = K67 * V6 = 252 L/h is comparable in magnitude to the parent Q (199 L/h). The value is used verbatim from Table III with no rescaling.
  • BLQ handling. Jin 2014 Methods describes a hybrid BLQ scheme: the first below-LLOQ observation in the disposition phase was imputed at half the LLOQ, and subsequent BLQ values were dropped. Simulation from the packaged model is unaffected (no BLQ in simulated output); the assumption is recorded so users fitting the model to original or external data can reproduce the original BLQ rule.
  • Dose-unit convention. The packaged model expects oral doses in nmol (matching the molar internal units of Jin 2014’s NONMEM analysis). The vignette converts milligrams to nanomoles via the simvastatin lactone molecular weight 418.57 g/mol. The simvastatin-acid hydroxyacid molecular weight 436.59 g/mol is not needed inside the ODEs because the molar interconversion is 1:1.
  • No covariates in final model. Age, body weight, and height were tested as candidate covariates on both parent and metabolite parameters and none reached the significance criterion (Results, parent and metabolite sections). The packaged model carries no covariate effects and therefore makes no demographic predictions beyond the cohort-typical values from a Korean adult male population.
  • No erratum located. A targeted search of PubMed and the Pharm Res landing page in May 2026 did not surface any erratum, corrigendum, or correction notice for this article. Should one be published in future, the model file’s reference field and the Table III source-trace comments should be updated to point at the corrected values.