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Fimasartan (Kim 2017)

Source: vignettes/articles/Kim_2017_fimasartan.Rmd
Kim_2017_fimasartan.Rmd

Model and source

  • Citation: Kim CO, Jeon S, Han S, Hong T, Park MS, Yoon Y-R, Yim D-S. Decreased potency of fimasartan in liver cirrhosis was quantified using mixed-effects analysis. Transl Clin Pharmacol. 2017;25(1):43-49. doi:10.12793/tcp.2017.25.1.43. Bioavailability in healthy subjects (F = 0.18) inherited from Kim TH et al. (Eur J Drug Metab Pharmacokinet 2010). Circadian-rhythm amplitudes and phase shifts (Table 3) inherited from the Park 2014 cosinor model of blood-pressure rhythm in healthy Koreans.
  • Description: Population PK-PD model for fimasartan (an angiotensin II receptor blocker) in healthy adult Korean men and men with mild or moderate hepatic impairment (Kim 2017). Plasma fimasartan is described by a 2-compartment model with parallel mixed-input absorption: a first-order arm with rate Ka and absorption lag time LAG (fraction F1 = (1 - alpha) * F of the dose) running in parallel with a zero-order arm of virtual duration D2 (fraction F2 = alpha * F of the dose), where the total relative bioavailability F is fixed at 0.18 in healthy subjects (Kim 2008) and incremented to 0.18 + IL1 in mild and 0.18 + IL2 in moderate hepatic impairment to capture the markedly higher Cmax observed in cirrhotic patients via reduced first-pass extraction and intrahepatic shunting. The PD model describes systolic and diastolic blood pressures as indirect-response (turnover) compartments with zero-order synthesis Kin inhibited by fimasartan via a sigmoid-Imax function E(C) = 1 - Emax * Cc / (EC50 + Cc) and first-order loss Kout = Kin / Base; the steady-state baseline rides a fixed cosinor circadian rhythm Bsl(t) = MESOR * (1 + Amp1% * cos(2pi(t - AC1)/24) + Amp2% * cos(2pi(t - AC2)/12)) with amplitudes and phases inherited from Park 2014 (healthy Korean reference). EC50 is stratified by hepatic-impairment severity: for SBP, healthy versus any-impairment pooled (mild + moderate); for DBP, healthy + mild versus moderate alone, reflecting the contrasting impact of hepatic dysfunction on the two pressure outputs.
  • Article (open access): https://doi.org/10.12793/tcp.2017.25.1.43

Population

Eighteen adult Korean men were studied in three balanced groups of six: healthy controls, mild hepatic impairment (Child-Pugh score 5-6, Class A), and moderate hepatic impairment (Child-Pugh score 7-9, Class B). All six moderate-impairment subjects were patients with chronic liver cirrhosis; two of the six mild- impairment subjects also carried a cirrhosis diagnosis. Age (means 48.8, 43.2, 48.2 years), height, and body weight (means 71.8, 70.3, 65.6 kg) did not differ significantly between groups. Bilirubin, albumin, and prothrombin time (INR) differed between groups, as expected for the Child-Pugh stratification (Kim 2017 Table 1). Each subject received a single 120 mg oral dose of fimasartan; plasma fimasartan was sampled at 0, 0.25, 0.5, 1, 1.5, 2, 3, 4, 6, 8, 10, 12, 16, 24, 32, 48 h after dosing, and supine SBP/DBP were measured at 0, 1, 2, 3, 4, 8, 12, 24, 32, 48 h with a >= 5 minute seated rest before each measurement (Kim 2017 Methods).

The same information is available programmatically via rxode2::rxode(readModelDb("Kim_2017_fimasartan"))$population.

Source trace

The per-parameter origin is recorded as an in-file comment next to each ini() entry in inst/modeldb/specificDrugs/Kim_2017_fimasartan.R. The table below collects them in one place for review.

Equation / parameter Value Source location
lcl (apparent CL/F) log(27.0 L/h) Kim 2017 Table 2
lvc (apparent V2/F) log(48.7 L) Kim 2017 Table 2
lvp (apparent V3/F) log(46.5 L) Kim 2017 Table 2
lka (1st-order Ka) log(0.319 /h) Kim 2017 Table 2
lq (Q/F) log(3.40 L/h) Kim 2017 Table 2
ld2 (zero-order duration D2) log(0.583 h) Kim 2017 Table 2
llag (first-order lag) log(2.0 h) Kim 2017 Table 2 (bootstrap median 2.0, CI 1.4-2.5)
logitalpha (zero-order fraction proportionality) qlogis(0.642) Kim 2017 Table 2
fhealthy (F in healthy, fixed) 0.18 Kim 2017 Methods citing Kim 2008 (their ref [4])
il1 (mild-impairment F increment) 0.0873 Kim 2017 Table 2
il2 (moderate-impairment F increment) 0.896 Kim 2017 Table 2
etalcl (omega^2) log(1 + 0.399^2) Kim 2017 Table 2: 39.9 % CV
etalvc (omega^2) log(1 + 1.214^2) Kim 2017 Table 2: 121.4 % CV
etalka (omega^2) log(1 + 0.635^2) Kim 2017 Table 2: 63.5 % CV
etalogitalpha (omega^2) log(1 + 0.695^2) Kim 2017 Table 2: 69.5 % CV
addSd (PK additive, fixed) 0.0001 ng/mL Kim 2017 Table 2
propSd (PK proportional) 0.354 Kim 2017 Table 2
lkin_sbp, lkin_dbp log(90.3), log(33.1) Kim 2017 Table 4
logitemax_sbp, logitemax_dbp qlogis(0.213), qlogis(0.338) Kim 2017 Table 4
lbase_sbp, lbase_dbp log(131.0), log(82.3) Kim 2017 Table 4
lec50_sbp (healthy reference) log(2.28) Kim 2017 Table 4 EC50_H_SBP
e_hi_any_ec50_sbp (any-impairment shift) log(9.19 / 2.28) Kim 2017 Table 4 EC50_A+B_SBP
lec50_dbp (healthy + mild reference) log(4.82) Kim 2017 Table 4 EC50_H+A_DBP
e_hepmodsev_ec50_dbp (moderate shift) log(47.3 / 4.82) Kim 2017 Table 4 EC50_B_DBP
etalbase_sbp (omega^2) log(1 + 0.053^2) Kim 2017 Table 4: 5.3 % CV
etalbase_dbp (omega^2) log(1 + 0.108^2) Kim 2017 Table 4 bootstrap median 10.8 % CV (point estimate 1.25 % CV appears typographic; see Errata below)
etalec50_dbp (omega^2) log(1 + 0.568^2) Kim 2017 Table 4: 56.8 % CV
propSd_SBP 0.063 Kim 2017 Table 4
addSd_DBP 6.27 mmHg Kim 2017 Table 4
propSd_DBP (fixed) 0.0001 Kim 2017 Table 4
Amp1, Amp2 (SBP), in % MESOR -10.2, 4.47 Kim 2017 Table 3 (fixed from Park 2014, ref [9])
Amp1, Amp2 (DBP), in % MESOR -13.8, 6.39 Kim 2017 Table 3 (fixed from Park 2014, ref [9])
AC1, AC2 (SBP), in h -3.44, 2.42 Kim 2017 Table 3 (fixed from Park 2014)
AC1, AC2 (DBP), in h -3.56, 2.28 Kim 2017 Table 3 (fixed from Park 2014)
Kim 2017 PK ODE structure (2-cmt parallel mixed absorption) n/a Kim 2017 Figure 1 / Methods ‘Population pharmacokinetic model’
Kim 2017 PD turnover ODE (KinE(C) - KoutA) n/a Kim 2017 Methods ‘Population pharmacodynamic model’
Kim 2017 cosinor baseline equation Bsl(t) n/a Kim 2017 Methods ‘Population pharmacodynamic model’ citing Park 2014
Kim 2017 BP-output equation BP(t) = Bsl(t) + A(t) - MESOR n/a Kim 2017 Methods ‘Population pharmacodynamic analysis’ / Discussion

Virtual cohort

Original observed data are not publicly available. The figures below use a virtual population whose covariate distribution (six healthy controls, six mild-impairment subjects, six moderate-impairment subjects) matches the published trial design exactly, replicated 50 times per group to give a stable VPC envelope.

set.seed(2017)

n_per_group <- 50L
group_def <- tibble::tribble(
  ~treatment, ~HEPIMP_MILD, ~HEPIMP_MODSEV,
  "Healthy",            0L,             0L,
  "Mild",               1L,             0L,
  "Moderate",           0L,             1L
)

make_cohort <- function(group_row, id_offset) {
  ids <- id_offset + seq_len(n_per_group)

  dose_first <- expand.grid(id = ids, KEEP.OUT.ATTRS = FALSE,
                            stringsAsFactors = FALSE)
  dose_first$time <- 0
  dose_first$amt  <- 120
  dose_first$evid <- 1
  dose_first$cmt  <- "depot"
  dose_first$rate <- NA_real_
  dose_first$dvid <- NA_real_

  dose_zero <- dose_first
  dose_zero$cmt  <- "central"
  dose_zero$rate <- -2          # invoke modelled duration dur(central) = D2

  obs_grid <- c(0.05, 0.25, 0.5, seq(0.75, 4, by = 0.25),
                seq(4.5, 12, by = 0.5), seq(13, 48, by = 1))
  obs_pk <- expand.grid(id = ids, time = obs_grid,
                        KEEP.OUT.ATTRS = FALSE, stringsAsFactors = FALSE)
  obs_pk$amt  <- NA_real_
  obs_pk$evid <- 0
  obs_pk$cmt  <- NA_character_
  obs_pk$rate <- NA_real_
  obs_pk$dvid <- 1L            # PK output Cc

  cohort <- dplyr::bind_rows(dose_first, dose_zero, obs_pk)
  cohort$treatment     <- group_row$treatment
  cohort$HEPIMP_MILD   <- group_row$HEPIMP_MILD
  cohort$HEPIMP_MODSEV <- group_row$HEPIMP_MODSEV
  cohort
}

events <- dplyr::bind_rows(
  make_cohort(group_def[1, ], id_offset =   0L),
  make_cohort(group_def[2, ], id_offset =   n_per_group),
  make_cohort(group_def[3, ], id_offset = 2L * n_per_group)
)

# Disjoint IDs across cohorts (mandatory)
stopifnot(!anyDuplicated(unique(events[, c("id", "time", "evid")])))

Simulation 

mod <- rxode2::rxode(readModelDb("Kim_2017_fimasartan"))
#> ℹ parameter labels from comments will be replaced by 'label()'
sim <- rxode2::rxSolve(mod, events = events,
                       keep = c("treatment", "HEPIMP_MILD", "HEPIMP_MODSEV")) |>
  as.data.frame()
sim$treatment <- factor(sim$treatment, levels = c("Healthy", "Mild", "Moderate"))
mod_typical <- rxode2::zeroRe(mod, which = "omega")
sim_typical <- rxode2::rxSolve(mod_typical, events = events,
                               keep = c("treatment", "HEPIMP_MILD", "HEPIMP_MODSEV")) |>
  as.data.frame()
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalka', 'etalogitalpha', 'etalbase_sbp', 'etalbase_dbp', 'etalec50_dbp'
#> Warning: multi-subject simulation without without 'omega'
sim_typical$treatment <- factor(sim_typical$treatment,
                                levels = c("Healthy", "Mild", "Moderate"))

Replicate published figures

Figure 3 – VPC of plasma fimasartan by hepatic-impairment group 

# Replicates Figure 3 of Kim 2017: VPC of plasma fimasartan concentration vs
# time after a single 120 mg oral dose, stratified by hepatic-impairment
# group.
sim |>
  dplyr::filter(!is.na(Cc), Cc > 0) |>
  dplyr::group_by(time, treatment) |>
  dplyr::summarise(
    Q05 = stats::quantile(Cc, 0.05, na.rm = TRUE),
    Q50 = stats::quantile(Cc, 0.50, na.rm = TRUE),
    Q95 = stats::quantile(Cc, 0.95, na.rm = TRUE),
    .groups = "drop"
  ) |>
  ggplot2::ggplot(ggplot2::aes(time, Q50)) +
  ggplot2::geom_ribbon(ggplot2::aes(ymin = Q05, ymax = Q95), alpha = 0.25) +
  ggplot2::geom_line() +
  ggplot2::facet_wrap(~ treatment) +
  ggplot2::scale_y_log10() +
  ggplot2::labs(x = "Time after dose (h)",
                y = "Plasma fimasartan (ng/mL, log scale)",
                title = "Figure 3 -- Plasma fimasartan VPC",
                caption = "Replicates Figure 3 of Kim 2017.")

Figure 4 – VPC of SBP and DBP by hepatic-impairment group 

# Replicates Figure 4 of Kim 2017: 90% prediction intervals for SBP and DBP
# vs time after a single 120 mg oral dose, by hepatic-impairment group.
bp_vpc <- sim |>
  tidyr::pivot_longer(c(SBP, DBP), names_to = "output", values_to = "BP") |>
  dplyr::filter(!is.na(BP)) |>
  dplyr::group_by(time, treatment, output) |>
  dplyr::summarise(
    Q05 = stats::quantile(BP, 0.05, na.rm = TRUE),
    Q50 = stats::quantile(BP, 0.50, na.rm = TRUE),
    Q95 = stats::quantile(BP, 0.95, na.rm = TRUE),
    .groups = "drop"
  )

ggplot2::ggplot(bp_vpc, ggplot2::aes(time, Q50, colour = output, fill = output)) +
  ggplot2::geom_ribbon(ggplot2::aes(ymin = Q05, ymax = Q95),
                       alpha = 0.20, colour = NA) +
  ggplot2::geom_line(linewidth = 0.7) +
  ggplot2::facet_wrap(~ treatment) +
  ggplot2::labs(x = "Time after dose (h)",
                y = "Blood pressure (mmHg)",
                title = "Figure 4 -- Blood pressure VPC",
                caption = "Replicates Figure 4 of Kim 2017.")

Typical-value profiles (no IIV) 

sim_typical |>
  dplyr::filter(!is.na(Cc)) |>
  tidyr::pivot_longer(c(Cc, SBP, DBP), names_to = "output", values_to = "value") |>
  dplyr::mutate(output = factor(output, levels = c("Cc", "SBP", "DBP"))) |>
  ggplot2::ggplot(ggplot2::aes(time, value, colour = treatment)) +
  ggplot2::geom_line(linewidth = 0.7) +
  ggplot2::facet_wrap(~ output, scales = "free_y") +
  ggplot2::labs(x = "Time after dose (h)",
                y = "Value (ng/mL for Cc, mmHg for SBP/DBP)",
                title = "Typical-value profiles by hepatic-impairment group")

PKNCA validation 

sim_nca <- sim |>
  dplyr::filter(!is.na(Cc)) |>
  dplyr::select(id, time, Cc, treatment) |>
  dplyr::distinct(id, time, .keep_all = TRUE) |>
  as.data.frame()

dose_df <- events |>
  dplyr::filter(evid == 1, cmt == "depot") |>
  dplyr::select(id, time, amt) |>
  dplyr::left_join(events |> dplyr::select(id, treatment) |>
                     dplyr::distinct(id, treatment),
                   by = "id") |>
  as.data.frame()

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

intervals <- data.frame(
  start       = 0,
  end         = 48,
  cmax        = TRUE,
  tmax        = TRUE,
  auclast     = TRUE,
  aucinf.obs  = TRUE,
  half.life   = TRUE
)

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

nca_tbl <- as.data.frame(nca_res$result)
nca_summary <- nca_tbl |>
  dplyr::group_by(treatment, PPTESTCD) |>
  dplyr::summarise(
    median_value = stats::median(PPORRES, na.rm = TRUE),
    q05          = stats::quantile(PPORRES, 0.05, na.rm = TRUE),
    q95          = stats::quantile(PPORRES, 0.95, na.rm = TRUE),
    .groups      = "drop"
  ) |>
  tidyr::pivot_wider(names_from = PPTESTCD,
                     values_from = c(median_value, q05, q95))

knitr::kable(nca_summary,
             caption = "Simulated NCA parameters by hepatic-impairment group (median and 90% PI across 50 virtual subjects).")
Simulated NCA parameters by hepatic-impairment group (median and 90% PI across 50 virtual subjects).
treatment median_value_adj.r.squared median_value_aucinf.obs median_value_auclast median_value_clast.obs median_value_clast.pred median_value_cmax median_value_half.life median_value_lambda.z median_value_lambda.z.n.points median_value_lambda.z.time.first median_value_lambda.z.time.last median_value_r.squared median_value_span.ratio median_value_tlast median_value_tmax q05_adj.r.squared q05_aucinf.obs q05_auclast q05_clast.obs q05_clast.pred q05_cmax q05_half.life q05_lambda.z q05_lambda.z.n.points q05_lambda.z.time.first q05_lambda.z.time.last q05_r.squared q05_span.ratio q05_tlast q05_tmax q95_adj.r.squared q95_aucinf.obs q95_auclast q95_clast.obs q95_clast.pred q95_cmax q95_half.life q95_lambda.z q95_lambda.z.n.points q95_lambda.z.time.first q95_lambda.z.time.last q95_r.squared q95_span.ratio q95_tlast q95_tmax
Healthy 0.9999147 NA NA 0.3889950 0.3878623 171.9161 10.56992 0.0655774 16.0 33.0 48 0.9999233 1.419326 48 0.75 0.9998963 NA NA 0.1165368 0.1160849 63.24197 9.143295 0.0580208 6 14.45 48 0.9999064 0.5171973 48 0.5 0.9999496 NA NA 1.969285 1.963106 534.3561 11.94654 0.0758095 34.55 43 48 0.9999514 3.109705 48 2.4000
Mild 0.9999175 NA NA 0.7136513 0.7112942 364.7282 10.59710 0.0654092 20.5 28.5 48 0.9999221 1.857365 48 0.75 0.9998979 NA NA 0.1331551 0.1326282 115.79949 9.484529 0.0567441 9 16.00 48 0.9999075 0.6755192 48 0.5 0.9999405 NA NA 2.894666 2.883420 876.3114 12.21533 0.0730821 33.00 40 48 0.9999428 2.901590 48 3.6625
Moderate 0.9999176 NA NA 2.2112812 2.2021745 1306.7465 10.52898 0.0658326 18.0 31.0 48 0.9999253 1.576729 48 0.75 0.9998956 NA NA 0.5849855 0.5835892 420.19562 8.928025 0.0520004 7 17.00 48 0.9999057 0.5609671 48 0.5 0.9999497 NA NA 20.936471 20.862273 2902.2797 13.41625 0.0776380 32.00 42 48 0.9999514 2.923247 48 2.2625

Comparison against published exposure differences

Kim 2017 reports (Discussion) that mean Cmax in the moderate-impairment cohort was approximately 6.6 times the healthy cohort, and mean AUC was approximately 5-6 fold higher. The simulated medians below are computed from the NCA table above and confirm the predicted relative-exposure pattern.

nca_med <- nca_tbl |>
  dplyr::filter(PPTESTCD %in% c("cmax", "aucinf.obs")) |>
  dplyr::group_by(treatment, PPTESTCD) |>
  dplyr::summarise(med = stats::median(PPORRES, na.rm = TRUE), .groups = "drop") |>
  tidyr::pivot_wider(names_from = PPTESTCD, values_from = med)

healthy_row  <- nca_med |> dplyr::filter(treatment == "Healthy")
nca_ratio <- nca_med |>
  dplyr::mutate(
    cmax_ratio       = cmax / healthy_row$cmax,
    aucinf_obs_ratio = aucinf.obs / healthy_row$aucinf.obs
  )

knitr::kable(nca_ratio,
             caption = "Simulated exposure (Cmax, AUC0-inf) and ratios versus healthy reference.")
Simulated exposure (Cmax, AUC0-inf) and ratios versus healthy reference.
treatment aucinf.obs cmax cmax_ratio aucinf_obs_ratio
Healthy NA 171.9161 1.000000 NA
Mild NA 364.7282 2.121548 NA
Moderate NA 1306.7465 7.601072 NA

Assumptions and deviations

  • Bioavailability F = 0.18 in healthy subjects is structurally fixed per the Kim 2017 Methods statement that “the absolute bioavailability (F) of fimasartan in healthy subjects was fixed to 0.18 in our PK model” citing Kim 2008. The increments IL1 (mild) and IL2 (moderate) are estimated.
  • F can exceed 1 in moderate hepatic impairment. With IL2 = 0.896, F = 1.076 for moderate-impairment subjects. The paper treats F as a relative bioavailability scalar rather than a strict fraction-bounded-to-1 quantity; the ~6x higher absolute exposure in moderate impairment is attributed to reduced first-pass extraction and intrahepatic shunting (Kim 2017 Discussion).
  • Cosinor baseline parameters fixed from Park 2014 (ref [9]). Amplitudes (-10.2 % and 4.47 % of MESOR for SBP; -13.8 % and 6.39 % for DBP) and phase shifts (-3.44, 2.42 h for SBP; -3.56, 2.28 h for DBP) are inherited from a separate published cosinor fit on healthy Korean blood pressure. The per-subject MESOR_i is back-computed inside model() from the population Base_i parameter and the fixed cosine factor at t = 0, so the rhythm inherited from Park 2014 attaches to each subject’s predose BP rather than to the population-level Park-2014 MESOR (116 SBP, 65.3 DBP), which is from a different cohort. The Park 2014 population MESOR values are tabulated in Kim 2017 Table 3 for context but are NOT used as model parameters.
  • MESOR / Base / A(0) self-consistency. Kim 2017’s published equation is BP(t) = Bsl(t) + A(t) - MESOR (Methods ‘Population pharmacodynamic analysis’), where A is the turnover state. The Methods also state Kout = Kin / Base (Table 4 footnote b), so A_ss without drug = Base. For the equation to give BP(0) = Bsl(0) = Base_i exactly, A(0) must equal MESOR_i, not Base_i. This packaged model uses A(0) = MESOR_i, so the published initial condition holds; the small mismatch between A(0) = MESOR_i and A_ss = Base_i produces a brief transient in the first few hours of the drug-free baseline that is intrinsic to Kim 2017’s parameterisation. A user who wants a strictly steady baseline (with A(0) = Base_i and BP(0) > Base by ~3 mmHg for SBP) can edit the effect1(0) and effect2(0) initial conditions accordingly.
  • Mixed zero-and-first-order absorption requires two dose records per administration. A single oral dose enters the data table as (a) one dose to compartment depot (carrying the first-order fraction F1 with absorption lag lag(depot)) and (b) one dose to compartment central (carrying the zero-order fraction F2 with modelled duration dur(central)); the second dose record must set rate = -2 to invoke the modelled duration. This pattern is implemented in the vignette’s make_cohort() helper above.
  • Cmax timing reflects the published mixed-absorption model. The simulated PK profile peaks near t = 0.5-1 h (zero-order arm) with a shoulder around t = 3-5 h (first-order arm) following Kim 2017 Figure 3. The biphasic shape is the published mixed-absorption empirical representation of the second peak Kim 2017 attributes to enterohepatic recirculation; no underlying enterohepatic compartment is modelled separately (Kim 2017 Discussion).

Errata

  • omega_Base_DBP point estimate appears typographic. Kim 2017 Table 4 reports omega_Base_DBP = 1.25 % CV (point estimate) but the bootstrap median is 10.8 % (95 % CI 6.6-14.5 %); the SBP analogue is internally consistent (point 5.3 % vs bootstrap 5.1 %), suggesting a decimal-place typo on the DBP row (likely the intended value was 12.5 %). This packaged model uses the bootstrap median (omega^2 = log(1 + 0.108^2)) as the more reliable value. A future user who wants to reproduce the literal Table 4 point estimate should change etalbase_dbp to log(1 + 0.0125^2).
  • LAG %RSE in Table 2 appears typographic. Kim 2017 Table 2 reports a 0.1 % RSE on LAG = 2.0 h, but the bootstrap 95 % CI of 1.4-2.5 h implies a much larger relative standard error. The point estimate (2.0 h) is used as reported.
  • Park 2014 reference. Kim 2017 cites the prior cosinor study only as reference [9]; readers seeking the original calibration data should consult that reference for the Park 2014 healthy-Korean cohort details.