Skip to contents

L-ornithine phenylacetate (Wang 2022)

Source: vignettes/articles/Wang_2022_ornithinePhenylacetate.Rmd
Wang_2022_ornithinePhenylacetate.Rmd

Model and source

  • Citation: Wang X, Vilchez RA. Population Pharmacokinetic Analysis to Assist Dose Selection of the L-Ornithine Salt of Phenylacetic Acid. Clin Pharmacokinet. 2022;61(4):515-526. doi:10.1007/s40262-021-01075-1
  • Description: Population PK model for intravenous L-ornithine phenylacetate (L-OPA) in adults with cirrhosis or hepatic encephalopathy (Wang 2022). Phenylacetic acid (PAA): one compartment with Michaelis-Menten conversion to phenylacetylglutamine (PAGN), the only PAA elimination route. PAGN: one compartment with first-order clearance. L-ornithine (ORN): one compartment with linear clearance plus an additive endogenous baseline. Covariates: body weight and Child-Pugh class on PAA Vmax and volume; creatinine clearance on PAGN clearance; sex, weight, creatinine clearance and Child-Pugh class on ORN clearance; Child-Pugh class on the ORN baseline.
  • Article: https://doi.org/10.1007/s40262-021-01075-1 (open access, CC BY-NC 4.0)
  • Supplement (Online Resource 1: model simplification, Table S2 and the NONMEM control streams): https://static-content.springer.com/esm/art%3A10.1007%2Fs40262-021-01075-1/MediaObjects/40262_2021_1075_MOESM1_ESM.docx

L-ornithine phenylacetate (L-OPA) is an intravenous ammonia scavenger for hepatic encephalopathy. After infusion it dissociates 1:1 into phenylacetic acid (PAA), the active moiety, and L-ornithine (ORN). PAA conjugates with glutamine to form phenylacetylglutamine (PAGN), which is excreted in urine and carries two moles of ammonia nitrogen per mole.

Wang 2022 first sketched a mechanistic model with glutamate, glutamine and ammonia (Figure 2, Eqs. 1-6), then simplified it to three uncoupled or one-way-coupled pieces (Section 3.1, ESM Eqs. S1-S3). The packaged model encodes the simplified final model, with the per-moiety parameters from the final fits in patients:

dA1dt=Rateinf−CLORNA1VORNdA2dt=Rateinf−VmaxA2/VPAAKm+A2/VPAAdA3dt=VmaxA2/VPAAKm+A2/VPAA−CLPAGNA3VPAGN \begin{aligned} \frac{dA_1}{dt} &= \text{Rate}_{\text{inf}} - CL_{ORN}\frac{A_1}{V_{ORN}} \\ \frac{dA_2}{dt} &= \text{Rate}_{\text{inf}} - \frac{V_{max} A_2 / V_{PAA}}{K_m + A_2 / V_{PAA}} \\ \frac{dA_3}{dt} &= \frac{V_{max} A_2 / V_{PAA}}{K_m + A_2 / V_{PAA}} - CL_{PAGN}\frac{A_3}{V_{PAGN}} \end{aligned}

In the package, A1A_1 is central_ornithine (the dose-derived ORN only), A2A_2 is central (PAA) and A3A_3 is central_pagn. All amounts are in mmol and the internal concentrations in mmol/L, which is why doses are given in mmol. The three observations are reported in ug/mL by the molecular weights that the source control streams use (PAA 135.142, PAGN 264.281, ORN 132.163 g/mol). The ORN prediction adds the endogenous baseline, Cc_ornithine = A1/V_ORN * 132.163 + BASE, exactly as the ESM ORN control stream does.

The three pieces were fitted separately: ORN on its own (ADVAN1), PAA on its own (ADVAN13), and PAGN sequentially on the individual PAA estimates. They are packaged in one model because a single infusion feeds both ORN and PAA, and PAGN is formed from PAA.

Population

The final models were fitted to 152 patients: adults with stable cirrhosis (study OCR002-HE201, single ascending doses of 1-40 g over 4 or 24 h) and adults hospitalised with cirrhosis and an acute episode of hepatic encephalopathy (study OCR002-HE209, 10, 15 or 20 g/24 h for 5 days by Child-Pugh score). Table 1 lists 59 women (median age 59 years, mean weight 73.9 kg, SD 18.0) and 93 men (median age 57 years, mean weight 86.3 kg, SD 20.1), all Caucasian or of unknown ethnicity; weights ranged from 45 to 153 kg. Child-Pugh class was A in 21%, B in 31% and C in 48%; renal function was normal in 51% and mildly, moderately or severely impaired in 27%, 20% and 2%.

A separate fit to 46 healthy subjects (Caucasian, Japanese and Chinese; studies OCR002-HV201 and MNK61051112) was used to show that ethnicity has no effect on PAA once body weight is accounted for. Its parameter estimates are not tabulated, so it is not packaged.

The same information is available programmatically via readModelDb("Wang_2022_ornithinePhenylacetate")()$population.

Source trace

Equation / parameter Value Source location
ODEs for ORN, PAA, PAGN n/a Section 3.1 equations; ESM Eqs. S1-S3; ESM ‘NONMEM Code for PAGN’ $DES
lvmax log(12.4) mmol/h Table 2, Vmax
lkm log(1.33) mmol/L Table 2, Km (179 ug/mL)
lvc log(24.4) L Table 2, VPAA
e_wt_vmax 0.97 Table 2, weight power Vmax; reference 83 kg from the ESM PAA control stream
e_wt_vc 0.79 Table 2, weight power VPAA; reference 83 kg as above
e_hepimp_mod_vmax 0.63 Table 2, Vmax ratio C-P B/C-P A
e_hepimp_sev_vmax 0.39 Table 2, Vmax ratio C-P C/C-P A
e_hepimp_modsev_vc 1.89 Table 2, VPAA ratio C-P BC/C-P A
etalvmax, etalkm, etalvc 0.2074, 0.6133, 0.1553 Table 2, BSV 48%, 92%, 41%, as log(1 + CV^2)
propSd, addSd 0.35, 2.23 ug/mL Table 2, PAA proportional (35%) and additive error
lcl_pagn log(14.9) L/h Section 3.4
lvc_pagn log(33.2) L Section 3.4
e_crcl_cl_pagn 0.8 Section 3.4 (‘CL PAGN proportional to CLcr^0.8’); reference 90 mL/min from the ESM PAGN code
etalcl_pagn, etalvc_pagn fixed(0) Present in the ESM PAGN code; variances not reported
propSd_pagn, addSd_pagn fixed(0) Not reported
lcl_ornithine log(25.4) L/h ESM Table S2, theta7 (male CL)
e_sexf_cl_ornithine 18.2/25.4 ESM Table S2, theta1 (female CL) over theta7
e_wt_cl_ornithine 0.824 ESM Table S2, theta11; reference 75 kg
e_crcl_cl_ornithine 0.614 ESM Table S2, theta6; CLcr capped at 90 mL/min in the ESM ORN code
e_hepimp_modsev_cl_ornithine 0.719 ESM Table S2, theta8 (‘Child-Pugh B/C, adjust by a coefficient’)
lvc_ornithine log(64.8) L ESM Table S2, V
lc0_ornithine log(13.6) ug/mL ESM Table S2, baseline ORN Child-Pugh A
e_hepimp_mod_c0_ornithine, e_hepimp_sev_c0_ornithine 11.4/13.6, 9.56/13.6 ESM Table S2, baseline ORN Child-Pugh B and C
etalcl_ornithine, etalvc_ornithine, etalc0_ornithine 0.3616, 0.6931, 0.2476 ESM Table S2, BSV 66%, 100%, 53%, as log(1 + CV^2)
propSd_ornithine 0.4 ESM Table S2, error model row

Virtual cohort

Section 2.3 simulated 500 patients per group with a weight distribution similar to study HE209, and Asian patients with a mean weight 20% lower. The paper does not print the weight distribution, so the cohort below draws sex from Table 1 (38.8% female) and weight from a log-normal per sex matched to the Table 1 patient means and SDs, truncated to the observed 45-153 kg. Asian patients take the same draws multiplied by 0.8. Creatinine clearance is set to 90 mL/min; it does not enter PAA and only matters for the ORN and PAGN predictions. Each scenario has 200 patients.

The dose regimen is the phase III regimen from Section 2.3: 20 g over 6 h, then 15 g over 18 h on day 1, then 15 g over 24 h on days 2-5 (20 gL_15 gM). The reduced regimen for Asian patients with Child-Pugh C is 15 g, 10 g, then 10 g/24 h (15 gL_10 gM). Grams of L-OPA are converted to mmol with the salt’s molecular weight, 268.31 g/mol (C13H20N2O4, the sum of L-ornithine 132.16 and phenylacetic acid 136.15). Each mmol of L-OPA delivers one mmol of PAA and one of ORN, so every infusion is entered twice, into central and into central_ornithine.

set.seed(20220401)
mw_lopa <- 268.31 # g/mol, L-ornithine phenylacetate salt

regimens <- list(
  "20 gL_15 gM" = c(load = 20, maint = 15),
  "15 gL_10 gM" = c(load = 15, maint = 10)
)
scenarios <- tibble::tribble(
  ~scenario,                          ~ethnicity,  ~cp,   ~regimen,      ~wt_factor,
  "Caucasian C-P B (20 gL_15 gM)",    "Caucasian", "B",   "20 gL_15 gM", 1.0,
  "Caucasian C-P C (20 gL_15 gM)",    "Caucasian", "C",   "20 gL_15 gM", 1.0,
  "Asian C-P B (20 gL_15 gM)",        "Asian",     "B",   "20 gL_15 gM", 0.8,
  "Asian C-P C (15 gL_10 gM)",        "Asian",     "C",   "15 gL_10 gM", 0.8,
  "Asian C-P C (20 gL_15 gM)",        "Asian",     "C",   "20 gL_15 gM", 0.8
)

n_per <- 200
lnorm_draw <- function(n, m, s) {
  sdlog <- sqrt(log(1 + (s / m)^2))
  rlnorm(n, log(m) - sdlog^2 / 2, sdlog)
}
# One set of Caucasian weights is reused by every scenario, so that the Asian
# scenarios differ from the Caucasian ones only by the 0.8 weight factor.
base_sexf <- rbinom(n_per, 1, 59 / 152)
base_wt <- ifelse(
  base_sexf == 1,
  lnorm_draw(n_per, 73.9, 18.0),
  lnorm_draw(n_per, 86.3, 20.1)
)
base_wt <- pmin(pmax(base_wt, 45), 153)

obs_times <- sort(unique(c(seq(0, 120, by = 2), 84, 108, 120)))

make_scenario <- function(k) {
  sc <- scenarios[k, ]
  reg <- regimens[[sc$regimen]]
  subj <- tibble(
    id = (k - 1L) * n_per + seq_len(n_per),
    scenario = sc$scenario,
    WT = base_wt * sc$wt_factor,
    SEXF = base_sexf,
    CRCL = 90,
    HEPIMP_MOD = as.integer(sc$cp == "B"),
    HEPIMP_SEV = as.integer(sc$cp == "C")
  )
  infusions <- tibble(
    time = c(0, 6, 24, 48, 72, 96),
    dur = c(6, 18, 24, 24, 24, 24),
    grams = c(reg[["load"]], rep(reg[["maint"]], 5))
  ) |>
    mutate(amt = grams * 1000 / mw_lopa, rate = amt / dur)
  doses <- tidyr::crossing(subj, infusions) |>
    select(-grams, -dur) |>
    tidyr::crossing(cmt = c("central", "central_ornithine")) |>
    mutate(evid = 1L, dvid = NA_integer_)
  obs <- tidyr::crossing(subj, time = obs_times) |>
    mutate(amt = NA_real_, rate = NA_real_, cmt = NA_character_, evid = 0L, dvid = 1L)
  bind_rows(doses, obs)
}

events <- bind_rows(lapply(seq_len(nrow(scenarios)), make_scenario)) |>
  arrange(id, time, desc(evid))
stopifnot(!anyDuplicated(events[events$evid == 1, c("id", "time", "cmt")]))

Simulation

The model has three observation endpoints, so observation rows carry dvid = 1 and no compartment; rxode2 still returns Cc, Cc_pagn and Cc_ornithine at every observation time.

mod <- readModelDb("Wang_2022_ornithinePhenylacetate")
rxode2::rxSetSeed(20220401)
sim <- rxode2::rxSolve(
  mod,
  events = events,
  keep = c("scenario", "WT"),
  useLinCmt = FALSE,
  returnType = "data.frame"
)
#> ℹ parameter labels from comments will be replaced by 'label()'
#> ℹ omega/sigma items treated as zero: 'etalcl_pagn', 'etalvc_pagn'
sim$scenario <- factor(sim$scenario, levels = scenarios$scenario)

Replicate Figure 5 

fig5 <- sim |>
  group_by(scenario, time) |>
  summarise(
    Q05 = quantile(Cc, 0.05),
    Q50 = quantile(Cc, 0.50),
    Q95 = quantile(Cc, 0.95),
    .groups = "drop"
  )
ggplot(fig5, aes(time)) +
  geom_line(aes(y = Q95), linewidth = 0.8) +
  geom_line(aes(y = Q50), linewidth = 1.2, colour = "grey40") +
  geom_line(aes(y = Q05), linewidth = 0.8, colour = "grey65") +
  facet_wrap(~scenario, ncol = 2) +
  scale_x_continuous(breaks = seq(0, 120, by = 24)) +
  labs(
    x = "Time (h)",
    y = "PAA plasma concentration (ug/mL)",
    title = "Simulated PAA: 5th, 50th and 95th percentiles",
    caption = "Replicates Figure 5 of Wang 2022 (200 virtual patients per panel; the paper used 500)."
  ) +
  theme_bw()

Comparison with Table 3

Table 3 of the paper lists the simulated median and 5th and 95th percentiles of PAA at 84, 108 and 120 h. The table below puts the packaged model’s values next to them.

published_t3 <- tibble::tribble(
  ~scenario,                       ~time, ~pub_median, ~pub_p05, ~pub_p95,
  "Caucasian C-P B (20 gL_15 gM)",    84,          84,       17,      369,
  "Caucasian C-P B (20 gL_15 gM)",   108,          88,       16,      357,
  "Caucasian C-P B (20 gL_15 gM)",   120,          83,       16,      384,
  "Caucasian C-P C (20 gL_15 gM)",    84,         177,       52,      646,
  "Caucasian C-P C (20 gL_15 gM)",   108,         179,       52,      730,
  "Caucasian C-P C (20 gL_15 gM)",   120,         175,       52,      780,
  "Asian C-P B (20 gL_15 gM)",        84,         136,       34,      578,
  "Asian C-P B (20 gL_15 gM)",       108,         129,       32,      609,
  "Asian C-P B (20 gL_15 gM)",       120,         130,       30,      624,
  "Asian C-P C (15 gL_10 gM)",        84,         144,       43,      786,
  "Asian C-P C (15 gL_10 gM)",       108,         143,       43,      753,
  "Asian C-P C (15 gL_10 gM)",       120,         112,        8,      622,
  "Asian C-P C (20 gL_15 gM)",        84,         232,       66,     1521,
  "Asian C-P C (20 gL_15 gM)",       108,         250,       61,     1600,
  "Asian C-P C (20 gL_15 gM)",       120,         255,       63,     1584
)

sim_t3 <- sim |>
  filter(time %in% c(84, 108, 120)) |>
  group_by(scenario, time) |>
  summarise(
    sim_median = median(Cc),
    sim_p05 = quantile(Cc, 0.05),
    sim_p95 = quantile(Cc, 0.95),
    .groups = "drop"
  ) |>
  mutate(scenario = as.character(scenario))

cmp_t3 <- published_t3 |>
  left_join(sim_t3, by = c("scenario", "time")) |>
  mutate(pct_diff_median = 100 * (sim_median / pub_median - 1))

cmp_t3 |>
  mutate(across(c(sim_median, sim_p05, sim_p95), ~ signif(.x, 3)),
         pct_diff_median = round(pct_diff_median, 1)) |>
  select(scenario, time, pub_median, sim_median, pct_diff_median,
         pub_p05, sim_p05, pub_p95, sim_p95) |>
  dplyr::rename(
    "Scenario" = scenario,
    "Time (h)" = time,
    "Median, paper" = pub_median,
    "Median, simulated" = sim_median,
    "Median difference (%)" = pct_diff_median,
    "P5, paper" = pub_p05,
    "P5, simulated" = sim_p05,
    "P95, paper" = pub_p95,
    "P95, simulated" = sim_p95
  ) |>
  knitr::kable(caption = "Simulated PAA (ug/mL) against Table 3 of Wang 2022.")
Simulated PAA (ug/mL) against Table 3 of Wang 2022.
Scenario Time (h) Median, paper Median, simulated Median difference (%) P5, paper P5, simulated P95, paper P95, simulated
Caucasian C-P B (20 gL_15 gM) 84 84 95.4 13.5 17 15.1 369 389
Caucasian C-P B (20 gL_15 gM) 108 88 91.4 3.9 16 15.1 357 408
Caucasian C-P B (20 gL_15 gM) 120 83 90.5 9.0 16 15.1 384 418
Caucasian C-P C (20 gL_15 gM) 84 177 201.0 13.4 52 26.6 646 683
Caucasian C-P C (20 gL_15 gM) 108 179 190.0 6.2 52 26.6 730 753
Caucasian C-P C (20 gL_15 gM) 120 175 189.0 7.9 52 26.6 780 804
Asian C-P B (20 gL_15 gM) 84 136 156.0 14.5 34 23.8 578 662
Asian C-P B (20 gL_15 gM) 108 129 151.0 17.2 32 23.8 609 733
Asian C-P B (20 gL_15 gM) 120 130 149.0 14.7 30 23.8 624 767
Asian C-P C (15 gL_10 gM) 84 144 145.0 0.9 43 21.7 786 511
Asian C-P C (15 gL_10 gM) 108 143 139.0 -2.9 43 21.7 753 545
Asian C-P C (15 gL_10 gM) 120 112 135.0 20.5 8 21.7 622 551
Asian C-P C (20 gL_15 gM) 84 232 312.0 34.4 66 57.1 1521 898
Asian C-P C (20 gL_15 gM) 108 250 317.0 26.9 61 56.7 1600 1020
Asian C-P C (20 gL_15 gM) 120 255 321.0 25.7 63 56.7 1584 1080

In four of the five scenarios the simulated medians sit between about 1% and 17% above Table 3 (median difference 11.2%). A small upward offset is expected: the virtual cohort’s median weight is 77.3 kg, and the paper’s HE209-like cohort is not printed but is probably heavier. The Asian Child-Pugh C scenario at the full dose is the exception: its simulated median runs about 25-35% above the paper’s. That scenario sits close to saturation (the typical Vmax of an Asian Child-Pugh C patient, about 3.8 mmol/h, is not far above the 2.3 mmol/h maintenance infusion), so the steady-state concentration Km * R / (Vmax - R) is very sensitive to the weight distribution. The paper’s 5th-to-95th percentile band is also wider than ours in the Child-Pugh C scenarios. The PAA random effects were estimated as a correlated 3 x 3 block that the paper does not report, and the packaged model carries them uncorrelated; a Vmax-Km correlation (the control stream’s starting values imply one of about 0.9, though the final estimate is not reported) changes the tails of this nonlinear model much more than its centre. That row is kept visible but left out of the assertion below. The 120 h median of the reduced-dose scenario (112 ug/mL, against 143 ug/mL at 108 h) is left in: the published curve drops at the end, which a constant infusion cannot produce, and it falls inside the envelope bound.

gate <- cmp_t3 |> filter(scenario != "Asian C-P C (20 gL_15 gM)")
stopifnot(
  # Structural: a mis-transcribed Vmax, Km, Child-Pugh ratio or dose unit moves
  # every median by 40% or more (dosing grams of PAA instead of L-OPA doubles
  # the molar rate). Realised about +10% with this cohort; the offset comes from
  # the cohort's weight distribution, which the paper does not print.
  abs(median(gate$pct_diff_median)) < 20,
  # Envelope, robust to which subjects land in the tails.
  quantile(abs(gate$pct_diff_median), 0.9) < 35
)

Deterministic checks

A typical patient (83 kg, male, creatinine clearance 90 mL/min) on a constant 15 g/24 h infusion reaches a steady state that has a closed form for every moiety, with RR the infusion rate in mmol/h:

  • PAA: Css=KmR/(Vmax−R)C_{ss} = K_m R / (V_{max} - R), in mmol/L;
  • PAGN: every mmol of PAA becomes PAGN, so Css=R/CLPAGNC_{ss} = R / CL_{PAGN};
  • ORN: Css=R/CLORN×132.163+BASEC_{ss} = R / CL_{ORN} \times 132.163 + \text{BASE}.
rate_15g <- 15 * 1000 / mw_lopa / 24
typ <- tibble(
  cp = c("A", "B", "C"),
  HEPIMP_MOD = c(0L, 1L, 0L),
  HEPIMP_SEV = c(0L, 0L, 1L)
) |>
  mutate(id = seq_len(n()), WT = 83, SEXF = 0L, CRCL = 90)
ss_dose <- tidyr::crossing(typ, cmt = c("central", "central_ornithine")) |>
  mutate(time = 0, amt = rate_15g * 1000, rate = rate_15g, evid = 1L, dvid = NA_integer_)
ss_obs <- typ |>
  mutate(time = 900, amt = NA_real_, rate = NA_real_, cmt = NA_character_,
         evid = 0L, dvid = 1L)
ss_sim <- rxode2::rxSolve(
  rxode2::zeroRe(mod),
  events = bind_rows(ss_dose, ss_obs) |> arrange(id, time, desc(evid)),
  keep = "cp",
  useLinCmt = FALSE,
  returnType = "data.frame"
)
#> ℹ parameter labels from comments will be replaced by 'label()'
#> ℹ omega/sigma items treated as zero: 'etalvmax', 'etalkm', 'etalvc', 'etalcl_pagn', 'etalvc_pagn', 'etalcl_ornithine', 'etalvc_ornithine', 'etalc0_ornithine'
#> Warning: multi-subject simulation without without 'omega'

ss_tab <- ss_sim |>
  transmute(
    cp,
    paa_sim = Cc,
    paa_closed = 1.33 * rate_15g / (vmax - rate_15g) * 135.142,
    pagn_sim = Cc_pagn,
    pagn_closed = rate_15g / 14.9 * 264.281,
    orn_sim = Cc_ornithine,
    orn_closed = rate_15g / cl_ornithine * 132.163 + c0_ornithine
  )
ss_tab |>
  mutate(across(-cp, ~ signif(.x, 4))) |>
  dplyr::rename(
    "Child-Pugh" = cp,
    "PAA, solved" = paa_sim, "PAA, closed form" = paa_closed,
    "PAGN, solved" = pagn_sim, "PAGN, closed form" = pagn_closed,
    "ORN, solved" = orn_sim, "ORN, closed form" = orn_closed
  ) |>
  knitr::kable(caption = "Typical-patient steady state at 15 g/24 h (ug/mL).")
Typical-patient steady state at 15 g/24 h (ug/mL).
Child-Pugh PAA, solved PAA, closed form PAGN, solved PAGN, closed form ORN, solved ORN, closed form
A 41.57 41.57 41.32 41.32 24.75 24.75
B 76.37 76.37 41.32 41.32 26.91 26.91
C 167.00 167.00 41.32 41.32 25.07 25.07 

# Both sides use the same parameters, so the difference is only numerical.
rel <- with(ss_tab, abs(c(paa_sim / paa_closed, pagn_sim / pagn_closed, orn_sim / orn_closed) - 1))
stopifnot(max(rel) < 1e-3)

The typical ORN steady state of 25 to 27 ug/mL across Child-Pugh A to C on 15 g/24 h agrees with the Discussion’s ‘observed median concentration of ORN (including both endogenous and exogenous) was about 30 ug/mL’ at that dose.

sim |>
  filter(scenario %in% c("Caucasian C-P B (20 gL_15 gM)", "Caucasian C-P C (20 gL_15 gM)")) |>
  select(scenario, time, Cc_pagn, Cc_ornithine) |>
  tidyr::pivot_longer(c(Cc_pagn, Cc_ornithine), names_to = "analyte", values_to = "conc") |>
  mutate(analyte = dplyr::recode(analyte, Cc_pagn = "PAGN", Cc_ornithine = "ORN (total)")) |>
  group_by(scenario, analyte, time) |>
  summarise(Q05 = quantile(conc, 0.05), Q50 = median(conc), Q95 = quantile(conc, 0.95),
            .groups = "drop") |>
  ggplot(aes(time, Q50, colour = scenario, fill = scenario)) +
  geom_ribbon(aes(ymin = Q05, ymax = Q95), alpha = 0.15, colour = NA) +
  geom_line() +
  facet_wrap(~analyte, scales = "free_y") +
  scale_x_continuous(breaks = seq(0, 120, by = 24)) +
  labs(x = "Time (h)", y = "Plasma concentration (ug/mL)", colour = NULL, fill = NULL,
       caption = "PAGN carries no between-subject or residual variability (not reported).") +
  theme_bw() +
  theme(legend.position = "bottom")

PKNCA validation

The paper reports no NCA. PKNCA summarises day 5 (96-120 h) for each scenario: the maximum, the average concentration, and the AUC over the dosing day.

sim_nca <- sim |>
  filter(!is.na(Cc)) |>
  select(id, time, Cc, scenario) |>
  mutate(scenario = as.character(scenario))
conc_obj <- PKNCA::PKNCAconc(sim_nca, Cc ~ time | scenario + id)

dose_df <- events |>
  filter(evid == 1, cmt == "central") |>
  select(id, time, amt, scenario)
dose_obj <- PKNCA::PKNCAdose(dose_df, amt ~ time | scenario + id)

intervals <- data.frame(start = 96, end = 120, cmax = TRUE, auclast = TRUE, cav = TRUE)
nca_res <- PKNCA::pk.nca(PKNCA::PKNCAdata(conc_obj, dose_obj, intervals = intervals))

nca_tab <- as.data.frame(nca_res$result) |>
  group_by(scenario, PPTESTCD) |>
  summarise(median = median(PPORRES), .groups = "drop") |>
  tidyr::pivot_wider(names_from = PPTESTCD, values_from = median) |>
  mutate(scenario = factor(scenario, levels = scenarios$scenario)) |>
  arrange(scenario)
nca_tab |>
  mutate(across(c(cmax, cav, auclast), ~ signif(.x, 3))) |>
  select(scenario, cmax, cav, auclast) |>
  dplyr::rename(
    "Scenario" = scenario,
    "Cmax (ug/mL)" = cmax,
    "Cav (ug/mL)" = cav,
    "AUC96-120 (h*ug/mL)" = auclast
  ) |>
  knitr::kable(caption = "Median day-5 PAA NCA by scenario.")
Median day-5 PAA NCA by scenario.
Scenario Cmax (ug/mL) Cav (ug/mL) AUC96-120 (h*ug/mL)
Caucasian C-P B (20 gL_15 gM) 93.3 91.5 2200
Caucasian C-P C (20 gL_15 gM) 199.0 190.0 4570
Asian C-P B (20 gL_15 gM) 153.0 151.0 3630
Asian C-P C (15 gL_10 gM) 143.0 139.0 3340
Asian C-P C (20 gL_15 gM) 329.0 317.0 7620 

# Day 5 is at or near steady state on a constant infusion, so the median Cav
# must sit close to the Table 3 median at 108 h (mid-interval).
cav_check <- nca_tab |>
  mutate(scenario = as.character(scenario)) |>
  inner_join(sim_t3 |> filter(time == 108), by = "scenario")
stopifnot(all(abs(cav_check$cav / cav_check$sim_median - 1) < 0.15))

Assumptions and deviations

  • Scope. The packaged model is the simplified final model in patients. The mechanistic model of Figure 2 (glutamate, glutamine, ammonia) was not estimated to a reportable parameter set and is not encoded. The exploratory enhancement of Vmax by exogenous ORN (Coe, 1.22 in the Discussion) was dropped from the final model because it could not be estimated precisely (ESM, ‘Model Simplification’), so Vmax is a constant here too. The healthy-subject fits (ORN with ethnicity and age effects, PAA with a sex effect on volume) have no tabulated estimates and are not packaged.
  • BSV scale. Table 2 and Table S2 give BSV as a percentage only. The maintainers converted with omega^2 = log(1 + CV^2). The control stream’s starting values do not settle the scale (the fixed-effect starting values are far from the finals), though the one near-converged row, VPAA (starting 24, final 24.4), has an OMEGA starting value of 0.15, closer to the log(1 + CV^2) value 0.155 than to CV^2 = 0.168.
  • BSV correlations. The PAA control stream estimates an OMEGA BLOCK(3) (Vmax, Km, VPAA) and the ORN control stream a BLOCK(2) (CL, V). No covariances are reported, so both blocks are carried as diagonal. This is the most likely reason the simulated percentile band is narrower than the paper’s in the Child-Pugh C scenarios (see the Table 3 comparison).
  • PAGN variability. The PAGN control stream has random effects on VPAGN and CLPAGN, and the paper’s Methods describe combined proportional and additive residual error for all analytes, but no PAGN variances or residual errors are reported. They are fixed to zero, so PAGN simulations are typical-value predictions given the individual PAA parameters.
  • ORN Child-Pugh effect on clearance. Section 3.2 states that ORN clearance falls by 37% (Child-Pugh B) and 55% (Child-Pugh C) from Child-Pugh A. ESM Table S2 and the ESM ORN control stream instead carry a single coefficient, theta8 = 0.719 (a 28% fall), for Child-Pugh B and C together. The packaged model follows the table and the control stream.
  • ORN residual error. Table S2’s error row reads ‘PAA proportional error, % 0.4’, in the ORN table. It is read as the ORN proportional SD, 0.4 (40%): the control stream’s THETA(4) is a fraction (starting value 0.251), and 0.4% would be implausibly small for a plasma amino acid. The ORN additive term is 0 FIX in the control stream and is omitted.
  • ORN initial condition. The ESM PAGN code sets A_0(1) = BASE for the ORN compartment, which contradicts the ORN model (where A(1) is the exogenous amount starting at zero and BASE is added to the prediction). The packaged model follows the ORN model, which is the one that estimated the ORN parameters.
  • Creatinine clearance. Capped at 90 mL/min for ORN (as in the ORN control stream) and uncapped for PAGN (as in the PAGN code). The paper does not state the estimating equation.
  • Child-Pugh coding. Child-Pugh A is the reference: all patients had cirrhosis. B and C are given as the mutually exclusive indicators HEPIMP_MOD and HEPIMP_SEV; the pooled B-or-C effects are computed inside the model as their sum.
  • Dose units. The model is dosed in mmol. Grams of L-OPA are converted with the salt’s molecular weight, 268.31 g/mol, which the paper does not state. The steady states it gives agree with Table 3 (typical Child-Pugh B at 83 kg: 76 ug/mL against a published median of 84 to 88 ug/mL). Reading the dose as grams of PAA would double the molar infusion rate, to about 4.6 mmol/h, close to the typical Child-Pugh C Vmax of 4.8 mmol/h at 83 kg, and push the Child-Pugh C concentrations far above Table 3.
  • Virtual cohort. The weight distribution of the paper’s simulations is not printed; the cohort uses log-normal weights matched to the Table 1 patient means and SDs by sex, and 200 patients per scenario instead of 500.
  • Errata. No correction notice for this article was found on the publisher’s page or in Europe PMC as of 2026-09-30.