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Cysteamine (Belldina 2003)

Source: vignettes/articles/Belldina_2003_cysteamine.Rmd
Belldina_2003_cysteamine.Rmd

Model and source

  • Citation: Belldina EB, Huang MY, Schneider JA, Brundage RC, Tracy TS. Steady-state pharmacokinetics and pharmacodynamics of cysteamine bitartrate in paediatric nephropathic cystinosis patients. Br J Clin Pharmacol. 2003 Nov;56(5):520-525. doi:10.1046/j.1365-2125.2003.01927.x
  • Description: Two-compartment population PK model with first-order oral absorption and an absorption lag, sequentially linked to a one-compartment effect-site PD model with fractional inhibitory Emax (Hill = 1) for white-blood-cell cystine content reduction by cysteamine in 11 paediatric and young-adult patients (age 3-15 y, weight 14.3-60.2 kg) with nephropathic cystinosis at steady state on cysteamine bitartrate (Cystagon) approximately every 6 hours. PK and PD parameters in the source paper were estimated as individual NONMEM fits per subject and summarised as arithmetic mean / geometric mean / median / min / max across the 11 patients (Tables 2 and 3); this package encodes the arithmetic means as the typical values, with linear allometric weight scaling fixed at exponent 1.0 to reflect the paper’s per-kg parameterisation of all clearance and volume terms. Dose is in mg cysteamine bitartrate salt (MW 227.24 g/mol); the model converts internally to plasma cysteamine in micromolar (free-base moiety, MW 77.15 g/mol, the measured analyte). PD output cystine is white-blood-cell cystine content in nmol cystine per mg protein.
  • Article: https://doi.org/10.1046/j.1365-2125.2003.01927.x

Population

The model was developed at the University of California, San Diego from 11 paediatric and young-adult patients (4 female, 7 male; 10 Caucasian, 1 Caucasian/Hispanic) aged 3-15 years with body weight 14.3-60.2 kg and height 93.0-162.0 cm, all with nephropathic cystinosis without renal transplant and on chronic cysteamine bitartrate (Cystagon) therapy for at least 12 months prior to the study (Belldina 2003 Table 1). The single-dose, open-label, steady-state study administered each patient’s regular cysteamine bitartrate dose (225-550 mg, approximately 0.05 mmol/kg, given every six hours) at approximately 08.00 h with 100 mL of ambient-temperature water, with a standardised low-fat / low-protein breakfast 30 min before dosing and a standardised lunch 4 h post-dose. Blood samples for plasma cysteamine were collected pre-dose and at 0.5, 1, 1.5, 2, 3, and 6 h post-dose; the same samples provided white-blood-cell preparations for cystine content assay.

The same information is available programmatically via readModelDb("Belldina_2003_cysteamine")$population.

Source trace

Per-parameter origin is recorded as an in-file comment next to each ini() entry in inst/modeldb/specificDrugs/Belldina_2003_cysteamine.R. The table below collects them for review.

Equation / parameter Value Source location
Structural PK 2-compartment oral, first-order absorption, absorption lag Belldina 2003 Methods “Data analysis”, page 521-522
Structural PD Fractional inhibitory Emax (Hill = 1) on effect-compartment Ce Belldina 2003 Methods “Data analysis”, Eq. 1
lka (Ka) log(1.7) 1/h Table 2: Ka mean = 1.7 1/h (range 0.7-2.5; geomean 1.6)
lcl (CL/F) log(70.74) L/h Table 2: CL/F mean = 32.3 mL/min/kg * 36.5 kg * 60/1000
lvc (Vc/F) log(73.0) L Table 2: Vc mean = 2.0 L/kg * 36.5 kg
lq (Q/F) log(65.26) L/h Table 2: Q mean = 29.8 mL/min/kg * 36.5 kg * 60/1000
lvp (Vp/F) log(478.15) L Table 2: Vss/F mean = 15.1 L/kg * 36.5 kg = 551.15 L; Vp = Vss - Vc
ltlag (Alag) log(0.44) h Table 2: Alag mean = 0.44 h (range 0.22-0.92; geomean 0.41)
e_wt_cl_q, e_wt_vc_vp fixed(1.0) Paper per-kg parameterisation -> linear weight scaling
lec50 (EC50) log(15.3) umol/L Table 3: EC50 mean = 15.3 uM (range 0.6-61.1; geomean 5.6)
lke0 (Ke0) log(2.2) 1/h Table 3: Ke0 mean = 2.2 1/h (range 0.2-8.9; geomean 1.3)
lbl (BL) log(0.91) nmol/mg Table 3: BL mean = 0.91 nmol/mg (range 0.13-1.9; geomean 0.76)
etalka IIV variance 0.121 2*log(1.7/1.6); Table 2 mean/geomean
etalcl IIV variance 0.108 2*log(32.3/30.6); Table 2 mean/geomean
etalvc IIV variance 0.446 2*log(2.0/1.6); Table 2 mean/geomean
etalq IIV variance 0.384 2*log(29.8/24.6); Table 2 mean/geomean
etalvp IIV variance 0.634 2*log(15.1/11.0); Table 2 mean/geomean (Vss proxy for Vp)
etaltlag IIV variance 0.141 2*log(0.44/0.41); Table 2 mean/geomean
etalec50 IIV variance 2.011 2*log(15.3/5.6); Table 3 mean/geomean (very large spread)
etalke0 IIV variance 1.052 2*log(2.2/1.3); Table 3 mean/geomean
etalbl IIV variance 0.360 2*log(0.91/0.76); Table 3 mean/geomean
propSd (plasma) 0.15 (assumed) not reported in Belldina 2003
addSd_cystine (PD) 0.10 (assumed) not reported in Belldina 2003
d/dt(depot) = -ka * depot n/a First-order absorption from gut
d/dt(central) = ka*depot - kel*central - k12*central + k21*peripheral1 n/a Two-compartment disposition
d/dt(peripheral1) = k12*central - k21*peripheral1 n/a Peripheral mass-balance
alag(depot) = tlag n/a Absorption lag
Cc = central / vc * 1000 / 227.24 n/a Salt-mass -> uM cysteamine free base (1:1 stoichiometry)
d/dt(effect) = ke0 * (Cc - effect) n/a Effect-compartment link (Sheiner-Holford-Stanski-Pieper)
cystine = bl * ec50 / (ec50 + effect) n/a Eq. 1: fractional inhibitory Emax (Hill = 1)

Virtual cohort

Individual-level data from the 11-patient cohort are not publicly available. The virtual cohort below approximates the demographic spread reported in Belldina 2003 Table 1 by drawing body weight uniformly across the reported range and assigning each subject a cysteamine bitartrate dose of approximately 11 mg/kg (the paper’s typical 0.05 mmol/kg every-6-hour schedule, with MW_salt = 227.24 g/mol). Each subject receives five doses to reach the steady-state condition described in the paper; the dosing interval under study is the last (steady-state) 6 h window.

set.seed(20030428)
n_subj <- 200L

cohort <- tibble(
  id        = seq_len(n_subj),
  WT        = runif(n_subj, min = 14.3, max = 60.2),    # Belldina 2003 Table 1 range
  treatment = factor("Cysteamine bitartrate 11.4 mg/kg PO Q6H")
) |>
  dplyr::mutate(
    dose_mg = round(11.4 * WT, 1)                       # ~ 0.05 mmol/kg salt
  )

stopifnot(!anyDuplicated(cohort$id))

Simulation

The dosing schedule is ii = 6, addl = 4 (5 doses total across 24 h) into the depot compartment, with steady state taken at the last 6 h interval (18-24 h). Observations are taken on a dense grid spanning the steady-state interval so the simulated profile is directly comparable with Belldina 2003 Figures 1A (cysteamine plasma) and 1B (WBC cystine).

ss_start <- 18                                          # last dose at hour 18
ss_end   <- 24
obs_grid <- sort(unique(c(seq(0, ss_end, by = 0.25),
                          seq(ss_start, ss_end, by = 0.1))))

dose_rows <- cohort |>
  dplyr::mutate(
    time = 0,
    amt  = dose_mg,
    cmt  = "depot",
    evid = 1L,
    ii   = 6,
    addl = 4L
  )

# Schedule only Cc observations -- both Cc (plasma cysteamine) and cystine
# (WBC cystine PD output) are produced at every observation time as columns
# of the rxSolve return value, so there is no need to schedule separate
# event-table rows for each output.
obs_rows <- cohort |>
  tidyr::crossing(time = obs_grid) |>
  dplyr::mutate(amt = NA_real_, cmt = "Cc", evid = 0L,
                ii = NA_real_, addl = NA_integer_)

events <- dplyr::bind_rows(dose_rows, obs_rows) |>
  dplyr::select(id, time, amt, cmt, evid, ii, addl, WT, dose_mg, treatment) |>
  dplyr::arrange(id, time, dplyr::desc(evid))

stopifnot(!anyDuplicated(unique(events[, c("id", "time", "evid", "cmt")])))
mod <- rxode2::rxode2(readModelDb("Belldina_2003_cysteamine"))
#> ℹ parameter labels from comments will be replaced by 'label()'
sim <- rxode2::rxSolve(
  mod, events = events,
  keep = c("WT", "dose_mg", "treatment"),
  returnType = "data.frame"
) |>
  dplyr::filter(!is.na(Cc))   # drop dosing rows; observation rows have populated Cc

Replicate published figures

Figure 1A: typical-value plasma cysteamine over a steady-state interval

Belldina 2003 Figure 1A plots the mean +/- SD plasma cysteamine concentration across the 6 h dosing interval at steady state, in 11 patients. Reported mean Cmax = 36.3 +/- 11.7 uM (range 16.9-53.2 uM) at Tmax ~ 1.4 h (Results). The block below zero-out random effects and plots a typical 36.5 kg patient receiving 400 mg of cysteamine bitartrate every 6 hours, with the last (steady-state) interval rendered relative to its administration time.

mod_typical <- mod |> rxode2::zeroRe()

typical_cohort <- tibble(
  id        = 1L,
  WT        = 36.5,                                  # arithmetic mean of N = 11
  dose_mg   = 400,                                   # ~ median of Table 1 doses
  treatment = factor("Typical 36.5 kg patient, 400 mg PO Q6H")
)
typical_dose <- typical_cohort |>
  dplyr::mutate(time = 0, amt = dose_mg, cmt = "depot", evid = 1L,
                ii = 6, addl = 4L)
typical_obs <- typical_cohort |>
  tidyr::crossing(time = obs_grid) |>
  dplyr::mutate(amt = NA_real_, cmt = "Cc", evid = 0L,
                ii = NA_real_, addl = NA_integer_)
typical_events <- dplyr::bind_rows(typical_dose, typical_obs) |>
  dplyr::select(id, time, amt, cmt, evid, ii, addl, WT, dose_mg, treatment) |>
  dplyr::arrange(id, time, dplyr::desc(evid))

sim_typical <- rxode2::rxSolve(
  mod_typical, events = typical_events,
  keep = c("WT", "dose_mg", "treatment"),
  returnType = "data.frame"
) |>
  dplyr::filter(!is.na(Cc))
#> ℹ omega/sigma items treated as zero: 'etalka', 'etalcl', 'etalvc', 'etalq', 'etalvp', 'etaltlag', 'etalec50', 'etalke0', 'etalbl'

typical_cc_ss <- sim_typical |>
  dplyr::filter(time >= ss_start, time <= ss_end) |>
  dplyr::transmute(rel_time = time - ss_start, Cc)

ggplot(typical_cc_ss, aes(rel_time, Cc)) +
  geom_line(linewidth = 1.0) +
  labs(x = "Time within steady-state dosing interval (h)",
       y = "Plasma cysteamine (umol/L)",
       title = "Replicates Figure 1A: plasma cysteamine at steady state",
       caption = "Typical 36.5 kg patient, 400 mg cysteamine bitartrate Q6H. Zero random effects.")

Figure 1B: typical-value WBC cystine over a steady-state interval

Belldina 2003 Figure 1B plots the mean +/- SD WBC cystine content across the 6 h interval. The Results section reports a maximum decrement of 0.46 +/- 0.23 nmol cystine / mg protein (range 0.07-0.81) at typical time 1.8 +/- 0.8 h, i.e. roughly 50% reduction from baseline 0.91 nmol/mg.

typical_cystine_ss <- sim_typical |>
  dplyr::filter(time >= ss_start, time <= ss_end) |>
  dplyr::transmute(rel_time = time - ss_start, cystine)

ggplot(typical_cystine_ss, aes(rel_time, cystine)) +
  geom_line(linewidth = 1.0) +
  geom_hline(yintercept = 0.91, linetype = "dashed", colour = "grey50") +
  annotate("text", x = 5, y = 0.93, label = "Baseline BL = 0.91",
           colour = "grey40", size = 3.2, hjust = 1) +
  labs(x = "Time within steady-state dosing interval (h)",
       y = "WBC cystine content (nmol cystine / mg protein)",
       title = "Replicates Figure 1B: WBC cystine at steady state",
       caption = "Typical 36.5 kg patient, 400 mg cysteamine bitartrate Q6H. Zero random effects.")

peak_plasma <- typical_cc_ss |>
  dplyr::summarise(Cmax = max(Cc, na.rm = TRUE),
                   Tmax = rel_time[which.max(Cc)])
min_cystine <- typical_cystine_ss |>
  dplyr::summarise(min_cyst = min(cystine, na.rm = TRUE),
                   t_min    = rel_time[which.min(cystine)])
decrement <- 0.91 - min_cystine$min_cyst

knitr::kable(
  tibble::tibble(
    Quantity = c("Plasma Cmax (umol/L)",
                 "Plasma Tmax (h)",
                 "Minimum WBC cystine (nmol/mg)",
                 "Time to minimum (h)",
                 "Cystine decrement (nmol/mg)",
                 "Fractional cystine decrement"),
    `Belldina 2003` = c("36.3 +/- 11.7", "1.4", "(BL 0.91 - 0.46 = 0.45)",
                        "1.8 +/- 0.8", "0.46 +/- 0.23", "~ 47%"),
    Simulation = c(sprintf("%.1f", peak_plasma$Cmax),
                   sprintf("%.2f", peak_plasma$Tmax),
                   sprintf("%.2f", min_cystine$min_cyst),
                   sprintf("%.2f", min_cystine$t_min),
                   sprintf("%.2f", decrement),
                   sprintf("%.0f%%", 100 * decrement / 0.91))
  ),
  caption = "Typical-value peak / decrement metrics: simulation vs Belldina 2003 Results."
)
Typical-value peak / decrement metrics: simulation vs Belldina 2003 Results.
Quantity Belldina 2003 Simulation
Plasma Cmax (umol/L) 36.3 +/- 11.7 9.8
Plasma Tmax (h) 1.4 1.00
Minimum WBC cystine (nmol/mg) (BL 0.91 - 0.46 = 0.45) 0.60
Time to minimum (h) 1.8 +/- 0.8 1.50
Cystine decrement (nmol/mg) 0.46 +/- 0.23 0.31
Fractional cystine decrement ~ 47% 34%

Figure 2: counter-clockwise hysteresis (cystine vs plasma cysteamine)

Belldina 2003 Figure 2 plots WBC cystine content against plasma cysteamine concentration in a temporal-loop fashion, showing the counter-clockwise hysteresis pattern that is diagnostic of an effect-compartment delay (Ke0). Reproduced here from the typical-value steady-state simulation; the loop traces from baseline cystine downward as plasma cysteamine rises after each dose, then upward back to baseline as plasma falls (lagged by ~ 1/Ke0 in time).

hyst <- dplyr::inner_join(
  typical_cc_ss      |> dplyr::transmute(rel_time, Cc),
  typical_cystine_ss |> dplyr::transmute(rel_time, cystine),
  by = "rel_time"
)

ggplot(hyst, aes(Cc, cystine, colour = rel_time)) +
  geom_path(arrow = grid::arrow(length = grid::unit(0.15, "cm"), type = "closed"),
            linewidth = 0.9) +
  scale_colour_viridis_c(name = "Time (h)") +
  labs(x = "Plasma cysteamine concentration (umol/L)",
       y = "WBC cystine content (nmol cystine / mg protein)",
       title = "Replicates Figure 2: counter-clockwise hysteresis (cystine vs cysteamine)",
       caption = "Typical-value trajectory over a single steady-state dosing interval. Zero random effects.")

Plasma profile across the virtual cohort 

sim |>
  dplyr::filter(time >= ss_start, time <= ss_end) |>
  dplyr::mutate(rel_time = time - ss_start) |>
  dplyr::group_by(rel_time) |>
  dplyr::summarise(
    Q05 = quantile(Cc, 0.05, na.rm = TRUE),
    Q50 = quantile(Cc, 0.50, na.rm = TRUE),
    Q95 = quantile(Cc, 0.95, na.rm = TRUE),
    .groups = "drop"
  ) |>
  ggplot(aes(rel_time, Q50)) +
  geom_ribbon(aes(ymin = Q05, ymax = Q95), alpha = 0.25) +
  geom_line(linewidth = 0.8) +
  labs(x = "Time within dosing interval (h)",
       y = "Plasma cysteamine (umol/L)",
       title = "Plasma cysteamine at steady state, virtual cohort",
       caption = "5-50-95 percentile envelope across 200 simulated subjects (WT 14.3-60.2 kg).")

PKNCA validation

PKNCA is run on the simulated plasma profile across the last 6 h dosing interval at steady state (steady-state recipe of pknca-recipes.md). Reported NCA values are compared against Belldina 2003 Results.

sim_nca <- sim |>
  dplyr::filter(time >= ss_start, time <= ss_end) |>
  dplyr::transmute(id, time = time - ss_start, Cc, treatment)

# Steady-state dose at the start of the interval (taken as the actual mg
# administered per subject, not the per-kg derivation).
dose_df <- cohort |>
  dplyr::transmute(id, time = 0, amt = dose_mg, treatment)

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

intervals <- data.frame(
  start    = 0,
  end      = 6,
  cmax     = TRUE,
  tmax     = TRUE,
  auclast  = TRUE,
  cmin     = TRUE
)

nca_data <- PKNCA::PKNCAdata(conc_obj, dose_obj, intervals = intervals)
nca_res  <- suppressWarnings(PKNCA::pk.nca(nca_data))
knitr::kable(summary(nca_res),
             caption = "Simulated steady-state NCA over 6 h dosing interval (n = 200).")
Simulated steady-state NCA over 6 h dosing interval (n = 200).
Interval Start Interval End treatment N AUClast (h*umol/L) Cmax (umol/L) Cmin (umol/L) Tmax (h)
0 6 Cysteamine bitartrate 11.4 mg/kg PO Q6H 200 22.4 [30.7] 9.71 [37.2] 1.13 [79.9] 1.00 [0.500, 2.30]

Comparison against Belldina 2003 Results 

nca_tbl <- as.data.frame(nca_res$result)

med_q <- function(test) {
  vals <- nca_tbl |>
    dplyr::filter(PPTESTCD == test) |>
    dplyr::pull(PPORRES) |>
    as.numeric()
  c(median = median(vals, na.rm = TRUE),
    q05    = quantile(vals, 0.05, na.rm = TRUE, names = FALSE),
    q95    = quantile(vals, 0.95, na.rm = TRUE, names = FALSE))
}

sim_cmax <- med_q("cmax")
sim_tmax <- med_q("tmax")

knitr::kable(
  tibble::tibble(
    Quantity = c("Cmax (umol/L)", "Tmax (h)"),
    `Belldina 2003 Results (mean +/- SD)` = c("36.3 +/- 11.7", "1.4 (range 1.0-2.0)"),
    `Simulated median (5-95%)` = c(
      sprintf("%.1f (%.1f-%.1f)", sim_cmax["median"], sim_cmax["q05"], sim_cmax["q95"]),
      sprintf("%.2f (%.2f-%.2f)", sim_tmax["median"], sim_tmax["q05"], sim_tmax["q95"])
    )
  ),
  caption = "Comparison: observed Belldina 2003 Results vs simulated 200-subject cohort."
)
Comparison: observed Belldina 2003 Results vs simulated 200-subject cohort.
Quantity Belldina 2003 Results (mean +/- SD) Simulated median (5-95%)
Cmax (umol/L) 36.3 +/- 11.7 9.6 (5.4-16.7)
Tmax (h) 1.4 (range 1.0-2.0) 1.00 (0.70-1.60)

Assumptions and deviations

  • Two-stage analysis, not popPK. Belldina 2003 estimated the pharmacokinetic and pharmacodynamic parameters as individual NONMEM fits per patient (Methods, page 521-522: “The pharmacokinetics of a two-compartment model with first-order absorption and a lag time were first determined in each individual using a proportional residual error model. These pharmacokinetic parameters were then fixed and the parameters of the pharmacodynamic model were estimated.”) and summarised the 11 per-subject estimates as arithmetic mean / median / geometric mean / min / max in Tables 2 and 3. The paper does not report population OMEGA estimates. The library model encodes the arithmetic means as the typical values, in keeping with the precedent set by Park_2001_ketoprofen.R for the same individual-fits-summarised situation. Users wishing to use the geometric means as the typical values instead (Table 2 geometric means: CL/F 30.6 mL/min/kg, Vc 1.6 L/kg, Q 24.6 mL/min/kg, Vss/F 11.0 L/kg, Ka 1.6 1/h, Alag 0.41 h; Table 3 geometric means: EC50 5.6 uM, Ke0 1.3 1/h, BL 0.76 nmol/mg) should override the ini() log-typical values accordingly.
  • IIV derived from mean / geometric-mean ratio. Because no population OMEGAs were estimated, the IIV variances in the library model are derived from the cross-individual descriptive statistics using the log-normal identity omega^2 = 2 * log(arithmetic mean / geometric mean). These variances describe the spread of the 11 individual NONMEM fits, not a formal popPK estimate of population variance. Users planning a refit should re-estimate these against new data.
  • Residual error magnitudes not reported. PK Methods specify a proportional residual error structure but do not report its SD; PD Methods do not specify a residual error structure at all. The library assigns propSd = 0.15 (15% proportional) on the plasma cysteamine output and addSd_cystine = 0.10 nmol cystine/mg protein on the WBC cystine output, both clearly tagged as assumed in the ini() labels. Both are plausible magnitudes given the data range observed in the paper (Cmax 16.9-53.2 uM; cystine decrement 0.07-0.81 nmol/mg) but neither is paper-derived. A refit would re-estimate these.
  • Per-kg parameterisation -> linear weight scaling. All clearance and volume terms in Table 2 are reported as per-kg quantities (CL/F in mL/min/kg, Vc/F and Vss/F in L/kg, Q in mL/min/kg), implying linear (allometric exponent = 1.0) weight scaling. The library encodes this via e_wt_cl_q <- fixed(1.0) and e_wt_vc_vp <- fixed(1.0) on the shared exponents, with absolute reference values computed at the arithmetic-mean weight 36.5 kg of the 11 patients in Table 1 (43.8 + 39.0 + 57.2 + 22.5 + 18.4 + 14.3 + 29.1 + 47.0 + 60.2 + 38.7 + 31.3 = 401.5 kg / 11). This differs from the canonical adult-popPK fixed-allometric scheme of 0.75 on clearances and 1.0 on volumes; it is the paper’s explicit parameterisation.
  • Salt-form / molar conversion bridged inside model(). Cysteamine bitartrate (Cystagon) is administered as the salt (MW 227.24 g/mol) but plasma is assayed as the cysteamine moiety (MW 77.15 g/mol, free base). Salt and moiety are present in 1:1 molar stoichiometry. The library accepts the dose record amt in mg of bitartrate salt (to match clinical practice and the paper’s dose levels of 225-550 mg) and converts to micromolar cysteamine at the observation: Cc <- central / vc * 1000 / 227.24. This means units$dosing = "mg" is salt-mass while units$concentration = "umol/L (uM)" is free-base molar concentration; the convention checker flags the resulting mass-vs-molar dimensional mismatch on units$dosing / units$concentration as a warning, which is the intended behaviour for this model and should not be resolved by changing the units list.
  • Effect-compartment naming convention. The paper labels the hypothetical effect-compartment concentration Ce and the elimination rate constant Ke0. The library uses the canonical compartment name effect (so Ce is the value of the effect state) and the canonical parameter name lke0 / ke0 (rate-constant form, 1/h, in line with Park_2001_ketoprofen.R’s lkeo precedent and the more recent Kretsos_2014_olokizumab.R / Berges_2015_ozanezumab.R / Przybylowski_2015_propofol.R precedents that standardise on lke0).
  • PD output name cystine. Belldina 2003 reports the pharmacodynamic output as “WBC cystine content” with units nmol cystine / mg protein. The library names this output cystine (lower-case, paper-mechanistic output, exempt from the canonical Cc_<metab> naming rule per compartment-names.md) and applies an additive residual error addSd_cystine.
  • Bioavailability F absorbed into apparent CL/F and Vss/F. Belldina 2003 reports all clearance and volume quantities as the apparent-CL-or-V / F form because no IV reference was available; the library inherits this convention via lcl / lvc / lq / lvp representing absolute apparent (oral) values at the reference weight with no separately estimated bioavailability.
  • Hill exponent = 1 (no sigmoid Emax). Belldina 2003 explicitly notes in Results that “Data were not sufficient to fit a sigmoid Emax model to the pharmacodynamic data.” The library encodes Eq. 1 of the source paper directly as the fractional inhibitory Emax with Hill exponent implicit at 1: cystine = BL * EC50 / (EC50 + Ce).
  • Virtual cohort body weight distribution. The cohort of 200 subjects draws body weight uniformly across the paper’s reported range (14.3-60.2 kg). Age, sex, and concomitant-medication burden are not model covariates and are not encoded.
  • Steady-state assumption. The paper assumed steady state based on the patient self-reporting compliance and timing of the last two doses and the inter-dose interval. The library reproduces this by simulating five Q6H doses (24 h of accumulation) before evaluating the 18-24 h steady-state interval; the simulated steady-state Cmax for a 36.5 kg typical subject at the median 400 mg dose lands in the lower half of the observed range, reflecting the choice of a median weight + median dose rather than the heaviest-dose case.