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[68Ga]Ga- and [177Lu]Lu-HA-DOTATATE theranostics (Siebinga 2023)

Source: vignettes/articles/Siebinga_2023_hadotatate.Rmd
Siebinga_2023_hadotatate.Rmd

Model and source

This paper develops two semi-physiological population PK models that share a single six-compartment structure: one for the diagnostic radioligand [68Ga]Ga-HA-DOTATATE and one for the therapeutic radioligand [177Lu]Lu-HA-DOTATATE. They are packaged as two model files (the authors built them as two models, with different fu, different k10, a different placement of interindividual variability, and five parameters estimated as fold differences), and documented in this one vignette.

  • Citation: Siebinga H, de Wit-van der Veen BJ, Beijnen JH, Stokkel MPM, Dorlo TPC, Huitema ADR, Hendrikx JJMA. Predicting [177Lu]Lu-HA-DOTATATE kidney and tumor accumulation based on [68Ga]Ga-HA-DOTATATE diagnostic imaging using semi-physiological population pharmacokinetic modeling. EJNMMI Phys. 2023;10(1):48. doi:10.1186/s40658-023-00565-4
  • Article: https://doi.org/10.1186/s40658-023-00565-4
  • Diagnostic model: Siebinga_2023_ga68hadotatate
  • Therapeutic model: Siebinga_2023_lu177hadotatate

The upstream whole-body PBPK model that the structural parameters were fixed from is Siebinga et al., EJNMMI Res. 2023;13:8, https://doi.org/10.1186/s13550-023-00958-7.

Structure

Compartments one to six are blood, spleen, kidney, tumor lesions, a lumped SSTR-expressing organ compartment (sstr: lungs, pancreas, stomach, thyroid and liver) and a lumped rest compartment (other). Every transfer is unidirectional blood-to-tissue: Table 2 reports no return rate constants (k21, k31, k41, k51, k61) and every arrow in Figure 2 other than k10 leaves the system from a tissue.

Uptake into the four SSTR-expressing compartments follows Equation 1,

dA/dt = kin * fu * A_blood * (1 - A / bmax) - kout * A

so the blood-to-tissue flux is gated by the unoccupied fraction of the receptor pool and only the unbound fraction is available. bmax is reported as a concentration and converted to an amount by multiplying by the compartment volume (“B MAX amounts were calculated based on the compartment volume”), which is why a larger tumor automatically carries a larger binding capacity.

Population

Nine evaluable patients with neuroendocrine tumors (ten enrolled; patient one excluded because every lesion was under 2 cm in diameter, and patient two’s kidney data excluded because only one kidney could be quantified). Median (range) age 70 years (44-76), weight 75.0 kg (55.0-108), height 174 cm (160-189), creatinine clearance 68.8 mL/min (53.6-111); 5 of 9 (56%) female (Table 1).

Each patient received a diagnostic [68Ga]Ga-HA-DOTATATE PET/CT at approximately 45 min post-injection (median 96.0 MBq, 5.23 ug peptide) within six months before the first [177Lu]Lu-HA-DOTATATE therapy cycle (median 7271 MBq, 151 ug peptide), followed by planar scintigraphy at 0.5, 4, 24 and 72 h plus SPECT/CT at 24 h. No blood samples were drawn. Median (range) target-lesion tumor volume was 80.0 mL (7.81-212) and total tumor volume 283 mL (22.4-644).

The same information is available programmatically via readModelDb("Siebinga_2023_lu177hadotatate")()$population.

Source trace

Per-parameter provenance is recorded as an in-file comment next to each ini() entry in inst/modeldb/specificDrugs/Siebinga_2023_ga68hadotatate.R and inst/modeldb/specificDrugs/Siebinga_2023_lu177hadotatate.R. Collected here for review. “Fixed” and “estimated” follow Table 2, whose header states that an RSE is given for estimated values only.

Equation / parameter [68Ga]Ga- [177Lu]Lu- Source location
Six-compartment structure, unidirectional transfers n/a n/a Figure 2; Methods “Semi-physiological PK model”
Capacity-limited uptake dA/dt = kin*fu*A_blood*(1 - A/bmax) - kout*A n/a n/a Equation 1, p. 5
Exponential IIV P_i = P_pop * exp(eta_i) n/a n/a Equation 2, p. 6
Proportional RUV C_obs = C_pred * (1 + eps) n/a n/a Equation 3, p. 6
Tumor-sink effect k12_cov = k12_pop * exp(0.4 * (-V_tumor_total)) fixed fixed Equation 4, p. 6
Tumor-burden power effect k14_cov = k14_pop * (V_tumor_cmt / V_tumor_cmt_median)^eff fixed fixed Equation 5, p. 6
kel (k10, 1/h) 0.25 fixed 0.575 fixed Table 2; k10 for [177Lu] from CL 2.3 L/h (Puszkiel 2019, ref 31) divided by V1 = 4 L
kin_spleen (k12, 1/h) 0.21 fixed 0.0607 (0.29-fold, RSE 15%) Table 2
kin_kidney (k13, 1/h) 0.22 fixed 0.107 (0.49-fold, RSE 15%) Table 2
kin_tumor (k14, 1/h) 0.11 fixed 0.157 (1.43-fold, RSE 14%) Table 2
kin_sstr (k15, 1/h) 2.5 fixed 2.5 fixed Table 2
kin_other (k16, 1/h) 1 fixed 1 fixed Table 2
kdeg_spleen / kdeg_kidney / kdeg_sstr / kdeg_other (1/h) 0.01 fixed 0.01 fixed Table 2; Methods “fixed to 0.01 h-1”
kdeg_tumor (k40, 1/h) 0.01 fixed 0.00375 (0.38-fold, RSE 35%) Table 2
lvc (V1, L) 4 fixed 4 fixed Table 2; organ volumes from ICRP Publication 89
v_spleen / v_kidney / v_sstr / v_other (L) 0.21 / 0.3 / 4 / 50 same Table 2 (V2, V3, V5, V6)
v_tumor (L) TUM_VOL_TARGET/1000 same Methods: “The tumor compartment volume was based on individual measured tumor volumes”
fu 0.69 fixed 0.57 fixed Table 2; [177Lu] value from Lubberink 2020 (ref 35)
lbmax_spleen (nmol/L) 16.7 fixed 16.7 fixed Table 2, BMAX compartment 2
lbmax_kidney (nmol/L) 6.7 fixed 6.7 fixed Table 2, BMAX compartment 3
lbmax_tumor (nmol/L) 30 fixed 30 fixed Table 2, BMAX compartment 4
lbmax_sstr (nmol/L) 2.4 fixed 2.4 fixed Table 2, BMAX compartment 5
e_tum_vol_total_kin_spleen 0.4 fixed 0.4 fixed Equation 4 coefficient; “the extent of this effect was based on previous PBPK simulations”
e_tum_vol_target_kin_tumor 1 fixed 0.67 (RSE 17%) Table 2 “Tumor volume on k14”
IIV on kel (CV%) 31.6 fixed 31.6 fixed Table 2 IIV k10
IIV, 50% CV on kin_spleen, kin_kidney, kin_tumor on bmax_spleen, bmax_kidney, bmax_tumor Table 2 IIV rows + footnote **
IIV, 31.6% CV on kin_sstr on bmax_sstr Table 2 IIV row + footnote **
propSd_* (proportional RUV) 0.316 fixed 0.316 fixed Table 2 RUV proportional error 31.6% CV
mw (g/mol) 1628.5 1628.5 Not in this paper - Siebinga 2023 EJNMMI Res 13:8, Table 3 “Molecular weight”

Virtual cohort

Original observed data are not publicly available. The simulations below use a virtual population whose tumor-volume distribution reproduces the Table 1 marginal medians and ranges.

set.seed(20230848)

n_sub <- 120

# Table 1 reports the two tumor volumes only as marginal median (range), with no
# joint distribution and no distributional family. Target-lesion volume is drawn
# log-uniformly across the observed range so the reported extremes are honoured
# without inventing a shape; total tumor volume is then generated from the
# median ratio 283/80 with modest multiplicative scatter and clipped to its own
# reported range. See "Assumptions and deviations".
log_unif <- function(n, lo, hi) exp(stats::runif(n, log(lo), log(hi)))

subjects <- tibble::tibble(
  id = seq_len(n_sub),
  TUM_VOL_TARGET = log_unif(n_sub, 7.81, 212),
  TUM_VOL_TOTAL = pmin(
    644,
    pmax(22.4, TUM_VOL_TARGET * (283 / 80) * exp(stats::rnorm(n_sub, 0, 0.25)))
  )
)

# Per-agent dosing (Table 1 median peptide amounts) and imaging windows. The
# diagnostic scan is a single acquisition at ~45 min; the therapy scans run to
# 72 h. Observation rows point at ODE STATE names (never at an algebraic
# observable such as Cc) and carry a dvid, which this multi-endpoint model
# requires.
make_events <- function(dose_ug, tmax, n_obs, id_offset = 0L) {
  s <- subjects |> dplyr::mutate(id = id + id_offset)
  dosing <- s |>
    dplyr::mutate(time = 0, amt = dose_ug, evid = 1L,
                  cmt = "blood", dvid = NA_integer_)
  obs <- s |>
    tidyr::crossing(time = seq(0, tmax, length.out = n_obs)) |>
    dplyr::mutate(amt = NA_real_, evid = 0L,
                  cmt = "tumor", dvid = 1L)
  dplyr::bind_rows(dosing, obs) |>
    dplyr::arrange(id, time, dplyr::desc(evid))
}

ev_ga <- make_events(dose_ug = 5.23, tmax = 2, n_obs = 121, id_offset = 0L)
ev_lu <- make_events(dose_ug = 151, tmax = 72, n_obs = 289, id_offset = 1000L)

stopifnot(!anyDuplicated(unique(ev_ga[, c("id", "time", "evid")])))
stopifnot(!anyDuplicated(unique(ev_lu[, c("id", "time", "evid")])))

Simulation 

mod_ga <- readModelDb("Siebinga_2023_ga68hadotatate")
mod_lu <- readModelDb("Siebinga_2023_lu177hadotatate")

# useLinCmt = FALSE: rxode2's automatic ODE -> linCmt conversion corrupts the
# dvid -> cmt mapping for multi-output models like this one.
sim_ga <- rxode2::rxSolve(
  mod_ga, ev_ga,
  keep = c("TUM_VOL_TARGET", "TUM_VOL_TOTAL"),
  useLinCmt = FALSE, returnType = "data.frame"
)
#> ℹ parameter labels from comments will be replaced by 'label()'
sim_lu <- rxode2::rxSolve(
  mod_lu, ev_lu,
  keep = c("TUM_VOL_TARGET", "TUM_VOL_TOTAL"),
  useLinCmt = FALSE, returnType = "data.frame"
)
#> ℹ parameter labels from comments will be replaced by 'label()'

# rxSolve occasionally drops subjects silently; assert the count survived.
stopifnot(dplyr::n_distinct(sim_ga$id) == n_sub)
stopifnot(dplyr::n_distinct(sim_lu$id) == n_sub)

Replicate published figures

Figure 3 - concentration-time profiles in spleen, kidney and tumor

Figure 3 of Siebinga 2023 shows the individually observed decay-corrected peptide concentrations for both radiopharmaceuticals, stratified by patient. The panels below are the corresponding simulated population profiles (median with 5th-95th percentile band).

to_long <- function(sim, agent) {
  sim |>
    dplyr::select(id, time, Cspleen, Ckidney, Ctumor) |>
    tidyr::pivot_longer(
      c(Cspleen, Ckidney, Ctumor),
      names_to = "compartment", values_to = "conc"
    ) |>
    dplyr::mutate(
      agent = agent,
      compartment = dplyr::recode(compartment,
        Cspleen = "Spleen", Ckidney = "Kidney", Ctumor = "Tumor")
    )
}

prof <- dplyr::bind_rows(
  to_long(sim_ga, "[68Ga]Ga-HA-DOTATATE"),
  to_long(sim_lu, "[177Lu]Lu-HA-DOTATATE")
) |>
  dplyr::filter(time > 0) |>
  dplyr::group_by(agent, compartment, time) |>
  dplyr::summarise(
    Q05 = stats::quantile(conc, 0.05, na.rm = TRUE),
    Q50 = stats::quantile(conc, 0.50, na.rm = TRUE),
    Q95 = stats::quantile(conc, 0.95, na.rm = TRUE),
    .groups = "drop"
  )

ggplot(prof, aes(time, Q50)) +
  geom_ribbon(aes(ymin = Q05, ymax = Q95), alpha = 0.25) +
  geom_line() +
  facet_wrap(~agent + compartment, scales = "free", ncol = 3) +
  scale_y_log10() +
  labs(
    x = "Time (h)", y = "Peptide concentration (ug/L)",
    title = "Simulated concentration-time profiles",
    caption = "Replicates Figure 3 of Siebinga 2023 (median with 5th-95th percentile band)."
  )

Maximum receptor occupancy after [177Lu]Lu-HA-DOTATATE

The Results section reports that maximum receptor occupancy after [177Lu]Lu-HA-DOTATATE “ranged from 39 to 55% for spleen, 71-97% for kidney and 78-100% for tumors”. This is a direct, quantitative check on the capacity-limited uptake mechanism, so it is reproduced here from the typical-value profile of the median patient.

mw <- 1628.5

typ <- tibble::tibble(
  id = 1L, TUM_VOL_TARGET = 80.0, TUM_VOL_TOTAL = 283
)
ev_typ <- dplyr::bind_rows(
  typ |> dplyr::mutate(time = 0, amt = 151, evid = 1L,
                       cmt = "blood", dvid = NA_integer_),
  typ |> tidyr::crossing(time = seq(0, 72, length.out = 1441)) |>
    dplyr::mutate(amt = NA_real_, evid = 0L, cmt = "tumor", dvid = 1L)
) |>
  dplyr::arrange(time, dplyr::desc(evid))

sim_typ <- rxode2::rxSolve(
  rxode2::zeroRe(mod_lu), ev_typ,
  useLinCmt = FALSE, returnType = "data.frame"
)
#> ℹ parameter labels from comments will be replaced by 'label()'
#> ℹ omega/sigma items treated as zero: 'etalkel', 'etalbmax_spleen', 'etalbmax_kidney', 'etalbmax_tumor', 'etalbmax_sstr'

# bmax as an amount (ug) = concentration (nmol/L) * mw/1000 * volume (L)
bmax_amt <- c(
  Spleen = 16.7 * mw / 1000 * 0.21,
  Kidney = 6.7 * mw / 1000 * 0.30,
  Tumor = 30.0 * mw / 1000 * (80.0 / 1000)
)

occupancy <- tibble::tibble(
  Compartment = c("Spleen", "Kidney", "Tumor"),
  `Simulated maximum occupancy (%)` = round(100 * c(
    max(sim_typ$spleen) / bmax_amt[["Spleen"]],
    max(sim_typ$kidney) / bmax_amt[["Kidney"]],
    max(sim_typ$tumor) / bmax_amt[["Tumor"]]
  ), 1),
  `Published range (%)` = c("39-55", "71-97", "78-100")
)

knitr::kable(
  occupancy,
  caption = "Maximum receptor occupancy after [177Lu]Lu-HA-DOTATATE, typical patient (target-lesion volume 80.0 mL, total tumor volume 283 mL, 151 ug peptide). Published values from Results, 'Semi-physiological PK model'."
)
Maximum receptor occupancy after [177Lu]Lu-HA-DOTATATE, typical patient (target-lesion volume 80.0 mL, total tumor volume 283 mL, 151 ug peptide). Published values from Results, ‘Semi-physiological PK model’.
Compartment Simulated maximum occupancy (%) Published range (%)
Spleen 43.2 39-55
Kidney 84.8 71-97
Tumor 90.9 78-100

The paper’s contrasting statement for the diagnostic agent is that, at the very low administered peptide amount, “receptors are not close to full occupancy” – which is the stated rationale for placing interindividual variability on the uptake rate constants for [68Ga] but on the receptor expressions for [177Lu].

ev_typ_ga <- dplyr::bind_rows(
  typ |> dplyr::mutate(time = 0, amt = 5.23, evid = 1L,
                       cmt = "blood", dvid = NA_integer_),
  typ |> tidyr::crossing(time = seq(0, 2, length.out = 241)) |>
    dplyr::mutate(amt = NA_real_, evid = 0L, cmt = "tumor", dvid = 1L)
) |>
  dplyr::arrange(time, dplyr::desc(evid))

sim_typ_ga <- rxode2::rxSolve(
  rxode2::zeroRe(mod_ga), ev_typ_ga,
  useLinCmt = FALSE, returnType = "data.frame"
)
#> ℹ parameter labels from comments will be replaced by 'label()'
#> ℹ omega/sigma items treated as zero: 'etalkel', 'etalkin_spleen', 'etalkin_kidney', 'etalkin_tumor', 'etalkin_sstr'
i45 <- which.min(abs(sim_typ_ga$time - 0.75))

tibble::tibble(
  Compartment = c("Spleen", "Kidney", "Tumor"),
  `Occupancy at the 45-min scan (%)` = round(100 * c(
    sim_typ_ga$spleen[i45] / bmax_amt[["Spleen"]],
    sim_typ_ga$kidney[i45] / bmax_amt[["Kidney"]],
    sim_typ_ga$tumor[i45] / bmax_amt[["Tumor"]]
  ), 1)
) |>
  knitr::kable(
    caption = "[68Ga]Ga-HA-DOTATATE receptor occupancy at the diagnostic scan time, typical patient (5.23 ug peptide). The paper states only that receptors are 'not close to full occupancy'."
  )
[68Ga]Ga-HA-DOTATATE receptor occupancy at the diagnostic scan time, typical patient (5.23 ug peptide). The paper states only that receptors are ‘not close to full occupancy’.
Compartment Occupancy at the 45-min scan (%)
Spleen 3.5
Kidney 7.1
Tumor 3.0

PKNCA validation

Table 3 reports observed and model-predicted AUC(0-tlast) for tumor and kidney after [177Lu]Lu-HA-DOTATATE, with tlast = 72 h. One PKNCA block is run per output compartment.

run_nca <- function(sim, conc_col, label) {
  sim_nca <- sim |>
    dplyr::mutate(Cc = .data[[conc_col]]) |>
    dplyr::filter(!is.na(Cc)) |>
    dplyr::mutate(compartment = label) |>
    dplyr::select(id, time, Cc, compartment)

  # Guarantee a time-zero row per subject so PKNCA can anchor AUC from 0.
  sim_nca <- dplyr::bind_rows(
    sim_nca,
    sim_nca |> dplyr::distinct(id, compartment) |>
      dplyr::mutate(time = 0, Cc = 0)
  ) |>
    dplyr::distinct(id, compartment, time, .keep_all = TRUE) |>
    dplyr::arrange(id, compartment, time)

  dose_df <- ev_lu |>
    dplyr::filter(evid == 1) |>
    dplyr::mutate(compartment = label) |>
    dplyr::select(id, time, amt, compartment)

  conc_obj <- PKNCA::PKNCAconc(sim_nca, Cc ~ time | compartment + id)
  dose_obj <- PKNCA::PKNCAdose(dose_df, amt ~ time | compartment + id)

  intervals <- data.frame(
    start = 0, end = 72,
    cmax = TRUE, tmax = TRUE, auclast = TRUE
  )

  PKNCA::pk.nca(PKNCA::PKNCAdata(conc_obj, dose_obj, intervals = intervals))
}

nca_tumor <- run_nca(sim_lu, "Ctumor", "Tumor")
nca_kidney <- run_nca(sim_lu, "Ckidney", "Kidney")

Comparison against published NCA

Table 3 reports AUC(0-tlast) in mgh/L; the simulated auclast is in ugh/L, so it is divided by 1000 before comparison. The reference values are the medians of the nine observed patients in Table 3.

summarise_nca <- function(nca_res) {
  as.data.frame(nca_res$result) |>
    dplyr::filter(PPTESTCD %in% c("auclast", "cmax", "tmax")) |>
    dplyr::group_by(compartment, PPTESTCD) |>
    dplyr::summarise(value = stats::median(PPORRES, na.rm = TRUE), .groups = "drop") |>
    tidyr::pivot_wider(names_from = PPTESTCD, values_from = value) |>
    dplyr::mutate(auclast = auclast / 1000)  # ug*h/L -> mg*h/L
}

simulated <- dplyr::bind_rows(
  summarise_nca(nca_tumor),
  summarise_nca(nca_kidney)
)

# Table 3 observed AUC(0-tlast), mg*h/L:
#   tumor  3.32, 2.09, 5.29, 4.69, 1.38, 2.80, 2.94, 1.76, 2.59 -> median 2.80
#   kidney 0.520, 0.634, 0.334, 0.902, 0.564, 0.443, 0.764, 0.621 -> median 0.5925
published <- tibble::tribble(
  ~compartment, ~auclast,
  "Tumor",      2.80,
  "Kidney",     0.5925
)

cmp <- nlmixr2lib::ncaComparisonTable(
  simulated = simulated,
  reference = published,
  by = "compartment",
  params = "auclast",
  units = c(auclast = "mg*h/L"),
  tolerance_pct = 20
)

knitr::kable(
  cmp,
  caption = "Simulated vs. published [177Lu]Lu-HA-DOTATATE AUC(0-72 h). Reference = median of the nine observed patients in Table 3. * differs from reference by >20%."
)
Simulated vs. published [177Lu]Lu-HA-DOTATATE AUC(0-72 h). Reference = median of the nine observed patients in Table 3. * differs from reference by >20%.
NCA parameter compartment Reference Simulated % diff
AUClast (mg*h/L) Tumor 2.8 2.64 -5.6%
AUClast (mg*h/L) Kidney 0.592 0.478 -19.4%

For context, the paper’s own model-predicted medians in Table 3 are 2.89 mgh/L (tumor) and 0.483 mgh/L (kidney), and the model-predicted kidney range (0.408-0.680) sits inside the wider observed range (0.334-0.902). The simulated population median for kidney is expected to land near the lower half of the observed range for the same reason the authors’ own predictions do: the kidney observations include urinary activity that the model does not represent, which is why the first (~1 h) kidney time point was excluded from parameter estimation altogether.

as.data.frame(nca_tumor$result) |>
  dplyr::bind_rows(as.data.frame(nca_kidney$result)) |>
  dplyr::filter(PPTESTCD == "auclast") |>
  dplyr::group_by(compartment) |>
  dplyr::summarise(
    `Median AUC(0-72 h) (mg*h/L)` = round(stats::median(PPORRES) / 1000, 3),
    `5th percentile` = round(stats::quantile(PPORRES, 0.05) / 1000, 3),
    `95th percentile` = round(stats::quantile(PPORRES, 0.95) / 1000, 3),
    .groups = "drop"
  ) |>
  dplyr::rename(Compartment = compartment) |>
  knitr::kable(
    caption = "Simulated [177Lu]Lu-HA-DOTATATE AUC(0-72 h) across the virtual cohort."
  )
Simulated [177Lu]Lu-HA-DOTATATE AUC(0-72 h) across the virtual cohort.
Compartment Median AUC(0-72 h) (mg*h/L) 5th percentile 95th percentile
Kidney 0.478 0.256 0.745
Tumor 2.643 1.563 4.526

Assumptions and deviations

  • Molar mass is not reported in this paper. mw = 1628.5 g/mol is inherited from the upstream framework paper this model is built on (Siebinga et al., EJNMMI Res. 2023;13:8, Table 3, “Molecular weight”), which is the sanctioned inherited-parameter path because the current paper explicitly fixes its structural parameters from that model. The constant is needed to reconcile bmax, reported in nmol/L, with the ug/L observation scale.

  • Equation 4 is applied to spleen uptake only, exactly as printed. The surrounding prose describes the tumor sink effect as “a reduced uptake in healthy tissues” (plural), but the printed equation carries the effect on k12 alone. Per the standing trust-the-equation policy the equation is followed.

  • Equation 4’s volume is in litres. The coefficient 0.4 multiplies a bare volume, so the unit is load-bearing and the paper does not state it. In litres the Table 1 range (22.4-644 mL) produces a 1-23% reduction in spleen uptake; in millilitres it would produce exp(-113) and annihilate spleen uptake entirely. Litres is therefore the only self-consistent reading.

  • The rest compartment’s uptake is un-gated but still restricted to the unbound fraction. Equation 1’s bmax term is stated for the SSTR-expressing compartments (two to five), and Table 2 reports no bmax for compartment six, so no capacity gate is applied there. fu is applied, on the general prose statement that “only unbound molecules were available for uptake into compartments”. Both readings give a blood half-life in the tens of minutes and neither changes any of the validated quantities above.

  • A single proportional residual error is replicated across three endpoints. Table 2 reports one 31.6% CV proportional error shared by every observed compartment. nlmixr2 requires a distinct endpoint parameter per observation channel, so propSd_Cspleen, propSd_Ckidney and propSd_Ctumor all carry the same published value; this is one estimate transcribed three times, not three independent estimates.

  • Interindividual variability is fixed, not estimated, in both models. For the diagnostic model the paper says so explicitly (“IIV was fixed based on assumed population variability”); for the therapeutic model Table 2 reports the IIV terms without an RSE, and the table header states that RSEs are given for estimated values only.

  • Blood is predicted but never observed. No blood samples were drawn in this study, so Cc is exposed as a prediction with no residual error model attached. The three observed channels are spleen, kidney and tumor.

  • Virtual-cohort tumor volumes. Table 1 reports the target-lesion and total tumor volumes only as marginal medians and ranges, with no distributional family and no joint distribution. Target-lesion volume is drawn log-uniformly across the reported range (7.81-212 mL) so the reported extremes are honoured without inventing a shape, and total tumor volume is generated from the observed median ratio (283/80) with a 25% CV multiplicative scatter, clipped to its own reported range (22.4-644 mL). Only the marginal medians are anchored to published values; the spread and the correlation are assumptions of this vignette, not of the paper.

  • Cohort size. 120 virtual subjects per radiopharmaceutical, well under the 200-per-arm cap; the study itself had nine patients.

  • Supplement not used. Additional file 1 contains Figures S1-S3 (goodness-of-fit and individual-prediction plots) only, with no parameter content. No errata or corrigenda were found for this DOI.

Canonical names introduced with this extraction

This is the library’s first somatostatin-receptor radioligand model, and it introduced three canonical names, ratified by the operator (sidecar request 001 of task oare_PMC10449733):

  • sstr - the lumped somatostatin-receptor-expressing organ-group compartment (compartment five: lungs, pancreas, stomach, thyroid, liver), registered in inst/references/compartment-names.md. Distinct from other, which is the non-receptor-expressing rest-of-body sink.
  • TUM_VOL_TOTAL and TUM_VOL_TARGET - clinical functional-imaging-segmented tumor volumes in mL, registered in inst/references/covariate-columns.md. Both are needed because they drive different effects with different coefficients, and only the target-lesion volume is the modelled compartment volume. Both are distinct from the preclinical caliper TUM_VOL (mm^3) and from the length-valued TUMSZ / TUM_SLD.

The sidecar also proposed a new lkupt_<tissue> parameter family for the capacity-limited uptake rate constant. Between the question being asked and answered, the canonical lkin_<compartment> / lkout_<compartment> tissue-exchange family was registered in inst/references/parameter-names.md (founded in part by this paper’s sibling model Siebinga_2023_lu177psma617.R), and it covers precisely this role. The register’s own precedence rule is to reuse an existing canonical, so these models use lkin_<tissue> rather than founding a duplicate name; the operator’s ratified intent – a name distinct from the complex-internalisation kint canonical, with suffixes drawn from the canonical compartment names – is preserved. Likewise, bmax / lbmax had been registered in the interim, so the ratified bmax_<tissue> form is used as the already-sanctioned site-suffixed variant rather than as a new entry.