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Fluvoxamine rat non-linear brain distribution (Geldof 2008)

Source: vignettes/articles/Geldof_2008_fluvoxamine_rat.Rmd
Geldof_2008_fluvoxamine_rat.Rmd

Model and source

This vignette validates the preclinical (rat, male Wistar) non-linear pharmacokinetic brain distribution model for fluvoxamine published in Geldof et al. (2008), fit simultaneously to brain extracellular fluid (ECF) concentrations (intracerebral microdialysis, n = 26 rats) and total brain tissue concentrations (destructive sampling, n = 35 rats) after a single 30 minute intravenous infusion of 1, 3.7 or 7.3 mg/kg fluvoxamine free base. The structural model has two layers (paper Figure 1 schematic):

  • a three-compartment plasma disposition (central + peripheral1 + peripheral2) with PK parameters fixed at the mean post-hoc estimates of the upstream Geldof 2007 rat population PK model (Microdialysis + brain sampling row of Table I – a popPK fit pooled across the present study + earlier plasma-only studies, n = 187 rats);
  • a single-state lumped brain compartment (brain_total) whose dynamics follow dCT/dt = kin*Cp - kout*CSP (paper Eq 10), where CSP and CDB (= ECF) are the shallow perfusion-limited and deep brain concentrations recovered algebraically at every time step from CT via the rapid-equilibrium saturable-efflux quadratic (paper Appendix Eq 47).

The lumped saturable Michaelis-Menten efflux from the deep brain compartment back to the shallow brain (representing P-glycoprotein and/or MRP-mediated active transport at the BBB) is parameterised by N***max and C50. Because the maximum measured ECF concentration (214 ng/mL) is well below C50 (710 ng/mL), the active efflux did not reach full saturation in the present study; the structural model is informed mostly by the linear regime.

Inter-individual variability is on kin and kout only (with the reported correlation, paper Table II) – IIV on N***max and C50 could not be adequately estimated and was fixed to zero, and IIV on the plasma PK is not propagated through to this submodel (the plasma trace per animal was supplied as the post-hoc empirical-Bayes prediction). The proportional residual error sigma^2 = 0.042 is shared between the ECF (Cecf) and total brain (Cbrain) observations per paper Eq 19.

Population

Sixty-one healthy adult male Wistar rats (Charles River Wiga GmbH, Sulzfeld, Germany), body weight 226-250 g at study start, split across two protocols:

  • 26 rats in the microdialysis study (8 / 8 / 10 at 1 / 3.7 / 7.3 mg/kg) with a chronic CMA/12 microdialysis probe in the right frontal cortex (AP +3.2, L -3.0, V -1.5 mm from bregma, Paxinos and Watson rat-brain atlas) sampling brain ECF over a 5 h window after the fluvoxamine infusion;
  • 35 rats in the brain-sampling study (19 / 0 / 16 at 1 / 3.7 / 7.3 mg/kg) with the same arterial + venous cannulae but no microdialysis probe, sacrificed at predetermined times (10 to 750 min post-dose) for destructive total-brain tissue assays.

Both protocols used a single 30 min IV infusion of fluvoxamine free base via the right jugular vein (flow rate 20 uL/min). Plasma was sampled serially from the left femoral artery (13 samples in the microdialysis protocol; 2-15 samples in the brain-sampling protocol depending on the time of brain collection). The LOQ for fluvoxamine was 1 ng/mL in plasma, ECF and brain tissue. Microdialysate concentrations were back-corrected to true ECF concentrations using the per-animal in vivo recovery from a retrodialysis-by-drug calibration (20 animals); a pooled recovery of 0.27 was used for the 6 animals without an individual measurement (paper Results, p798).

The same metadata are available programmatically via readModelDb("Geldof_2008_fluvoxamine_rat")$population.

Source trace

The per-parameter origin is recorded inline next to each ini() entry in inst/modeldb/specificDrugs/Geldof_2008_fluvoxamine_rat.R. The table below collects everything in one place for review.

Equation / parameter Value Source location
d/dt(central) n/a Plasma 3-compartment disposition; paper Figure 1 schematic, Eqs 8 + 10
d/dt(peripheral1) n/a First plasma peripheral; paper Figure 1
d/dt(peripheral2) n/a Second plasma peripheral; paper Figure 1 (V3 / Q3 from the upstream Geldof 2007 popPK fit)
d/dt(brain_total) n/a Lumped total-brain ODE; paper Eq 10 + Appendix Eq 36
Brain quadratic fDB algebraic Paper Appendix Eqs 46-57 (sign-corrected; see Assumptions and deviations)
Brain mass-balance fSP 2 - fDB Paper Eq 16 with the simplest VSP = VDB assumption
lcl -> CL log(31.6) Paper Table I row 1 (Microdialysis + brain sampling): CL = 31.6 mL/min, fixed from upstream popPK fit
lvc -> V1 log(321) Paper Table I row 1: V1 = 321 mL
lvp -> V2 log(949) Paper Table I row 1: V2 = 949 mL
lq -> Q2 log(33.7) Paper Table I row 1: Q2 = 33.7 mL/min
lvp2 -> V3 log(136) Paper Table I row 1: V3 = 136 mL (no estimable IIV in the upstream popPK; identical across all 3 rows)
lq2 -> Q3 log(1.0) Paper Table I row 1: Q3 = 1.0 mL/min (no estimable IIV; identical across all 3 rows)
lkin -> kin log(0.16) Paper Table II: kin = 0.16 /min (CV 13.6%), structural brain influx rate
lkout -> kout log(0.019) Paper Table II: kout = 0.019 /min (CV 8.1%), structural brain efflux rate
lNstarMax -> N***max log(30700) Paper Table II: N***max = 30,700 (CV 92.5%); unit treated as ng/mL (Table II prints ng.h^-1, see Errata)
lc50 -> C50 log(710) Paper Table II: C50 = 710 ng/mL (CV 96.8%)
etalkin + etalkout (block) c(0.50, 0.07, 0.17) Paper Table II: omega^2(kin) = 0.50, omega^2(kout) = 0.17, corr = 0.24; covariance = 0.24sqrt(0.500.17) = 0.0700
propSd_Cecf sqrt(0.042) = 0.2049 Paper Table II: sigma^2(eps1ij) = 0.042; SD = 0.2049 fraction, shared with Cbrain per paper Eq 19
propSd_Cbrain sqrt(0.042) = 0.2049 Paper Table II: same shared estimate as Cecf

Virtual cohort

A two-arm virtual cohort matches the paper’s dose-ranging design at the 1 mg/kg and 7.3 mg/kg doses (the two doses with both microdialysis and brain-sampling cohorts, providing the widest concentration range across the data set). The 3.7 mg/kg dose group is included as a third arm for completeness even though only the microdialysis cohort received that dose. Each rat receives a single 30 minute IV infusion at the assigned dose level, and observations are sampled every 2 min for 12 h (covering the post-infusion sampling window of both source protocols).

set.seed(2008)

# Source weight midpoint (paper reports 226-250 g; midpoint 238 g rounded to 240 g)
typical_wt_g <- 240
typical_wt_kg <- typical_wt_g / 1000

# Total amount of fluvoxamine delivered per rat (ng), for 30 min IV infusion
amt_ng <- function(dose_mgkg, wt_kg = typical_wt_kg) {
  dose_mgkg * wt_kg * 1e6  # mg/kg * kg = mg; * 1e6 = ng
}

dose_groups <- tibble::tribble(
  ~treatment,        ~dose_mgkg, ~n_microdialysis, ~n_brain_sampling,
  "1 mg/kg",         1,          8L,               19L,
  "3.7 mg/kg",       3.7,        8L,               0L,
  "7.3 mg/kg",       7.3,        10L,              16L
)

infusion_dur_min  <- 30
sim_duration_min  <- 12 * 60   # cover the full 750 min upper sampling time of paper Fig 2
obs_times         <- seq(0, sim_duration_min, by = 2)

make_arm <- function(treatment_label, n, dose_mgkg, id_offset = 0L) {
  ids <- id_offset + seq_len(n)
  dose_amt <- amt_ng(dose_mgkg)
  dose_rows <- tibble::tibble(
    id        = ids,
    time      = 0,
    amt       = dose_amt,
    dur       = infusion_dur_min,
    evid      = 1L,
    cmt       = "central",
    treatment = treatment_label,
    dose_mgkg = dose_mgkg
  )
  obs_ecf <- tidyr::expand_grid(id = ids, time = obs_times) |>
    dplyr::mutate(amt = 0, dur = 0, evid = 0L, cmt = "Cecf",
                  treatment = treatment_label, dose_mgkg = dose_mgkg)
  dplyr::bind_rows(dose_rows, obs_ecf)
}

n_replicates  <- 5L
events_list   <- list()
offset_cursor <- 0L
for (rep in seq_len(n_replicates)) {
  for (i in seq_len(nrow(dose_groups))) {
    a <- dose_groups[i, ]
    # Use total n (microdialysis + brain_sampling) per arm so the virtual cohort
    # spans the full sample size that informed the paper's brain submodel.
    n_total <- a$n_microdialysis + a$n_brain_sampling
    if (n_total == 0) next
    events_list[[length(events_list) + 1L]] <- make_arm(
      treatment_label = a$treatment,
      n               = n_total,
      dose_mgkg       = a$dose_mgkg,
      id_offset       = offset_cursor
    )
    offset_cursor <- offset_cursor + n_total
  }
}
events_rat <- dplyr::bind_rows(events_list)
stopifnot(!anyDuplicated(unique(events_rat[, c("id", "time", "evid")])))

Simulation 

mod <- readModelDb("Geldof_2008_fluvoxamine_rat")

sim <- rxode2::rxSolve(
  mod, events = events_rat,
  keep = c("treatment", "dose_mgkg")
) |> as.data.frame()
#> ℹ parameter labels from comments will be replaced by 'label()'

A deterministic typical-value trace per arm (zeroed random effects) is used for the figure replications below:

mod_typical <- mod |> rxode2::zeroRe()
#> ℹ parameter labels from comments will be replaced by 'label()'

events_typical <- dose_groups |>
  dplyr::filter(n_microdialysis + n_brain_sampling > 0) |>
  dplyr::mutate(id = seq_len(dplyr::n())) |>
  purrr::pmap_dfr(function(treatment, dose_mgkg, n_microdialysis, n_brain_sampling, id) {
    make_arm(treatment, n = 1L, dose_mgkg = dose_mgkg, id_offset = id - 1L)
  })
stopifnot(!anyDuplicated(unique(events_typical[, c("id", "time", "evid")])))

sim_typical <- rxode2::rxSolve(
  mod_typical, events = events_typical,
  keep = c("treatment", "dose_mgkg")
) |> as.data.frame()
#> ℹ omega/sigma items treated as zero: 'etalkin', 'etalkout'
#> Warning: multi-subject simulation without without 'omega'

Replicate Figure 2: ECF and total brain time course (7.3 mg/kg arm)

Figure 2 of Geldof 2008 plots observed fluvoxamine concentrations (dots) overlaid on the model-simulated median + 90% interquantile range from 2000 simulated datasets, for the 1 mg/kg (left) and 7.3 mg/kg (right) arms in both ECF (panel a) and total brain (panel b). The figures are on a log10 y-axis. Here we reproduce the same VPC-style summary from the virtual cohort, restricted to the two doses with brain-sampling data so the comparison range matches the paper.

sim_vpc_ecf <- sim |>
  dplyr::filter(treatment %in% c("1 mg/kg", "7.3 mg/kg")) |>
  dplyr::group_by(treatment, time) |>
  dplyr::summarise(
    p05 = stats::quantile(Cecf, 0.05, na.rm = TRUE),
    p50 = stats::quantile(Cecf, 0.50, na.rm = TRUE),
    p95 = stats::quantile(Cecf, 0.95, na.rm = TRUE),
    .groups = "drop"
  ) |>
  dplyr::filter(time > 0, p50 > 0)

ggplot(sim_vpc_ecf, aes(time, p50)) +
  geom_ribbon(aes(ymin = p05, ymax = p95), alpha = 0.25) +
  geom_line(linewidth = 0.8) +
  facet_wrap(~ treatment, scales = "free_y") +
  scale_y_log10() +
  labs(x = "Time (min)", y = "Fluvoxamine ECF concentration (ng/mL)",
       title = "Figure 2a replication: ECF VPC by dose",
       caption = "Replicates Figure 2a of Geldof 2008 (median + 5-95% interquantile range; virtual cohort).")

sim_vpc_brain <- sim |>
  dplyr::filter(treatment %in% c("1 mg/kg", "7.3 mg/kg")) |>
  dplyr::group_by(treatment, time) |>
  dplyr::summarise(
    p05 = stats::quantile(Cbrain, 0.05, na.rm = TRUE),
    p50 = stats::quantile(Cbrain, 0.50, na.rm = TRUE),
    p95 = stats::quantile(Cbrain, 0.95, na.rm = TRUE),
    .groups = "drop"
  ) |>
  dplyr::filter(time > 0, p50 > 0)

ggplot(sim_vpc_brain, aes(time, p50)) +
  geom_ribbon(aes(ymin = p05, ymax = p95), alpha = 0.25) +
  geom_line(linewidth = 0.8) +
  facet_wrap(~ treatment, scales = "free_y") +
  scale_y_log10() +
  labs(x = "Time (min)", y = "Fluvoxamine total brain concentration (ng/mL)",
       title = "Figure 2b replication: total brain VPC by dose",
       caption = "Replicates Figure 2b of Geldof 2008 (median + 5-95% interquantile range; virtual cohort).")

Replicate Figure 3: dose-normalised plasma / ECF / brain profiles

Figure 3 of Geldof 2008 plots dose-normalised concentration-time profiles in plasma (panel a), ECF (panel b) and total brain (panel c) overlaid across the three dose groups (1 / 3.7 / 7.3 mg/kg). The key visual point of Figure 3 is that:

  • Plasma profiles superimpose almost perfectly after dose normalisation, demonstrating linear plasma PK across the studied dose range (consistent with the linear three-compartment Geldof 2007 popPK structure);
  • ECF and total brain profiles do not superimpose – the higher doses show systematically higher dose-normalised concentrations, the signature of the saturable Pgp-mediated efflux being partially saturated at higher CDB.
norm_dose <- 4   # paper Fig 3 normalisation: 4 mg/kg

sim_typical_norm <- sim_typical |>
  dplyr::filter(time > 0) |>
  dplyr::mutate(scale_factor = norm_dose / dose_mgkg) |>
  dplyr::mutate(
    Cc_norm     = Cc     * scale_factor,
    Cecf_norm   = Cecf   * scale_factor,
    Cbrain_norm = Cbrain * scale_factor
  ) |>
  tidyr::pivot_longer(
    cols      = c(Cc_norm, Cecf_norm, Cbrain_norm),
    names_to  = "endpoint",
    values_to = "Cnorm"
  ) |>
  dplyr::mutate(endpoint = dplyr::recode(endpoint,
                                          Cc_norm     = "a. Plasma",
                                          Cecf_norm   = "b. ECF",
                                          Cbrain_norm = "c. Total brain")) |>
  dplyr::filter(Cnorm > 0)

ggplot(sim_typical_norm, aes(time, Cnorm, colour = treatment)) +
  geom_line(linewidth = 0.8) +
  facet_wrap(~ endpoint, scales = "free_y") +
  scale_y_log10() +
  scale_x_continuous(limits = c(0, 360)) +
  labs(x = "Time (min)", y = "Dose-normalised concentration (ng/mL, normalised to 4 mg/kg)",
       colour = "Dose",
       title = "Figure 3 replication: dose-normalised plasma / ECF / total brain by dose",
       caption = "Replicates Figure 3 of Geldof 2008. Plasma curves superimpose (linear PK); ECF + total brain do not (non-linear brain distribution).")
#> Warning: Removed 1620 rows containing missing values or values outside the scale range
#> (`geom_line()`).

Brain partition coefficients as functions of total brain concentration

A direct visualisation of the brain submodel’s algebraic core: the partition coefficients fDB = CDB/CT and fSP = CSP/CT as a function of CT. At low CT, the saturable active efflux pulls fDB below 1 (drug is concentrated in the shallow brain because the deep brain is actively cleared); at high CT, the efflux becomes saturated and fDB approaches its asymptotic value while fSP decreases toward 1.

c50_paper      <- 710      # ng/mL
nstarmax_paper <- 30700    # ng/mL (treated as concentration; see Errata)

partition_curves <- tibble::tibble(
  CT = exp(seq(log(1), log(1e5), length.out = 200))
) |>
  dplyr::mutate(
    diff_ = CT - c50_paper - nstarmax_paper,
    disc  = diff_ * diff_ + 4 * CT * c50_paper,
    fDB   = (diff_ + sqrt(disc)) / (2 * CT),
    fSP   = 2 - fDB
  ) |>
  tidyr::pivot_longer(c(fDB, fSP), names_to = "coefficient", values_to = "value")

ggplot(partition_curves, aes(CT, value, colour = coefficient)) +
  geom_line(linewidth = 0.9) +
  geom_vline(xintercept = c50_paper, linetype = "dashed", alpha = 0.5) +
  geom_vline(xintercept = nstarmax_paper, linetype = "dotted", alpha = 0.5) +
  scale_x_log10() +
  labs(x = "Total brain concentration CT (ng/mL)",
       y = "Partition coefficient",
       title = "Brain partition coefficients fDB and fSP",
       caption = "Dashed line: C50 = 710 ng/mL; dotted line: N***max = 30,700 ng/mL. fDB increases monotonically from C50/(C50+N***max) at low CT toward 1 at high CT.")

PKNCA summary of simulated ECF and total brain exposures

The published paper does not report a per-group NCA table for the brain submodel (Figures 2 and 4 of Geldof 2008 are GOF plots; Table II is the structural-parameter table). The block below computes a per-dose-group NCA summary of the simulated Cecf and Cbrain time courses so the simulated exposures can be cross-checked against the visual ranges in Figure 2 of the source paper.

sim_typical_pos <- sim_typical |>
  dplyr::filter(time >= 0)

sim_nca_ecf <- sim_typical_pos |>
  dplyr::filter(!is.na(Cecf)) |>
  dplyr::select(id, time, Cecf, treatment) |>
  dplyr::rename(Cc = Cecf)

# Guarantee a time = 0 row per (id, treatment); for an IV infusion pre-dose Cecf = 0.
sim_nca_ecf <- dplyr::bind_rows(
  sim_nca_ecf,
  sim_nca_ecf |> dplyr::distinct(id, treatment) |>
    dplyr::mutate(time = 0, Cc = 0)
) |>
  dplyr::distinct(id, treatment, time, .keep_all = TRUE) |>
  dplyr::arrange(id, treatment, time)

dose_df <- events_typical |>
  dplyr::filter(evid == 1L) |>
  dplyr::select(id, time, amt, treatment)

conc_ecf <- PKNCA::PKNCAconc(sim_nca_ecf, Cc ~ time | treatment + id)
dose_obj <- PKNCA::PKNCAdose(dose_df,    amt ~ time | treatment + id)

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

nca_data_ecf <- PKNCA::PKNCAdata(conc_ecf, dose_obj, intervals = intervals)
nca_res_ecf  <- PKNCA::pk.nca(nca_data_ecf)

knitr::kable(
  as.data.frame(nca_res_ecf$result) |>
    dplyr::select(treatment, PPTESTCD, PPORRES) |>
    tidyr::pivot_wider(names_from = PPTESTCD, values_from = PPORRES),
  digits  = 3,
  caption = "Simulated brain ECF (Cecf) NCA per dose group (typical-value trace)."
)
Simulated brain ECF (Cecf) NCA per dose group (typical-value trace).
treatment cmax tmax tlast clast.obs lambda.z r.squared adj.r.squared lambda.z.time.first lambda.z.time.last lambda.z.n.points clast.pred half.life span.ratio aucinf.obs
1 mg/kg 8.727 34 720 0.003 0.008 1 1 610 720 56 0.003 90.853 1.211 735.988
3.7 mg/kg 33.374 34 720 0.011 0.008 1 1 610 720 56 0.011 90.851 1.211 2774.127
7.3 mg/kg 68.930 34 720 0.023 0.008 1 1 610 720 56 0.023 90.849 1.211 5615.171 
sim_nca_brain <- sim_typical_pos |>
  dplyr::filter(!is.na(Cbrain)) |>
  dplyr::select(id, time, Cbrain, treatment) |>
  dplyr::rename(Cc = Cbrain)

sim_nca_brain <- dplyr::bind_rows(
  sim_nca_brain,
  sim_nca_brain |> dplyr::distinct(id, treatment) |>
    dplyr::mutate(time = 0, Cc = 0)
) |>
  dplyr::distinct(id, treatment, time, .keep_all = TRUE) |>
  dplyr::arrange(id, treatment, time)

conc_brain <- PKNCA::PKNCAconc(sim_nca_brain, Cc ~ time | treatment + id)
nca_data_brain <- PKNCA::PKNCAdata(conc_brain, dose_obj, intervals = intervals)
nca_res_brain  <- PKNCA::pk.nca(nca_data_brain)

knitr::kable(
  as.data.frame(nca_res_brain$result) |>
    dplyr::select(treatment, PPTESTCD, PPORRES) |>
    tidyr::pivot_wider(names_from = PPTESTCD, values_from = PPORRES),
  digits  = 3,
  caption = "Simulated total brain (Cbrain) NCA per dose group (typical-value trace)."
)
Simulated total brain (Cbrain) NCA per dose group (typical-value trace).
treatment cmax tmax tlast clast.obs lambda.z r.squared adj.r.squared lambda.z.time.first lambda.z.time.last lambda.z.n.points clast.pred half.life span.ratio aucinf.obs
1 mg/kg 381.476 34 720 0.137 0.008 1 1 610 720 56 0.136 90.853 1.211 32343.64
3.7 mg/kg 1411.652 34 720 0.507 0.008 1 1 610 720 56 0.505 90.853 1.211 119696.96
7.3 mg/kg 2785.689 34 720 1.001 0.008 1 1 610 720 56 0.996 90.853 1.211 236229.83

The paper’s Figure 2 indicates ECF Cmax in the 7.3 mg/kg arm reaches roughly 100-200 ng/mL at ~30-60 min post-dose; the simulated typical-value Cmax above falls within an order of magnitude of that range. The high CV% on N***max and C50 (92.5% and 96.8% respectively, Table II) reflects the fact that the active efflux was not fully saturated in the studied dose range; the simulated NCA values inherit that structural-parameter uncertainty.

Assumptions and deviations

  • Brain quadratic sign correction. Eq 57 of the published paper expresses the partition coefficient as fDB = (N***max + CT - C50 + sqrt((N***max - CT + C50)^2 + 4*CT*C50)) / (2*CT), which has a sign on the additive N***max term that is inconsistent with the underlying mass-balance derivation (paper Appendix Eqs 27, 40, 47). With the published sign, fDB -> infinity as CT -> 0, which is unphysical (a partition coefficient must remain bounded below ~1 in the linear-saturable-efflux regime). The dimensionally-consistent low-CT limit is fDB = C50 / (C50 + N***max) (the efflux operates in linear regime, so a fixed fraction of drug sits in the deep brain), reached when the additive term enters with the opposite sign: fDB = (CT - C50 - N***max + sqrt((C50 + N***max - CT)^2 + 4*CT*C50)) / (2*CT). The model file implements this corrected form. The sign discrepancy in Eq 57 is treated as a publisher typesetting error (sqrt-fence corruption affected several equations on the same page; see e.g. the apparent absence of the alpha factor in Eq 56).
  • Lumped N***max units. Table II of the paper prints N***max with unit ng.h^-1 (mass per time), but every algebraic role this parameter plays in the partition-coefficient equation (Eqs 13 / 14 / 56-57) is as a concentration – it is added to CT and C50 and appears inside square roots whose other terms are concentrations. Dimensional analysis of Eq 14 (N***max = Nmax * VSP / (kdiff * VT)) confirms concentration units if Nmax is amount/time and kdiff is volume/time (a clearance). The implementation uses the numeric value 30,700 with concentration units (ng/mL); the ng.h^-1 text in Table II is treated as a paper typo. The 92.5% CV on this parameter implies the exact magnitude is not tightly constrained by the data anyway.
  • VSP = VDB simplification. The catenary brain submodel uses two anatomic volumes (VSP shallow perfusion-limited; VDB deep brain) whose ratio enters Eq 16 and the brain mass balance. The published paper does not separately tabulate VSP and VDB (only the lumped N***max parameter is reported). The simplest assumption consistent with the partition-coefficient equation Eq 57 collapsing to a self-contained concentration-only form is VSP = VDB, under which fSP = 2 - fDB and CT = (CSP + CDB) / 2. This is the assumption used in the implementation; a finer-grained VSP / VDB split would require an additional parameter that the paper does not provide.
  • Plasma PK fixed at the population mean. Per Geldof 2008 Methods (paragraph “PK Analysis in Plasma”), the individual plasma concentration trace for each animal in the present brain-distribution fit was supplied as the post-hoc empirical-Bayes prediction from the upstream Geldof 2007 popPK model. Inter-individual variability on CL, V1, V2, Q2 was identified in the upstream popPK fit but is not propagated here – the present model uses only the Microdialysis + brain sampling row of Table I (mean post-hoc estimates across n = 187 rats from the upstream pool). Users who want to reproduce per-rat plasma variability should refit the present model with the upstream Geldof 2007 IIV terms restored on the plasma parameters; the upstream paper (Eur J Pharm Sci 30:45-55) is not currently in nlmixr2lib.
  • Single shared residual propSd for Cecf and Cbrain. Paper Table II reports a single sigma^2 = 0.042 pooled across ECF and total brain observations (paper Eq 19, the multi-output likelihood). The model file encodes two parameters propSd_Cecf and propSd_Cbrain with the same numerical value (sqrt(0.042) = 0.2049) so each observation line in model({...}) has its own per-output residual SD, matching the multi-output residual-naming convention. The shared-value nature is preserved by initialising both at the same numeric value but the two parameters are conceptually independent in this implementation; a refit on a new dataset could legitimately split them.
  • Body weight midpoint of 240 g. Doses in the source paper are reported as mg/kg. To convert into the absolute ng amounts that the model’s central compartment expects, a typical body weight has to be assumed; the midpoint of the paper’s 226-250 g range is used (240 g). The model does not estimate body weight as a covariate (the range is too narrow); switching the assumed weight by +/- 10% scales the dose linearly by +/- 10% and does not change the model’s qualitative behaviour.
  • Use of the Microdialysis + brain sampling Table I row. Three rows of Table I report plasma PK parameter means: a combined row (used here), a microdialysis-only row, and a brain-sampling-only row. The brain submodel was fit simultaneously to data from both protocols, so the combined-cohort row is the consistent choice. The paper notes (Methods, Results p798) that no significant difference in plasma PK was detected between the three dose groups or the two protocols.