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Quinidine BBB transport in kainate-treated rats (Syvanen 2012)

Source: vignettes/articles/Syvanen_2012_quinidine_rat.Rmd
Syvanen_2012_quinidine_rat.Rmd

Model and source

The packaged model is a faithful translation of the paper’s final NONMEM VI ADVAN6 fit (paper Figure 2 schematic, Table II “Estimation” column, Table IV equations). It is a preclinical (rat) brain-microdialysis popPK model with:

  • Two-compartment plasma disposition (central plasma V1, peripheral plasma V2, inter-compartmental clearance Q, systemic clearance CL).
  • A brain extracellular fluid (ECF) compartment V_Br sampled by hippocampal microdialysis, exchanging with central plasma via asymmetric BBB clearances (Q_in for influx, Q_out for efflux). The paper parameterises Q_in = f1 * Q_out with Q_out FIXED at 10.8 mL/min from a bootstrap-stability analysis.
  • A third observed output, total brain tissue concentration C_brain_deep, modelled as the algebraic equilibrium multiple C_brain_deep = f2 * C_brain_csf. The paper could not estimate separate rate constants for the deep brain (the brain tissue sample was taken only at end-of-experiment), so the deep brain is not a dynamic state.

Two binary covariates modify the model:

  • CONMED_TARIQUIDAR (1 = 15 mg/kg IP tariquidar pre-administered 30 min before quinidine; selective P-glycoprotein inhibitor) shifts CL, Q_out, Q_in, and f2.
  • DIS_POSTSE_KAINATE (1 = rat at 7 days post-kainate-induced status epilepticus; rat temporal-lobe-epilepsy paradigm) shifts CL, V2, and V_Br.

The headline biological findings the model encodes are: tariquidar pre-administration is predicted to raise the steady-state brain ECF-to-plasma concentration ratio by 2.65 / 0.366 = 7.24-fold and the total brain-to-plasma ratio by 2.65 / 0.366 * 5.66 = 40.9-fold (paper Results p91); kainate post-SE treatment lowers systemic clearance (1.86-fold) and brain ECF volume (1.69-fold) without statistically significant effects on Q_in, Q_out, or f2 (paper Table III).

Population

64 evaluable adult male Sprague-Dawley rats (Harlan, Horst, The Netherlands), 200-249 g body weight on arrival, housed >= 1 week before instrumentation. 58 of those 64 rats contributed PK data; the other 6 contributed in-vivo retrodialysis probe-recovery calibration (paper Table I, p88).

Treatment allocation:

  • Control rats received quinidine in one of three IV infusion arms: 12.5 ug/min over 4 h (3000 ug cumulative; n = 7 vehicle + 6 TQD), 25 ug/min over 4 h (6000 ug cumulative; n = 8 vehicle + 8 TQD), or 100 ug/min over 30 min (3000 ug cumulative; n = 9 vehicle + 7 TQD).
  • Kainate-treated rats received only the 100 ug/min over 30 min arm (n = 8 vehicle + 8 TQD).

Half of each arm received tariquidar 15 mg/kg IP 30 min before quinidine; the other half received 5% glucose / saline vehicle. Kainate induction (paper Methods “Animals”, p88): an initial 10 mg/kg IP dose of kainic acid followed by 5 mg/kg IP every 30-60 min until stage IV / V seizures on Racine’s scale, or a 30 mg/kg cumulative cap. Rats reached SE within ~20 min of the last injection and were studied 7 days later.

The same metadata are available programmatically via readModelDb("Syvanen_2012_quinidine_rat")$population.

Source trace

The per-parameter origin is recorded as an in-file comment next to each ini() entry in inst/modeldb/specificDrugs/Syvanen_2012_quinidine_rat.R. The table below collects everything in one place for review.

Equation / parameter Value Source location
d/dt(central) n/a Paper Fig. 2 schematic; IV infusion + bidirectional BBB + V2 exchange
d/dt(peripheral1) n/a Paper Fig. 2 schematic; Q-mediated exchange with central plasma
d/dt(brain_csf) n/a Paper Fig. 2 schematic; Q_in influx + Q_out efflux
Cbrain_deep = f2 * Cbrain_csf n/a Paper Results “Development of the Pharmacokinetic Model”, p90 (algebraic-only)
lcl (CL) log(32.1) mL/min Table II “Estimation - 2898” column: CL = 32.1 mL/min (RSE 5.1%)
lvc (V1) log(146) mL Table II: V1 = 146 mL (RSE 42%)
lq (Q) log(66.6) mL/min Table II: Q2 = 66.6 mL/min (RSE 11%)
lvp (V2) log(1840) mL Table II: V2 = 1840 mL (RSE 6.5%)
lqout (Q_out) fixed(log(10.8)) Table II: Q_out = 10.8 mL/min FIXED; Results p90 explains the bootstrap rationale
lf1 (f1 = Q_in / Q_out) log(0.0619) Table II: f1 = 0.0619 (RSE 8.2%)
lvbr (V_Br) log(269) mL Table II: V_Br = 269 mL (RSE 14%)
lf2 (f2) log(8.67) Table II: f2 = 8.67 (RSE 2.7%)
e_dis_postse_kainate_cl log(0.537) Table II + Table IV: theta_kainate(CL) = 0.537 (RSE 8.5%)
e_dis_postse_kainate_vp log(0.678) Table II + Table IV: theta_kainate(V2) = 0.678 (RSE 7.0%)
e_dis_postse_kainate_vbr log(0.592) Table II + Table IV: theta_kainate(V_Br) = 0.592 (RSE 13%)
e_conmed_tariquidar_cl log(0.835) Table II + Table IV: theta_tariquidar(CL) = 0.835 (RSE 6.8%)
e_conmed_tariquidar_qout log(0.366) Table II + Table IV: theta_tariquidar(Q_out) = 0.366 (RSE 14%)
e_conmed_tariquidar_qin log(2.65) Table II + Table IV: theta_tariquidar(Q_in) = 2.65 (RSE 17%)
e_conmed_tariquidar_f2 log(5.66) Table II + Table IV: theta_tariquidar(f2) = 5.66 (RSE 33%)
etalcl (omega^2(CL)) 0.0682 Table II: omega^2(CL) = 0.0682 (RSE 20%, shrinkage 6%)
etalvc (omega^2(V1)) 1.92 Table II: omega^2(V1) = 1.92 (RSE 30%, shrinkage 18%) – high IIV per paper
etalvp (omega^2(V2)) 0.0686 Table II: omega^2(V2) = 0.0686 (RSE 34%, shrinkage 15%)
etalqin (omega^2(Q_in)) 0.101 Table II: omega^2(Q_in) = 0.101 (RSE 19%, shrinkage 13%)
etalvbr (omega^2(V_Br)) 0.196 Table II: omega^2(V_Br) = 0.196 (RSE 31%, shrinkage 16%)
propSd (plasma) sqrt(0.270) = 0.520 Table II: sigma^2(plasma) = 0.270 (RSE 7.0%)
propSd_Cbrain_csf sqrt(0.185) = 0.430 Table II: sigma^2(brain ECF) = 0.185 (RSE 9.4%)
propSd_Cbrain_deep sqrt(0.694) = 0.833 Table II: sigma^2(total brain) = 0.694 (RSE 21%)

Virtual cohort

The published data are not in a public repository. Below we build a four-arm virtual cohort matched to the paper’s 100 ug/min over 30 min experimental arm (the only arm in which all four covariate combinations were studied per Table I):

  • control + vehicle
  • control + TQD
  • kainate + vehicle
  • kainate + TQD

Each arm contains n_per_arm = 25 virtual rats. The dose unit is ng so the 100 ug/min over 30 min infusion is encoded as a 3 000 000 ng amount delivered at 100 000 ng/min for 30 min.

set.seed(20120101)
n_per_arm <- 25L

obs_times <- c(seq(0, 30, by = 2),
               seq(35, 120, by = 5),
               seq(130, 240, by = 10),
               seq(260, 420, by = 20))

make_arm <- function(arm, kainate, tariquidar, id_offset) {
  ids <- id_offset + seq_len(n_per_arm)
  dose_rows <- tibble(
    id   = ids,
    time = 0,
    amt  = 3e6,                # 3,000,000 ng = 3 mg = 3000 ug cumulative
    rate = 1e5,                # 100,000 ng/min = 100 ug/min
    evid = 1L,
    cmt  = "central",
    DIS_POSTSE_KAINATE     = kainate,
    CONMED_TARIQUIDAR  = tariquidar,
    arm  = arm
  )
  obs_rows <- tidyr::expand_grid(id = ids, time = obs_times) |>
    mutate(
      amt   = 0,
      rate  = 0,
      evid  = 0L,
      cmt   = "Cc",
      DIS_POSTSE_KAINATE    = kainate,
      CONMED_TARIQUIDAR = tariquidar,
      arm   = arm
    )
  bind_rows(dose_rows, obs_rows)
}

events <- bind_rows(
  make_arm("control + vehicle",  kainate = 0, tariquidar = 0, id_offset =   0L),
  make_arm("control + TQD",      kainate = 0, tariquidar = 1, id_offset = 100L),
  make_arm("kainate + vehicle",  kainate = 1, tariquidar = 0, id_offset = 200L),
  make_arm("kainate + TQD",      kainate = 1, tariquidar = 1, id_offset = 300L)
)

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

Simulation 

mod <- rxode2::rxode2(readModelDb("Syvanen_2012_quinidine_rat"))
#> ℹ parameter labels from comments will be replaced by 'label()'

sim <- rxode2::rxSolve(
  mod,
  events = events,
  keep   = c("arm", "DIS_POSTSE_KAINATE", "CONMED_TARIQUIDAR")
) |>
  as.data.frame()

For the typical-value reference trajectories (reproducing the deterministic shape of the published figure without the very large IIV on V1), zero out the random effects:

mod_typical <- mod |> rxode2::zeroRe()
sim_typical <- rxode2::rxSolve(
  mod_typical,
  events = events,
  keep   = c("arm", "DIS_POSTSE_KAINATE", "CONMED_TARIQUIDAR")
) |>
  as.data.frame()
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalvp', 'etalqin', 'etalvbr'
#> Warning: multi-subject simulation without without 'omega'

Replicate published figures

Figure 1 – plasma and brain ECF time-courses

Figure 1 of Syvanen 2012 plots mean plasma (upper panel) and brain ECF (lower panel) concentrations during and after the 100 ug/min over 30 min IV infusion, for each of the four covariate arms. The plot below reproduces the typical-value trajectories from the packaged model.

# Replicates Figure 1 upper panel of Syvanen 2012: plasma concentration vs time
# in the 100 ug/min over 30 min arm, split by kainate and tariquidar status.
sim_typical |>
  filter(time > 0, time <= 420) |>
  ggplot(aes(time, Cc, colour = arm)) +
  geom_line(linewidth = 0.7) +
  scale_y_log10() +
  labs(
    x        = "Time (min)",
    y        = "Plasma Cc (ng/mL, log scale)",
    colour   = "Arm",
    title    = "Figure 1 (upper panel) -- plasma quinidine, typical values",
    caption  = "Reproduces Figure 1 upper panel of Syvanen 2012 (100 ug/min over 30 min IV arm)."
  ) +
  theme_minimal()

# Replicates Figure 1 lower panel of Syvanen 2012: brain ECF concentration vs
# time, same four arms.
sim_typical |>
  filter(time > 0, time <= 420) |>
  ggplot(aes(time, Cbrain_csf, colour = arm)) +
  geom_line(linewidth = 0.7) +
  scale_y_log10() +
  labs(
    x       = "Time (min)",
    y       = "Brain ECF Cbrain_csf (ng/mL, log scale)",
    colour  = "Arm",
    title   = "Figure 1 (lower panel) -- brain ECF quinidine, typical values",
    caption = "Reproduces Figure 1 lower panel of Syvanen 2012 (same arms)."
  ) +
  theme_minimal()

Verify the headline TQD effects

The paper Results “TQD Treatment” (p91) derives two headline ratios from the parameter estimates:

  • Brain ECF concentration is raised theta_tariquidar(Q_in) / theta_tariquidar(Q_out) = 2.65 / 0.366 = 7.24-fold by tariquidar (acting on both Q_in and Q_out).
  • Total brain concentration is raised 2.65 / 0.366 * theta_tariquidar(f2) = 2.65 / 0.366 * 5.66 = 41.0-fold (the additional f2 effect on the intra-brain redistribution).

We check that the packaged model reproduces these analytical ratios directly:

# Pull the e_conmed_tariquidar_* coefficients straight from the parsed
# rxode2 model so the check is sourced from the live model object, not
# hand-copied numbers.
theta_tbl  <- mod$theta
get_e <- function(name) theta_tbl[[name]]

ratio_qin  <- exp(get_e("e_conmed_tariquidar_qin"))    # expected 2.65
ratio_qout <- exp(get_e("e_conmed_tariquidar_qout"))   # expected 0.366
ratio_f2   <- exp(get_e("e_conmed_tariquidar_f2"))     # expected 5.66

tibble(
  quantity = c("theta_tariquidar(Q_in)",
               "theta_tariquidar(Q_out)",
               "theta_tariquidar(f2)",
               "brain-ECF-to-plasma ratio TQD/vehicle (= Q_in_ratio / Q_out_ratio)",
               "total-brain-to-plasma ratio TQD/vehicle (= the above * f2_ratio)"),
  packaged = c(ratio_qin, ratio_qout, ratio_f2,
               ratio_qin / ratio_qout,
               ratio_qin / ratio_qout * ratio_f2),
  paper    = c(2.65, 0.366, 5.66, 7.24, 41.0)
) |>
  mutate(across(c(packaged, paper), \(x) round(x, 3))) |>
  knitr::kable(caption = "Tariquidar effects: packaged model vs paper headline ratios.")
Tariquidar effects: packaged model vs paper headline ratios.
quantity packaged paper
theta_tariquidar(Q_in) 2.650 2.650
theta_tariquidar(Q_out) 0.366 0.366
theta_tariquidar(f2) 5.660 5.660
brain-ECF-to-plasma ratio TQD/vehicle (= Q_in_ratio / Q_out_ratio) 7.240 7.240
total-brain-to-plasma ratio TQD/vehicle (= the above * f2_ratio) 40.981 41.000

End-of-experiment total-brain : plasma ratios

The paper Results “Kainate Treatment” (p91) reports the OBSERVED total-brain-to-plasma ratios measured at the end of the 7 h experiment (brain tissue sampled at terminal decapitation):

Arm Observed total-brain : plasma ratio (mean +/- SD)
control + vehicle 0.9 +/- 0.6
control + TQD 114 +/- 80
kainate + vehicle 0.6 +/- 0.4
kainate + TQD 45 +/- 29

The packaged-model typical-value predictions at the same 420 min sampling time:

endpoint <- sim_typical |>
  filter(abs(time - 420) < 1e-6) |>
  group_by(arm) |>
  summarise(
    Cc_ng_per_mL          = mean(Cc),
    Cbrain_deep_ng_per_mL = mean(Cbrain_deep),
    ratio_total_to_plasma = mean(Cbrain_deep / Cc),
    .groups = "drop"
  )

knitr::kable(endpoint,
             caption = "Typical-value end-of-experiment (t = 420 min) brain:plasma ratios.")
Typical-value end-of-experiment (t = 420 min) brain:plasma ratios.
arm Cc_ng_per_mL Cbrain_deep_ng_per_mL ratio_total_to_plasma
control + TQD 17.397725 950.866100 54.6546242
control + vehicle 7.663316 5.721639 0.7466271
kainate + TQD 50.389783 1665.521396 33.0527598
kainate + vehicle 23.933562 15.105604 0.6311473

The packaged-model ratios sit comfortably within +/- 1 SD of the paper’s observed means (control + vehicle ~0.75 vs observed 0.9 +/- 0.6; control + TQD ~55 vs observed 114 +/- 80, low end of the +/-1 SD interval; kainate + TQD ~30 vs observed 45 +/- 29, within +/- 1 SD). The observed-mean values are higher than the typical-value predictions partly because the paper’s mean is computed from a small sample with skewed distributions and partly because the brain has not fully reached pseudo-equilibrium with plasma at 7 h (during a single 30 min infusion, plasma is already in terminal decay while the brain is still equilibrating, so the brain : plasma ratio is still rising at terminal sampling). The theoretical pseudo-steady-state ratios verified in the previous section (7.24 / 41.0) would be approached only under a much longer infusion that holds plasma at constant Cc.

PKNCA validation on plasma Cc 

sim_nca <- sim |>
  filter(!is.na(Cc), time > 0) |>
  select(id, time, Cc, arm)

conc_obj <- PKNCA::PKNCAconc(sim_nca, Cc ~ time | arm + id)

dose_df <- events |>
  filter(evid == 1L) |>
  select(id, time, amt, arm)

dose_obj <- PKNCA::PKNCAdose(dose_df, amt ~ time | arm + id)

intervals <- data.frame(
  start      = 0,
  end        = 420,
  cmax       = TRUE,
  tmax       = TRUE,
  auclast    = TRUE,
  half.life  = TRUE
)

nca_data <- PKNCA::PKNCAdata(conc_obj, dose_obj, intervals = intervals)
nca_res  <- PKNCA::pk.nca(nca_data)
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nca_sum  <- as.data.frame(summary(nca_res))
knitr::kable(nca_sum, caption = "Simulated plasma NCA parameters by arm.")
Simulated plasma NCA parameters by arm.
start end arm N auclast cmax tmax half.life
0 420 control + TQD 25 NC 1570 [29.9] 30.0 [30.0, 30.0] 101 [30.1]
0 420 control + vehicle 25 NC 1510 [14.8] 30.0 [30.0, 30.0] 60.1 [19.7]
0 420 kainate + TQD 25 NC 2210 [23.0] 30.0 [30.0, 30.0] 93.6 [31.3]
0 420 kainate + vehicle 25 NC 2170 [20.7] 30.0 [30.0, 30.0] 90.9 [32.3]

Assumptions and deviations

  • High V1 IIV taken at face value. Table II reports omega^2(V1) = 1.92 (approximate CV 240%), much larger than typical popPK V1 variability. The bootstrap re-fit reports the same magnitude (omega^2(V1) = 2.03) so the value appears stable rather than a transcription error. The packaged model uses 1.92 as the variance on the log scale. Stochastic simulations will therefore show wide between-subject scatter on plasma trajectories driven by V1 variability; the validation figures above use rxode2::zeroRe() to suppress this for visual clarity.

  • Three independent residual-error streams. Table II reports three separate sigma^2 values (one for plasma, one for brain ECF, one for total brain), so the packaged model declares three independent proportional-error parameters (propSd, propSd_Cbrain_csf, propSd_Cbrain_deep). Each output has its own residual SD; no shared / cross-output residual structure is implied.

  • Total brain is an algebraic output, not a state. Paper Results “Development of the Pharmacokinetic Model” (p90) and Discussion (p93) state explicitly that “rate constants for distribution to and from the total brain compartment could not be estimated based on the present data set. Therefore, concentration of quinidine in brain tissue was in the final pharmacokinetic model described as a multiple (f2) of the free brain ECF concentration.” The packaged model does NOT declare a separate brain_deep ODE state; the third observed output is the derived quantity Cbrain_deep = f2 * Cbrain_csf.

  • Q_out FIXED at 10.8 mL/min. Paper Results p90 explains that this value was obtained when Q_out was free in the final model fit; it was then fixed in the published estimation because in some bootstrap replicates V_Br was estimated to an unrealistically high value while the ratio V_Br / Q_out remained stable. The packaged model wraps lqout <- fixed(log(10.8)) to preserve this provenance; downstream users who refit the model will see Q_out held constant.

  • Q_in is constructed as f1 * Q_out_base. Paper Table IV writes the final-model Q_in as f1 * THETA8 * THETA13^TARIQUIDAR * exp(eta5) where THETA8 is the BASE Q_out (10.8 mL/min) before its own tariquidar modification THETA9. The packaged model preserves this convention so the BBB influx and efflux clearances are independently parameterised under tariquidar; setting CONMED_TARIQUIDAR = 1 raises Q_in 2.65-fold (via THETA13) and separately lowers Q_out 2.73-fold (via THETA9), each picking up its own multiplier off the shared 10.8 mL/min anchor.

  • No weight covariate in the final model. Animal weight on the experimental day was tested as a covariate in the screening step (Table III) and significantly reduced OFV by 9.5 units when fitted on plasma alone. When the brain compartments were added (the full final model), weight no longer reached the p < 0.01 threshold for any parameter and was dropped (paper Results “Development of the Pharmacokinetic Model” p90). The packaged model follows the paper and does NOT include a weight effect.

  • Kainate effect on f2 not retained. Paper Results “Kainate Treatment” (p91) notes a numerically lower observed total-brain : plasma ratio in kainate-treated than control rats but reports that “in the population model kainate as a covariate for f2 … did not result in a significant drop of OFV (Table III)” – delta-OFV of -0.73, below the 6.63 threshold. The packaged model follows the paper and does NOT include a kainate effect on f2.

  • Dose-unit choice. The paper reports infusion rates in ug/min and concentrations in ng/mL. The packaged model uses ng for dose amounts and ng/mL for concentrations so the volumes (mL) and clearances (mL/min) can stay in the paper’s reported units without an explicit conversion factor in the ODE block. The vignette dose amt = 3e6 ng corresponds to the paper’s 3 mg (= 3000 ug) cumulative dose; analogously for the 6000 ug cumulative arm.