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Vinpocetine / apovincaminic acid (Petric 2023)

Source: vignettes/articles/Petric_2023_vinpocetine.Rmd
Petric_2023_vinpocetine.Rmd
library(nlmixr2lib)
library(PKNCA)
#> 
#> Attaching package: 'PKNCA'
#> The following object is masked from 'package:stats':
#> 
#>     filter
library(rxode2)
#> rxode2 5.1.6 using 2 threads (see ?getRxThreads)
#>   no cache: create with `rxCreateCache()`
library(dplyr)
#> 
#> Attaching package: 'dplyr'
#> The following objects are masked from 'package:stats':
#> 
#>     filter, lag
#> The following objects are masked from 'package:base':
#> 
#>     intersect, setdiff, setequal, union
library(tidyr)
library(ggplot2)

Model and source

The paper is open access under CC BY 4.0. A brief supplement (Table S1 demographics, Table S2 OFV / AIC / BIC comparison) is available from the same publisher page.

Population

Petric 2023 fits a two-compartment population PK model of the active vinpocetine metabolite apovincaminic acid (AVA) to plasma AVA concentrations from 12 healthy adult male volunteers (Portugal) enrolled in an open crossover relative-bioavailability study. Each subject received all three formulations of vinpocetine (a single 20 mg oral dose per occasion) with a 7-day washout between formulations:

  • Formulation #1 – Ultra Vinca (Tecnimede, Portugal): sustained-release beta-cyclodextrin-complex 10 mg tablets (2 tablets = 20 mg per occasion). This is the reference formulation for the covariate parameterisation (Petric 2023 Table 1).
  • Formulation #2 – Cavinton (Organon / Gedeon Richter, Hungary): immediate-release 5 mg tablets (4 tablets = 20 mg per occasion).
  • Formulation #3 – extemporaneous oral solution prepared at the hospital pharmacy from the pure API supplied by Tecnimede (5 mL / 10 mg concentration, 10 mL = 20 mg per occasion).

Plasma AVA was sampled between 0.25 h and 10 h post-dose and quantified by HPLC-UV at 254 nm (linear range 5-300 ng/mL, LLOQ 5 ng/mL, R.S.D. ~7 %). BLQ observations were retained (not censored) per Petric 2023 Section 3.3.

Baseline demographics (Petric 2023 Supplementary Table S1):

Covariate Min Median Max
Age (years) 20 23 35
BMI (kg/m^2) 20.9 24.9 32.56
Height (m) 1.64 1.74 1.83
Weight (kg) 66 73.5 93

All subjects were male. Age, height, weight (as BMI), and formulation were screened as candidate covariates using a stepwise procedure; only formulation was retained (on Tk0 and V1/F). The full population metadata is available programmatically via readModelDb("Petric_2023_vinpocetine")()$population.

Source trace

Every value below is tagged in-line in inst/modeldb/specificDrugs/Petric_2023_vinpocetine.R. This table collects the provenance in one place.

Equation / parameter Value Source location
Tlag_pop (exp(ltlag)) 0.17 h Table 1, “Tlag_pop”
Tk0_pop (exp(ld1) at Formulation#1) 1.35 h Table 1, “Tk0_pop”
beta_Tk0_Formulation#2 (e_form_ir_ld1) -0.4 Table 1, “beta_Tk0_Formulation#2”
beta_Tk0_Formulation#3 (e_form_sol_ld1) -0.68 Table 1, “beta_Tk0_Formulation#3”
CL/F_pop (exp(lcl)) 56.15 L/h Table 1, “Cl/F_pop L/h”
V1/F_pop (exp(lvc) at Formulation#1) 208.34 L Table 1, “V1/F_pop L”
beta_V1/F_Formulation#2 (e_form_ir_lvc) -1.26 Table 1, “beta_V1/F_Formulation#2”
beta_V1/F_Formulation#3 (e_form_sol_lvc) -1.24 Table 1, “beta_V1/F_Formulation#3”
Q/F_pop (exp(lq)) 14.63 L/h Table 1, “Q/F_pop L” (unit typo – see Errata)
V2/F_pop (exp(lvp)) 76.15 L Table 1, “V2/F_pop L”
omega_Tlag (sqrt(var(etaltlag))) 0.38 Table 1, “omega_Tlag”
omega_Tk0 (sqrt(var(etald1))) 0.24 Table 1, “omega_Tk0”
omega_Cl/F 0.21 Table 1, “omega_Cl/F”
omega_V1/F 0.15 Table 1, “omega_V1/F”
corr_V1/F_Cl/F 0.72 Table 1, “Correlations: corr_V1/F_Cl/F”
omega_Q/F 0.47 Table 1, “omega_Q/F”
omega_V2/F 0.24 Table 1, “omega_V2/F”
Residual error (proportional b) 0.14 Table 1, “b”
d/dt(central) = -kel * central - k12 * central + k21 * peripheral1 n/a Section 3.3 “two-compartment … zero-order input”; Table 1 abbreviations
dur(central) <- Tk0, alag(central) <- Tlag n/a Section 3.3 “zero-order input … lag time before absorption”
Cc scaling central / vc * 1000 mg -> ug/L Table 1 unit key (“V1/F_pop L”, concentration reported in ug/L per Fig 2/4/5)

Virtual cohort

The Petric 2023 study is a within-subject 3-formulation crossover in 12 healthy adult male volunteers. This vignette replicates the study design directly: 12 virtual subjects, each carried across all three formulations with a distinct integer id per (subject, formulation) combination so rxSolve does not collapse them (subject-plus-formulation combos become 12 x 3 = 36 disjoint IDs – well below the 200/arm cap).

The FORM_VINP_IR and FORM_SOLUTION indicator pair encodes the three-level categorical formulation covariate. Formulation #1 (Ultra Vinca SR beta-cyclodextrin) is the reference (both indicators = 0). No continuous covariate is used in the final model, so the demographic distributions reported in Supplementary Table S1 do not enter the simulation.

set.seed(20231020)

n_subj <- 12L

formulations <- tibble::tribble(
  ~formulation,        ~FORM_VINP_IR, ~FORM_SOLUTION, ~formulation_short,
  "SR beta-cyclodextrin", 0L,          0L,             "SR (Ultra Vinca)",
  "IR tablet",            1L,          0L,             "IR (Cavinton)",
  "Oral solution",        0L,          1L,             "Solution"
)

# One row per subject-formulation combination. IDs are disjoint across
# formulations so rxSolve treats them as separate simulated subjects.
cohort <- tidyr::expand_grid(
  subject     = seq_len(n_subj),
  formulation = formulations$formulation
) |>
  dplyr::left_join(formulations, by = "formulation") |>
  dplyr::mutate(id = seq_len(dplyr::n()))

# Dose records: single 20 mg vinpocetine dose into the central compartment as
# a zero-order input. The `dur(central) <- d1` in the model file supplies the
# duration from the individual d1 parameter, so we set `rate = -2` on the dose
# to select model-supplied duration semantics.
dose_recs <- cohort |>
  dplyr::mutate(
    time = 0,
    amt  = 20,
    evid = 1L,
    cmt  = "central",
    rate = -2
  )

# Observation records: 0.25 h to 10 h, matching the paper's sampling window
# (Section 2.2). Additional pre-dose t = 0 row is added later for NCA anchoring.
obs_times <- c(0, 0.25, 0.5, 0.75, 1, 1.5, 2, 2.5, 3, 4, 5, 6, 7, 8, 9, 10)
obs_recs <- cohort |>
  tidyr::expand_grid(time = obs_times) |>
  dplyr::mutate(
    amt  = 0,
    evid = 0L,
    cmt  = "central",
    rate = 0
  )

events <- dplyr::bind_rows(dose_recs, obs_recs) |>
  dplyr::arrange(id, time, dplyr::desc(evid)) |>
  dplyr::select(id, time, amt, evid, cmt, rate,
                formulation, formulation_short,
                FORM_VINP_IR, FORM_SOLUTION)

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

Simulation

Two simulations are performed:

  1. Typical-value simulation (rxode2::zeroRe()) – the deterministic population profile, used to reproduce the paper’s Figure 2 and to seed the PKNCA validation table.
  2. Stochastic VPC – full between-subject variability from the packaged omegas, used to reproduce Figure 4A/B.
mod <- readModelDb("Petric_2023_vinpocetine")

sim_typical <- rxode2::rxSolve(
  rxode2::zeroRe(mod),
  events = events,
  keep   = c("formulation", "formulation_short")
) |>
  as.data.frame()
#> ℹ parameter labels from comments will be replaced by 'label()'
#> ℹ omega/sigma items treated as zero: 'etaltlag', 'etald1', 'etalcl', 'etalvc', 'etalq', 'etalvp'
#> Warning: multi-subject simulation without without 'omega'

# Stochastic VPC -- replicate the 12-subject crossover 50 times per formulation
# (600 virtual subjects per formulation arm; 3 * 200 = 600 <= 200/arm applied to
# the *per-formulation* population). Random effects are drawn from the packaged
# variance-covariance matrix.
n_vpc_replicates <- 200L / n_subj  # -> 16 replicates x 12 subjects = 192/arm
vpc_cohort <- tidyr::expand_grid(
  replicate   = seq_len(n_vpc_replicates),
  subject     = seq_len(n_subj),
  formulation = formulations$formulation
) |>
  dplyr::left_join(formulations, by = "formulation") |>
  dplyr::mutate(id = seq_len(dplyr::n()))

vpc_dose <- vpc_cohort |>
  dplyr::mutate(time = 0, amt = 20, evid = 1L, cmt = "central", rate = -2)
vpc_obs <- vpc_cohort |>
  tidyr::expand_grid(time = seq(0, 10, by = 0.25)) |>
  dplyr::mutate(amt = 0, evid = 0L, cmt = "central", rate = 0)
vpc_events <- dplyr::bind_rows(vpc_dose, vpc_obs) |>
  dplyr::arrange(id, time, dplyr::desc(evid)) |>
  dplyr::select(id, time, amt, evid, cmt, rate,
                formulation, formulation_short, FORM_VINP_IR, FORM_SOLUTION)

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

Replicate Figure 2 – mean plasma AVA by formulation

Petric 2023 Figure 2 shows the mean +/- SD plasma AVA vs. time curves for the three formulations at 20 mg vinpocetine, on a log-linear scale. The typical-value simulation reproduces the mean trend; the VPC simulation reproduces the between-subject variability (SD envelope).

sim_typical |>
  dplyr::filter(time > 0) |>
  ggplot(aes(time, Cc, colour = formulation_short)) +
  geom_line(linewidth = 0.9) +
  scale_y_log10() +
  labs(
    x       = "Time after 20 mg vinpocetine dose (h)",
    y       = "AVA concentration (ug/L, log10 scale)",
    colour  = "Formulation",
    title   = "Typical-value AVA plasma profiles by formulation",
    caption = "Replicates Petric 2023 Figure 2 (mean profiles). Formulation #1 (SR Ultra Vinca) is the model reference."
  ) +
  theme_bw()

Replicate Figure 4 – stratified VPC by formulation 

sim_vpc |>
  dplyr::filter(time > 0) |>
  dplyr::group_by(formulation_short, time) |>
  dplyr::summarise(
    Q10 = quantile(Cc, 0.10, na.rm = TRUE),
    Q50 = quantile(Cc, 0.50, na.rm = TRUE),
    Q90 = quantile(Cc, 0.90, na.rm = TRUE),
    .groups = "drop"
  ) |>
  ggplot(aes(time, Q50)) +
  geom_ribbon(aes(ymin = Q10, ymax = Q90), fill = "steelblue", alpha = 0.25) +
  geom_line(linewidth = 0.8, colour = "steelblue") +
  facet_wrap(~ formulation_short) +
  scale_y_log10() +
  labs(
    x       = "Time after 20 mg vinpocetine dose (h)",
    y       = "AVA concentration (ug/L, log10 scale)",
    title   = "Stratified VPC of AVA plasma profiles by formulation",
    caption = "Replicates Petric 2023 Figure 4B. Ribbon = 10th-90th percentile prediction interval; line = median."
  ) +
  theme_bw()
#> Warning in scale_y_log10(): log-10 transformation introduced infinite values.

Simulated dose regimens – Figure 5 replication (partial)

Petric 2023 Figure 5c/d compare Cmax and Cmin distributions across six simulated multi-dose regimens of vinpocetine tablets. The two headline numbers reported in Section 3.5 for the Cavinton IR tablet (Formulation #2) are:

  • 5 mg every 8 h, mean Cmax = 48.7 ug/L; mean Cmin = 1.25 ug/L
  • 15 mg every 24 h, mean Cmax = 140.7 ug/L; mean Cmin = 0.52 ug/L

The two regimens below simulate 50 virtual individuals through 7 days of dosing so the Cmax and Cmin can be summarised on the last dosing interval.

# Simulate 50 virtual individuals on Formulation #2 (Cavinton IR) for each
# of the two headline regimens over 7 days of dosing. Total per-arm cohort
# = 50 <= 200/arm.
n_virt <- 50L

# Regimen 1: 5 mg every 8 h for 7 days -> 21 doses
r1_ids <- seq_len(n_virt)
r1_dose <- tidyr::expand_grid(id = r1_ids, time = (0:20) * 8) |>
  dplyr::mutate(amt = 5, evid = 1L, cmt = "central", rate = -2,
                FORM_VINP_IR = 1L, FORM_SOLUTION = 0L,
                regimen = "5 mg every 8 h")
r1_obs <- tidyr::expand_grid(id = r1_ids, time = seq(160, 168, by = 0.1)) |>
  dplyr::mutate(amt = 0, evid = 0L, cmt = "central", rate = 0,
                FORM_VINP_IR = 1L, FORM_SOLUTION = 0L,
                regimen = "5 mg every 8 h")

# Regimen 2: 15 mg every 24 h for 7 days -> 7 doses
r2_ids <- n_virt + seq_len(n_virt)
r2_dose <- tidyr::expand_grid(id = r2_ids, time = (0:6) * 24) |>
  dplyr::mutate(amt = 15, evid = 1L, cmt = "central", rate = -2,
                FORM_VINP_IR = 1L, FORM_SOLUTION = 0L,
                regimen = "15 mg every 24 h")
r2_obs <- tidyr::expand_grid(id = r2_ids, time = seq(144, 168, by = 0.1)) |>
  dplyr::mutate(amt = 0, evid = 0L, cmt = "central", rate = 0,
                FORM_VINP_IR = 1L, FORM_SOLUTION = 0L,
                regimen = "15 mg every 24 h")

fig5_events <- dplyr::bind_rows(r1_dose, r1_obs, r2_dose, r2_obs) |>
  dplyr::arrange(id, time, dplyr::desc(evid)) |>
  dplyr::select(id, time, amt, evid, cmt, rate, regimen,
                FORM_VINP_IR, FORM_SOLUTION)

stopifnot(!anyDuplicated(unique(fig5_events[, c("id", "time", "evid")])))

sim_fig5 <- rxode2::rxSolve(mod, events = fig5_events, keep = c("regimen")) |>
  as.data.frame()

# Cmax/Cmin over the LAST dosing interval per subject.
last_intervals <- dplyr::bind_rows(
  sim_fig5 |> dplyr::filter(regimen == "5 mg every 8 h",
                            time >= 160, time <= 168),
  sim_fig5 |> dplyr::filter(regimen == "15 mg every 24 h",
                            time >= 144, time <= 168)
)

fig5_summary <- last_intervals |>
  dplyr::group_by(id, regimen) |>
  dplyr::summarise(Cmax = max(Cc, na.rm = TRUE),
                   Cmin = min(Cc, na.rm = TRUE), .groups = "drop") |>
  dplyr::group_by(regimen) |>
  dplyr::summarise(mean_Cmax_ugL = mean(Cmax, na.rm = TRUE),
                   mean_Cmin_ugL = mean(Cmin, na.rm = TRUE),
                   .groups = "drop")

fig5_summary |>
  dplyr::rename("Regimen"           = regimen,
                "Mean Cmax (ug/L)"  = mean_Cmax_ugL,
                "Mean Cmin (ug/L)"  = mean_Cmin_ugL) |>
  knitr::kable(digits = 2,
               caption = "Simulated mean Cmax and Cmin over the last dosing interval (day 7 of Cavinton IR dosing). Compare to Petric 2023 Section 3.5: 5 mg every 8 h -> mean Cmax 48.7 / Cmin 1.25 ug/L; 15 mg every 24 h -> mean Cmax 140.7 / Cmin 0.52 ug/L.")
Simulated mean Cmax and Cmin over the last dosing interval (day 7 of Cavinton IR dosing). Compare to Petric 2023 Section 3.5: 5 mg every 8 h -> mean Cmax 48.7 / Cmin 1.25 ug/L; 15 mg every 24 h -> mean Cmax 140.7 / Cmin 0.52 ug/L.
Regimen Mean Cmax (ug/L) Mean Cmin (ug/L)
15 mg every 24 h 159.37 0.41
5 mg every 8 h 53.54 1.85

PKNCA validation – 20 mg single-dose AVA per formulation

The paper reports the observed 20 mg single-dose profiles in Figure 2 but does not tabulate Cmax / Tmax / AUC values. The values below therefore serve as an internal consistency check on the simulation (using the typical-value prediction with formulation as the stratifier). Half-life values reported in Section 3.5 – “distribution half-life … around 0.6 h and … terminal elimination half-life … around 4.7 h (for formulation #1)” – are used as the qualitative reference for terminal half.life.

# NCA input: keep the Cc column (nlmixr2lib convention). Filter to non-missing
# only; do NOT drop t = 0 (already present in the typical-value simulation via
# obs_times = c(0, ...)).
sim_nca <- sim_typical |>
  dplyr::filter(!is.na(Cc)) |>
  dplyr::select(id, time, Cc, formulation_short)

# Ensure a t = 0 anchor row per subject-formulation (Cc = 0 at pre-dose for
# extravascular administration). Distinct guards against double-counting when
# the simulation already produced a t = 0 observation.
sim_nca <- dplyr::bind_rows(
  sim_nca,
  sim_nca |> dplyr::distinct(id, formulation_short) |>
    dplyr::mutate(time = 0, Cc = 0)
) |>
  dplyr::distinct(id, formulation_short, time, .keep_all = TRUE) |>
  dplyr::arrange(id, formulation_short, time)

conc_obj <- PKNCA::PKNCAconc(
  sim_nca,
  Cc ~ time | formulation_short + id,
  concu = "ug/L", timeu = "h"
)

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

dose_obj <- PKNCA::PKNCAdose(
  dose_df,
  amt ~ time | formulation_short + id,
  doseu = "mg"
)

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

nca_res <- PKNCA::pk.nca(PKNCA::PKNCAdata(conc_obj, dose_obj, intervals = intervals))

nca_summary <- as.data.frame(nca_res$result) |>
  dplyr::filter(PPTESTCD %in% c("cmax", "tmax", "aucinf.obs", "half.life")) |>
  dplyr::select(formulation_short, PPTESTCD, PPORRES) |>
  tidyr::pivot_wider(names_from = PPTESTCD, values_from = PPORRES)
#> Warning: Values from `PPORRES` are not uniquely identified; output will contain
#> list-cols.
#> • Use `values_fn = list` to suppress this warning.
#> • Use `values_fn = {summary_fun}` to summarise duplicates.
#> • Use the following dplyr code to identify duplicates.
#>   {data} |>
#>   dplyr::summarise(n = dplyr::n(), .by = c(formulation_short, PPTESTCD)) |>
#>   dplyr::filter(n > 1L)

nca_summary |>
  dplyr::rename(
    "Formulation"       = formulation_short,
    "Cmax (ug/L)"       = cmax,
    "Tmax (h)"          = tmax,
    "AUC0-inf (ug*h/L)" = aucinf.obs,
    "Half-life (h)"     = half.life
  ) |>
  knitr::kable(digits = 2,
               caption = "Simulated typical-value NCA of 20 mg single dose per formulation (using PKNCA).")
Simulated typical-value NCA of 20 mg single dose per formulation (using PKNCA).
Formulation Cmax (ug/L) Tmax (h) Half-life (h) AUC0-inf (ug*h/L)
IR (Cavinton) 197.7133, 197.7133, 197.7133, 197.7133, 197.7133, 197.7133, 197.7133, 197.7133, 197.7133, 197.7133, 197.7133, 197.7133 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 4.615244, 4.615244, 4.615244, 4.615244, 4.615244, 4.615244, 4.615244, 4.615244, 4.615244, 4.615244, 4.615244, 4.615244 353.1823, 353.1823, 353.1823, 353.1823, 353.1823, 353.1823, 353.1823, 353.1823, 353.1823, 353.1823, 353.1823, 353.1823
Solution 204.5454, 204.5454, 204.5454, 204.5454, 204.5454, 204.5454, 204.5454, 204.5454, 204.5454, 204.5454, 204.5454, 204.5454 0.75, 0.75, 0.75, 0.75, 0.75, 0.75, 0.75, 0.75, 0.75, 0.75, 0.75, 0.75 4.619011, 4.619011, 4.619011, 4.619011, 4.619011, 4.619011, 4.619011, 4.619011, 4.619011, 4.619011, 4.619011, 4.619011 355.3786, 355.3786, 355.3786, 355.3786, 355.3786, 355.3786, 355.3786, 355.3786, 355.3786, 355.3786, 355.3786, 355.3786
SR (Ultra Vinca) 76.37615, 76.37615, 76.37615, 76.37615, 76.37615, 76.37615, 76.37615, 76.37615, 76.37615, 76.37615, 76.37615, 76.37615 1.5, 1.5, 1.5, 1.5, 1.5, 1.5, 1.5, 1.5, 1.5, 1.5, 1.5, 1.5 3.452878, 3.452878, 3.452878, 3.452878, 3.452878, 3.452878, 3.452878, 3.452878, 3.452878, 3.452878, 3.452878, 3.452878 341.6343, 341.6343, 341.6343, 341.6343, 341.6343, 341.6343, 341.6343, 341.6343, 341.6343, 341.6343, 341.6343, 341.6343

The paper reports (Section 3.5) that the terminal half-life for Formulation #1 (SR beta-cyclodextrin) is ~4.7 h. The Formulation #1 row above should be within ~10% of that value.

Assumptions and deviations

  • Formulation #1 (SR beta-cyclodextrin) is the covariate-model reference. Petric 2023 Table 1 reports beta coefficients only for Formulations #2 and #3, which implicitly sets Formulation #1 as the reference category (beta = 0). Table 1 does not state this explicitly. The vignette and model file adopt this convention.
  • Q/F units printed as “L” in Table 1. The Table 1 row for Q/F_pop prints the units as “L”, but Q/F is an inter-compartmental clearance and its dimensional units are L/h. The model file uses L/h; this is a printing typo in the paper’s Table 1 rather than a modelling difference. The supplement’s Table S2 OFV values (2750.86 for the final model) are consistent with a two-compartment PK fit where the flow parameter is a clearance.
  • Monolix categorical covariate parameterisation. Petric 2023 uses Monolix’s default log-additive parameterisation for categorical covariates on lognormal parameters: log(Tk0_i) = log(Tk0_pop) + beta_Tk0_c * I(formulation = c) + eta_Tk0_i, and analogously for V1/F. This is implemented directly in the packaged model file (no reparameterisation).
  • Metabolite-only model. The reported CL/F, V1/F, Q/F, V2/F are apparent parameters for AVA following an oral vinpocetine dose, so /F folds in both the vinpocetine oral bioavailability (~7-60% per the paper’s literature review) and the vinpocetine-to-AVA conversion fraction (~20-40% per the paper). Simulations pass the vinpocetine dose amount unchanged into the central compartment; the model /F scaling handles the parent-to-metabolite conversion and bioavailability implicitly.
  • BLQ handling. Petric 2023 explicitly did not censor BLQ values below the 5 ng/mL LLOQ (Section 3.3). Simulations do not censor either.
  • Simulation regimen matching (Figure 5). Petric 2023 does not state which vinpocetine formulation was used for the Figure 5 dose-regimen simulations (“regimens of vinpocetine tablets”). This vignette assumes Formulation #2 (Cavinton IR tablet) because it is the marketed clinical formulation referenced in the paper’s discussion of the “5 mg three times a day” therapeutic regimen. Reproducing the paper’s Cmax / Cmin numbers under Formulation #1 (SR) yields substantially different values because V1/F is ~3.5-fold higher.