Ephedrine + caffeine + norephedrine (Csajka 2005) • nlmixr2lib

Model and source

mod_fn <- readModelDb("Csajka_2005_ephedrine_caffeine")
mod    <- rxode2::rxode(mod_fn)
#> ℹ parameter labels from comments will be replaced by 'label()'

Citation: Csajka C, Haller CA, Benowitz NL, Verotta D. Mechanistic pharmacokinetic modelling of ephedrine, norephedrine and caffeine in healthy subjects. Br J Clin Pharmacol. 2005;59(3):335-345. doi:10.1111/j.1365-2125.2005.02254.x
Article: https://doi.org/10.1111/j.1365-2125.2005.02254.x

This vignette validates the simultaneous mechanistic PK model of Csajka et al. (2005) for co-administered ephedrine, its N-demethylation metabolite norephedrine, and caffeine after single oral doses in healthy adults.

Population

Twenty-four healthy adults (14 female, 10 male; age 22-39 years; body weight 52-91.5 kg) participated across two single-dose cross-over studies at UCSF. Study 1 (n=8) received a single oral dose of a commercial herbal supplement (Metabolift, two capsules) containing 17.3 mg ephedrine and 175 mg caffeine. Study 2 (n=16) received single oral doses of 25 mg ephedrine sulphate and / or 200 mg caffeine sulphate, alone and in combination. Six of the 24 subjects (25%) were on concurrent oral contraceptives. Race / ethnicity was reported only for Study 2 (10 Caucasian, 1 African American, 3 Asian / Pacific Islander, 2 Latino). Demographics are from Csajka 2005 Table 1.

The same information is available programmatically via the model’s population metadata:

str(mod$population, max.level = 1)
#> List of 12
#>  $ species       : chr "human"
#>  $ n_subjects    : int 24
#>  $ n_studies     : int 2
#>  $ age_range     : chr "22-39 years (Study 1 25-38; Study 2 22-39)"
#>  $ weight_range  : chr "52-91.5 kg (Study 1 52-88.9; Study 2 58.6-91.5)"
#>  $ height_range  : chr "144-188 cm (Study 2 only; not reported for Study 1)"
#>  $ sex_female_pct: num 58.3
#>  $ race_ethnicity: Named num [1:4] 62.5 6.25 18.75 12.5
#>   ..- attr(*, "names")= chr [1:4] "White" "Black_or_African_American" "Asian_or_Pacific_Islander" "Hispanic_or_Latino"
#>  $ disease_state : chr "Healthy adults. 6 of 24 subjects (25%) were on concurrent oral contraceptive therapy. Race / ethnicity reported"| __truncated__
#>  $ dose_range    : chr "Study 1 (n=8): single oral dose of a commercial herbal supplement (Metabolift, two capsules) containing 17.3 mg"| __truncated__
#>  $ regions       : chr "USA (University of California, San Francisco)"
#>  $ notes         : chr "Csajka 2005 Table 1 demographics. 379 ephedrine, 352 norephedrine, 417 caffeine plasma samples and 40 urinary e"| __truncated__

Source trace

The per-parameter origin is recorded as an in-file comment next to each ini() entry in inst/modeldb/specificDrugs/Csajka_2005_ephedrine_caffeine.R. The table below collects them in one place.

Equation / parameter	Value	Source location
`lka_caf` (caffeine ka_C)	log(0.064 1/min)	Csajka 2005 Table 3
`lcl_caf` (caffeine CL_C/F_C)	log(0.083 L/min)	Csajka 2005 Table 3
`lvc_caf` (caffeine V_C/F_C)	log(38.6 L)	Csajka 2005 Table 3
`e_conmed_birthcontrol_cl_caf`	0.54	Csajka 2005 Table 3 (d_OC_CL)
`lka` (ephedrine ka_E)	log(0.036 1/min)	Csajka 2005 Table 3
`lcl_renal` (CL_RE/F_E)	log(0.34 L/min)	Csajka 2005 Table 3
`lvc` (V_E/F_E)	log(181 L)	Csajka 2005 Table 3
`ltlag` (ephedrine lag)	log(16.7 min)	Csajka 2005 Table 3
`lfdepot` (F_E,pharm)	fixed(log(0.59))	Csajka 2005 Table 3
`lvmax_neph` (Vmax/V_NE)	log(1.96e-4 mg/(min*L))	Csajka 2005 Table 3
`lkm` (Michaelis-Menten Km)	log(2.77 mg)	Csajka 2005 Table 3
`lkel_neph` (norephedrine ke_NE)	log(0.037 1/min)	Csajka 2005 Table 3, Methods text
`la50_caf` (ka_E,50)	log(31.4 mg)	Csajka 2005 Table 3
`d_caf`	fixed(0.99)	Csajka 2005 Table 3 (d = expit(theta_e = 19.5))
`propSd` (ephedrine plasma)	0.17	Csajka 2005 Table 3
`propSd_caf` (caffeine plasma)	0.17	Csajka 2005 Table 3
`propSd_neph` (norephedrine)	0.15	Csajka 2005 Table 3
IIVs (omega^2 = log(CV^2 + 1))	derived from %CV	Csajka 2005 Table 3
Caffeine equation	n/a	Csajka 2005 Methods ‘Caffeine pharmacokinetics’, equation 1
Ephedrine + norephedrine MM	n/a	Csajka 2005 Methods ‘Ephedrine and norephedrine pharmacokinetics’, equation 6
Caffeine effect on ephedrine ka	n/a	Csajka 2005 Methods ‘Interaction of caffeine and ephedrine’, equations 10b / 10e (final)
OC effect on caffeine CL	n/a	Csajka 2005 Methods ‘Caffeine pharmacokinetics’, equation 5

Virtual cohort

Original observed data are not publicly available. The virtual cohort below mirrors the Study 2 design (single oral 25 mg ephedrine + 200 mg caffeine, no oral contraceptive use), with a small parallel oral-contraceptive cohort to demonstrate the d_OC_CL effect on caffeine.

set.seed(20260604)

obs_times <- c(0, 15, 30, 45, 60, 75, 90, 120, 150, 180, 210, 240, 300, 360, 420,
               480, 600, 660, 720, 840, 960, 1080, 1200, 1320, 1440)

make_cohort <- function(n, cohort_label, oc_status, id_offset) {
  cov <- tibble(
    id = id_offset + seq_len(n),
    CONMED_BIRTHCONTROL = oc_status
  )
  doses <- bind_rows(
    cov |> mutate(time = 0, amt = 25,  cmt = "depot",     evid = 1L),
    cov |> mutate(time = 0, amt = 200, cmt = "depot_caf", evid = 1L)
  )
  obs <- tidyr::crossing(cov, tibble(time = obs_times)) |>
    mutate(amt = NA_real_, cmt = "Cc", evid = 0L)
  bind_rows(doses, obs) |>
    arrange(id, time, evid) |>
    mutate(cohort = cohort_label)
}

events <- bind_rows(
  make_cohort(60, "Study 2 pharmaceutical (no OC)", 0, id_offset = 0L),
  make_cohort(20, "Study 2 pharmaceutical (with OC)", 1, id_offset = 100L)
)

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

Simulation

sim <- rxode2::rxSolve(
  mod,
  events  = events,
  keep    = c("cohort", "CONMED_BIRTHCONTROL"),
  addCov  = TRUE,
  nStud   = 1
) |>
  as.data.frame()

sim_typical <- rxode2::rxSolve(
  rxode2::zeroRe(mod),
  events  = events,
  keep    = c("cohort", "CONMED_BIRTHCONTROL"),
  addCov  = TRUE
) |>
  as.data.frame()
#> ℹ omega/sigma items treated as zero: 'etalka_caf', 'etalcl_caf', 'etalvc_caf', 'etalka', 'etalcl_renal', 'etalvc', 'etaltlag', 'etalvmax_neph', 'etalkm', 'etalkel_neph'
#> Warning: multi-subject simulation without without 'omega'

Replicate published figures

Figure 2 - Caffeine plasma profile, +/- oral contraceptive

sim_typical |>
  filter(time <= 24 * 60) |>
  mutate(Cc_caf_ug_per_L = Cc_caf * 1000,
         OC = ifelse(CONMED_BIRTHCONTROL == 1, "On oral contraceptive", "Not on oral contraceptive")) |>
  distinct(time, OC, .keep_all = TRUE) |>
  ggplot(aes(time / 60, Cc_caf_ug_per_L, colour = OC)) +
  geom_line(linewidth = 0.7) +
  labs(x = "Time (h)", y = "Plasma caffeine (ug/L)",
       colour = "Cohort",
       title = "Figure 2 - caffeine plasma profile",
       caption = "Pharmaceutical 200 mg caffeine; typical-value simulation.\nReplicates the shape of Csajka 2005 Figure 2.")

Figure 3 - Norephedrine plasma profile from ephedrine metabolism

sim_typical |>
  filter(time <= 24 * 60, cohort == "Study 2 pharmaceutical (no OC)") |>
  mutate(Cc_neph_ug_per_L = Cc_neph * 1000) |>
  distinct(time, .keep_all = TRUE) |>
  ggplot(aes(time / 60, Cc_neph_ug_per_L)) +
  geom_line(linewidth = 0.7) +
  labs(x = "Time (h)", y = "Plasma norephedrine (ug/L)",
       title = "Figure 3 - plasma norephedrine from saturable conversion",
       caption = "Pharmaceutical 25 mg ephedrine; typical-value simulation.\nReplicates the shape of Csajka 2005 Figure 3 (solid line = MM model).")

Figure 4 - Ephedrine plasma profile

sim_typical |>
  filter(time <= 24 * 60, cohort == "Study 2 pharmaceutical (no OC)") |>
  mutate(Cc_ug_per_L = Cc * 1000) |>
  distinct(time, .keep_all = TRUE) |>
  ggplot(aes(time / 60, Cc_ug_per_L)) +
  geom_line(linewidth = 0.7) +
  labs(x = "Time (h)", y = "Plasma ephedrine (ug/L)",
       title = "Figure 4 - plasma ephedrine after pharmaceutical 25 mg",
       caption = "Caffeine-modulated absorption (d_caf = 0.99, ka_E,50 = 31.4 mg).\nReplicates the shape of Csajka 2005 Figure 4.")

PKNCA validation

Three independent PKNCA blocks - one per plasma output (caffeine, ephedrine, norephedrine). The treatment grouping (cohort + id) carries the with / without oral-contraceptive subgroups so per-cohort half-lives can be compared against the paper.

# Caffeine plasma NCA, both cohorts (no OC and with OC).
sim_caf <- sim |>
  filter(!is.na(Cc_caf)) |>
  mutate(Cc_caf_ug_per_L = Cc_caf * 1000) |>
  select(id, time, Cc_caf_ug_per_L, cohort)

dose_caf <- events |>
  filter(evid == 1, cmt == "depot_caf") |>
  select(id, time, amt, cohort)

conc_caf  <- PKNCA::PKNCAconc(sim_caf, Cc_caf_ug_per_L ~ time | cohort + id,
                              concu = "ug/L", timeu = "min")
dose_caf  <- PKNCA::PKNCAdose(dose_caf, amt ~ time | cohort + id, doseu = "mg")
ints_caf  <- data.frame(start = 0, end = Inf, cmax = TRUE, tmax = TRUE,
                        aucinf.obs = TRUE, half.life = TRUE)
nca_caf   <- PKNCA::pk.nca(PKNCA::PKNCAdata(conc_caf, dose_caf, intervals = ints_caf))

nca_caf_tbl <- nca_caf$result |>
  filter(PPTESTCD %in% c("cmax", "tmax", "aucinf.obs", "half.life")) |>
  group_by(cohort, PPTESTCD) |>
  summarise(median = median(PPORRES, na.rm = TRUE),
            q05    = quantile(PPORRES, 0.05, na.rm = TRUE),
            q95    = quantile(PPORRES, 0.95, na.rm = TRUE), .groups = "drop")
knitr::kable(nca_caf_tbl, caption = "Simulated caffeine NCA (per cohort).", digits = 2)

Simulated caffeine NCA (per cohort).
cohort	PPTESTCD	median	q05	q95
Study 2 pharmaceutical (no OC)	aucinf.obs	2461784.34	1334984.00	5189510.48
Study 2 pharmaceutical (no OC)	cmax	4666.71	3409.00	6005.30
Study 2 pharmaceutical (no OC)	half.life	348.98	166.65	746.42
Study 2 pharmaceutical (no OC)	tmax	60.00	44.25	120.00
Study 2 pharmaceutical (with OC)	aucinf.obs	5729865.73	3097906.72	11064482.70
Study 2 pharmaceutical (with OC)	cmax	5145.44	3803.88	5844.68
Study 2 pharmaceutical (with OC)	half.life	704.08	355.13	1506.85
Study 2 pharmaceutical (with OC)	tmax	67.50	45.00	121.50

# Ephedrine plasma NCA, no-OC cohort only (no OC effect on ephedrine).
sim_eph <- sim |>
  filter(!is.na(Cc), cohort == "Study 2 pharmaceutical (no OC)") |>
  mutate(Cc_ug_per_L = Cc * 1000) |>
  select(id, time, Cc_ug_per_L, cohort)

dose_eph <- events |>
  filter(evid == 1, cmt == "depot", cohort == "Study 2 pharmaceutical (no OC)") |>
  select(id, time, amt, cohort)

conc_eph  <- PKNCA::PKNCAconc(sim_eph, Cc_ug_per_L ~ time | cohort + id,
                              concu = "ug/L", timeu = "min")
dose_eph  <- PKNCA::PKNCAdose(dose_eph, amt ~ time | cohort + id, doseu = "mg")
ints_eph  <- data.frame(start = 0, end = Inf, cmax = TRUE, tmax = TRUE,
                        aucinf.obs = TRUE, half.life = TRUE)
nca_eph   <- PKNCA::pk.nca(PKNCA::PKNCAdata(conc_eph, dose_eph, intervals = ints_eph))

nca_eph_tbl <- nca_eph$result |>
  filter(PPTESTCD %in% c("cmax", "tmax", "aucinf.obs", "half.life")) |>
  group_by(PPTESTCD) |>
  summarise(median = median(PPORRES, na.rm = TRUE),
            q05    = quantile(PPORRES, 0.05, na.rm = TRUE),
            q95    = quantile(PPORRES, 0.95, na.rm = TRUE), .groups = "drop")
knitr::kable(nca_eph_tbl, caption = "Simulated ephedrine NCA (no-OC cohort).", digits = 2)

Simulated ephedrine NCA (no-OC cohort).
PPTESTCD	median	q05	q95
aucinf.obs	43446.79	38198.10	49823.70
cmax	65.32	47.99	87.91
half.life	377.24	258.74	517.66
tmax	150.00	75.00	210.00

# Norephedrine plasma NCA, no-OC cohort. Norephedrine is a metabolite
# (no direct dose), so a dose object is omitted from PKNCAdata.
sim_neph <- sim |>
  filter(!is.na(Cc_neph), cohort == "Study 2 pharmaceutical (no OC)") |>
  mutate(Cc_neph_ug_per_L = Cc_neph * 1000) |>
  select(id, time, Cc_neph_ug_per_L, cohort)

conc_neph <- PKNCA::PKNCAconc(sim_neph, Cc_neph_ug_per_L ~ time | cohort + id,
                              concu = "ug/L", timeu = "min")
ints_neph <- data.frame(start = 0, end = Inf, cmax = TRUE, tmax = TRUE,
                        auclast = TRUE, half.life = TRUE)
nca_neph  <- PKNCA::pk.nca(PKNCA::PKNCAdata(conc_neph, intervals = ints_neph))
#> No dose information provided, calculations requiring dose will return NA.

nca_neph_tbl <- nca_neph$result |>
  filter(PPTESTCD %in% c("cmax", "tmax", "auclast", "half.life")) |>
  group_by(PPTESTCD) |>
  summarise(median = median(PPORRES, na.rm = TRUE),
            q05    = quantile(PPORRES, 0.05, na.rm = TRUE),
            q95    = quantile(PPORRES, 0.95, na.rm = TRUE), .groups = "drop")
knitr::kable(nca_neph_tbl, caption = "Simulated norephedrine NCA (no-OC cohort).", digits = 2)

Simulated norephedrine NCA (no-OC cohort).
PPTESTCD	median	q05	q95
auclast	4890.96	1587.31	8915.80
cmax	4.88	1.68	8.78
half.life	601.30	335.96	1284.42
tmax	210.00	120.00	300.00

Comparison against published NCA

The paper reports terminal half-lives derived from the population PK fit (not full NCA tables). Compare the simulated half-lives below against the reported values.

Analyte / cohort	Simulated median t1/2 (h)	Published t1/2 (h)	Source
Caffeine, no oral contraceptive	5.8	5.3	Csajka 2005 Results ‘Caffeine pharmacokinetics’
Caffeine, on oral contraceptive	11.7	11.8	Csajka 2005 Results ‘Caffeine pharmacokinetics’
Ephedrine, no oral contraceptive	6.3	6.1	Csajka 2005 Results ‘Ephedrine and norephedrine pharmacokinetics’

A peak-amount sanity check against the paper’s observed-concentration ranges (Csajka 2005 Results):

Analyte	Simulated median Cmax (ug/L)	Published observed range (ug/L)
Caffeine, no OC	4667	0 - 8470
Ephedrine, no OC	65	1.59 - 101.40
Norephedrine	4.88	0.51 - 8.18

Assumptions and deviations

Pharmaceutical formulation default. The model’s ini() carries the pharmaceutical-formulation values (F_E,pharm = 0.59, no caffeine absorption lag). For herbal-formulation simulations, override lfdepot <- log(0.78) for F_E,herbal and prepend a 22.2-minute time shift to caffeine doses (the herbal caffeine lag); the paper reports no significant difference in caffeine bioavailability between formulations, so no herbal lfdepot_caf is required.
Norephedrine metabolic pathway treated as formation-only. The Michaelis-Menten conversion term vmax_neph * mm_factor drives the norephedrine pseudo-concentration but does NOT subtract from ephedrine central. The paper (Csajka 2005, Discussion paragraph 3) characterises this pathway as “minor compared with the renal elimination of ephedrine”; the published Vmax/V_NE is a compound parameter that pins the norephedrine concentration rate but does not identify the absolute Vmax required to deplete the parent. This is the standard mechanistic simplification for a saturable-but-minor conversion; ephedrine cumulative urinary recovery in the no-OC cohort matches the paper’s observed 0-24 h range (7.35 - 22.2 mg) under this simplification, which it would not under a fully-coupled depletion form.
Norephedrine compartment carries a pseudo-concentration. Because the norephedrine volume V_NE is unidentifiable, central_neph stores the norephedrine concentration directly (= A5 / V_NE), and the reported Vmax/V_NE is the rate of change of that concentration when the MM is saturated. The observation Cc_neph is therefore central_neph itself (no division by a volume).
Caffeine baseline omitted. The paper integrates a per-subject baseline caffeine concentration C0 (range 14.2 - 3820 ug/L due to dietary intake) for 22 of 24 subjects. The model file defaults to C0 = 0 (washout); users who want to reproduce the paper’s pre-dose concentrations can add an earlier-time dose or initialise central_caf accordingly.
OCR-derived unit ambiguity in Vmax/V_NE. Csajka 2005 Table 3 reports Vmax/V_NE = 1.96e-4 with a unit heading rendered ambiguously in the source PDF / trimmed-markdown (the character that should be “mu g” is rendered as “m g”); the same OCR rendering applies to plasma concentrations (e.g. “8470 m g L^-1” for caffeine, which can only mean “ug / L”). The numerical interpretation that reproduces the paper’s observed norephedrine concentration range (0.51 - 8.18 ug/L) is 1.96e-4 mg / (min L) (equivalently 0.196 ug / (min L)); the model file uses this interpretation, which is consistent with the table heading taken literally as mg. If a future re-extraction confirms that the heading was meant to be ug with no compensating order-of-magnitude shift elsewhere in the paper, the model file should be updated accordingly.
Km on amount, not concentration. Csajka 2005 Table 3 reports Km = 2.77 in the same heading-ambiguous unit as Vmax/V_NE. The model file encodes Km as a mg amount (compared against the ephedrine central state amount, not the central concentration); under this encoding the MM transitions from saturated to linear over the observed ephedrine concentration range, which is the structural improvement the paper attributes to the MM term (DOBJ = -124 vs the linear-formation alternative).
No effect of caffeine on its own absorption from the ephedrine indirect-action model. The paper confirms “No statistically significant effect of ephedrine on caffeine absorption was observed.” The caffeine ODE is independent of the ephedrine state.
OC encoding inverted from the paper’s source column. The paper’s source column is named OC (1 = on oral contraceptive); the canonical CONMED_BIRTHCONTROL has the same 1 = on-OC orientation, so no value transformation is required (covariateData$CONMED_BIRTHCONTROL$source_name = "OC").
Urine pH covariate excluded. The paper reports a post-hoc inverse linear association between urine pH and ephedrine renal clearance (CL_R = 0.4723 - 0.0172 * pH, p = 0.013) but does not retain pH in the final population PK model; the model file documents the screen via covariatesDataExcluded$URINE_PH rather than introducing pH as a covariate effect.
Norephedrine elimination unit. Csajka 2005 Table 3 prints the ke_NE row’s unit heading as “L / h” which is dimensionally wrong for a first-order rate constant. The prose text in the Results section gives the correct unit (“0.037 1 min^-1”); the model file uses the prose value.