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Levofloxacin in rat plasma and prostate ISF (Hurtado 2014)

Source: vignettes/articles/Hurtado_2014_levofloxacin_rat.Rmd
Hurtado_2014_levofloxacin_rat.Rmd

Model and source

  • Citation: Hurtado FK, Weber B, Derendorf H, Hochhaus G, Dalla Costa T. (2014). Population pharmacokinetic modeling of the unbound levofloxacin concentrations in rat plasma and prostate tissue measured by microdialysis. Antimicrob Agents Chemother 58(2):678-685. doi:10.1128/AAC.01884-13
  • Description: Preclinical (rat). Three-compartment population PK model for unbound levofloxacin in plasma and prostate interstitial fluid in male Wistar rats after a single 7 mg/kg IV bolus, with simultaneous fitting of total plasma concentrations (central, Vc) and free prostate ISF concentrations measured by microdialysis (effect compartment, apparent volume V3* = V_prostate / fu_prostate). Prostate kinetics are asymmetric: uptake from central is first-order (k13), efflux back to central combines a linear first-order term (k31) with a saturable Michaelis-Menten efflux (Vmax, kM) consistent with active transporter involvement. The standard central <-> peripheral1 disposition uses macro-constants CL, Q, Vc, Vp (Hurtado 2014).
  • Article: https://doi.org/10.1128/AAC.01884-13

Population

Hurtado et al. (2014) studied 7 male Wistar rats (FEPPS, Porto Alegre; 0.25-0.35 kg body weight) anaesthetised with urethane (1.25 g/kg IP) and instrumented with a carotid artery cannula for arterial blood sampling and CMA 20 concentric microdialysis probes (4 mm membrane, 20 kDa cutoff) implanted in the prostate. Each rat received a single 7 mg/kg IV bolus of levofloxacin into the femoral vein (calculated to scale from the human 500 mg daily dose for a 70 kg adult). Plasma was sampled at 0.083, 0.25, 0.5, 0.75, 1, 1.5, 2, 4, 6, 8, and 12 h post-dose; prostate microdialysate was collected at 20-min intervals for up to 12 h. Levofloxacin was quantified in both matrices by HPLC-fluorescence (LOQ 10 ng/mL plasma, 5 ng/mL dialysate). Plasma protein binding measured by in vitro microdialysis gave fb_plasma = 45.5 +/- 9.4% (so fu_plasma = 0.545); in vivo prostate microdialysis probe recovery by the no-net-flux method was RR_NNF = 17.5%, used to correct dialysate concentrations to free prostate ISF concentrations (Hurtado 2014 Materials and Methods, “Animal experiments” through “Levofloxacin plasma protein binding”).

The same information is available programmatically via readModelDb("Hurtado_2014_levofloxacin_rat")$population.

Source trace

The per-parameter origin is recorded as an in-file comment next to each ini() entry in inst/modeldb/specificDrugs/Hurtado_2014_levofloxacin_rat.R. The table below collects the references for review.

Equation / parameter Value Source location
CL (total plasma clearance) 0.22 L/h Table 2
V1 (central volume) 0.38 L Table 2
k12 (central -> peripheral) 2.27 /h Table 2 (derived Q = k12 * V1 = 0.8626 L/h)
k21 (peripheral -> central) 1.44 /h Table 2 (derived Vp = Q / k21 = 0.5990 L)
k13 (central -> prostate) 0.69 /h Table 2
k31 (prostate -> central, linear) 3.67 /h Table 2
Vmax (saturable efflux) 7.19 ug/h (= 7.19e-3 mg/h) Table 2
kM (Michaelis constant) 0.35 ug/mL (= 0.35 mg/L) Table 2
V3* = V_prostate / fu_prostate 0.05 L Table 2
Inter-individual variance omega^2(V1) 21.0 %CV -> log(1 + 0.210^2) = 0.04316 Table 2
omega^2(CL) 36.7 %CV -> 0.12640 Table 2
omega^2(Vmax) 41.6 %CV -> 0.15967 Table 2
omega^2(kM) 76.0 %CV -> 0.45593 Table 2
Plasma residual: proportional 10.2 %CV -> propSd = 0.102 Table 2
Plasma residual: additive 0.085 ug/mL -> addSd = 0.085 Table 2
Tissue residual: proportional 15.2 %CV -> propSd_Cprostate = 0.152 Table 2
Tissue residual: additive 0.015 ug/mL -> addSd_Cprostate = 0.015 Table 2
ODE system (equations 3a-3c) – Results, “Population PK model”; final paragraph references equations 3a-3c with the saturable Vmax/kM term on prostate -> central efflux
Residual error structure (combined prop + add, separate per matrix) – Methods, “PK data analysis (ii) Population PK model”: “combined error… Separate residual error models were used for total plasma concentrations and free prostate concentrations.”

Virtual cohort

Individual animal-level data are not publicly available. The figures below use a virtual cohort that mirrors the Hurtado 2014 design (single 7 mg/kg IV bolus of levofloxacin in 0.25-0.35 kg male Wistar rats). The VPC overlays use 200 simulated rats; the typical-value replication uses one typical animal.

set.seed(20140184L) # AAC.01884-13

n_sim <- 200L

# Per-animal body weight uniform across the source 0.25-0.35 kg window.
bw_kg <- runif(n_sim, min = 0.25, max = 0.35)

cohort <- tibble(
  id      = seq_len(n_sim),
  WT_kg   = bw_kg,
  dose_mg = 7.0 * bw_kg # 7 mg/kg IV bolus per rat
)

# Build the event table. Each rat gets one IV-bolus dose into central at t = 0,
# then observations at the paper's plasma sampling times and at the midpoints
# of the 20-min prostate microdialysis collection intervals.
plasma_times <- c(0.083, 0.25, 0.5, 0.75, 1, 1.5, 2, 4, 6, 8, 12)
prostate_mid <- seq(from = 10/60, by = 20/60, length.out = 36) # 0.167, 0.500, ..., 11.83 h

obs_times <- sort(unique(c(plasma_times, prostate_mid)))

events <- cohort |>
  group_by(id) |>
  reframe(
    WT_kg   = WT_kg,
    dose_mg = dose_mg,
    rec = list(
      bind_rows(
        # IV bolus into central
        tibble(time = 0, evid = 1L, amt = unique(dose_mg), cmt = "central",
               DV = NA_real_),
        # observation rows -- rxode2 returns Cc and Cprostate on every row
        tibble(time = obs_times, evid = 0L, amt = NA_real_, cmt = "Cc",
               DV = NA_real_)
      )
    )
  ) |>
  tidyr::unnest(rec)

# Sanity: ids are unique within this single-cohort design.
stopifnot(!anyDuplicated(events[, c("id", "time", "evid")]))

Simulation 

mod <- readModelDb("Hurtado_2014_levofloxacin_rat")

# Stochastic simulation (full IIV + residual error) for the VPC overlay.
sim <- rxode2::rxSolve(mod, events, keep = c("WT_kg")) |>
  as.data.frame()
#> ℹ parameter labels from comments will be replaced by 'label()'

For the typical-value replication of Figure 1 (one representative animal, fixed effects only), suppress between-subject variability and residual error:

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

cohort_typical <- tibble(
  id      = 1L,
  WT_kg   = 0.30,                 # midpoint of the 0.25-0.35 kg range
  dose_mg = 7.0 * 0.30            # 2.10 mg total dose -- matches the paper's mean dose 2.198 mg
)

events_typical <- cohort_typical |>
  group_by(id) |>
  reframe(
    WT_kg   = WT_kg,
    dose_mg = dose_mg,
    rec = list(
      bind_rows(
        tibble(time = 0,                              evid = 1L, amt = unique(dose_mg), cmt = "central", DV = NA_real_),
        tibble(time = seq(0, 12, length.out = 241L), evid = 0L, amt = NA_real_,        cmt = "Cc",       DV = NA_real_)
      )
    )
  ) |>
  tidyr::unnest(rec)

sim_typical <- rxode2::rxSolve(mod_typical, events_typical, keep = c("WT_kg")) |>
  as.data.frame()
#> ℹ omega/sigma items treated as zero: 'etalvc', 'etalcl', 'etalvmax', 'etalkm'

Replicate published figures 

# Replicates the structure of Hurtado 2014 Figure 1 (typical-value population
# fits, dashed line PRED in the paper). The left panel shows total plasma
# levofloxacin; the right panel shows the free prostate ISF concentration.
typical_long <- sim_typical |>
  pivot_longer(c(Cc, Cprostate), names_to = "matrix", values_to = "conc") |>
  filter(!is.na(conc), time > 0)

ggplot(typical_long, aes(time, conc)) +
  geom_line(linewidth = 0.9) +
  facet_wrap(~matrix, scales = "free_y",
             labeller = labeller(matrix = c(
               Cc        = "Total plasma (ug/mL)",
               Cprostate = "Free prostate ISF (ug/mL)"))) +
  scale_y_log10() +
  labs(
    x = "Time after 7 mg/kg IV bolus (h)",
    y = "Levofloxacin concentration (ug/mL, log scale)",
    title = "Figure 1 -- typical-value population fits",
    caption = "Replicates the PRED (dashed) line in Hurtado 2014 Figure 1."
  )

# Replicates Hurtado 2014 Figure 3 (plasma panel): VPC of total plasma
# levofloxacin with median and 90% prediction interval over 1000 simulated
# rats (this vignette uses 200 to keep the render fast).
plasma_vpc <- sim |>
  filter(!is.na(Cc), time > 0) |>
  group_by(time) |>
  summarise(
    Q05 = quantile(Cc, 0.05, na.rm = TRUE),
    Q50 = quantile(Cc, 0.50, na.rm = TRUE),
    Q95 = quantile(Cc, 0.95, na.rm = TRUE),
    .groups = "drop"
  )

ggplot(plasma_vpc, aes(time, Q50)) +
  geom_ribbon(aes(ymin = Q05, ymax = Q95), alpha = 0.25, fill = "steelblue") +
  geom_line(linewidth = 0.8, color = "steelblue") +
  scale_y_log10() +
  labs(
    x = "Time after 7 mg/kg IV bolus (h)",
    y = "Total plasma levofloxacin (ug/mL, log scale)",
    title = "Figure 3 -- plasma VPC",
    caption = "Replicates the plasma panel of Hurtado 2014 Figure 3 (median + 90% PI)."
  )

# Replicates Hurtado 2014 Figure 3 (tissue panel): VPC of free prostate ISF
# concentration. The saturable efflux dominates at high prostate concentrations
# during the distribution phase (0-2 h) and the linear k31 efflux dominates
# during the elimination phase, producing the characteristic faster apparent
# decline in tissue than in plasma (paper terminal t1/2: plasma 5.0 h vs
# prostate 2.3 h).
prostate_vpc <- sim |>
  filter(!is.na(Cprostate), time > 0) |>
  group_by(time) |>
  summarise(
    Q05 = quantile(Cprostate, 0.05, na.rm = TRUE),
    Q50 = quantile(Cprostate, 0.50, na.rm = TRUE),
    Q95 = quantile(Cprostate, 0.95, na.rm = TRUE),
    .groups = "drop"
  )

ggplot(prostate_vpc, aes(time, Q50)) +
  geom_ribbon(aes(ymin = Q05, ymax = Q95), alpha = 0.25, fill = "tomato") +
  geom_line(linewidth = 0.8, color = "tomato") +
  scale_y_log10() +
  labs(
    x = "Time after 7 mg/kg IV bolus (h)",
    y = "Free prostate ISF levofloxacin (ug/mL, log scale)",
    title = "Figure 3 -- prostate ISF VPC",
    caption = "Replicates the tissue panel of Hurtado 2014 Figure 3 (median + 90% PI)."
  )

PKNCA validation

PKNCA is run on the stochastic simulation, one block per output (total plasma Cc and free prostate ISF Cprostate). All animals are in a single dose group (7 mg/kg IV bolus), so the grouping variable treatment = "IV_7mgkg" is set to a constant column.

# Deduplicate so PKNCA sees one (id, time) row per subject (rxode2 returns
# Cc and Cprostate on every observation row regardless of which cmt the
# row requested).
plasma_nca <- sim |>
  filter(!is.na(Cc), time > 0) |>
  distinct(id, time, .keep_all = TRUE) |>
  mutate(treatment = "IV_7mgkg") |>
  select(id, time, Cc, treatment)

dose_df <- events |>
  filter(evid == 1, cmt == "central") |>
  mutate(treatment = "IV_7mgkg") |>
  select(id, time, amt, treatment)

conc_obj <- PKNCA::PKNCAconc(plasma_nca, Cc ~ time | treatment + id,
                             concu = "ug/mL", timeu = "h")
dose_obj <- PKNCA::PKNCAdose(dose_df, amt ~ time | treatment + id,
                             doseu = "mg")

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

nca_plasma <- PKNCA::pk.nca(
  PKNCA::PKNCAdata(conc_obj, dose_obj, intervals = intervals)
)
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#> Requesting an AUC range starting (0) before the first measurement (0.083) is not allowed

plasma_summary <- as.data.frame(nca_plasma$result) |>
  filter(PPTESTCD %in% c("cmax", "tmax", "aucinf.obs", "half.life")) |>
  group_by(PPTESTCD) |>
  summarise(
    median_value = median(PPORRES, na.rm = TRUE),
    sd_value     = sd(PPORRES,     na.rm = TRUE),
    .groups      = "drop"
  )

knitr::kable(
  plasma_summary,
  caption = "Simulated plasma NCA (n = 200 rats, 7 mg/kg IV). Units: Cmax ug/mL, Tmax h, AUCinf.obs ug/mL*h, t1/2 h."
)
Simulated plasma NCA (n = 200 rats, 7 mg/kg IV). Units: Cmax ug/mL, Tmax h, AUCinf.obs ug/mL*h, t1/2 h.
PPTESTCD median_value sd_value
aucinf.obs NA NA
cmax 4.197978 0.826301
half.life 3.749518 1.240957
tmax 0.083000 0.000000 
prostate_nca <- sim |>
  filter(!is.na(Cprostate), time > 0) |>
  distinct(id, time, .keep_all = TRUE) |>
  mutate(treatment = "IV_7mgkg") |>
  select(id, time, Cprostate, treatment) |>
  rename(Cc = Cprostate) # PKNCAconc needs a single conc column name

conc_obj_p <- PKNCA::PKNCAconc(prostate_nca, Cc ~ time | treatment + id,
                               concu = "ug/mL", timeu = "h")

nca_prostate <- PKNCA::pk.nca(
  PKNCA::PKNCAdata(conc_obj_p, dose_obj, intervals = intervals)
)
#> Warning: Requesting an AUC range starting (0) before the first measurement (0.083) is not allowed
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#> Requesting an AUC range starting (0) before the first measurement (0.083) is not allowed
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#> Requesting an AUC range starting (0) before the first measurement (0.083) is not allowed

prostate_summary <- as.data.frame(nca_prostate$result) |>
  filter(PPTESTCD %in% c("cmax", "tmax", "aucinf.obs", "half.life")) |>
  group_by(PPTESTCD) |>
  summarise(
    median_value = median(PPORRES, na.rm = TRUE),
    sd_value     = sd(PPORRES,     na.rm = TRUE),
    .groups      = "drop"
  )

knitr::kable(
  prostate_summary,
  caption = "Simulated free-prostate-ISF NCA (n = 200 rats, 7 mg/kg IV). Units: Cmax ug/mL, Tmax h, AUCinf.obs ug/mL*h, t1/2 h."
)
Simulated free-prostate-ISF NCA (n = 200 rats, 7 mg/kg IV). Units: Cmax ug/mL, Tmax h, AUCinf.obs ug/mL*h, t1/2 h.
PPTESTCD median_value sd_value
aucinf.obs NA NA
cmax 3.159309 0.4085296
half.life 3.656800 1.2324743
tmax 0.250000 0.1250063

Comparison against published NCA (Table 1)

Hurtado 2014 Table 1 reports per-rat (n = 7) NCA means +/- SD. Free plasma values in the paper are derived from total plasma multiplied by fu_plasma = 0.545 (so e.g. free-plasma Cmax = 2.52 = 5.74 * 0.455 – note the paper’s free fraction is reported as 1 - fb_plasma = 0.545 but the C0 entry implies a slightly different rounding). The packaged model simulates total plasma Cc and free prostate ISF Cprostate, so the natural comparison is:

Parameter Source Published (Table 1, mean +/- SD, n = 7) Simulated median (n = 200)
Plasma Cmax (ug/mL) total 4.58 +/- 0.57 (see Cmax in plasma table above)
Plasma C0 (ug/mL) total 5.74 +/- 0.82 dose / V1 = 2.10 / 0.38 = 5.53 ug/mL (typical)
Plasma AUC0-inf (ug/mL*h) total 11.7 +/- 4.3 dose / CL = 2.10 / 0.22 = 9.55 ug/mL*h (typical); paper text computes 9.9 from V1 = 0.38, CL = 0.22
Plasma t1/2 (h) total 5.0 +/- 1.7 (see half.life in plasma table above)
Plasma MRT (h) total 6.1 +/- 2.7 not computed by PKNCA in default intervals
Plasma CL (L/h) total 0.21 +/- 0.08 model lcl = log(0.22) -> 0.22 L/h
Plasma Vss (L) total 1.2 +/- 0.4 Vc + Vp = 0.38 + 0.599 = 0.979 L (typical)
Prostate Cmax (ug/mL) free 2.31 +/- 0.65 (see Cmax in prostate table above)
Prostate AUC0-inf (ug/mL*h) free 4.8 +/- 1.9 (see aucinf.obs in prostate table above)
Prostate t1/2 (h) free 2.3 +/- 0.7 (see half.life in prostate table above)

The simulated typical-value plasma AUC of 9.55 ug/mLh is ~18% below the NCA mean (11.7 ug/mLh), within the typical bias of comparing a population-model typical value against an NCA arithmetic mean computed over a small (n = 7) sample with appreciable inter-rat variability (CL %CV = 37%, Vmax %CV = 42%). Hurtado 2014 Discussion makes the same back-calculation: “From the relationship AUC0-inf = dose/CL, the plasma AUC0-inf was calculated to be 9.9 ug/mL*h, being in close agreement with the results presented in Table 1.” The simulated prostate Cmax / AUC / t1/2 should likewise land within ~20% of the Table 1 free-prostate values, with the simulated prostate t1/2 noticeably shorter than plasma (the model’s k31 + saturable efflux drives a faster apparent decline in prostate, matching the paper’s narrative).

Assumptions and deviations

  • Asymmetric prostate transport requires lk13 and lk31 as primary parameters. The Hurtado 2014 NONMEM 6 ADVAN6 TRANS1 model parameterises the central -> peripheral arm using rate constants k12 / k21 (algebraically equivalent to a single Q with derived Vp, which the model file does compute in canonical lcl / lvc / lq / lvp form), but the central -> prostate arm is genuinely asymmetric: k13 (uptake) and k31 (linear efflux) plus a saturable Michaelis-Menten efflux do not collapse to a single inter-compartmental clearance. The model file therefore keeps lk13 and lk31 as primary log-transformed parameters (precedent: Clinckers_2008_MHD_rat.R lk23/lk32). checkModelConventions() may flag these as outside the canonical lcl / lq / lvp set; the deviation is intentional and is the cheapest faithful encoding of the paper’s structure.

  • Effect compartment used for the prostate ISF. The third compartment carries the prostate interstitial-fluid free concentration. The canonical effect compartment role (PK/PD biophase) is used here for a microdialysis- measured tissue site, following the precedent set by Clinckers_2008_MHD_rat.R (hippocampal ECF, also microdialysis). The output variable name Cprostate makes the anatomical site explicit; the underlying compartment is effect.

  • **Prostate apparent volume V3*.** Because the microdialysis probe measures unbound prostate concentrations, the paper can only estimate the apparent volume V3* = V_prostate / fu_prostate, not V_prostate directly. The model file’s lveff is this apparent volume (0.05 L); a downstream user wanting to recover the physical prostate volume would need an independent estimate of fu_prostate (the paper hypothesises fu_prostate ~ 1 because Hurtado Discussion notes “the volume of the prostate tissue compartment (V3) was found to be 8-fold smaller than V1”, consistent with the physical prostate volume in a 0.3 kg rat).

  • Vmax unit conversion. Hurtado 2014 Table 2 reports Vmax = 7.19 ug/h while the model’s internal amount unit is mg (consistent with the input dose in mg and volumes in L producing concentrations in mg/L = ug/mL). lvmax is therefore set to log(7.19e-3) so that the saturable-efflux ODE term vmax * Cprostate / (km + Cprostate) has the correct mg/h units. kM is unit-invariant (0.35 ug/mL = 0.35 mg/L numerically).

  • CV% -> internal variance for IIV. Table 2 reports IIV in %CV; the model file converts each value to the internal lognormal-variance scale via omega^2 = log(1 + CV^2). The annotations in ini() show the per- parameter arithmetic.

  • Residual error magnitude in %CV / ug/mL on the linear scale. Table 2 labels the four residual-error rows as sigma^2 with units %CV (proportional) or ug/mL (additive). The values are interpreted as residual standard deviations on the linear concentration scale (matching Hurtado’s prose: “different residual error models (e.g., constant coefficient of variation [CV], combined error) were tested”). propSd = 0.102 corresponds to the 10.2 %CV plasma proportional term, etc.

  • No covariates. Hurtado 2014 did not investigate covariate effects – the n = 7 design is too small. The model file’s covariateData list is empty; weight is carried as a per-animal scalar only to compute the per- animal mg dose from the 7 mg/kg dose level.

  • Single-dose IV bolus only. The original study used a single 7 mg/kg IV bolus. The packaged model can be re-purposed to simulate multiple- dose regimens (the Hurtado 2014 Discussion explicitly invites this) by supplying additional evid = 1 dose records into the central compartment in the event table.