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Somatropin / rhGH preclinical rat (Thorsted 2016)

Source: vignettes/articles/Thorsted_2016_somatropin_rat.Rmd
Thorsted_2016_somatropin_rat.Rmd

Model and source 

mod <- readModelDb("Thorsted_2016_somatropin_rat")
ui  <- rxode2::rxode(mod)
#> ℹ parameter labels from comments will be replaced by 'label()'
cat(ui$reference, sep = "\n")
#> Thorsted A, Thygesen P, Agerso H, Laursen T, Kreilgaard M. Translational mixed-effects PKPD modelling of recombinant human growth hormone - from hypophysectomized rat to patients. Br J Pharmacol. 2016 Jun;173(11):1742-55. doi:10.1111/bph.13473.
  • Description: Preclinical (hypophysectomized Sprague-Dawley rat). Mixed-effects PKPD model for recombinant human growth hormone (rhGH / somatropin) describing PK as a two-compartment model with parallel linear (CL) and Michaelis-Menten (Vmax, KM) elimination, parallel first-order subcutaneous absorption (ka1 direct path, ka2 delayed through one transit compartment, with bioavailabilities F1 and F2), an indirect response model for IGF-1 induction (stimulation of kin via a three-compartment effect-delay chain feeding an Emax/EC50 stimulation), and a linear bodyweight-gain model driven by IGF-1 above baseline. Reference rat body weight is 0.1 kg (100 g) and the allometric exponents (0.75 / 1.0) are fixed.
  • Article: Br J Pharmacol 173(11):1742-55

The Thorsted 2016 paper develops a mixed-effects PKPD model for recombinant human growth hormone (rhGH, INN: somatropin) in hypophysectomized male Sprague-Dawley rats following i.v. and s.c. administration. The PK is a two-compartment model with parallel linear clearance (CL) and Michaelis-Menten (Vmax, KM) elimination, and parallel first-order s.c. absorption (a direct ka1 path and a transit-delayed ka2 path with bioavailabilities F1 and F2). The PD has two layers: an indirect-response model for IGF-1 (Emax stimulation of kin via a three-compartment effect-delay chain), and a linear bodyweight-gain submodel driven by IGF-1 above the per-animal baseline.

Population 

str(ui$population)
#> List of 10
#>  $ species       : chr "rat (Sprague-Dawley, hypophysectomized; male, 90-110 g, age 6-8 weeks)"
#>  $ n_subjects    : int 230
#>  $ n_studies     : int 6
#>  $ age_range     : chr "6-8 weeks at study start (hypophysectomized at 4 weeks; acclimatized 1-2 weeks)"
#>  $ weight_range  : chr "90-110 g (approximately 0.1 kg)"
#>  $ sex_female_pct: num 0
#>  $ disease_state : chr "Hypophysectomized rat model of growth hormone deficiency (pituitary gland surgically removed at age 4 weeks); p"| __truncated__
#>  $ dose_range    : chr "rhGH 11-3319 ug as i.v. tail-vein bolus or s.c. injection into the scruff of the neck; six study cohorts in tot"| __truncated__
#>  $ regions       : chr "Denmark (Novo Nordisk A/S, Maaloev)"
#>  $ notes         : chr "230 male hypophysectomized Sprague-Dawley rats from Taconic M&B (Ejby, Denmark); 304 rhGH plasma concentrations"| __truncated__

The rat cohort is 230 male hypophysectomized Sprague-Dawley rats (90-110 g, approximately 0.1 kg) acclimatized 1-2 weeks after surgery and acclimatization (Thorsted 2016 Methods, Animals). The dataset combines one single-dose PKPD study (i.v. tail-vein and s.c. neck routes, sampling from pre-dose through 48 h) and five multiple-dose PD studies (daily s.c. injections through 28 days, with PD samples retained only through 168 h because of anti-drug-antibody formation thereafter; see Thorsted 2016 Methods, Data exclusion and Table 1).

Source trace

Per-parameter source citations are also recorded as inline comments in inst/modeldb/specificDrugs/Thorsted_2016_somatropin_rat.R.

Equation / parameter Value Source
Structural PKPD diagram n/a Thorsted 2016 Figure 2
CL - linear clearance 0.0285 L/h Table 2
Vmax - non-linear elimination capacity 11.5 ug/h Table 2
KM - non-linear elimination half-saturation 358 ug/L Table 2
Vc - central volume 0.0069 L Table 2
Q - inter-compartmental clearance 0.0101 L/h Table 2
Vp - peripheral volume 0.0081 L Table 2
ka1 - direct SC absorption rate 3.02 1/h Table 2
ka2 - transit-delayed SC absorption rate 1.22 1/h Table 2
F1 - bioavailability ka1 path 0.0316 Table 2
F2 - bioavailability ka2 path 0.833 Table 2
kout - IGF-1 degradation rate 0.0913 1/h Table 2
R0 - baseline IGF-1 29.4 ng/mL Table 2
Emax (PKPD-study cohort) 9.88 Table 2
EC50 - half-maximal stimulation 16.3 ug/L Table 2
kCPLAG - GH effect-delay rate 0.599 1/h Table 2
SLD - bodyweight-gain slope 0.000309 g per ng/mL per h Table 2
WT_BASE - baseline bodyweight 106 g Table 2
Allometric exponent CL / Q / Vmax 0.75 (fixed) Methods / Results
Allometric exponent Vc / Vp 1.0 (fixed) - rat Methods / Results
Allometric exponent ka1 / ka2 -0.25 (fixed) Methods
IIV CL 11.6% CV Table 2
IIV Vp 18.4% CV (correlated with CL, rho = -0.568) Table 2 / Results
IIV ka2 9.3% CV Table 2
IIV R0 17.0% CV Table 2
IIV WT_BASE 5.2% CV Table 2
Proportional residual error (PK) 0.233 Table 2
Additive residual SD (PK) 0.279 ng/mL Table 2
Additive residual SD (IGF-1, PKPD) 21.3 ng/mL Table 2
Additive residual SD (BW) 2.38 g Table 2

Virtual cohort

The original observed data are not publicly available. The simulations below use a small virtual cohort of 100-g rats. SC dosing requires two dose events per administration (one into the depot compartment, one into depot2; the model’s f(depot) and f(depot2) bioavailabilities split the systemic input between the two parallel absorption paths). IV dosing uses a single event into the central compartment.

set.seed(20260516)

make_sc_cohort <- function(n, dose_ug, regimen_label, id_offset = 0L,
                           obs_grid = c(0, 0.08, 0.17, 0.33, 0.5, 1, 2, 4, 6,
                                        8, 10, 12, 24)) {
  ids <- id_offset + seq_len(n)
  doses_depot  <- tidyr::expand_grid(id = ids, time = 0,
                                     evid = 1, amt = dose_ug,
                                     cmt = "depot")
  doses_depot2 <- doses_depot |> dplyr::mutate(cmt = "depot2")
  obs <- tidyr::expand_grid(id = ids, time = obs_grid) |>
    dplyr::mutate(evid = 0, amt = 0, cmt = "Cc")
  events <- dplyr::bind_rows(doses_depot, doses_depot2, obs) |>
    dplyr::arrange(id, time, evid) |>
    dplyr::mutate(WT = 0.1, cohort = regimen_label)
  events
}

make_iv_cohort <- function(n, dose_ug, regimen_label, id_offset = 0L,
                           obs_grid = c(0, 0.08, 0.17, 0.33, 0.5, 1, 2, 4, 6,
                                        8, 10, 12)) {
  ids <- id_offset + seq_len(n)
  doses <- tidyr::expand_grid(id = ids, time = 0,
                              evid = 1, amt = dose_ug,
                              cmt = "central")
  obs <- tidyr::expand_grid(id = ids, time = obs_grid) |>
    dplyr::mutate(evid = 0, amt = 0, cmt = "Cc")
  events <- dplyr::bind_rows(doses, obs) |>
    dplyr::arrange(id, time, evid) |>
    dplyr::mutate(WT = 0.1, cohort = regimen_label)
  events
}

events <- dplyr::bind_rows(
  make_iv_cohort(40, 1106, "IV 1106 ug",  id_offset =   0L),
  make_iv_cohort(40, 3319, "IV 3319 ug",  id_offset =  40L),
  make_sc_cohort(40,  221, "SC 221 ug",   id_offset = 100L),
  make_sc_cohort(40, 1106, "SC 1106 ug",  id_offset = 200L),
  make_sc_cohort(40, 3319, "SC 3319 ug",  id_offset = 300L)
)

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

Typical-value simulation

The chunk below uses rxode2::zeroRe() to suppress between-animal variability and produce typical-value (population-mean) trajectories for rhGH plasma concentration after single i.v. and s.c. doses.

mod_typ <- rxode2::zeroRe(mod)
#> ℹ parameter labels from comments will be replaced by 'label()'
sim_typ <- rxode2::rxSolve(mod_typ, events = events,
                           keep = c("cohort", "WT")) |>
  as.data.frame()
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvp', 'etalka2', 'etalr0', 'etalwtbase'
#> Warning: multi-subject simulation without without 'omega'
sim_typ |>
  dplyr::filter(time > 0) |>
  ggplot(aes(time, Cc, colour = cohort)) +
  geom_line(size = 0.8) +
  scale_y_log10() +
  labs(x = "Time (h)", y = "rhGH plasma concentration (ng/mL)",
       title = "Typical-value rhGH PK in 100 g hypophysectomized rats",
       caption = "Replicates the shape of Thorsted 2016 Figure 1A (i.v.) / Figure 1B (s.c.).")
#> Warning: Using `size` aesthetic for lines was deprecated in ggplot2 3.4.0.
#> ℹ Please use `linewidth` instead.
#> This warning is displayed once per session.
#> Call `lifecycle::last_lifecycle_warnings()` to see where this warning was
#> generated.

IGF-1 and bodyweight from a single SC dose

A single s.c. dose drives a delayed IGF-1 induction (through the three-compartment effect-delay chain) and a small bodyweight increase proportional to the IGF-1 excursion above the per-animal baseline.

events_pd <- make_sc_cohort(
  n = 10, dose_ug = 1106, regimen_label = "SC 1106 ug",
  id_offset = 1000L,
  obs_grid = c(0, 24, 48, 72, 96, 120, 144, 168)
)
sim_pd <- rxode2::rxSolve(mod_typ, events = events_pd,
                          keep = c("cohort", "WT")) |>
  as.data.frame()
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvp', 'etalka2', 'etalr0', 'etalwtbase'
#> Warning: multi-subject simulation without without 'omega'
sim_pd |>
  dplyr::filter(time > 0) |>
  dplyr::distinct(time, .keep_all = TRUE) |>
  ggplot(aes(time, IGF1)) +
  geom_line(size = 0.8, colour = "tomato") +
  geom_hline(yintercept = 29.4, linetype = "dashed") +
  labs(x = "Time (h)", y = "IGF-1 (ng/mL)",
       title = "Typical-value IGF-1 after single 1106 ug s.c. rhGH dose",
       caption = "Dashed line at R0 = 29.4 ng/mL. Replicates Thorsted 2016 Figure 1C.")

sim_pd |>
  dplyr::filter(time > 0) |>
  dplyr::distinct(time, .keep_all = TRUE) |>
  ggplot(aes(time, BW)) +
  geom_line(size = 0.8, colour = "steelblue") +
  labs(x = "Time (h)", y = "Bodyweight (g)",
       title = "Typical-value bodyweight trajectory after single 1106 ug s.c. dose",
       caption = "Replicates Thorsted 2016 bodyweight time course (Figure 1E shape).")

NCA validation of rhGH after i.v. dosing

PKNCA is used to compute simulated rhGH NCA parameters for the i.v. cohorts, where a clean concentration profile makes NCA most interpretable. The model includes parallel linear and Michaelis-Menten elimination, so the apparent half-life is a function of the concentration range sampled.

sim_nca <- sim_typ |>
  dplyr::filter(time > 0, grepl("^IV ", cohort)) |>
  dplyr::select(id, time, Cc, cohort)

dose_df <- events |>
  dplyr::filter(evid == 1, grepl("^IV ", cohort)) |>
  dplyr::select(id, time, amt, cohort)

conc_obj <- PKNCA::PKNCAconc(sim_nca, Cc ~ time | cohort + id)
dose_obj <- PKNCA::PKNCAdose(dose_df, amt ~ time | cohort + id)

intervals <- data.frame(
  start      = 0,
  end        = 12,
  cmax       = TRUE,
  tmax       = TRUE,
  aucinf.obs = 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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knitr::kable(summary(nca_res),
             caption = "Simulated NCA for rhGH after i.v. bolus (typical-value rat).")
Simulated NCA for rhGH after i.v. bolus (typical-value rat).
start end cohort N cmax tmax half.life aucinf.obs
0 12 IV 1106 ug 40 103000 [0.000] 0.0800 [0.0800, 0.0800] 0.659 [0.000] NC
0 12 IV 3319 ug 40 309000 [0.000] 0.0800 [0.0800, 0.0800] 0.659 [0.000] NC

Assumptions and deviations

  • Dual Emax collapsed to the single-dose value. Thorsted 2016 Table 2 reports two separate Emax estimates: 9.88 for the single-dose PKPD cohort and 23.9 for the repeated-dose PD cohorts (the latter explained in the Discussion as a physiological adaptation - increased GH-receptor / GH-binding-protein expression with repeated dosing). The packaged model carries only the single-dose Emax = 9.88 because that is the value the paper itself carries forward to the human projection (Table 3). Users who want to simulate the repeated-dose PD cohort response should override lemax with log(23.9) in ini().

  • Dual IGF-1 residual SD collapsed to the single-dose value. Symmetrically, Table 2 reports two additive residual SDs for the IGF-1 model: 21.3 ng/mL for the PKPD cohort and 78.2 ng/mL (with 58.8% CV IIV on the residual term) for the PD cohorts. The packaged model uses 21.3 (the PKPD-cohort value) without IIV on residual. Override addSd_IGF1 (and add etalAddSdIGF1 IIV if needed) to recover the PD-cohort residual model.

  • Parallel-absorption dosing convention. SC doses require two event records per administration in user-supplied datasets (one with cmt = "depot" and one with cmt = "depot2", same amt); the model’s f(depot) and f(depot2) bioavailability functions partition the systemic input across the two paths. Provide a single event record with cmt = "central" for i.v. doses.

  • Bodyweight is reported in grams. The model state bw and the residual error addSd_BW = 2.38 are in grams (matching Table 2), while the WT covariate used for allometric scaling is in kg per the nlmixr2lib convention. Set WT = 0.1 for a 100-g reference rat.