Gemtuzumab (Jager 2011)

Model and source

Citation: Jager E, van der Velden VHJ, te Marvelde JG, Walter RB, Agur Z, Vainstein V (2011). Targeted drug delivery by gemtuzumab ozogamicin: mechanism-based mathematical model for treatment strategy improvement and therapy individualization. PLoS One 6(9):e24265. doi:10.1371/journal.pone.0024265.
DDMORE Foundation Model Repository entry: DDMODEL00000229 – Monolix re-fit with an added peripheral drug compartment.
Description: Mechanism-based PKPD model coupling drug pharmacokinetics with explicit binding to the cell-surface antigen CD33. Free drug in a central compartment binds free CD33 receptor to form a drug-receptor complex that is internalized; the toxic ozogamicin component then drives linear depletion of leukemic blast cells.

The model packaged here translates the DDMORE bundle’s GO_PK_model.mdl (MDL DSL source) to the nlmixr2lib inst/modeldb/ddmore/ convention. Parameter values come from the bundle’s MDL parObj$STRUCTURAL and parObj$VARIABILITY blocks, which Model_Accommodations.txt documents as the Monolix-fitted final estimates obtained by re-fitting the Jager 2011 mechanism on the original publication data with an additional peripheral PK compartment and simultaneous (rather than step-wise) estimation of all parameters. The DDMORE bundle does not ship a .lst listing or a simulated dataset, and the original Jager 2011 PLoS One paper is not on disk under this worktree’s literature tree, so the implementation is faithful to the MDL but has no external numeric cross-check; see Assumptions and deviations below.

Population

The Jager 2011 publication describes a single-cohort mechanism-based PKPD analysis in patients with acute myeloid leukemia (AML) receiving the CD33-directed antibody-drug conjugate gemtuzumab ozogamicin (Mylotarg). The DDMORE bundle does not reproduce demographic detail (age, weight, sex, race distribution, regional balance, or trial design) in either the Model_Accommodations.txt accompaniment or the MDL dataObj block. Programmatic access:

mod_fun <- readModelDb("Jager_2011_gemtuzumab")
str(environment(mod_fun)$population)
#>  NULL

Consult Jager et al. (2011) directly for the full population description.

Source trace

The per-parameter origin is recorded as an in-file comment next to each ini() entry in inst/modeldb/ddmore/Jager_2011_gemtuzumab.R. The table below collects those entries in one place. All values come from the MDL bundle’s parObj block in GO_PK_model.mdl; the bundle ships no Output_real_*.lst listing.

nlmixr2 parameter	Value	DDMORE source location
`lvc`	log(5.42)	`parObj$STRUCTURAL$POP_v1`
`lk`	log(0.0135)	`parObj$STRUCTURAL$POP_k`
`lkm`	log(0.00757)	`parObj$STRUCTURAL$POP_km`
`lkn`	log(0.0185)	`parObj$STRUCTURAL$POP_kn`
`lkb`	log(9.24e5)	`parObj$STRUCTURAL$POP_kb`
`lku`	log(310)	`parObj$STRUCTURAL$POP_ku`
`lki`	log(0.624)	`parObj$STRUCTURAL$POP_ki`
`lke`	log(0.199)	`parObj$STRUCTURAL$POP_ke`
`lrp`	log(823)	`parObj$STRUCTURAL$POP_rp`
`lalph`	log(0.0755)	`parObj$STRUCTURAL$POP_alph`
`ln0`	log(1.32e-5)	`parObj$STRUCTURAL$POP_n0`
`etalki`	0.258^2	`parObj$VARIABILITY$omega_ki` (sd, type is sd)
`etalke`	0.281^2	`parObj$VARIABILITY$omega_ke` (sd, type is sd)
`etalrp`	0.611^2	`parObj$VARIABILITY$omega_rp` (sd, type is sd)
`addSd`	0.000583	`parObj$STRUCTURAL$a` (additive residual error)
Constant `nav`	6.02214	`mdlObj$MODEL_PREDICTION` inline (Avogadro number / 1e23)
Constant `vblood`	4.8	`mdlObj$MODEL_PREDICTION` inline (assumed blood volume, L)
ODE `central`	n/a	`mdlObj$MODEL_PREDICTION$DEQ` `A1`
ODE `target`	n/a	`mdlObj$MODEL_PREDICTION$DEQ` `A2` (init = rp / ke)
ODE `complex`	n/a	`mdlObj$MODEL_PREDICTION$DEQ` `A3` (init = 0)
ODE `cells`	n/a	`mdlObj$MODEL_PREDICTION$DEQ` `A4` (init = n0)
ODE `peripheral1`	n/a	`mdlObj$MODEL_PREDICTION$DEQ` `A5` (init = 0)
Output `Cc`	n/a	`mdlObj$MODEL_PREDICTION$output1 = A1 / v1`

Virtual cohort

The DDMORE bundle for DDMODEL00000229 ships no event dataset and the Jager 2011 paper is not on disk, so no published clinical regimen is available to reproduce. The vignette exercises the packaged ODEs on a single typical-individual scenario (one 50 mg IV bolus into the central compartment) so that the simulated trajectories can be inspected for mechanistic plausibility – not as a clinically-grounded dosing regimen.

events <- data.frame(
  id   = 1L,
  time = c(0, seq(0.25, 336, by = 0.25)),
  amt  = c(50, rep(NA_real_, length(seq(0.25, 336, by = 0.25)))),
  evid = c(1L, rep(0L,  length(seq(0.25, 336, by = 0.25)))),
  cmt  = c("central", rep("central", length(seq(0.25, 336, by = 0.25))))
)

Simulation

mod  <- rxode2::rxode2(readModelDb("Jager_2011_gemtuzumab"))
#> ℹ parameter labels from comments will be replaced by 'label()'
mod_typ <- rxode2::zeroRe(mod)
sim  <- rxode2::rxSolve(mod_typ, events = events)
#> ℹ omega/sigma items treated as zero: 'etalki', 'etalke', 'etalrp'

Mechanistic sanity checks

The DDMORE bundle does not link to a .lst listing or a published NCA / VPC figure that this packaged model can be compared against numerically, and the structural model has no NCA-amenable PK arm in the ordinary sense (drug elimination is split across linear elimination, target-mediated internalization, and a peripheral PK compartment with two rate constants that are not in CL/Q form). Validation therefore consists of mechanistic sanity checks: each ODE has the qualitative behavior its mechanism implies.

Drug central concentration declines monotonically after the bolus

ggplot(sim, aes(time, Cc)) +
  geom_line() +
  scale_y_log10() +
  labs(x = "Time (h)", y = "Cc (mg/L; assumed unit, see Errata)",
       title = "Central drug concentration")

stopifnot(sim$Cc[1] > 8)               # initial ~= amt / vc = 50 / 5.42 ~= 9.2
stopifnot(all(diff(sim$Cc) < 0))       # monotonic decline (no rebound)
stopifnot(tail(sim$Cc, 1) > 0)

Free CD33 receptor depletes upon drug arrival, then recovers as drug clears

The receptor is at steady state rp / ke ~= 4135 at t = 0, but the incoming dose drives a fast binding pulse that depletes free target by several orders of magnitude before target slowly recovers as drug – and complex – fall.

ggplot(sim, aes(time, target)) +
  geom_line() +
  scale_y_log10() +
  labs(x = "Time (h)", y = "Free CD33 target (relative units)",
       title = "Free target dynamics")

target_steady <- with(environment(mod_fun), exp(log(823) - log(0.199)))  # rp / ke
stopifnot(min(sim$target) < 1)                       # transient near-zero depletion
stopifnot(tail(sim$target, 1) > min(sim$target) * 5) # partial recovery
stopifnot(target_steady > 4000 && target_steady < 4200)

Drug-receptor complex peaks early and decays as drug clears

ggplot(sim, aes(time, complex)) +
  geom_line() +
  labs(x = "Time (h)", y = "Drug-receptor complex (relative units)",
       title = "Complex dynamics")

stopifnot(sim$complex[1] > 0)
stopifnot(max(sim$complex) > 1000)
peak_idx  <- which.max(sim$complex)
final_idx <- nrow(sim)
stopifnot(sim$complex[final_idx] < sim$complex[peak_idx])

Leukemic blast cells decline at the typical-population rate `alph`

The cell ODE is d/dt(cells) = -alph * cells, so cells decay exponentially at typical-value rate alph = 0.0755 1/h (half-life log(2) / alph ~= 9.18 h). The simulated trajectory should match this analytically.

ggplot(sim, aes(time, cells)) +
  geom_line() +
  scale_y_log10() +
  labs(x = "Time (h)", y = "Leukemic blasts (relative units)",
       title = "Blast cell depletion")

alph_typ <- 0.0755
expected <- 1.32e-5 * exp(-alph_typ * sim$time)
rel_err  <- abs(sim$cells - expected) / expected
stopifnot(max(rel_err) < 0.001)  # within 0.1% of the analytical solution

Drug peripheral compartment fills then re-distributes

ggplot(sim, aes(time, peripheral1)) +
  geom_line() +
  labs(x = "Time (h)", y = "Drug in peripheral1 (mg)",
       title = "Peripheral drug compartment")

stopifnot(sim$peripheral1[1] > 0)
stopifnot(any(diff(sim$peripheral1) > 0))      # at least transient accumulation
stopifnot(any(diff(sim$peripheral1) < 0))      # then re-distribution / decline

Assumptions and deviations

The DDMORE Foundation Model Repository entry DDMODEL00000229 ships only the MDL DSL source (GO_PK_model.mdl), its PharmML XML rendering (GO_PK_model.xml), the Model_Accommodations.txt reference note, and RDF / scraper metadata – there is no Output_real_*.lst, Output_simulated_*.lst, or simulated event dataset. The Jager 2011 publication itself is not on disk in this worktree’s literature tree. The following assumptions and deviations apply.

Parameter values come from the MDL parObj block, not a .lst listing. The bundle has no NONMEM listing file with a MINIMIZATION SUCCESSFUL block whose final estimates can be read off, and the DDMORE-source skill’s default rule (read final estimates from Output_real_*.lst) cannot apply. The MDL parObj$STRUCTURAL and parObj$VARIABILITY values are treated as the bundle’s authoritative final estimates per Model_Accommodations.txt, which describes the parObj as the Monolix re-fit of the Jager 2011 model on the publication’s data.
Bundle is a Monolix re-fit, not a literal reproduction of Jager 2011. Model_Accommodations.txt documents two material differences from the publication:
1. The PK structure was extended from the published one-compartment drug PK (linear elimination only) to a two-compartment drug PK with linear elimination plus a peripheral compartment (rate constants km, kn).
2. All parameters were estimated simultaneously in Monolix, in contrast with Jager 2011’s step-wise estimation. As a result, the parObj values for parameters that exist in both formulations (e.g., kb, ku, ki, ke, rp, k, alph, n0, v1) differ from the values reported in the original publication.
The packaged model reproduces the DDMORE bundle’s Monolix-re-fit formulation, not the published Jager 2011 formulation.
No external numeric cross-check. Without the publication PDF on disk and without a .lst listing in the bundle, neither published parameter tables nor the bundle’s own re-fit objective function / per-subject predictions are available for verification. Source-trace comments point at the MDL parObj lines; reviewers wishing to verify against the original Monolix run should consult the live DDMORE repository entry at https://repository.ddmore.eu/model/DDMODEL00000229.
Units of dose, central concentration, additive error, receptor, and cell counts are MDL-native. The MDL dataObj block declares AMT : { use is amt, variable = A1 } and DV : { use is dv, variable = Y } with no explicit unit annotations. The packaged units field declares dosing = "mg" and concentration = "mg/L" based on the observation that a 50-unit dose into central produces an initial Cc = amt / vc ~= 9.22, which is consistent with a clinical mg-scale gemtuzumab ozogamicin bolus (typical adult IV ~6-18 mg) and a central volume v1 = 5.42 L. Receptor units (target, complex, rp) and cell-count units (cells, n0) are MDL-native and are mechanism-specific scalings rather than physical receptor or cell numbers; the inline constants nav = 6.02214 (Avogadro / 1e23) and vblood = 4.8 L in the central ODE convert the per-cell binding flux into a plasma-equivalent rate. Reviewers concerned about the exact unit interpretation should consult Jager 2011 directly.
OMEGA correlation block is dropped as vestigial. The MDL parObj declares an OMEGA block with type is corr over six etas (ETA_k, ETA_alph, ETA_n0, ETA_v1, ETA_kn, ETA_km), but every individual omega_X for those six parameters is 0.0 (type is sd). Mathematically, a correlation among zero-variance random effects has no effect on simulation; the packaged model omits the correlation block and applies IIV only to ki, ke, and rp (the three etas whose omega_X parObj sd is non-zero).
Compartment name cells is non-canonical. nlmixr2lib::checkModelConventions() flags cells as not in the canonical compartment list. The model’s biology is leukemic blast cell count, which has no canonical short name in the register; cells was chosen by analogy with the circ / precursor1..4 naming used in the DDMORE bundle for Friberg_2002_paclitaxel. A GitHub issue should ratify a canonical name for cell-count compartments before this convention is reused for additional models.
Population demographics absent. The population metadata for this model uses NA_* placeholders for age range, weight range, sex ratio, region, and study count because the DDMORE bundle does not ship that detail and the publication itself is not on disk. Consult Jager 2011 for the population description.
No PKNCA validation. The structural model is not a standard PK model, lacks NCA-amenable single-arm PK output for which Cmax / AUC / half-life are clinically interpretable in isolation, and has no published reference NCA values or VPC figure available locally to compare against. Validation in this vignette is reduced to mechanistic sanity (each ODE behaves as its mechanism implies) and an analytical match for the leukemic-blast depletion ODE.