Fibrodysplasia ossificans progressiva is an ultra-rare autosomal-dominant disorder in which a single recurrent mutation in ACVR1/ALK2 (c.617G>A, p.R206H, >95% of classic cases) turns activin A — normally a non-signalling competitive inhibitor of wild-type ALK2 — into a full agonist. Resident fibro/adipogenic progenitors in skeletal muscle connective tissue respond by running the complete endochondral ossification programme in the wrong place, converting muscle, tendon, ligament and fascia into mature, marrow-containing bone. The bone is never removed. Patients accumulate an irreversible skeleton-outside-the-skeleton, lose one joint after another, and die at a median age of 56 years, most often of cardiorespiratory failure from thoracic insufficiency syndrome.

Almost every mechanistic map of FOP ends at "heterotopic bone". That is where the interesting problem starts, because FOP has an unusual property: the disease is a stock, and every drug and every trial endpoint is a rate. The whole model is organised around four consequences of that, and each one is derived from published numbers rather than asserted.

The 36-month natural history study (NHS, PMID 36152026) reports four numbers in one cohort. Multiplying three of them against the fourth settles a question the paper never asks:

A drug that abolished 100% of flare-ups would remove ~30% of new heterotopic bone and no more. Two independent corroborations: 47% of patients report progression without obvious flare-ups (PMID 27025942), and in LUMINA-1 placebo only 12/29 (41%) of new lesions were co-located with a flare (PMID 39216107). Most heterotopic bone in FOP forms quietly, without a flare to announce it.

The model therefore runs two parallel routes — episodic and smouldering — and keeps them exactly separable by holding the receptor step linear in activin A (justified: FOP serum activin A is ~434 pg/mL, PMID 37165433, far below receptor saturation). Glucocorticoids, NSAIDs, mast-cell stabilisers and IL-1 blockade enter only the episodic route, so they cannot beat φ_FL — by construction, which is the point. Simulated: perfect abolition of every flare gives 28.8%; real-world glucocorticoid bursts give 3.4%.

Heterotopic bone remodels internally but is not resorbed (KRESORB = 0), and surgical excision provokes explosive recurrence. So the trial endpoint (annualised new HO volume) is a slope while disability is the area under it. One simulation of the MOVE regimen produces both:

Both numbers are correct descriptions of the same trial. A trial that reports only the first is not wrong; it is answering a different question from the one the patient is asking.

The NHS velocity profile is non-monotonic: 21.9 mL/yr at 8–<15, 41.5 at 15–<25, then a collapse to 4.6 at 25–65. The model reproduces all four band values (see below) from a somatic growth curve (anchored to human growth, not fitted to HO data) multiplied by a chondrogenic-competence factor that falls at skeletal maturity.

Two candidate mechanisms for the adult collapse were tested and one was rejected by the fit:

• Territory exhaustion — adults have run out of ossifiable tissue. A territory-limited model cannot reproduce the adolescent peak while keeping adults progressing; forcing it costs 18% on the 15–<25 velocity.
• Loss of chondrogenic competence at skeletal maturity — fits all four bands. It also explains, with the same parameter, why the physeal hazard of a retinoid disappears once the plates fuse. One mechanism, two independent observations.

This distinction is clinically decisive: under competence decline adults are not out of substrate, so an adult who is operated on or injured can still ossify catastrophically — which is what the clinical record shows, and what a territory-exhaustion model would wrongly call safe.

The consequence for treatment, simulated across five starting ages:

Note also what the model refuses to report: under any saturating model, "lifetime HO averted" is the wrong endpoint, because slowing formation changes when a burden is reached, not the final total. The honest currencies are burden at a fixed age and years of delay.

Palovarotene works by blocking chondrogenic commitment. The growth plate is chondrogenesis. MOVE delivered 54–60% reduction in new HO together with premature physeal closure in 21/57 (36.8%) of children under 14, reduced vertebral BMD and increased vertebral fracture risk (PMID 36583535); daily dosing ablates growth plates in mice (PMID 30226468).

The model does not assume the two effects are separable — it solves for the implied selectivity from those two published numbers and gets R_SEL = EC50(PPC)/EC50(HO) ≈ 3.7-fold (conditional on the assumed maximal physeal hazard, which is stated as a parameter). Then it sweeps the dose:

At ~3.7-fold selectivity there is no dose that reaches 50% suppression at an acceptable physeal hazard while the plates are open. The only separation axis is skeletal maturity — i.e. time — and by then Axis 3 has cut the remaining benefit to about a tenth. The R_SEL slider in the Shiny app answers the design question directly: a next-generation retinoid needs roughly an order of magnitude more physeal selectivity to be usable in the age group that needs it.

LUMINA-1 (garetosmab) reported a failed primary endpoint and a striking secondary one. Total lesion activity by PET-CT missed (p = 0.0741) while new HO lesion development was suppressed (0% vs 40.9%, p = 0.0027). The model produces both from one mechanism: total NaF activity sums the new mineralising front and ongoing remodelling of the mature stock the drug cannot touch. In the model's LUMINA-1 cohort only 39% of the NaF signal comes from new lesions, so a 91% reduction in new lesions shows up as a 38% reduction in total lesion activity — a real effect on a diluted endpoint, in a trial of 20 versus 24 patients.

The LUMINA-1 placebo arm formed bone ~12× faster than an NHS-average adult (1.21 new lesions per patient in 28 weeks versus ~0.1). The model cannot reproduce the trial's event rate from population parameters without an explicit 12-fold activity enrichment — a quantitative measure of how selected that cohort was, and a warning about the design MOVE used.

MOVE was single-arm against untreated NHS controls. Under this model the apparent effect is (drug effect) × (intrinsic activity ratio between the cohorts), and the two are not separable from the data:

A cohort with 40% of the external control's intrinsic activity would show a ~60% "reduction" with no drug whatsoever — the entire MOVE effect size, manufactured by selection. This does not show that palovarotene is inactive; it shows the design cannot separate the two, which is exactly why the MOVE analysis was so sensitive to a square-root transformation (99.4% versus 65.4% posterior probability). The model reproduces that fragility too: with between-subject variability the same simulated trial gives a 50.5% reduction in the mean but 30.1% after a square-root transform, at a coefficient of variation of 0.92.

Reproduce everything:

dot -Tsvg fop_qsp_model.dot -o fop_qsp_model.svg
dot -Tpng -Gdpi=150 fop_qsp_model.dot -o fop_qsp_model.png
Rscript fop_mrgsolve_model.R          # runs all 15 scenarios + calibration table
Rscript -e 'shiny::runApp("fop_shiny_app.R")'

Drug PK (15) — palovarotene (oral, 2-cpt, CYP3A4), garetosmab (IV, 2-cpt + target-mediated disposition), ALK2 kinase inhibitor (fidrisertib/zilurgisertib class), saracatinib, sirolimus, prednisone, anakinra.

Signalling (12) — trigger, inflammatory amplifier (mast cells, macrophages, IL-1), HIF-1α, mTORC1, free activin A split into smouldering and episodic pools, garetosmab–activin complex, pSMAD1/5/8 split the same way, activated FAPs, fibroproliferative lesion, chondrogenic anlagen.

Lesion maturation and bone (7) — hypertrophic/vascular-invasion stage, osteoblastic osteoid, mineralised thoracic HO, mineralised appendicular HO, mature-stock NaF remodelling pool, cumulative new HO, cumulative lesion count.

Clinical and safety (8) — CAJIS, FVC % predicted, cumulative mortality hazard, cumulative physeal-closure hazard, vertebral BMD Z, height Z, mucocutaneous retinoid AE burden, cumulative flare count.

The classes differ in where they cap out, not only in how potent they are. Because R206H loses the FKBP12 clamp, some signal is ligand-independent, so no anti-ligand antibody can reach it however completely it neutralises activin A.

KCOMMIT/(KCOMMIT + KRESOLVE) = 0.269 is the published day-84 ossification probability of an imaged flare (14/52). A commitment blocker does not abolish ossification — it shifts lesions from the ossifying branch into the resolving branch. That is why 85% maximal blockade yields an 80.6% ceiling, and why flare-triggered-only dosing achieves just 14% against chronic dosing's 57%: by the time a flare is symptomatic, part of the lesion has already crossed the checkpoint.

Fitted parameters: KF_HO, CMIN_C, A50C_C, AWC_C (to the four velocity bands); H0_MORT (to median survival); EC50_PAL (to the MOVE reduction); R_SEL (to the PPC rate); CL_GAR (to C_trough). Everything else is either taken from a publication or fixed a priori.

FVC = 35 + 65 · K/(K + HO_thoracic) with a small K saturates early. That was chosen because Botman et al. (PMID 33748352) found restrictive physiology already present in childhood and, in 4 of 5 patients, thoracic HO progressing into adulthood with no further FVC decline. The model reproduces this (FVC 71% at age 8 → 47% at 20 → 43.5% at 30 → 42.8% at 45) and it carries a sobering implication that follows from the shape alone: the pulmonary damage is front-loaded, so preventing later thoracic HO buys very little lung function.

1. The NHS dataset is internally inconsistent, and the model shows by how much. Integrating the study's own longitudinal velocities from its own childhood baseline (68.8 mL at 2–<8, then 21.9 and 41.5 mL/yr) puts a patient at ~650 mL by age 25 — already above the same study's cross-sectional 25–65 band mean of 575.2 mL. The model was fitted to the prospectively measured longitudinal velocities (the study's primary outcome and the quantity every trial uses as its endpoint) and consequently overshoots the cross-sectional adult stock by +29%. This is not repairable by tuning: you cannot have 41.5 mL/yr running through the twenties and only 575 mL by mid-life. Plausible causes are on the data side — cross-sectional band means over a 40-year age range dominated by younger participants, survivor effects, and unequal follow-up in the velocity estimates.
2. Territory is not identifiable from these data, and a free fit silently deleted it. Allowed to float, the optimiser drove HOMAX to 10^16 and GAMMA_T to 10^5 — voiding the mechanism while fitting every velocity perfectly. HOMAX is therefore fixed a priori at 2000 mL (about 39% consumed by age 56) rather than fitted, and the model's late-life plateau is an assumption, not a result.
3. The competence transition sits on its lower bound. AWC_C fits to 0.50 yr — the width limit allowed. Two adjacent NHS band means of 41.5 then 4.6 mL/yr demand a near-step loss of chondrogenic competence in the mid-twenties, possibly sharper than this model permits. That is a strong biological claim and it is the data's, not the model's.
4. CAJIS is not numerically calibrated. It is implemented on its true 0–30 scale, monotone in appendicular stock, saturating in late-stage disease, and validated in shape only. No published cohort mean was used to pin it. Read CAJIS output as ordinal; the model does not claim a CAJIS of 15.9 is measurably distinct from 15.5.
5. Survival and life-years are extrapolation, not evidence. No FOP trial has ever measured a functional or survival endpoint. The model's projection that a 57%-effective commitment blocker started at age 8 raises median survival from 56.0 to 68.5 years is the model reasoning out loud about what the volume endpoints imply — it is a hypothesis generator, not a result.

Nine, all fixed: multi-line : continuations that broke @annotated parsing; a signalling steady state written with the leak term on the wrong side, so the initial conditions sat off equilibrium; an ACTAFL_0 expression with a term multiplied by zero; the episodic/smouldering ratio initialised as 0.74 instead of 0.295 — inverted, which would have made the anti-flare ceiling the opposite of the finding; $OMEGA random effects drawn by default, making every "deterministic" scenario silently stochastic; interpolation at a time point outside the output grid returning NA and propagating into every reported percentage; a garetosmab TMDD V_max so large it eliminated 80% of each dose, putting C_trough 75-fold below the published value; scenarios started at age 15 or 33 while carrying a 5-year-old's 60 mL of heterotopic bone, which corrupted every percent-of-total-volume statement (Axis 2); and an adult LUMINA-1 cohort rendered completely inert by territory exhaustion, producing zeroes in every cell of that scenario.

This is an educational and research-grade QSP model, built from public literature and not independently validated. It must not be used for clinical decisions, prescribing, or regulatory submission. Parameters are illustrative approximations; fitting and qualification against patient-level data would be required for any applied use. Where the model extrapolates beyond published endpoints — survival, life-years, CAJIS trajectories — it says so.