A Quantitative Systems Pharmacology model of idiopathic intracranial hypertension built around a single equation and the bound hiding inside it:

ICP = I_f · R_out + P_sss

Every drug ever licensed or trialled for IIH — acetazolamide, topiramate, furosemide, GLP-1 receptor agonists, 11β-HSD1 inhibitors — acts on I_f, the CSF formation rate. P_sss, the dural sinus pressure, is additive. So as any secretion-blocking drug approaches perfection, ICP approaches P_sss and stops. That floor is a term no drug in the disease touches, and in a substantial minority of patients it sits above the pressure that defines remission.

Every number in this README is printed by iih_reference_check.py — a pure standard-library Python implementation of the same equations the R model integrates. Nothing here is quoted from memory:

python3 iih_reference_check.py          # full report (~5 min)
python3 iih_reference_check.py --brief  # headline results only

Idiopathic intracranial hypertension is raised CSF pressure (> 25 cmH₂O) without a mass lesion, hydrocephalus or venous thrombosis, occurring overwhelmingly in women of reproductive age with central obesity and recent weight gain. Its incidence tracks obesity prevalence. Papilloedema threatens permanent visual field loss — the outcome that matters — while headache dominates quality of life and often outlives the pressure that caused it. Three mechanisms are pathologically entangled: obesity raises intra-abdominal and thence central venous pressure, impeding cerebral venous drainage; the transverse sinuses are stenosed in almost every patient, adding a trans-stenotic pressure gradient upstream of CSF absorption; and CSF secretion is modulated by an IIH-specific androgen signature acting on choroid-plexus transporters. Treatment reflects the confusion: a carbonic anhydrase inhibitor titrated to the limit of tolerability, weight loss up to bariatric surgery, venous sinus stenting, CSF diversion, and optic nerve sheath fenestration — interventions whose relative merits are argued largely from single-arm pressure series.

In steady state the Davson relation holds by conservation of volume:

ICP = I_f · R_out + P_sss

What makes IIH more than plumbing is that P_sss is not a constant. The transverse sinus is a collapsible tube inside the skull, so CSF pressure squeezes it:

P_sss = P_cv + G(ICP),      γ = dG/dICP > 0

Together these are a positive feedback loop. Closed-loop sensitivity to any input is the open-loop sensitivity times 1/(1−γ), and the bound becomes the self-consistent venous floor:

ICP_floor = P_cv + G(ICP_floor)

This is not a modelling convenience. Lalou 2020 (PMID 31832847) measured it: in pseudotumour cerebri, CSF and sagittal sinus pressure track each other (R = 0.96 at baseline, R = 0.92 during infusion), and during CSF drainage they keep tracking until the sinus pressure bottoms out while CSF pressure continues to fall — γ > 0 while the sinus is collapsible, γ → 0 once it is open. The floor equation is the arithmetic of that observation.

The ICP relaxation time constant is ~10 minutes, so a lumbar puncture and a CSF infusion study are inside the model rather than bolted on — which is what makes the identifiability analysis (§6) possible.

The mechanistic map colours every therapy node by which term of the equation it acts on, because that — not potency — decides whether it can work: blue = secretion (I_f), green = outflow resistance (no licensed drug), orange = the venous floor (stenting), pink = P_cv via the abdomen (weight loss), purple = bypasses the equation entirely (shunt, LP, fenestration).

Physiological constants, not fitted: IF0 (0.35 mL/min), ELAST (0.11 /mL, Marmarou), IOP (15 mmHg), KTRANS. Structural choices with no data to fix them, varied in the sensitivity analysis: the collapse curve (GMAX, ICPCOL, WCOL), papilloedema resolution time constant (42 d, from the clinical course), and the entire slow R_out/lymphatic remodelling loop — which has no human quantitative anchor in IIH and is included only because chronicity and relapse need one.

Each phenotype below is pinned to its published baseline pressure; what differs between rows is only the composition of that pressure — and the composition is exactly what no drug trial in IIH has ever measured.

Hold one patient at exactly 37 cmH₂O and sweep only the gradient:

† R_out below the normal 6 mmHg/(mL/min) range — non-physiological, and that constraint is what bounds how venous a patient can be.

The therapeutic room available to every drug in this disease varies more than two-fold across patients who are clinically indistinguishable without venography. In the same stenosis-dominated patient:

A drug that abolishes CSF secretion completely does not reach remission; a stent does, with no drug at all. They are not interchangeable at any potency, because they act on different terms: the drug scales I_f·R_out, the stent moves the floor the drug is bounded by. In a virtual population of 300 admissible patients, the ordering reverses across the composition:

A real stented cohort reached < 25 cmH₂O in 40/50 (80%, PMID 29871989) — those patients were selected for a demonstrated gradient, i.e. the bottom row, not the population average.

The loop gain is measurable from published data, and it is not zero. Stenting lowers sagittal sinus pressure by 8.1 mmHg (PMID 29922401) and CSF pressure by 16.8 cmH₂O = 12.4 mmHg (PMID 29871989) — a ratio of 1.53. A passive, non-collapsible sinus forces that ratio to be exactly 1: lowering P_sss by x lowers ICP by x and nothing else changes. A ratio above 1 is only possible if the sinus is collapsible, and 1/(1−γ) = 1.53 gives γ ≈ 0.35. Both known biases across that interval push the other way (the acetazolamide dose fell from 950 to 300 mg/day and weight rose 1.1 kg), so the gain is if anything under-estimated.

ICP is a state; vision is an integral. Forced to the same day-180 pressure, a step intervention (drug) delivers 1.26× the visual gain of a ramp (weight loss: 1.23 vs 0.97 dB), because permanent loss tracks the integral of translaminar gradient above threshold, which the endpoint pressure has already forgotten. A six-month ICP endpoint therefore systematically over-values weight loss — and the weight component of GLP-1 agonists — against drugs, stents and shunts.

Timing beats potency where the floor is high. In the fulminant phenotype, stenting delayed by 120 days still leaves less permanent damage (79% axon loss, PMD −15.2 dB) than maximal acetazolamide given immediately (96% axon loss, PMD −20.5 dB), because the drug cannot cross the floor while the stent moves it. This is the clinical rule — fulminant IIH needs mechanical decompression, not dose escalation — arriving as a structural consequence rather than an assumption.

The ICP endpoint cannot separate drug potency from loop gain. It constrains only the product ε·I_f·R_out/(1−γ); every (γ, ε) pair on that curve fits the trial exactly. Worse, the classical CSF infusion test measures R_out/(1−γ), not R_out, so in IIH it over-states resistance by exactly the amplification factor, and any drug effect predicted from it is over-stated with it. What breaks the tie is not more pressure data but one simultaneous sinus pressure trace, which yields dP_sss/dICP directly. That is this model's practical recommendation.

① The IIHTT placebo arm falls ~5× more than any weight mechanism allows. Its 3.45 kg of weight loss buys at most 0.97 cmH₂O at the randomised IIH:WT slope (0.28 cmH₂O/kg); the observed fall was 5.24 cmH₂O — an implied slope of 1.52 cmH₂O/kg against 0.28 (IIH:WT 12 mo), 0.31 (24 mo) and 0.51 (very-low- calorie diet cohort). Fitted to each arm's absolute fall, the model's shortfalls are −49.7 mmH₂O (acetazolamide) and −46.8 mmH₂O (placebo). Those being nearly equal is the finding: an arm-independent offset is what a non-treatment effect looks like — enrolment required a raised opening pressure, and lumbar-puncture opening pressure has large within-subject variance, which is the textbook setup for regression to the mean.

The methodological consequence is sharp. Reading the trial at face value requires acetazolamide to suppress CSF formation by 0.53, at or above the ceiling for carbonic anhydrase inhibition; the randomisation-protected between-arm reading requires 0.28. Same trial, two defensible readings, a 1.9-fold difference in inferred potency — and a QSP model fitted to absolute arm trajectories, which is the common practice, silently picks the first and inherits the artefact as drug potency. This model uses the second.

② Weight mediates ~20% of the pressure effect but a reported 4% of the vision effect, and the model cannot close that gap. IIHTT's own mediation analysis put the weight-mediated part of the visual benefit at 0.03 dB of 0.71 dB. The model reproduces the pressure share (18.7% against ~20%) and gets the vision share wrong (~16% against 4%). The step-versus-ramp timing asymmetry is real but supplies only 1.26× of the ~5× required. Either the 4% is a decomposition of noise — IIHTT's total PMD effect was 0.71 dB with a 95% CI of 0 to 1.43 and p = 0.050, and ~16% sits well inside that interval — or weight loss lowers pressure without protecting the nerve proportionally, which would require the ocular chain to be driven by something other than the pressure fed to it here. The model cannot decide, and the discrepancy is left standing.

Calibrated on the IIHTT between-arm differences, because that is the randomisation-protected estimand:

Out-of-sample tests (never fitted): IIH:WT's ~24% weight loss for remission → model 29.7% (average slope 0.272 cmH₂O/kg, within 3% of the trial slope it was built on); IIHTT's RGCL numbers reproduced with essentially zero true axon loss, which is the correct reading of a mild-visual-loss cohort.

• It over-predicts the visual value of pressure control (between-arm PMD 1.31 vs 0.71 dB) and of weight loss (~16% vs 4% mediation). The excess is the same size as the placebo-arm visual improvement it cannot generate (0.12 predicted vs 0.71 observed). Until that is resolved the ocular chain here is too responsive to pressure.
• The exenatide anchor is only just reachable. The observed −5.7 cmH₂O at 2.5 hours forces the GLP-1R maximal secretory effect to ~0.5, essentially equal to acetazolamide's ceiling, and forces 10 µg bid to sit near saturation. That is falsifiable: higher doses or weekly analogues should not deepen the acute ICP fall, only the weight-mediated ramp. The trial's own time course (−5.7 at 2.5 h, −6.4 at 24 h, −5.6 at 12 weeks) is also non-monotone in a way this model structurally cannot produce while weight is falling.
• Baseline papilloedema is too high (456 µm RNFL against typical reported IIH values of ~250–350 µm). Only RNFL change is compared with the trial, and PMD/Frisén are normalised to baseline, so the pressure conclusions do not depend on it — but the absolute OCT scale should not be quoted.
• The remission-threshold prediction is 24% too high (29.7% vs 24%), because the model's pressure-per-kilogram slope is not constant: as pressure falls the sinus re-opens, the loop gain drops, and each further kilogram buys slightly less.
• The slow outflow-remodelling loop is unanchored. It produces chronicity and relapse, which the disease has, but no human IIH data constrain it.
• Headache is a hypothesis, not a prediction. The large central- sensitisation term exists because headache is famously poorly coupled to pressure; it is structurally motivated and quantitatively unanchored.
• Per-patient floors must never be quoted without that patient's own manometry. The sensitivity analysis shows the qualitative bound survives across the whole plausible parameter range, and its exact numerical value does not.

Fourteen prebuilt scenarios in IIH_simulate_scenarios(): natural history · IIHTT placebo · IIHTT acetazolamide 2.5 g/day · acetazolamide at the 4 g/day target · topiramate · very-low-calorie diet · bariatric surgery · exenatide · venous sinus stenting · stent + acetazolamide · maximal triple drug therapy against the floor · CSF shunt · fulminant IIH (drug vs urgent stent) · acetazolamide withdrawal and relapse. Plus IIH_infusion_study() and IIH_lumbar_puncture(), the two diagnostic manoeuvres that would identify the model, and IIH_drug_ceiling_table(), which computes the bound directly.

Disclaimer. This is an educational and research QSP model, assembled from public literature and not independently validated. It must not be used for clinical decisions, prescribing, or regulatory submission. Its parameters are illustrative approximations, and its central quantity — an individual patient's venous floor — requires catheter manometry that none of the drug trials it is calibrated against performed.