Quantitative Systems Pharmacology model of chronic insomnia built around the claim that insomnia is not a deficiency of sleep drive. Process S and Process C are close to normal in most patients. What is abnormal is a third process — 24-hour hyperarousal — that raises the wake side of the VLPO/ascending-arousal flip-flop switch, and a learned behavioural loop that keeps arousal there. Hypnotics push the switch from the other side. CBT-I enters the loop. That difference is why two treatments with the same effect size at week 4 behave completely differently at week 12, and reproducing it is what this model is for.

Scale: 217 nodes · 19 clusters · 329 edges in the map · 63 ODE compartments · 19 prebuilt scenarios (17 interventions + 2 matched untreated controls) · 9 dashboard tabs · 105 PubMed-verified references.

Chronic insomnia disorder is difficulty initiating or maintaining sleep, with daytime consequences, on at least three nights a week for at least three months, despite adequate opportunity to sleep. That last clause is the whole problem: these patients are not sleep-deprived, they are sleep-unable. Polysomnography in insomnia is often nearly normal, and the objective deficit (20–60 min of lost sleep) is far smaller than the subjective one. What is reliably abnormal is arousal, measured every way it has been measured: high-frequency beta and gamma EEG intruding on NREM, whole-brain metabolic rate that fails to fall from wake to NREM on FDG-PET, a flattened evening cortisol nadir with nyctohemeral HPA activation, raised muscle sympathetic nerve activity and reduced heart-rate variability. Insomnia is therefore best modelled as a disorder of the wake side of the sleep switch, not of sleep drive.

The second half of the disease is learned. Spielman's 3-P model says a predisposed person (trait anxiety, ruminative style, short-sleep phenotype) is tipped into insomnia by a precipitating stressor, and then kept there by what they do about it: they go to bed earlier and lie there longer, which spreads the same homeostatic sleep pressure across more hours and lowers sleep efficiency; the extra wakefulness in bed conditions the bed itself as a wake cue; and trying harder to sleep is itself arousing. The precipitant can resolve entirely and the insomnia persists, because the loop is now self-sustaining.

한국어 요약: 만성 불면장애는 잠잘 기회가 충분한데도 입면 또는 수면 유지가 어려운 상태가 주 3회 이상 3개월 넘게 지속되는 질환입니다. 이 모델의 출발점은 "불면은 수면 구동이 부족해서 생기는 것이 아니다"라는 관점입니다. 실제로 항상성 수면압 (Process S)과 일주기 리듬(Process C)은 대체로 정상이며, 이상이 있는 것은 24시간 지속되는 과각성(피질 β/γ 침입, 전뇌 대사율 상승, 야간 코르티솔 nadir 소실, 교감신경 항진)입니다. 여기에 스필만의 3-P 모형이 말하는 학습된 유지 고리(침상시간 연장 → 수면압 희석 → 침대의 각성 조건화 → 수면 노력 증가 → 과각성 강화)가 더해지면서 촉발 요인이 사라진 뒤에도 불면이 스스로 지속됩니다. 수면제는 스위치를 반대쪽에서 밀 뿐 이 고리에 개입하지 않고, CBT-I는 고리 자체를 표적합니다. 이 비대칭을 재현하는 것이 본 모델의 핵심 목적입니다.

19 clusters, 217 nodes, 329 edges. Click the image for the full-detail SVG.

63 ODE compartments. time is in hours and clock time is TIME mod 24, so a schedule (bedtime, rise time, light, dosing) is a first-class part of the model rather than a covariate.

Everything reported by the model — SOL, WASO, TST, sleep efficiency, N3 and REM minutes, awakening count — is read out of one continuous variable:

drive = wS·S + wA·adenosine_eff + E_BzRA + E_melatonergic + E_5HT2A
        − wT·ΔcoreTemp − C(t) − AROUSAL − W_ascending − ultradian − θ

SLP   = opportunity × SLPmax / (1 + exp(−drive / k))

W_ascending is itself driven by 1 − SLP, so the noradrenergic, histaminergic and orexinergic tones collapse once sleep begins and rise once it ends. That feedback makes the switch bistable, which is the point: sleep onset and awakening are transitions, not gradual slides, and the model shows genuine hysteresis.

Awakenings are not stochastic. An ultradian oscillator whose phase advances only during sleep (so it effectively resets at each sleep onset) produces a ~90-minute trough in sleep drive that deepens as Process S dissipates. A good sleeper's margin over threshold absorbs it; an insomniac's does not. This reproduces the clinical pattern that fragmentation concentrates in the last third of the night — when S has dissipated, cortisol is rising and the ultradian troughs are deepest.

good_sleeper, chronic_insomnia, severe_insomnia, sleep_onset, sleep_maintenance, elderly, comorbid_depression, delayed_phase, shift_worker. A phenotype is not a set of target sleep numbers — it is a starting point on the 3-P loop, defined mostly by constitutive arousal A0 plus, where relevant, circadian period, pineal output and SWS capacity. The sleep metrics are outputs.

source("ins_mrgsolve_model.R")

# one arm: daridorexant 50 mg for 12 weeks in a chronic-insomnia patient
r  <- ins_run_scenario("7. Daridorexant 50 mg nightly", weeks = 12)
head(r$nightly)          # night-by-night SOL / WASO / TST / SE / ISI ...

# a custom arm
sim <- ins_simulate(
  phenotype      = "elderly",
  weeks          = 8,
  param          = list(PAIN = 0.4),                       # patient covariates
  treat          = list(BLTON = 1, BLTLUX = 10000),        # starts at randomisation
  events         = ev_nightly("DARD", 25, days = 56),
  cbti_start_day = 15
)
ins_nightly(sim)

# every prebuilt arm, summarised at weeks 1, 4 and 12
ins_run_all()

Every simulation runs a 150-day untreated lead-in first, so the patient is at their chronic equilibrium at randomisation rather than mid-transient. Only the post-lead-in window is returned, with time re-zeroed.

Full numbers, including week-1/4/12 tables and the change from each arm's matched control, are in the calibration block at the end of ins_mrgsolve_model.R. The headline comparison, week 4, change from the matched untreated control:

The untreated baseline the model settles on for the chronic-insomnia phenotype — SOL 47 min, WASO 100 min, TST 399 min, SE 74.6%, ISI 18.8, subjective TST 292 min — matches the pooled entry criteria and baselines of the recent Phase 3 hypnotic programmes. Sleep architecture comes out in the right direction too: DORAs raise REM (130–137 min vs 88 untreated), ethanol suppresses it (56), trazodone raises N3 (97 vs 86), BzRA suppress N3 slightly, and the elderly phenotype retains about 40% of young N3 (37 min).

• There is no placebo response. Real placebo arms improve LPS by 10–20 min and WASO by 15–25 min, so every Δ above is larger than the corresponding placebo-subtracted trial delta by roughly that amount. Comparisons between active arms are the ones this model is built to make.
• There is a TST ceiling. Total sleep time cannot exceed SLPMAX × TIB, so once a hypnotic consolidates sleep to near continuity, every effective drug converges on the same TST at a fixed time in bed. The model therefore cannot rank suvorexant, lemborexant, daridorexant 50 mg and zolpidem on total sleep time — only on latency, on the shape of the night, on residual sedation, and on what happens when the drug stops.
• CBT-I is a responder, not an average. Arm 13 reaches ISI 6.4 at week 4 and 4.9 at week 12. Real CBT-I trials report ~60–70% response and ~40–50% remission; a single deterministic patient cannot represent that spread.
• Awakenings repeat. The ultradian mechanism gives the same patient the same awakening pattern every night.
• The loop is genuinely bistable, which is deliberate (it is Spielman's model taken literally) but means outcomes are steep in A0 near the threshold — small covariate changes there produce large predicted differences.

Both CBT-I and a hypnotic drop ISI by a similar amount at week 4. At week 12, with nothing being taken, CBT-I has held and zolpidem has not — and arm 2 ends worse than the untreated arm (ISI 22.0 vs 19.7) because the rebound nights re-conditioned the bed.

No parameter was set to produce that. It follows from where the two act: CBT-I removes terms from the arousal equation (COND, SEFF, DBAS) and compresses TIBS, all of which are state variables that persist; the drug adds a term proportional to a concentration, which is gone when the concentration is. If that asymmetry did not fall out of the structure, the model would be wrong about what insomnia is.

shiny::runApp("ins_shiny_app.R")

Nine tabs: patient profile and arousal decomposition · two-process core and the switch (with the hysteresis loop) · circadian phase, light and melatonin · drug PK and target occupancy · nightly sleep metrics against a matched control · sleep architecture · the 3-P perpetuating loop · clinical endpoints and safety · side-by-side scenario comparison. Every run simulates the matched untreated control alongside the active arm.

chronic-insomnia-disorder/
├── README.md                  이 문서
├── ins_qsp_model.dot          기계론적 지도 소스 (Graphviz)
├── ins_qsp_model.svg          지도 (벡터, 전체 해상도)
├── ins_qsp_model.png          지도 (150 dpi)
├── ins_mrgsolve_model.R       63-ODE QSP 모델 + 19개 시나리오 + 검증 블록
├── ins_shiny_app.R            9-탭 인터랙티브 대시보드
└── ins_references.md          105편 (PubMed 검증 완료)

Rebuild the map with:

dot -Tsvg ins_qsp_model.dot -o ins_qsp_model.svg
dot -Tpng -Gdpi=150 ins_qsp_model.dot -o ins_qsp_model.png

교육 및 연구 목적의 정성적·반정량적 QSP 모델입니다. 공개 문헌과 임상시험 데이터를 바탕으로 구성되었으나 독립적으로 검증·인증되지 않았으며, 실제 임상 의사결정, 처방, 또는 규제 제출에 직접 사용해서는 안 됩니다. 특히 수면제 선택·용량·중단은 반드시 의료진과 상의하십시오.