CBT-I Sleep Restriction Titration Simulator

Patient Profile

Physiological sleep need 7.0 h

Starting time-in-bed (TIB) 9.0 h

Titration step per week 20 min

Night-to-night variability Medium

DTx Program Control

This Week

Prescribed TIB

9.00 h

Week / Night

1 / 0

Avg. sleep efficiency

—

Avg. total sleep time

—

Program not started — click "+1 Night" or "Run Full Week".

How it works

This models a real prescription digital therapeutic for chronic insomnia (CBT-I delivered as software, e.g. Somryst — the first FDA-cleared prescription DTx). The engine underneath is the two-process model of sleep regulation (Borbély):

Process S (homeostatic pressure), during wake:
  S(t) = 1 − (1 − S0)·e^(−t/τw),  τw ≈ 18 h
During sleep, S discharges:
  S(t) = S0·e^(−t/τs),  τs ≈ 4.2 h

Sleep onset latency (SOL) falls as pressure at bedtime rises:
  SOL = SOLmin + k·(1 − S_bed)

Sleep efficiency:  SE = TST / TIB × 100%

Each simulated night, prior wake time builds sleep pressure; that pressure sets both how fast the patient falls asleep and how much total sleep time (TST) the restricted time-in-bed (TIB) window can hold, with random night-to-night noise layered on top. This is exactly the quantity a CBT-I app measures from a sleep diary or wearable.

After every 7-night week, the app's real titration rule fires — the same logic used in clinical sleep-restriction therapy:

SE ≥ 90% — sleep is efficient, so TIB is increased by the titration step (more time allowed in bed).
SE ≤ 80% — sleep is fragmented, so TIB is decreased by the titration step (further restriction to rebuild sleep drive).
80% < SE < 90% — TIB is held steady for another week.

Over several weeks this closed loop converges TIB toward the patient's true physiological sleep need while keeping efficiency high — the core mechanism regulators evaluate for clinical-endpoint clearance and the mechanism plotted in the 3D helix: each night is one instanced block, height = TST, color = that night's efficiency, arranged along a rising weekly spiral.

High efficiency (≥90%) Moderate (80–90%) Low (<80%)

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