Two-Process Sleep Model — Circadian Rhythm & Sleep Homeostasis

😴 Two-Process Sleep Model

Borbély's Two-Process Model: sleep is regulated by the interaction between Process S (homeostatic sleep pressure, driven by adenosine buildup) and Process C (circadian clock from the SCN). Sleep begins when S hits the upper threshold, waking occurs when S falls to the lower threshold.

🎛 Parameters

Circadian amplitude 0.20 τ_wake — buildup time const (h) 18.0 τ_sleep — decay time const (h) 4.5 Sleep deprivation extra (h) 0 Circadian phase offset (h) 0.0

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📐 Statistics

Avg sleep/night

7.8 h

Sleep efficiency

88%

Peak S value

0.92

Sleep onset

23:15

ℹ️ Key Concepts

Process S: rises exponentially toward 1 during wake (τ_w ≈ 18h), decays toward 0 during sleep (τ_s ≈ 4.5h). Linked to adenosine accumulation.

Process C: 24h sinusoidal oscillation from the suprachiasmatic nucleus (SCN), modulated by light-dark cycle.

Thresholds: H_upper (sleep trigger) and H_lower (wake trigger) track the circadian wave.