Pharyngeal Collapse: Critical Closing Pressure Simulator

Airway Mechanics

Critical closing pressure P_crit +2.0 cmH₂O

Genioglossus (dilator) tone 30%

Respiratory drive 10 cmH₂O

CPAP splint pressure 0 cmH₂O

Live State

Airway open

Min. cross-section

100%

Inspiratory flow

0.00 L/s

Local pressure @ throat

0.0 cmH₂O

Breath phase

insp.

How it works

The pharynx has no bony support, so it behaves like a Starling resistor: a collapsible tube running between a fixed upstream pressure (atmosphere, plus any CPAP) and a variable downstream pressure set by the diaphragm. The tube collapses wherever local intraluminal pressure P falls below the tissue's critical closing pressure P_crit:

collapsed if  P(z) < P_crit_eff
P_crit_eff = P_crit_anatomic − k · (dilator muscle tone)

Flow is not driven directly by the diaphragm pressure alone — it is solved self-consistently, because narrowing raises local flow velocity, and by Bernoulli's principle that lowers local static pressure further, narrowing the tube more. This simulator lumps viscous and convective pressure loss per segment as R ∝ 1/A², then iterates:

ΔP_total = P_upstream − P_alveolar(t)  =  Q² · Σ R_i
P_local(z) = P_upstream − Q² · Σ_{j≤z} R_j
A(z) = A₀(z) · sigmoid( (P_local(z) − P_crit_eff) / w )

That feedback loop is exactly why real obstructive apneas snap shut abruptly rather than narrowing gradually — once flow accelerates enough at the narrowest point (the velopharynx), the local pressure drop outruns the muscle's ability to hold the wall open.

P_crit — the anatomical/fat-loading term; positive values (obese, retrognathic anatomy) predict severe OSA, negative values a resistant airway.
Dilator tone — genioglossus/tensor-palatini activation, which falls sharply in sleep (especially REM); it linearly lowers the effective P_crit.
Respiratory drive — the diaphragm's inspiratory suction; higher drive paradoxically worsens collapse because it accelerates flow through the narrowed segment.
CPAP — continuous positive airway pressure pneumatically splints the tube by raising the whole pressure profile above P_crit, the actual mechanism (not muscle stimulation) behind why CPAP treats OSA.

Pressures, areas and flow are illustrative order-of-magnitude values calibrated to real clinical ranges for P_crit (≈ −8 to +6 cmH₂O) — the collapse instability itself is the physically accurate part; absolute flow numbers are simplified for a single idealized cross-section.

Open airway Narrowed / flow-limited Collapsed (apnea)

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