This is a 2D longitudinal-profile view of the exact same Starling-resistor physics as the companion 3D pharynx model: the airway has no bony support, so it behaves like a collapsible tube running between a fixed upstream pressure (atmosphere, plus any CPAP) and a variable downstream pressure set by the diaphragm. It collapses wherever local intraluminal pressure P falls below the tissue's critical closing pressure Pcrit:
collapsed if P(z) < P_crit_eff
P_crit_eff = P_crit_anatomic − k · (dilator muscle tone)
Flow is solved self-consistently: narrowing raises local velocity, Bernoulli's principle drops local static pressure further, which narrows the tube more. Viscous + convective loss per segment is lumped as R ∝ 1/A², iterated every frame:
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 )
v(z) = Q / A(z) (mass continuity along the tube)
That feedback loop is exactly why real obstructive apneas snap shut abruptly once flow accelerates enough at the narrowest point (the velopharynx, shown as the pinch in the silhouette below) — the local pressure drop outruns the muscle's ability to hold the wall open. Flow-carrying particles are drawn at their true local speed v=Q/A(z), so they visibly accelerate through the narrowed throat exactly as continuity requires.
- Pcrit — 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 Pcrit.
- Respiratory drive — the diaphragm's inspiratory suction; higher drive paradoxically worsens collapse because it accelerates flow through the narrowed segment (verified numerically: at full opening, throat pressure already reaches −12 cmH₂O by Bernoulli alone once effort hits 20 cmH₂O, before any active narrowing).
- CPAP — continuous positive airway pressure pneumatically splints the tube by raising the whole pressure profile above Pcrit, the actual mechanism behind why CPAP treats OSA.
Pressures, areas and flow are illustrative order-of-magnitude values calibrated to real clinical ranges for Pcrit (≈ −8 to +6 cmH₂O) — the collapse instability itself is the physically accurate part; absolute flow numbers are simplified for a single idealized cross-section. This 2D view solves the identical equations as the 3D radial-tube rendering but displays them as a longitudinal silhouette instead, so the two are complementary readouts of one mechanism, not duplicates.