Coronary Artery Stenosis & Poiseuille's Law

Coronary Stenosis

Stenosis (diameter reduction) 50%

—

Stenosis

50%

Remaining radius

50%

Flow rate (Poiseuille, r⁴)

6.3% of normal

If flow scaled linearly with diameter

would be 50% of normal

How it works

Poiseuille's law says the volumetric flow rate through a cylindrical vessel scales with the vessel radius raised to the fourth power, for a fixed pressure gradient, length and viscosity:

Q = (π · ΔP · r⁴) / (8 · η · L)
Q(stenosis) / Q(normal) = (r_narrowed / r_normal)⁴
                        = (1 − stenosis%)⁴

Stenosis slider — percent reduction in vessel diameter from atherosclerotic plaque; the remaining radius fraction is 1 − stenosis%.
Flow rate readout — computed by raising that remaining-radius fraction to the fourth power, not by a linear rule. A 50% diameter reduction leaves 50% of the radius, but only (0.5)⁴ ≈ 6.25% of the original flow survives — a ~94% drop.
Flow-vs-stenosis curve — has a long flat "shoulder" through moderate narrowing (the heart compensates and nothing feels wrong) then a steep "cliff" once narrowing crosses roughly 70–80%, where each further percent of plaque removes flow far faster.
Particle stream — its overall throughput rate tracks the computed flow ratio, so it visibly crawls once stenosis crosses the critical range.

Real-world relevance: this fourth-power relationship is why coronary artery disease can progress "silently" for years — moderate plaque buildup barely dents blood supply — and then trigger angina or a heart attack once a critical narrowing threshold is crossed, since flow collapses far faster than the anatomy appears to change on an angiogram.

Drag to orbit, scroll to zoom the 3D artery cross-section.

Blood flow particles Vessel wall Plaque (stenosis)

⚠ Couldn't load the 3D engineThree.js failed to load from the CDN. Check your connection and reload.

Flow rate vs. stenosis % — the "shoulder then cliff" curve