Collateral Flow Network in Peripheral Artery Disease

Disease Severity

Stenosis / occlusion 80%

Collateral vessels 3

Perfusion pressure ΔP 60 mmHg

Arteriogenesis

Hemodynamics

Total limb flow

-- mL/min

Via collaterals

--%

ΔP across lesion

-- mmHg

Collateral radius

-- mm

Wall shear (collat.)

-- dyn/cm²

Remodeling time

0 days

How it works

Blood flow through each vessel segment is modeled with the Hagen–Poiseuille law, exactly as in lumped-parameter hemodynamic models used to study peripheral artery disease (PAD):

R = 8ηL / (πr⁴)       (vascular resistance)
Q = ΔP / R           (flow, Ohm's-law analog)
τ_w = 4ηQ / (πr³)      (wall shear stress)

The narrowed native artery and the collateral vessels form a parallel resistor network bridging the diseased segment. Because resistance scales as 1/r⁴, a severe stenosis raises the main pathway's resistance enormously — and because it is fourth-power, even a small collateral carries flow disproportionate to its size once the stenosis is tight enough.

Stenosis / occlusion — narrows the diseased segment's lumen radius, driving its resistance up as 1/r⁴.
Collateral vessels — sets how many parallel bypass channels the network has, each with its own resistance.
Perfusion pressure ΔP — the driving pressure gradient across the limb segment (proximal minus distal pressure).
Start Remodeling — integrates a shear-stress feedback loop: flow forced through a narrow collateral raises its wall shear stress τ_w far above the ~8 dyn/cm² homeostatic set-point, and the endothelium responds by triggering outward remodeling (arteriogenesis) — the vessel enlarges, exactly as genicular and profunda femoris collaterals do over weeks in real PAD. Growth is capped near native-artery caliber, matching the biological ceiling on collateral enlargement.

Particle color encodes local flow velocity (blue = slow, red = fast) — note the high-velocity jet through the stenosis, the same phenomenon that produces elevated peak systolic velocity on duplex ultrasound at a real stenosis.

Slow flow Fast / jet flow

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