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Arterial Stenosis Hemodynamics

An interactive reduced-order model of blood flow through an atherosclerotic artery. Adjust the plaque and blood properties and watch velocity, pressure, and wall shear stress respond in real time — built on conservation of mass, Bernoulli, and Poiseuille relations derived from the incompressible Navier–Stokes equations.

Longitudinal 2-D section Newtonian · incompressible Reduced-order (not clinical CFD) Teaching tool
Velocity heat map Particles / streamlines Velocity vectors Wall shear stress Pressure band
Velocity
0––
m/s

Bright throat = flow acceleration (continuity). Converging particles show streamline crowding; slow/reversed dim particles downstream mark predicted flow separation. Wall tint: warm = high shear near the throat, magenta = low/disturbed shear in the recirculation zone.

Velocity vs. axial position

Cross-sectional mean velocity U(x) = Q / A(x)

mean U(x)plaque

Pressure vs. axial position

Static pressure relative to inlet

p(x)plaque

Wall shear stress vs. axial position

τw on each wall (sign = flow direction)

top wallbottom wall

What each control does

—
↑ Stenosis severity
Smaller lumen area → higher throat velocity (continuity) → larger pressure loss and higher wall shear stress at the throat.
↑ Plaque asymmetry
Shifts the high-velocity jet toward one wall; drives an asymmetric velocity profile and one-sided downstream separation.
↑ Inlet velocity
Raises Reynolds number, increases the stenotic jet velocity, and amplifies velocity gradients and pressure losses.
↑ Viscosity
Lowers Reynolds number and damps flow disturbances, while increasing viscous (Poiseuille) resistance and pressure loss.
↑ Diameter / ↓ severity
Larger lumen lowers velocity for the same flow; Re = ρVD/μ scales directly with diameter.

Governing equations & model

Incompressible Navier–Stokes is the physical basis:

∇ · u = 0
ρ(∂u/∂t + u·∇u) = −∇p + μ∇²u

A full 2-D/3-D solver is too heavy for a live browser tool, so this uses a quasi-1-D reduced-order model:

# continuity (axisymmetric)
U(x) = U₀ (D / H(x))²
# Reynolds number
Re = ρ V D / μ
# wall shear (Poiseuille)
τ_w = 8 μ U / H
# viscous loss
dp/dx = 32 μ U / H²
# throat + expansion loss
Δp = ½ρ(U_t²−U₀²) + ½ρ(U_t−U₀)²

Blood as a Newtonian fluid is the default. Real blood is shear-thinning (non-Newtonian): apparent viscosity rises sharply at low shear rate (< ~100 s⁻¹, e.g. venous flow, recirculation zones) as red cells aggregate — a Carreau–Yasuda or Casson model captures this. In fast arterial flow the Newtonian assumption is reasonable.

How to read the numbers

Directly calculated from governing equations: continuity U(x), Reynolds number, flow rate, min lumen diameter, % area reduction, Poiseuille wall shear stress, viscous pressure loss.
Estimated with simplified models: Bernoulli throat pressure dip, Borda–Carnot expansion loss, separation/recirculation extent, Womersley number, per-wall shear asymmetry.
Qualitative only (visualization): particle pacing, jet-spreading shape, recirculation vortex rendering, heat-map smoothing.

This is a conceptual teaching model. It is not a validated, patient-specific clinical CFD simulation and should not be used for diagnosis. Default values are adjustable examples, not universal physiological constants.