Pulsed-wave Doppler measures the frequency shift of ultrasound reflected off moving red blood cells. For a beam at angle θ to the flow direction, with transducer frequency f₀ and sound speed in tissue c ≈ 1540 m/s:
f_d = 2 f₀ v cos(θ) / c
Unambiguous (Nyquist) velocity limit set by the
pulse repetition frequency (PRF):
v_N = PRF · c / (4 f₀ cos θ)
Color Doppler maps f_d to a red↔blue scale (toward/away from the probe, brightness ∝ speed). Because PRF sets a maximum unambiguous shift, any true velocity beyond ±v_N cannot be told apart from a smaller velocity of the opposite sign — the color map wraps around and flips, exactly the aliasing artifact seen clinically as a sudden red→blue speckle in the center of a fast jet.
- Peak velocity — sets how fast the simulated pulsatile jet moves at systole; flow follows a Poiseuille-like profile (fastest at the vessel center, near-zero at the wall).
- Insonation angle θ — the angle between the ultrasound beam and the vessel axis; steeper angles (θ → 90°) shrink the measured shift toward zero (cos θ → 0), which is why sonographers keep θ below ~60° in practice.
- Transducer frequency f₀ — higher frequency gives a larger Doppler shift for the same velocity, but also a lower Nyquist limit for a fixed PRF.
- PRF — raising it raises v_N (less aliasing) at the cost of shallower maximum imaging depth in a real machine (not modeled here).
Real-world relevance: this is the exact physics behind color-flow and spectral Doppler ultrasound used to assess stenosis, DVT, fetal circulation and cardiac valve flow — and why a sonographer lowers the "scale" (PRF) to see slow flow, or raises it to stop a fast jet from aliasing.