Infographics / Ultrasound Physics

Doppler equation and insonation angle

An ultrasound beam from a transducer insonates a blood vessel at angle theta to the flow direction. The detected Doppler shift depends only on the along-beam velocity component v times cosine theta, following the equation delta f equals 2 f0 v cosine theta divided by c. A graph shows the shift is maximum at 0 degrees (beam parallel to flow), falls to zero at 90 degrees (perpendicular), and is most accurate below 60 degrees.

Doppler angle dependence in ultrasound An ultrasound beam from a transducer insonates a blood vessel at angle theta to the flow direction. The detected Doppler shift depends only on the along-beam velocity component v times cosine theta, following the equation delta f equals 2 f0 v cosine theta divided by c. A graph shows the shift is maximum at 0 degrees (beam parallel to flow), falls to zero at 90 degrees (perpendicular), and is most accurate below 60 degrees. Δf = ( 2 · f₀ · v · cos θ ) / c beam meets vessel at angle θ v blood flow (velocity v) ultrasound beam transducer θ v cos θ (detected) angle dependence of the shift max, θ = 0° (parallel) zero, θ = 90° (⊥) best accuracy θ < 60° 0° 60° 90° insonation angle θ Doppler shift ∝ cos θ Higher f₀ → larger shift; higher sound speed c → smaller shift ( Δf ∝ f₀ , Δf ∝ 1/c ). Toward probe → positive shift; away → negative. Factor of 2 = echo shifted on transmit and return. Typical shifts are a few kHz (audible) on a MHz carrier; sound speed (~1540 m/s) is unchanged by motion.
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