IMG-33

Doppler shift

Blood-flow US.

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ImagingDoppler

Governing equation

\\Delta f=2 f_0 v\\cos\\theta/c

where

f_0: f0 (MHz)
v: Flow (m/s)
\theta: Angle (°)
\Delta f: df (kHz)

Lecture brief

Historical brief

Larmor precession, CT Beer projections, SNR and Nyquist sampling are why MRI and CT images exist as numbers. The lab computes frequency, dose and resolution limits. This sheet (IMG-33 — Doppler shift) is the form associated with Doppler. Working symbols: $f_0$ , $v$ , $\theta$ $\rightarrow$ $\Delta f$ . Blood-flow US.

Purpose

Purpose: compute

\Delta f

from

f_0

v

\theta

in Medical imaging via

\\Delta f=2 f_0 v\\cos\\theta/c

Blood-flow US. Use it when a real medical imaging question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

f_0 = 5.000\,\mathrm{MHz}

v = 0.500\,\mathrm{m/s}

\theta = 30.000\,\mathrm{^{\circ}}

, the governing relation

\\Delta f=2 f_0 v\\cos\\theta/c

yields

\Delta f = 2.812\,\mathrm{kHz}

. Blood-flow US. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

f0 f_05 MHzFlow v0.5 m/sAngle \theta30 °

Outputs

df \Delta f2.812 kHz

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Narration of this film

Blood-flow US.

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