1.
Echo and Doppler Physics
Dr George Abraham, Royal Free Hospital.

2.
Waves
• Vibrations that transfer energy from place to
place without the transfer of matter.
• Sound waves travel through a medium and set
up patterns of disturbance – vibrations.
• Light is a transverse wave and sound is a
longitudinal wave.

3.
• Amplitude is maximum disturbance from the resting state
• Frequency is the number of waves produced by the source every second

4.
• Wavelength of a wave is the distance
between a point on one wave and the
same point on the next wave.

5.
What’s the frequency?
• Measured in Hz – 1
wave/second
• Normal range of human
hearing: 20Hz-20kHz
• kHz = 10,000; MHz =
10,000,000
• Sound waves travel fastest in
solids, then liquids, then gases.
• The speed of sound in the
heart is 1560 m/s

6.
Velocity of a wave
• 𝑉 = 𝑓 λ
• Velocity = frequency X wavelength
• Frequency = 1/time period
• Higher frequencies will thus give a shorter
wavelength.

7.
• They can reflect off a smooth surface in a
predictable way.
• Rough surfaces scatter waves in all directions.
• Diffraction happens when waves pass through
a gap.
• Refraction happens when waves change speed
entering a different density medium.
What can waves do?

8.
US and Reflection
• Frequencies above 20kHz are Ultrasound.
• US Machines use frequencies 1.5-7 MHz.
• In ultrasound, a detector placed near the source of the
US can measure the time taken for the sound to
bounce back and hence the distance from the source.
• Pulse Repetition Period or PRP is the time between
the onset of one pulse till the onset of the next pulse.
This parameter includes the time the pulse is “on” and
the listening time when the ultrasound machine is
“off”.
• Pulse Repetition Frequency is the number of
pulses/second and relates to frame rate.

9.
Reflection

10.
Diffraction

11.
Refraction
Refraction happens when waves pass from one
medium to another at an angle and change speed.

12.
Attenuation
• The resolution of a recording is the ability to
distinguish 2 objects close together.
• Higher frequencies have shorter wavelengths
hence higher resolution.
• As the ultrasound waves pass through a medium
they gradually lose energy as heat.
• In the body, the depth of penetration is around
200 wavelengths.
• At 1 MHz, the penetration is 30 cm
• At 5 Mz, the penetration is 6 cm

13.
Acoustic impedance
• Tissue density X Propagation velocity
• This in addition to the angle of incidence,
determines how much of the US is reflected:
the strength of the signal.

14.
High frequency beam with a short wavelength and
high pulse repetition frequency.
Depends on how narrow the
beam is: the ‘focus’

15.
US transducers
• PZT crystals are materials that vibrate and then transduce
an incoming signal to electricity.
• Backing materials reduce ringing after the current is gone
• Matching layers reduce impedance

16.
How are images produced?

17.
M Mode
• A single crystal
rapidly alternates
between
transmission and
receiver modes with
pulse repetition
frequencies
>1000Hz.
• Thus gives excellent
temporal resolution
and can be used to
visualise rapid
movement.

18.
Doppler Shift
• As sound waves move from a source towards
an observer the waves shorten in wavelength
and increase in frequency.
• As sound waves move from a source away
from an observer the waves lengthen in
wavelength and decrease in frequency.
• The change between the frequency
transmitted and received is the doppler shift
• The amount of doppler shift depends on the
velocity and this can be calculated

19.
Doppler spectral analysis
• The frequency range of doppler shift is
• -10 to + 10 kHz hence within the audible range
• The spectral display is a speed/time graph with
red blood cell velocities detected along the
beam at any given time point are depicted
ranging from zero to the peak velocity
• The brightness of the signal denotes the
amplitude of the signal received corresponding
to that velocity

20.
CW Doppler

21.
CW Doppler
• In CW Doppler the echo machine uses
continuous transmission and receiving of US
signals by 2 dedicated crystals
• The CW Doppler obtains signals along the
entire cursor line
• It cannot assess flow at any one specific point
• It can measure high velocities without aliasing

22.
Aliasing
The phenomenon of aliasing means PW doppler displays will not
represent the highest velocities accurately.
The sampling frequency of the PW probe has to be more than twice the
frequency of the wave.

23.
Aliasing

24.
Important Points for Revision
• Relationship of velocity to frequency and wavelength
• Know the speed of sound in tissues
• Understand principles of image formation by
measurement of reflected US waves from the
transducer
• Understand how moving sources give a doppler shift
• Know the limitations of PW doppler and CW doppler
• Know the simplified Bernoulli equation

25.
References
- David Houghton
- https://www.slideshare.net/jeetshitole/physic
s-of-ultrasound-and-echocardiography