DOPPLER EFFECT
Course: Ultrasound
Victor Ekpo
MSc Medical Physics programme, College of Medicine, University of Lagos, 2017.

OUTLINE
• Introduction
• Physics of Doppler Effect
• Conditions for Doppler Effect
• Classifications
• Types
• Modes
• Applications
• Artifacts in Doppler Imaging
• Conclusion
2

INTRODUCTION
• Ultrasound is sound waves with frequency greater than
20kHz (Medical Ultrasound range: >2MHz)
• Sound waves travelling through a medium can be
reflected, refracted, absorbed or transmitted.
• Reflection occurs at the point of acoustic impedance
mismatch.
3

MOVING SOUND
• One or both the sound source and receiver may be
stationary or moving.
• If the sound source moves towards the listener, the
sound is perceived to have a higher frequency/pitch, and
a lower frequency as it moves away from the
listener.
4

DOPPLER EFFECT
Doppler effect is the change in frequency of
sound (or any wave) due to the relative motion* of
the source and receiver.
Doppler Shift (Δf) = Reflected Frequency – Transmitted frequency
Doppler angle ( θ ) = Angle between the direction of source – direction of sound
5

CONDITIONS FOR DOPPLER SHIFT
The Doppler effect will NOT occur:
• If the source and observer both move in the same direction at the
same speed.
• Where one source/listener is at the centre of a circle while the
other is moving on it with uniform speed.
• If the source/receiver is at 900 to the receiver/source.
6

7
Longer wavelengths
Lower frequency
Shorter wavelengths
Higher frequency
TOWARDS AWAY FROM

8
Sound waves reflected from a moving object are compressed
(higher frequency) when moving towards the listener/
transducer,
…and expanded (lower frequency) when moving away from
the listener/transducer compared to the incident sound
wave frequency.

9

The velocity of sound (c) is given by the equation,
Speed, c =
𝑊𝑎𝑣𝑒𝑙𝑒𝑛𝑔𝑡ℎ (λ)
𝑃𝑒𝑟𝑖𝑜𝑑 (𝑇)
= Wavelength (λ) * frequency (f)
λo =
𝑐
𝑓 𝑜
Consider a sound source travelling at a velocity 𝒗 𝒔 towards a detector.
After time t, the new wavelength,
λ1 =
𝑐 − 𝒗 𝒔
𝑓 𝑜
10
PHYSICS OF DOPPLER EFFECT
𝒗 𝒔
c

With a shortened wavelength, the new frequency f1 is given by:
f1 =
𝑐
λ1
=
𝑐
(c−vs) / fo
f1 = fo
𝑐
( 𝑐 − 𝒗 𝒔
)
Δf = f1 - fo = fo
𝑐
( 𝑐 − 𝒗 𝒔
) - fo
= fo
𝑐
( 𝑐 − 𝒗 𝒔
) - 1
= fo
𝑐 −( 𝑐 −𝑣𝑠 )
( 𝑐 − 𝒗 𝒔
)
Δf = fo
𝑣 𝑠
( 𝑐 − 𝒗 𝒔
)
If c >> vs , then
Δf = fo
𝑣 𝑠
𝑐
11

A similar equation can be written for a detector moving towards a source,
Δf = fo
𝑣 𝑑
𝑐
It can be shown that for a source moving away,
λ1 =
𝑐 + 𝒗 𝒔
𝑓 𝑜
Δf = fo
−𝑣 𝑠
𝑐
OR fo
−𝑣𝑑
𝑐
For a 2-way motion where a transducer emits ultrasound of frequency f,
and it gets reflected back by moving blood of velocity v (and c>>v), then:
Δf = 2f
𝑣
𝑐
12

If direction of motion is oblique, then:
Δf = (2vf Cos θ) /c
where:
Δf = Doppler shift
f = transducer frequency
v = velocity of source/receiver
c = velocity of sound
θ = Doppler angle 13
PHYSICS OF DOPPLER EFFECT (contd.)

• Doppler shift, Δf increases with:
• increasing source velocity v, and
• increasing transducer frequency, f
• Δf is maximum at θ = 0o and minimum at θ = 90o.
• To experience Doppler effect, θ ≠ 90o
14
Δf = (2vfCos θ) /c
Doppler Shift = 2 x Velocity of Blood x Transducer Freq x Cos θ
Propagation Velocity of Sound
FACTORS AFFECTING DOPPLER SHIFT

If the object is moving perpendicular (θ=90o) to the ultrasound beam, there is no change
in frequency or wavelength.
By measuring the frequency shift, Doppler Ultrasonography can be used to determine
any or all of these 4:
• Speed
• Direction
• Flow (Laminar or Turbulent)
• Location
15
Δf = (2vfCos θ) /c

USES OF DOPPLER METHOD
With Doppler, US can be used for static and dynamic imaging.
The Doppler method can be used for:
• detection and characterization of blood flow,
• detection of foetal heartbeat,
• detection of air emboli,
• blood pressure monitoring, and
• localization of blood vessel occlusions.
16

17
CLASSIFICATIONS OF DOPPLER ULTRASONOGRAPHY
OUTPUTS/IMAGING MODESTYPES FUNCTIONS
PULSED
WAVE
DOPPLER
CONTINUOUS
WAVE
DOPPLER
COLOUR
DOPPLER
POWER
DOPPLER
SPECTRAL
DOPPLER
DUPLEX
MODE
TRIPLEX
MODE
TRANSCRANIAL
DOPPLER
TISSUE
DOPPLER
OTHERS

TYPES
• Continuous Wave Doppler
• Pulsed Wave Doppler
18

CONTINUOUS WAVE DOPPLER
• It is a continuous wave of ultrasound being sent into
the body.
• Measures mainly the velocity of moving blood.
19

CW: TRANSDUCER PROPERTIES
• CW uses a relatively narrow-band high-Q transducer, to
preserve velocity information.
20

CW: TRANSDUCER PROPERTIES
• The piezoelectric elements of the transducer are divided into 2:
• Transmitter: continuously transmitting US, and
• Receiver: detecting reflected echoes.
Doppler Shift = Received Freq – Transmitted Freq
21

22
Transmitter and Receiver are angled
against each other.
The Transmitter produces sinuosoidal US
waves of the form Cos 2πfot.
The received signal is of form:
Cos [ 2π (fo + fD) t ]
The Doppler signal is thus of form:
Cos 2πfDt , and can be recovered via
frequency demodulation of the
received signal.
Fig: CW Doppler Scan Geometry (angled Tx and Rx)

WALL FILTER: CW DOPPLER
• The Doppler signal contains very low frequency signals
(clutter) from moving specular reflectors, such as blood vessel
walls.
• A "Wall Filter" selectively removes these other low
frequencies.
23

BEAT: CW DOPPLER (contd.)
• The Doppler ultrasound signal is amplified to an audible
sound level (called Beat).
• Doppler Beat can be heard through a speaker or a
headphone.
24

CW DOPPLER (contd.)
• The audio indicates the spread of velocities involved in a
heart beat.
• It forms the basis of the ultrasound stethoscope for
foetal heartbeat monitoring.
25

Fig: Foetal Heart Rate (FHR) Doppler Detector
Some also display the Heart Rate in Beats Per Minute (BPM)
Uses the principle of Continuous Wave Doppler. 26

BEATS: CW DOPPLER (contd.)
• The higher the pitch, the greater the velocity.
• The harsher the sound, the greater the turbulence.
27
Δf = (2vfCos θ) /c

28
Fig: Block Diagram of CW Doppler System

CW DOPPLER (contd.)
• Output can also be displayed on a Spectrum analyser,
constructing a pixel grayscale.
• Quadrature Detection (type of signal processing) permits
determination of the direction of flow of blood in CWD, if
used.
29

CW DOPPLER SPECTRAL DISPLAY
• The pixel greyscale represents the magnitude of the short
time Fourier Transform of the Doppler signal.
• A pixel in a Doppler spectrum represents the proportion
of red blood cells (RBCs) in the field of view that was
moving at a particular velocity at a particular time.
30

LIMITATIONS OF CW DOPPLER
• Poor Spatial Resolution: resulting from the large area of overlap
between the transmitter and receiver beams.
• Range Ambiguity: Measures velocity, but not location.
• CW cannot be used to distinguish the flow of overlapping vessels
at different depths.
• Lack of TGC (time gain compensation).
31

ADVANTAGES OF CW DOPPLER
• For measuring fast flow (high velocities) without aliasing.
• Good for assessing deep-lying vessels.
• It is inexpensive.
32

PULSED WAVE DOPPLER
• It transmits a sequence of short pulses, rather than a
continuous sinusoidal wave.
• PW allows both velocity and depth information to be
obtained.
33

PW DOPPLER (contd.)
• One single group of array elements is used for both receiving and
transmitting.
• PW Doppler allows measurement from a small, specific blood volume
(region of interest), which is defined by a sample volume.
• After the pulse has traveled forth and back (travel time T), an electronic
range gate is opened for a short period of time to receive the echoes.
34

OPTIMIZING PW
• Doppler Shift measurement: Achieved using longer
spatial pulse length (SPL)/high Q-factor transducer.*
• Depth Selection: Achieved with an electronic time gate
circuit (or range gate) to reject all echo signals, except
those falling within the determined gate window.
35

SAMPLE AND HOLD OPERATION
As the echo from each successive transmission is received, a
single sample at the expected arrival time of echoes from the
range gate is acquired and held until the echo from the next
pulse is received.
36

Fig: Sample-and-
Hold Operation of
PW Doppler
37
If the reflectors are moving, the signal received from the range gate will
change with each subsequent pulse, and the sample-and-hold operation will
construct a staircase signal (as above).

PW DOPPLER (contd.)
• The second pulse should be transmitted no sooner than the
expected arrival time of the echoes from the range gate that arise
from the first pulse*.
• The pulse travel time T determines the shortest possible time
interval between two successive transmit pulses.
38

Pulse repetition Frequency (PRF) is the number of pulses that an ultrasound
system transmits into the body each second.
The PRF of the transmitted pulses is the effective sampling frequency.
PRF = 1/T
The maximum detectable frequency shift (Nyquist Limit) is determined by
the value of one-half PRF.
fmax = ½ PRF
39
NYQUIST LIMIT

CONDITION TO AVOID ALIASING:
The PRF must be at least twice the Nyquist Limit.
PRF ≥ 2 fmax
40
NYQUIST LIMIT
fmax = ½ PRF
PRF = 2 fmax
Otherwise, at high blood velocities, aliasing will occur.

Fig A: Aliasing as shown in spectral Doppler effect
41
Aliased signals wrap around to negative amplitude,
masquerading as reversed flow and underestimating velocity.
A

PW MAX. VELOCITY
• Recall Doppler frequency is given by:
Substituting Maximum PW Doppler Frequency fmax for Δf, we get:
fmax = (2 vmax f Cosθ ) /c
PRF/2 = (2 vmax f Cosθ ) /c
42
Δf = (2vfCos θ) /c
vmax = cPRF
4fCosθ

PW MAX VELOCITY
• vmax represents the maximum velocity of reflector (e.g.
RBCs) that can be measured without aliasing.
• For a range gate positioned at depth z,
z = ½ λ
PRF = c/2z
43
vmax = ___c2____
8 z f Cosθ
vmax = cPRF
4fCosθ

PW MAX. VELOCITY
• The maximum velocity that can be accurately
determined by Pulsed Doppler increases with PRF,
lower operating frequency, and increasing angle.
44
vmax = ___c2____
8 z f Cosθ
vmax = c PRF
4 f Cosθ

DISADVANTAGES OF PW DOPPLER
PW cannot accurately measure fast blood velocities due to aliasing.
To avoid aliasing:
• increase the PRF
• increase Doppler angle
• reduce the depth
• reduce the transducer frequency
• change the baseline
• use CW instead.
45
vmax = ___c2____
8 z f Cosθ

46
Fig: Block Diagram of a Pulsed Wave Doppler System

MULTIGATED (MG) PULSED WAVE DOPPLER
• This is a variation of Pulsed Wave Doppler.
• Whereas PW Doppler system can only provide information from a particular
sample, MG PW Doppler obtains information from several depths
simultaneously using multiple gates.
• After demodulation, the received signal is directed to a number of parallel
processing chains - each with slightly different range of gate settings. 47

MG PW DOPPLER (CONTD.)
• Velocity distribution profile across the vessel cross-section can be
determined.
• It is a useful diagnostic tool for presence of plaques and stenosis.
• Orientation and location of a desired vessel still remain a problem, which
can be solved by Duplex Scanning.
48

MODES OF DOPPLER IMAGING
To display Doppler information, one of 3 modes may be chosen:
• Color Doppler
• Power Doppler
• Spectral Doppler
49

(a)
Power Doppler 50
(b)
Colour Doppler
(c)
Spectral Doppler

COLOUR DOPPLER (CD or CCD)
• Color (flow) scanning involves displaying Colour Doppler data
on real time (B-mode) grayscale images.
• The superimposition is such that tissue volumes containing
• no detectable flow are displayed in greyscale,
• while those in motion are in colour (usually red and blue).
51

COLOUR DOPPLER
Colours are assigned, depending on:
• DIRECTION : motion towards (Positive Doppler shift) or
(Velocity Mode) away (Negative Doppler shift) from the transducer.
• FLOW (Variance Mode): Laminar or Turbulent flow
• VELOCITY MAGNITUDE: mapped to the colour intensity
52

53

LIMITATIONS OF COLOUR DOPPLER
• Clutter of slow-moving solid structures and noise can
overwhelm the smaller echoes from moving blood.
• Spatial resolution of the colour image is lower than
grayscale.
54

USES OF COLOUR DOPPLER
• Imaging the heart and major blood vessels in
applications for which mean flow velocity is a
diagnostically useful parameter.
• To recognize and localize vessels and vascular blockage.
55

POWER DOPPLER
• Power Doppler represents the total power in the
Doppler spectrum at each sample volume.
• Unlike colour Doppler, Power Doppler usually
uses a single colour.
56

POWER DOPPLER
1. Power Doppler uses the magnitude of return Doppler
signal strength / power /intensity / amplitude alone.
2. It ignores the angle and direction of flow (phase).
3. It adopts slower frame rates and thus has greater
sensitivity to motion of the patient, tissues, and
transducer. 57
Power α Intensity α Amplitude2

Fig: Power Doppler
58

59

60

ADVANTAGES OF POWER DOPPLER
• PW’s greater sensitivity to motion allows detection and interpretation of
very subtle and slow blood flow.
• Power Doppler provides a more continuous display of tortuous vessels.
• Helps to rule out vascular occlusions,
• Helps to differentiate between blood carrying vessels and other fluid
occurrences
• It is not prone to aliasing.
61

DISADVANTAGES OF POWER DOPPLER
• It is susceptible to flash artifacts, which are colour signals due to its greater
sensitivity to motion.
• No information on flow velocity and direction of flow.
• Evaluation of hemodynamic properties such as the pulsation of flow, is
limited, since, most often, the image frame rate is too low.
62

USES OF POWER DOPPLER
• Used for tumour imaging, where moving blood volume is a
diagnostically useful parameter.
63

SPECTRAL DOPPLER
• The Spectral Doppler uses the Doppler frequency shift of the
echo signal as a measure of flow velocity and direction of flow.
• The Doppler spectrum ascertains the distribution of flow
velocities and their frequencies of occurrence at a defined
sampling site as a function of time.
64

SAMPLING SITE: SPECTRAL DOPPLER
• The sampling site is determined by using B-mode, Color Doppler
or Power Doppler image display (Duplex imaging).
65
SPECTRAL DOPPLER

The spectra from within or directly behind a stenosis (numbers 2 to 4) show increased
velocities, turbulence and reverse flow.
These changes in spectrum provide information on flow in the blood vessels.
66

FLOW
• Laminar flow normally exists at the centre of large
smooth vessels.
• Turbulent flow occurs when the vessel is disrupted by
plaque and stenosis.
67

USES OF SPECTRAL DOPPLER
68
SPECTRAL DOPPLER
• Spectral Doppler provides a detailed qualitative, semi-
quantitative or quantitative evaluation of hemodynamic
changes in tissues.

DUPLEX SCANNING
• Duplex scanning combines 2D B-mode imaging and a Doppler
type (e.g. Colour Doppler).
• The duplex system allows estimation of the flow velocity directly
from the Doppler shift frequency.
69

Duplex mode : Combining B-mode Greyscale + Colour Doppler
70

TRIPLEX MODE
71
Combines 3 methods: B-Scale greyscale, Colour Doppler and Spectral Doppler

(SOFT) TISSUE DOPPLER IMAGING
• Used to image soft tissue using a low pass filter.
• A conventional Doppler system assumes blood flow is concentrated at
intermediate and high velocities, while scatterers moving at low
velocities correspond to soft tissue.
• Therefore to eliminate such low velocities, a high pass wall filter is
usually used.
72

(SOFT) TISSUE DOPPLER IMAGING
• Tissue Doppler Imaging replaces the high pass wall filter with a
low pass filter, thus allowing only low Doppler frequency signal,
corresponding to low velocity movements.
• Can be done in Pulsed Wave Doppler mode or Colour Doppler mode.
• Used in diagnosing regional abnormalities in ventricular wall motion.
73

TRANSCRANIAL DOPPLER ULTRASONOGRAPHY (TCD)
• TCD is a non-imaging Pulsed Wave Doppler technique measuring
local blood flow velocity and direction in the proximal portions
of large intracranial arteries.
• Used for evaluation and management of patients with risk of
cerebrovascular disease.
74

TCD: Stroke Prevention for Children with SCD
• In 2017, Dr. M. Adekunle and Prof. O. Akinyanju (of Sickle Cell
Foundation Nigeria) recommended annual screening of children
with Sickle Cell Disorder (SCD to assess risk of stroke.
• Children aged 2-16 years with Sickle Cell Disorder (SCD) have a
high risk of stroke, esp. children aged 2-8 years.
75

TCD: Stroke Prevention for Children with SCD
• Stroke occurs when part of the brain is damaged by inadequate
blood supply.
• Inadequate blood supply occurs due to cerebral bleeding
(bleeding from arteries) or thrombosis (blood clots), which
impede flow of blood in the arteries of the brain.
76

If the velocity in an artery exceeds 250cm/s, that area is at a higher risk of stroke
[Adams]. 77
Fig: Transcranial Doppler Ultrasound of blood vessels in the Circle of Willis of the brain

TCD: Stroke Prevention (contd.)
• Stroke can cause paralysis, seizures, loss of speech or reduced
intellectual capacity.
• Stroke prevention therapy can be carried out for affected children.
• Adekunle and Akinyanju recommend establishment of more TCD
centres across Nigeria.
78

79
KNOBOLOGY
Some ultrasound units have a knob for PW, CW, Colour, and Power Doppler modes.
(A) (B)

ARTIFACTS IN DOPPLER
• Aliasing
• Mirror Artifact
• Vibration Artifact (Bruit)
• Velocity Artifact
• Shadowing Artifact
80

ALIASING
• Aliasing is error due to insufficient sampling rate PRF
• It causes high velocity forward flow to appear as reverse flow.
• Occurs in Colour Doppler, but not Power Doppler.
81

82
Fig: Increasing PRF can solve Aliasing Artifact

Due to reverberations and mirroring at strong reflectors, images in Color or
Power Doppler show artifacts, similar to those observed in B-mode.
e.g. mirroring of hepatic vessels at the diaphragm.
83

Caused by tissue vibrations at the site of an arterial-venous fistula, occlusion or
stenosis. pulsating blood pressure is transmitted to adjacent tissue causing tissue
vibration.
This is due to pulsating blood pressure at occlusions transmitted to adjacent
tissue, recognized as a colour mosaic. 84

• Due to changing Doppler angle
and transducer type used.
• Occurs only in Colour Doppler
(Doppler angle does not affect
Power Doppler)
• It can lead to Reverse-Flow and
Flow Acceleration artifacts.
85
• Convex/Sector Transducer & Linear Vessels: Curved transducer aperture
introduces Doppler angles, causing inaccurate depiction of blood vessel velocities.
• Linear Transducer & Curved Vessels: Produces similar effect as the above.

In the display of blood flow in the verterbral column in the Power Doppler mode,
due to strong reflectors (bones), a shadow is cast on the blood vessels, making
them look interrupted.
86

OTHER FORMS OF ANGIOGRAPHY (DSA vs CT vs MR)
• Digital Subtracted Angiography is the ‘gold standard’ in arterial
imaging.
• It uses X-ray based fluoroscopy.
• It produces its image by subtracting a pre-contrast image with an image
taken after injection of a contrast medium.
• It is considered invasive, as it involves use of catheter.
• It requires the patient to be still, and thus not favoured for heart
imaging.
87

OTHER FORMS OF ANGIOGRAPHY (DSA vs CT vs MR)
CT Angiography (CTA) has the advantage of producing 3D
images. It is less invasive and stressful for the patient.
MR Angiography (MRA) avoids ionizing radiation and
nephrotoxic contrast agents.
88

CTA vs MRA
Advantages of CTA over MRA include:
• Visualization of calcified plaques and
• Insusceptibility to metallic vascular clips.
• Lower cost: Iodinated contrast material for CT angiography is
less expensive than the dose of gadolinium required for MR
angiography.
89

CTA vs MRA
• Coronary Artery Disease: CTA offers better sensitivity and
specificity better than MRA.
• Arterial Stenosis of the Aortoiliac and Renal Arteries: No
statistically significant difference between CTA and MRA.
90

CTA vs MRA
• Aorto-iliac Arterial Disease: CTA shows higher sensitivity
(98.7%) than CCD (96.2%) in the assessment of aorto-iliac
arterial disease [A. Osama et al, 2012 ].
• Agreement between DSA and CCD was 96.1%
91

• Doppler Ultrasonography has a relatively high sensitivity in
comparison with digital subtraction angiography.
• It is cheaper, less-invasive, non-ionizing and offers minimal risk
of bio-effects.
92
CONCLUSION

REFERENCES
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Wilkins. 2002.
W. Huda, R. Sloan. Review of Radiologic Physics. 3rd ed. Philadelphia: Lippincott Williams & Wilkins. 2009.
M. Adekunle, O. Akinyanju. Prevention of Stroke in Children with Sickle Cell Anaemia. Sickle Cell Bulletin.
Vol 8. No. 1. Sickle Cell Foundation Nigeria. 2017.
Siemens AG. Principles of Ultrasound Imaging. 1999: Med USSE
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Angiography in assessment of aorto-iliac arterial disease. Egyptian Journal of Radiology and Nuclear Medicine.
2012.
R. Herzig, et al. Comparison Of Ultrasonography, CT Angiography, and Digital Subtraction Angiography In Severe
Carotid Stenoses. European Journal of Neurology. 2004.
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THANK YOU
94