### Doppler10 - Medical Physics

```Doppler Ultrasound: Principles
Doppler Effect
• Shift in perceived frequency when either
source or listener are moving relative to
one another
• Familiar occurrence in audible sounds
• Also occurs in medical ultrasound
Waves from stationary and moving sources
Stationary
Moving
Please note: the ‘squishing’ of the wave-fronts in the middle diagram and the
stretching in the lower diagram are exaggerated. Realistically the Doppler shifts
are so small in ultrasound you would hardly see any difference in the wave-fronts
compared to the unshifted one on top. These are artists’ diagrams.
Doppler shift
• Doppler shift is the
difference between
the transmitted and
• Transmitted and
are in the MHz range
• Doppler shift
frequencies often in
audible range
Scattering from blood
• Source of signals for flow
imaging:
– Red blood cells
– Much smaller than l
– Rayleigh scatterers
• Scattering increases with
frequency
• Scattering increases with
number of targets
– Double the number of
scatterers, scattered
intensity doubles!
Scattering from blood increases with frequency
• Blood behaves as Rayleigh
scatterers
– Intensity varies with f4
– Double the frequency, intensity
increases by 2 x 2 x 2 x 2 = 16!
• High frequency enhances blood
signals if the path is short
• Attenuation prohibits use of super
high frequencies in most areas
40 MHz IVUS image of a
coronary artery
Doppler equation
• Relationship between Doppler shift (or just Doppler)
frequency, FD and reflector velocity, v:
2f o v cosθ
FD 
c
• fo is the ultrasound frequency, or the transmitted beam
frequency.
• v is the reflector velocity (m/s; cm/s)
• q is the Doppler angle
• c is the speed of sound
2f o v cosθ
FD 
c
2f o v cosθ
FD 
c
2f o v cosθ
FD 
c
If the beam direction is perpendicular to the
direction of flow, the Doppler frequency is
ZERO!
Cosine Function
h
cos q = a/h
q
a
h
a
cos 2o = 0.999
h
cos 60o = 0.5
a
The frequency of the Doppler shift is
proportional to the cosine of the Doppler angle
2f o v cosθ
FD 
c
• Angle formed by the ultrasound
beam and the direction of flow
• Doppler frequency varies with
the cosine of the angle.
– Cosine = 1 for 0o
– Cosine = ½ for 60o
– Cosine = 0 for 90o
– For angles between 0 and
10o, cosine is close to 1.
• The larger the angle (up to 90o),
the smaller the cosine
Angle Correct Cursor
• Angle correct is needed to
convert the Doppler
frequency to a reflector
velocity
parallel to the flow direction
• Machine then computes the
Doppler angle
Angle Correct Cursor
• Angle correct is needed to
convert the Doppler
frequency to a reflector
velocity
parallel to the flow direction
• Machine then computes the
Doppler angle
• Most displays indicate the
reflector velocity rather than
Doppler frequency
Angle Correct Error
Effect of 5o error in setting the
angle correct cursor
Actual velocity is 50 cm/s
Actual Angle
0o
20o
40o
60o
80o
Assumed Angle Estimated Velocity
5o
50.2 cm/s
25o
51.8 cm/s
45o
54.2 cm/s
65o
59.2 cm/s
85o
99.6 cm/s
Flow Patterns
• Laminar flow
– Highest in center
– Zero at wall
• Turbulent flow
– Larger distribution
of velocities
Ways to “analyze” complex Doppler signals
• Listen to signals on the loudspeaker
– Ear is sensitive to variations in loudness, pitch
– Interpretation is subjective
• Display analog signal derived from velocity or
flow rate
– Example: zero crossing detector
• Display Doppler signal spectrum
– Usually displayed as a velocity spectral waveform
Doppler Instrument with built-in ZeroCrossing Detector
• Provides an estimate of
Doppler signal
frequency vs. time.
• Output may be to a
chart recorder.
• Output may also be
superimposed on a
spectral display (rare).
Spectral analysis done using a FFT device
FFT = Fast Fourier Transform
Frequency (kHz)
Spectral Display (Frequency)
Calculate Velocity from Doppler
Frequency
2f o v cosθ
FD 
c
fD 
note
2
c FD
v
2fo cosθ
Spectral Display (velocity)
Mirror Image Artifact (Spectral Doppler)
Origin of artifact:
- ~ perpendicular to flow;
- over gaining
“Simplified” Doppler equation
(When the Doppler angle is zero)
• Let f0 be expressed as “F (MHz)”, such as 3, 5, etc; let v be V m/s;
also, let c=1540m/s
2fo v 2 F x 106 /s x V m/s 2 x 106 /s F V
FD 


 1.3F  V kHz
3
3
c
1.54 x 10 m/s
1.54 x 10
or
FD  (1.3 kHz)  F  V
74. With Doppler ultrasound, if the echo
frequency is lower than the transmitted
frequency, we can conclude that the reflector
is moving _______ the transducer.
A. toward
B. away from
C. perpendicular to
D. at a 60o angle to
2fo v cosθ 2fo v 2 (5x106 /s) 2m/s
3
FD 



12
.
98
x10
/s
3
c
c
1.54x10 m/s
75. If blood is flowing directly toward a 5 MHz
transducer at 2 m/s, the Doppler frequency
would be:
A. 1.3 Hz
B. 13 kHz
C. 4.087 MHz
D. 13 MHz
FD  (1.3 kHz)  F  V
75. If blood is flowing directly toward a 5 MHz
transducer at 2 m/s, the Doppler frequency
would be:
A. 1.3 Hz
B. 13 kHz
C. 4.087 MHz
D. 13 MHz
76. The pressure amplitude of scattered
echoes from red blood cells that produce
Doppler signals is LEAST affected by:
A.
B.
C.
D.
speed of sound
attenuation by soft tissue
transducer frequency
hematocrit
77. A peak Doppler shift of 4 kHz is detected in
a large artery. If the peak velocity in the
vessel were to double, the detected peak
Doppler shift would be:
A. 2 kHz
B. 4 kHz
C. 8 kHz
D. 16 kHz
78. A 5 MHz transducer detects a peak Doppler
shift of 12 kHz in an artery. With a 2.5 MHz
transducer, the same vessel would be
expected to produce a peak Doppler shift of:
A. 6 kHz
B. 12 kHz
C. 24 kHz
D. 10 MHz
79. An artery is interrogated with a 2 MHz beam
with a Doppler angle of 45o. A peak Doppler
shift of 1.8 kHz is detected. If the Doppler
angle is increased to 60o, you would expect
the peak Doppler shift to be:
A. 1.3 kHz
B. 1.8 kHz
C. 2.1 kHz
D. 2.3 kHz
80. A small error in the estimation of the Doppler
angle will result in the largest velocity
miscalculations when the Doppler angle is:
A. 0o
B. 10o
C. 45o
D. 80o
81. A Doppler device without a spectral analyzer
can NOT display:
A. peak velocity
B. mean velocity
C. velocity changes over time
D. instantaneous distribution of velocities
82. On most instruments, the wall filter
eliminates: ________ signals.:
A.
B.
C.
D.
low amplitude
high amplitude
low frequency
high frequency
Basic Hemodynamics
• Vascular system
– Arrangements of pumps, conduits,
valves
– Aorta-arteries-arteriolescapillaries-venules-veins-vena
cava
• Travels from high to low
pressure
– Pressure gradient exists over any
region
– Total area of vasculature system
varies with distance from the heart
Pulse Pressure = systolic pressure - ??
= measure of amplitude of blood
pressure wave
Laminar
Flow
r
• Ideal model
• Highest velocity in center, lowest near
walls
• Tortuousity, bends, branching all
change the velocity profile
P2
Laminar
Flow
r
P1
L
• Energy associated with moving fluid
– Potential
• Elastic expansion of vessels, like stretching a
spring
– Kinetic
• Energy due to motion and related to the
velocity
• Viscous losses tend to dissipate the
energy with increasing distance
Poiseuille (pwazourz)
Schooled in physics and mathematics Poiseuille
developed an improved method for measuring blood
pressure.
Poiseuille’s interest in the forces that affected the blood
flow in small blood vessels caused him to perform
meticulous tests on the resistance of flow of liquids
through capillary tubes. In 1846, he published a paper on
his experimental research. Using compressed air,
Poiseuille forced water (instead of blood due to the lack
of anti-coagulants) through capillary tubes. Because he
controlled the applied pressure and the diameter of the
tubes, Poiseuille’s measurement of the amount of fluid
flowing showed there was a relationship. He discovered
that the rate of flow through a tube increases
proportionately to the pressure applied and to the fourth
power of the tube diameter. Failing to find the constant of
proportionality, that work was left to two other scientists,
who later found it to be p/8. In honor of his early work
the equation for flow of liquids through a tube is called
Poiseuille's Law.
Poiseuille equation
P1
• V = velocity (cm/s, m/s)
• Q = volume flow rate (cm3/s,
l/s)
• Pressure Volume relationship
• P2 and P1 are pressures, r is
the radius, L is the length, and
h is the coefficient of viscosity.
• Viscosity: measure of a fluid’s
resistance to flow; describes
the internal frictionof a moving
fluid
– Syrup has a high viscosity
– Water has a low viscosity
Laminar
Flow
r
P2
L
p ( P1  P2 )r
Q
8Lh
4
P
1
 V 2  gz  Constant
 2
Bernoulli Equation
(Expresses conservation of energy)
The simplified version of the Bernoulli
Equation is
P
P
1
 V 2  gz  Constant
 2
The Bernoulli principle helps to explain how an
airplane wing works. The greater velocities just
above the wing result in a lower pressure on the
top-front of the wing than on the undersurface,
hence an upward force. (Lift also can be
associated with a downward component of the air
to the rear; Newton’s third law says there must be
an upward lift.)
1 2
 V  gz  Constant
 2
where P, , V, and z are pressure,
density, velocity and height,
respectively, and g is the acceleration
due to gravity.
The fact that the terms on the left
sum up to a constant means that if V
increases, P must decrease to keep
the quantity a constant.
P
1
 V 2  gz  Constant
 2
Applying the Bernoulli Equation
(Expresses conservation of energy)
The modified Bernoulli Equation is
P 
or
P
1
 V 2  gz  Constant
 2
P1
P  4V 2
P2
P
1
 V 2  gz  Const ant
 2
1
1
2
2
P1  V1  P2  V2
2
2
but usually V1  V2
P1  P2 
1
V2 2
2
1
760x530 2
2
V22  530V 2 
V

3
.
988
V
2
1.01x105
where P now is in mm Hg and V is
in m/s. The density, , of blood is
taken to be 1060 kg/m3, and the term
760/1.01 x 105 converts pressure
from n/m2 to mm Hg.
P
1
 V 2  gz  Constant
 2
Applying the Bernoulli Equation
(Expresses conservation of energy)
The modified Bernoulli Equation is
P 
P
1
 V 2  gz  Constant
 2
1
760x530 2
V22  530V 2 
V  3.988V 2
5
2
1.01x10
or
P  4V 2
where P now is in mm Hg and V is
in m/s. The density, , of blood is
taken to be 1060 kg/m3, and the term
760/1.01 x 105 converts pressure
from n/m2 to mm Hg.
The pressure drop on the left is about
4 x (5.8)2 = 135 mm Hg.
Velocity Profiles
Continuous Wave (CW) Doppler
• Ultrasound transmitted continuously
rather than in pulses
• Some units have two-element
transducers, 1 transmitting, the other
receiving
• Arrays are sometimes used with CW;
different groups transmit than recieve
~MHz
~MHz
Difference
(audible)
Common user controls:
-Volume
-Gain (sometimes)
-Wall filter (sometimes)
Directional Doppler
• Usually want to know
whether flow is towards or
away from the transducer
used
• Tracing shows velocities
above and below the
baseline
• Speakers present velocities
on left or right speaker,
depending on direction
Range (depth) selection
done by a procedure
called “gating”
Gating +beam dimensions,
define “sample volume”
Pulsed Doppler
Important User Controls
•
•
•
•
•
•
•
•
•
•
•
•
Output
Frequency (may be different than B-mode frequency)
Gain
Wall filter
Gate position
Gate size (SV length)
Beam angle
Angle Correct
Velocity scale (prf)
Spectral Display Sweep speed
Gray scale maps
….
Sample Volume (gate)
Nyquist Sampling Limit
• Require PRF = 2 x Doppler Frequency
• Example, 3 kHz Doppler signal
– Need 6 kHz PRF to sample
• Example, 6 kHz Doppler signal
– Need 12 kHz PRF to sample
Nyquist Sampling Limit
• The Maximum Doppler frequency that
can be sampled is ½ the PRF
• Example, if PRF = 8 kHz
– Max Doppler frequency is 4 kHz
• Example, if PRF = 4 kHz
– Max Doppler frequency is 2 kHz
If the Doppler frequency exceeds ½ the PRF,
aliasing occurs
Aliasing produces false frequencies, reversal, etc.
Manifestation of Aliasing
After increasing the Velocity Scale
(automatically increases the PRF)
PRF
• Maximum PRF depends on depth of
sample volume
– When sample volume is shallow, PRF can
be higher
– When it is deep, PRF must be lower
• Thus, for a given ultrasound frequency,
a higher velocity can be detected at
shallower depths than at deeper depths.
To get rid of aliasing:
• Change the
velocity scale
• Change the
baseline
• Use a lower
ultrasound
frequency
• Get closer!
• Precise depth at which flow is detected
can be specified
• Flow information from a small portion of
a vessel can be isolated and analyzed
without interference from flow in
• Instruments can be made extremely
simple, inexpensive
• Useful when you do not have good
information (such as a B-mode image)
to help pinpoint vessel of interest
• DOES NOT ALIAS
Maximum Detectable Velocity
• Minimum PRF to avoid aliasing = 2
times the Doppler frequency.
• Maximum PRF set by gate depth (must
wait between successive transmit
pulses).
• Establishes a maximum detectable
velocity, that depends on gate depth
AND ultrasound frequency.
Maximum Velocity Detectable:
v max
c c
c2


2d 4fo 8fo d
2fo v
FD 
, so theminimumP RF we need to avoidaliasing is
c
4fo v
PRFmin  2FD 
c
But when imaging to a depth,d, theminimum wait timebetween pulses, T is
2d
T
c
T hus, themaximumP RF we can haveis
1
c
PRFmax  
T 2d
T hemaximumvelocitywe can detect with thisP RF will be
PRFmin  2FD 
Solving for Vmax
v max
4fo v max
c
 PRFmax 
c
2d
we get
c c
c2


2d 4fo 8fo d
Introduces range
ambiguity.
Allows higher velocities
to be detected.
Duplex Mode (Duplex Doppler)
B-mode imaging + Doppler
Frame Rate High
Frame Rate Low
Frame Rate vs Color Box Width
• Wider color box requires more individual color
beam lines.
• Each color beam line requires several pulseecho sequences (pulse-packet size).
• More time is needed to acquire echo data for
the wide color box than the narrow color box.
• Lower frame rate for the wide color box.
Flow velocity is usually indicated by color
brightness.
In Spectral Doppler, the entire range of velocities within
a gated region is displayed. In color, only the mean
velocity is displayed from each region.
Variance Display
Most manufacturers allow the operator
to select from a variety of color maps.
Color Threshold (emphasis on B-mode)
Only echoes exceeding the gray level indicated by
the line through gray bar will be displayed in place
of color.
Color Threshold (emphasis on color)
Only echoes exceeding the gray level indicated by
the line through gray bar will be displayed in place
of color.
Color Aliasing
Energy Mode (Power mode; color power
angiography mode)
• Does not display
Doppler shift
frequency
• Displays amplitude,
intensity or energy
in the Doppler signal
Direction, Energy vs. Velocity
θ
Energy mode does not display direction.
(Energy also not as direction dependent.)
Aliasing not displayed in energy mode.
Aliasing, Velocity vs. Energy
Energy mode does not display aliasing.
How B-Flow Images are Formed
Digital
Encoder
Digital
Decoder
Probe
LOGIQ 9
Bmode Process
Display
Monitor
For each line in the B-Flow image:
1) Transmit coded sound waves
Body
2) Decoder enhances flow signal
3) Flow and tissue displayed as in B-mode
(Slides are based on a set given to Zagzebski by GE Medical. They are presented to
attempt to understand B-flow, a complimentary technology to color flow imaging.)
B-flow processing
(Previous)
How B-Flow images are formed?
Digital encoded ultrasound is used as an enabling technology. Coded
sound waves are transmitted into the body and vasculature and the
returning signals are then decoded and displayed as in B-mode.
(Next)
Enhancement of the returned signal from blood reflections is
necessary due to the relative weakness of blood reflectors compared
to tissue. (Tissue is typically 20 - 30 db > reflective than blood.)
Enhancement however increases the tissue signal as well so the
tissue must be equalized to show enhancement of the blood
reflectors only.
(Slides are based on a set given to Zagzebski by GE Medical. They are presented to
attempt to understand B-flow, a complimentary technology to color flow imaging.)
Detecting Blood Reflectors
Problem:
Blood echoes are very weak
Solution:
Use coded excitation to
1) Increase sensitivity to
Blood
Tissue
blood reflectors (codes can
Noise
2) Equalize tissue signal
(not sure how this is done)
(Slides are based on a set given to Zagzebski by GE Medical. They are presented to
attempt to understand B-flow, a complimentary technology to color flow imaging.)
B-Flow Processing
Blood Reflectors Seen in B-Mode
1 0 0 1 1
Body
Encoder
Blood Echo
• Increase sensitivity to flow
• Equalize tissue signal
+
Tissue Echo
1 1 0 0 1
Decoder
(Slides are based on a set given to Zagzebski by GE Medical. They are presented to
attempt to understand B-flow, a complimentary technology to color flow imaging.)
Conventional Color Doppler
Imaging
Overlay
• Overlay color on B
overwrite lumen
• Separate B-mode and color firings
• Flash artifact
obscures anatomy
frame rate hit
(Slides are based on a set given to Zagzebski by GE Medical. They are presented to
attempt to understand B-flow, a complimentary technology to color flow imaging.)
(Previous)
This is where the strength of digital encoded ultrasound lies in that the coded
signal may be decoded into separate tissue and blood signals. It is now
relatively simple to enhance the blood signal while preserving diagnostic gray
scale.
Detecting blood flow with Doppler methods provides valuable diagnostic information.
However, Doppler technology constraints limit our ability to detect flow. Limitations
such as:
•Aliasing
•Signal dropout at orthogonal detection angles
•Wall filter limitations
(Next)
•All affect our ability to detect all types of blood flow. As a B-mode imaging technology,
B-Flow provides direct visualization of blood reflectors with:
•High spatial resolution
•High frame rates
•Blood and tissue displayed together - no overlay
•Intuitive display
(Slides are based on a set given to Zagzebski by
•No complex parameters to optimize
GE Medical. They are presented to attempt to
understand B-flow, a complimentary technology
to color flow imaging.)
B-Flow Image
B-Flow
Process
B-mode Image
B-Flow Image
• Simultaneous tissue and flow without overlay
• Intuitive B-mode-like display with full field of view
• No separate firings for flow
higher frame rate
B-Flow provides visualization of blood reflectors with:
High spatial resolution
(Slides are based on a set given to Zagzebski by GE Medical.
High frame rates
They are presented to attempt to understand B-flow, a
complimentary technology to color flow imaging.)
83. Gating determines the:
A. transmitting frequency
B. Doppler frequency
C. sample volume length
D. sample volume width
84. How often a Doppler signal is sampled is
determined by the _______ frequency.
A. transmitted
C. Doppler shifted
D. pulse repetition
85. If a pulsed Doppler device is operating at a
PRF of 6000/s, what is the maximum Doppler
frequency that can be accurately detected?
A. 3 kHz
C. 12 kHz
B. 6 kHz
D. 18 kHz
86. Aliasing occurs at lower frequencies when
the sample volume is:
A.
B.
C.
D.
moved toward the transducer
moved away from the transducer
increased in width
operated in continuous wave mode
87. Methods of compensating for aliasing do
NOT include:
A.
B.
C.
D.
transmitting at a higher frequency
increasing the velocity scale range
switching to continuous wave
88. Range discrimination is POOREST with:
A.
B.
C.
D.
M-Mode
continuous wave Doppler
pulsed Doppler
color Doppler
89. The highest velocities can be accurately
evaluated by:
A.
B.
C.
D.
real-time B-mode
pulsed Doppler
continuous wave Doppler
color Doppler
90. Increasing the packet size results in:
A.
B.
C.
D.
better velocity estimates,
better velocity estimates,
worse velocity estimates,
worse velocity estimates,
higher frame rates
lower frame rates
higher frame rates
lower frame rates
91. The term “variance” refers to:
A.
B.
C.
D.
peak velocity
mean velocity
velocity range
velocity threshold
92. The most accurate display of the distribution of
velocities at a particular depth occurs with:
A.
B.
C.
D.
continuous wave Doppler
pulsed Doppler
color Doppler
B-mode imaging
```