Educational Course Imaging Ultrasound I
Triplex Mode
J. Brian Fowlkes, PhD*
University of Michigan
Department of Radiology and
Biomedical Engineering
*Equipment support from GE Medical and Toshiba Medical
fowlkes@umich.edu
Gas Molecules in a Sound Wave
Wave Propagation
λ  - Spatial
f - Temporal
Animation from Dr. Dan Russell, Kettering University"
Relationships
Velocity-Frequency-Wavelength
c = f λ
c = Sound Velocity"
f = Frequency"
λ = Wavelength"
Speed of Sound
c
(m/s)
Propagation
Reflection and Refraction
θi = θr "
Reflection"
sin θi/ sin θt = c1/c2 (Snellʼs Law)"
Refraction"
c2 < c1"
Reflection and Transmission
•  The reflection coefficient is
R = [(Z2-Z1)/(Z2+Z1)]2
•  The transmission coefficient is
T = (4Z2Z1)/(Z2+Z1)2
where Z1 and Z2 are the
impedances of the two media.
Specular Reflection
Noise or Structure?"
Speckle"
Electronic"
Image Statistics
Speckle
SNR=I/σ"
λ
CNR=(Io−Ib)/(σo2+σb2)1/2"
where averages are taken "
over an ROI"
Scatter dia << λ"
ATTENUATION COEFFICIENT
Attenuation
(from Absorption and Scatter)
Intensity"
I = Ioe-2µd"
d"
Depth"
2.5
5.0
7.5
Lateral Resolution"
I/Q Data
Approximately equal to the beamwidth W"
D"
•  Baseband result for a specified
carrier frequency
W"
F"
If φ < 50ο"
Wf = λF/D"
"= λ(F#)"
•  I - In phase
φ
•  Q - quadrature (shifted 900)
I = A(t)cos(ωt)cos(ω 0 t)
I = (A(t) /2)[cos(ωt + ω 0 t) + cos(ωt − ω 0 t)]
Q = (A(t) /2)[sin(ωt + ω 0 t) + sin(ωt − ω 0 t)]
€
BB = I + jQ
€
Q = A(t)cos(ωt)sin(ω 0 t)
Env =
2
I +Q
2
€
RF Data
20000
RF Data
15000
Phased Array Beam Steering
Amplitude
(a.u.)
10000
5000
0
Series1
0
2
4
6
8
10
12
14
-5000
-10000
-15000
-20000
Time
(microsec)
A-mode
16
18
20
Traditional
B-mode Imaging
Compound
Imaging
Transducer
Transducer
Compound
Imaging
Normal B-Mode
Compound Imaging
Speckle Reduction"
Example in Breast Imaging
Wave Fronts
Stationary Sound Source" Source moving with vsource <
vsound ( Mach 0.7 )"
Animation courtesy of Dr. Dan Russell, Kettering University"
Doppler Equation
Wave Fronts
fD = 2f cosθ vo/c"
f = Center frequency of
transmitted ultrasound"
θ = Angle of motion with
respect to sound
propagation"
vo = Velocity of blood"
c = Sound speed"
Stationary Sound Source" Source moving with vsource <
vsound ( Mach 0.7 )"
Animation courtesy of Dr. Dan Russell, Kettering University"
Spectrum of Doppler
Sum and Difference Frequencies"
Wall Filter"
cos(ω0 t)cos((ω0 + ω D )t) =
1
1
cos(2ω0 + ω D ) + cos(ω D )
2
2
Power"
Transmit"X" Receive"
ω0 = Transmit frequency"
ωD = Doppler shift frequency"
t = Time"
0
Frequency"
Fblood"
€
Frequency"
Power"
Frequency"
Scanner Display
Spectral Data Display
Time"
Frequency"
Time"
Time"
Power"
Power"
Doppler Spectra
Color Flow Velocity Estimation
(Time Domain Correlation)
Pulse 1
Pulse 2
Hepatic Artery
Response"
Portal Vein
Response"
Power Doppler Image
Power"
Spectrum of Bandpass
Δt
Frequency"
Power Doppler Image
Doppler"
Signal Power"
Why flow detected at poles?
Spectral Broadening
Spectrum of Bandpass
Power"
Mean Freq. = 0"
Integrated Power ≠ 0
0"
Frequency"
Color Flow Image
True Velocity
Imaging
Transducer
k1
k2
θ
Vx"
Vy"
x
y
Axial"
V"
12.5 cm
Integration of Doppler Velocity Vectors
-12.5 cm
orthogonal flow
steer left flow
steer right flow
Lateral"
C-plane - Torus surface
Results - varying flow
(doughnut)
imaging angle
Measured flow [mL/s]"
(lateral)
sweep angle
(elevational)
95% confidence
interval
two realizations:
X = aperture ⊥ tube
O = aperture ‖ tube
line fit:
Y = (1.09±0.06) • X - (0.36±0.52)
Pump setting [mL/s]"
Tissue Doppler Imaging
Tissue Doppler
Imaging
Ramnarine et al. Cardiovasc Ultrasound.
2003; 1: 17.
Speckle Tracking
Ramnarine et al. Cardiovasc Ultrasound.
2003; 1: 17.
Speckle Reduction
•  Tissue Motion Quantification (TMQ)
•  Post processing of image data
•  Time Motion Annular Displacement
(TMAD)
•  May be performed on pre or post
envelop (B-mode)
•  Can be thought of as filtering but
algorithms can be complex
Phantom Result on Scanner
Simple Example
No Speckle Reduction"
Phantom Result on Scanner
Speckle Reduction in Liver
Too Much? "
Speckle Reduction"
Optimization
•  Can be applied to b-mode or Doppler
•  Relies on commonly known imaging
behavior
•  Allows for quick adjustment
•  Use in conjunction with presets
Digital Encoding
•  Uses longer pulse sequences
Coded Sequences
110 10011110010110"
•  Relies on code recognition (pulse
compression)
•  Allow for extraction of low amplitude
signals
Pulsed B-mode"
Coded B-mode"
Possible Advantages-Coded
Sequences
•  Improved detection of weak signals
•  Multichannel processing
•  Applications to harmonic imaging
Zone Sonography
Rapid Zone Acquisition
• Acquires an image frame ~10X faster
• Akin to photography
Rapid Zone Acquisition: Acoustic
Currency
Channel Domain Memory
• Retains transducer element data
• Stores a “Virtual Patient”
90+% of Acoustic
Currency Available
Zero Acoustic Currency Left
Channel Domain Processing
• Enables iterative processing
• Leverages Moore’s Law
time
• Line-by-line echo acquisition
• Sequential processing of scan
lines
• Image formation tied to sound
speed
Acoustic Currency For
Advanced Modes
time
• Echo data acquired from zones
• SW processing of entire echo
data set
• Image formation tied to
computer speed
For the record...
Wavelength
(or Period)
Acoustic Pressure (MPa)
3
2
p +, p r
•  Nonlinear acoustic propagation has been
known for many years!!
•  Ultrasound contrast agents research led to
increased nonlinear acoustics research
1
0
p –, p c
-1
Distance (or Time)
•  Analysis pointed towards tissue nonlinearity
Nonlinear Propagation!
u"
c>c0!
c=c0+βu!
Propagation
speed changes
with particle
velocity u!
t' =t-z/ c0!
c=c0!
c=c0!
t'"
c<c0!
•  Physicians began commenting on image
quality improvements in harmonic imaging
without contrast
Nonlinear propagation in tissue!
time waveforms"
spectra"
Axial waveforms"
KZK simulation"
Circular source"
p0=0.45 MPa"
MI=1.2"
Retarded
time!
focus"
Harmonic bandwidth considerations!
WAVEFORM "
SPECTRUM"
best axial resolution"
Measurements in water!
P3-2 phased array!
Beam patterns!
MI=0.3!
z=d=10cm!
best harmonic
separation"
KZK simulation of
waveform at the focus"
Pulse inversion
time waveforms"
Conventional Processing
spectra"
Circular
source"
Tissue
Odd harmonics"
sin(nωt+nπ)=-sin(nωt)"
Transducer
Receive filters
Transducer
Transducer
After!
processing!
Harmonic Processing
Tissue
Acoustic!
field!
Shallow fat layers
Distorted sound beam
Acoustic!
field!
Transmitted signal
Transducer
After!
processing!
Receive filters
Clinical examples
Conventional imaging!
Tissue Harmonic Imaging!
Transducer
Shallow fat layers
Tissue
Receive filters
Harmonic
energy
Tissue
Harmonic Processing
Transmitted signal
Acoustic!
field!
Transmitted signal
Even harmonics"
sin(nωt+nπ)=sin(nωt)"
Motion!
addressed with more
than 2 pulses"
Fundamental
energy
Transducer
p0=0.45 MPa"
MI=1.2"
Clean image
After!
processing!
Clinical benefits of THI
Conventional imaging
Tissue Harmonic Imaging
Perfluorocarbon Microbubbles
Clinical Benefits
•  Cardiology
–  Reduced overall clutter level
–  Improved endocardial visualization
–  Difficult to image patients addressed
•  Radiology
–  Reduced haze / clutter
–  Improved contrast resolution
–  Improved border delineation
–  Difficult to image patients addressed
Insert Your Favorite
Carbonated Beverage
Counts
8000
6000
4000
2000
0
Rasor Associates, US Patent Number 4,442,843
0
1
2
3
Radius in um
4
5
Harder Drive - Subharmonic
1000000
3 µm
2 micron
1000
1micron
100
10
1
0
1
2
3
4
5
6
7
8
9
10 11
3 µm
100
80
60
40
20
0
-20
-40
-60
-80
-100
1000
Scattering Cross-section [µm^2]
10000
Change in Radius [%]
Scattering cross-section [micron^2]
6 micron
100000
0
1
Frequency[MHz]
2
3
4
100
10
1
0.1
0.01
5
0
Time [cycle]
2
4
6
8
Frequency [MHz]
baseline spectrum (dB) vs f (MHz)
60
40
20
0
0
2
4
6
6
contrast spectrum (dB) vs f (MHz)
25 dB Increase in"
Second Harmonic"
60
40
20
0
0
Linear Scattering"
+"
2
4
6
8
Nonlinear Scattering"
+"
10
Power Pulse Inversion
Microvascular Imaging
Assume breathing motion of 2 cm/s
This is 20 um per firing, ie. 4.8° phase shift @ 1 MHz
3600"
1800"
+
+
5°
Echo 1"
Echo 2"
5°
_
+
Echo 3"
10°
5°
2X"
Source: M Bruce, M Averkiou, K Tiemann, S Lohmaier, J Powers, K Beach
"Vascular flow and perfusion imaging with ultrasound contrast agents”
Ultrasound in Med. & Biol., Vol. 30, No. 6, pp. 735–743, 2004
Microvascular Imaging
Source: M Bruce, M Averkiou, K Tiemann, S Lohmaier, J Powers, K Beach
"Vascular flow and perfusion imaging with ultrasound contrast agents”
Ultrasound in Med. & Biol., Vol. 30, No. 6, pp. 735–743, 2004
One at a Time, Please
Source: Fuminori Moriyasu, M.D., Ph.D., Department of Gastroenterology &
Hepatology, Tokyo Medical University, Japan"
• Hemangioma. Both images with ultrasound
contrast agent. (A) conventional imaging (B) Pulse
inversion imaging (a)
Source: (a) Averkiou M., Powers J., Skyba D., Bruce M., and Jensen S. "Ultrasound
Contrast Imaging Research. " Ultrasound Quarterly Vol. 19, No. 1, pp. 27-37 (2003)
Hold It!!!
Source: Fuminori Moriyasu, M.D., Ph.D., Department of Gastroenterology &
Hepatology, Tokyo Medical University, Japan"
Developments to Watch
•  Compound Imaging
•  Advanced Image Postprocessing
•  Automation
•  Pulse Sequencing
–  Coded Sequences
–  Harmonics
Fraunhofer Institute"