Optimization of a Digital Clutter Filter for
Microvascular Volume Quantification
using Power Doppler Ultrasound
Ryan Fox
MBP 3970Z Six Week Project
Supervisor: Dr. James C. Lacefield
Department of Medical Biophysics
Western University
April 3, 2012
Motivation & Objectives
Methods
Results & Discussion
Conclusions & Future Work
Microvascular Volume Quantification
• Study and diagnosis of angiogenesis-related disease
– Cancer, psoriasis, atherosclerosis, etc.
• Development and monitoring of treatments in-vivo
• Typical hemodynamic parameter imaging modalities
– Magnetic resonance imaging (MRI)
– Positron emission tomography (PET)
– X-ray computed tomography (CT)
Motivation & Objectives
Methods
Results & Discussion
Conclusions & Future Work
Microvascular Volume Quantification
• A rapidly advancing, attractive alternative:
Power Doppler Ultrasound
• Longitudinal studies
– No repeated injections of contrast media
– Avoids exposure to ionizing radiation
• Portable, available, and relatively low-cost
Motivation & Objectives
Methods
Results & Discussion
Conclusions & Future Work
Conventional Ultrasound Imaging
• Brightness mode (B-mode)
• Piezoelectric element sends single
pulse (high-f sound wave)
• Information encoded in echo
amplitude
Source: http://www.medison.ru/uzi/eho327.htm
Motivation & Objectives
Methods
Results & Discussion
Conclusions & Future Work
Doppler Ultrasound
• L pulses / sample volume
• Superposition of echoes:
–
–
–
–
–
Slow flowing blood
Fast flowing blood
Stationary tissue
Slow flowing tissue
Flash artifacts
ft
ft + fd
v
Source: http://www.medison.ru/uzi/eho327.htm
Motivation & Objectives
Methods
Results & Discussion
Power Doppler
Signal and Spectrum
Conclusions & Future Work
Time-Domain Signal
• Parseval’s Theorem:
Frequency Spectrum
• Check:
P > Pthreshold?
Y
Inside Vessel
N
Outside Vessel
Motivation & Objectives
Methods
Results & Discussion
Conclusions & Future Work
Ideal High-Pass Filter
• fp – passband edge frequency [Hz]
Input
Filter
Output
f > f p?
Y
Unaffected
fp = 2.5kHz
N
Suppressed
Motivation & Objectives
Methods
Results & Discussion
Conclusions & Future Work
Realizable High-Pass Filter
0
PR = -4.8dB
-10
SR = -41.4dB
Magnitude (dB)
-20
-30
-40
-50
-60
0
0.5
1
1.5
2
2.5
3
Frequency (kHz)
3.5
4
fs = 2.0kHz fp = 2.5kHz
TB = fp – fs = 0.5kHz
4.5
Motivation & Objectives
Methods
Results & Discussion
Conclusions & Future Work
Wall Filter Cut-Off Velocity (VC)
VC too low
VC too high
1 mm
• false-positive artifacts
1 mm
• false-negative artifacts
• maintained vessel continuity • loss of vessel continuity
S.Z. Pinter and J.C. Lacefield, Ultrasound Med. Biol., 35:1217-1228, 2009.
Motivation & Objectives
Methods
Results & Discussion
Conclusions & Future Work
Wall Filter Selection Curve (WFSC)
1.2
CPD
1
0.8
0.6
0.4
0.2
0
0
1
2
3
4
5
Wall Filter Cut-Off Velocity (mm/s)
GE Logiq 5® Ultrasound System,
www.nationalultrasound.com
Motivation & Objectives
Methods
Results & Discussion
Conclusions & Future Work
Problem Summary
• For each data point on WFSC calculate
• Search for local maxima in normalized first difference
– Interval of Vc in between local maxima = “characteristic interval”
• Multi-step decision algorithm to select operating point within
interval (right edge or centre)
• Coarse sampling of WFSC due to reliance on user controls
– First difference is sensitive to distance between samples
– More finely sampled -> characteristic intervals in challenging vessels
Motivation & Objectives
Methods
Results & Discussion
Conclusions & Future Work
Project Objectives
• Simulate a realistic, tunable, and physiological-based power
Doppler ultrasound backscattered signal
• Investigate the relative importance of PR, SR, TB, and
transient response on wall filter performance
• Determine the effectiveness of various filter designs in the
capacity as clutter filters
• Gain insight into methods to reduce the impact of the transient
response
• Determine the optimal filter design and compare its
performance to the original filter used in Dr. Lacefield’s
laboratory
Motivation & Objectives
Methods
Results & Discussion
Conclusions & Future Work
Null Hypothesis
• The blood flow power estimation error cannot be significantly
reduced by means of selecting an optimal filter design
Motivation & Objectives
Methods
Results & Discussion
Conclusions & Future Work
Approach
Doppler Signal Simulation
Filter Design
Performance Comparison
Relative Importance of
Filter Characteristics
Optimal Filter Selection
Evaluate Performance Relative to Benchmark
Motivation & Objectives
Methods
Results & Discussion
Conclusions & Future Work
Benchmark Power Doppler Images
Commercial Scanner
(proprietary filter design)
Dr. Lacefield’s Lab
(3rd order Chebychev I)
Motivation & Objectives
Methods
Results & Discussion
Conclusions & Future Work
Methods
• MATLAB R2011b (The MathWorks Inc., Natick, MA)
~ 20,000 lines of novel code
• Doppler signal simulation
– Physiologically-relevant frequency spectrum mask generated from
256 * 13 samples (L = 13)
– Inverse Fourier transform to obtain complex power Doppler time-domain
signal
• Process Doppler signal with controlled parameter filters &
compare output power to ideal filter
• Signal power
– Zero time lag autocorrelation (R0)
Motivation & Objectives
Methods
Results & Discussion
Conclusions & Future Work
Power Doppler Signal Simulation
Clutter Spectrum
Frequency Spectrum
0.8
3.5
0.6
3
0.4
2.5
Magnitude
Magnitude
1
0.2
0
-5
-4
-3
-2
-1 0 1
Frequency [kHz]
2
3
4
Complex, Gaussian
distributed white noise
5
+
0.8
x
0.4
Magnitude
Magnitude
0.5
0
-5
3
0.6
1
-3
-2
-1 0 1
Frequency [kHz]
2
3
4
5
+
Noise Floor Spectrum
0
-5
-3
-2
-1 0 1
Frequency [kHz]
2
3
4
5
0.025
-4
-3
-2
-1 0 1
Frequency [kHz]
2
3
4
0.02
5
Magnitude
-4
-4
Time Domain Signal
=
2
0.2
0
-5
1.5
1
4
Blood Flow Spectrum
2
0.015
0.01
0.5
Magnitude
0.005
0
0
0
-5
-4
-3
-2
-1
0
1
Frequency [kHz]
2
3
4
5
500
1000
1500 2000 2500
Sample Number
3000 3500
Motivation & Objectives
Methods
Results & Discussion
Conclusions & Future Work
Power Doppler Signal Simulation
• Clutter-to-Flow Ratio (CFR)
– CFR = 0dB for high ft (> 20MHz) - research
– CFR = 20dB for low ft - clinical
Case 2
2.5
2.5
2.5
2
2
2
1.5
1
1.5
1
0.5
0
-5 -4 -3 -2 -1 0 1 2 3 4 5
Frequency [kHz]
1.5
1
0.5
0
-5 -4 -3 -2 -1 0 1 2 3 4 5
Frequency [kHz]
Case 4
0
-5 -4 -3 -2 -1 0 1 2 3 4 5
Frequency [kHz]
Case 5
Case 6
3
3
2.5
2.5
2.5
2
2
2
1.5
1
0.5
0
-5 -4 -3 -2 -1 0 1 2 3 4 5
Frequency [kHz]
1.5
1
0.5
0
-5 -4 -3 -2 -1 0 1 2 3 4 5
Frequency [kHz]
Magnitude
3
Magnitude
Magnitude
Magnitude
3
0.5
CFR = 20dB
Case 3
3
Magnitude
CFR = 0dB
Magnitude
Case 1
3
1.5
1
0.5
0
-5 -4 -3 -2 -1 0 1 2 3 4 5
Frequency [kHz]
Motivation & Objectives
Methods
Results & Discussion
Conclusions & Future Work
1.5
Digital Filter Design Classes
Amplitude
1
• Finite Impulse Response (FIR)
0.5
0
-4
Ex: y(n) = 3x(n) – 2x(n-1) + x(n-2)
x(n)
-3
-2
-1
0
1
Sample Number
h(n)
2
3
4
Y(n)
• Infinite Impulse Response (IIR)
Ex: y(n) = y(n-1) + x(n) – x(n-1)
• Regression
Ex: y(n) = x(n) – 2n + n2
Motivation & Objectives
Methods
Results & Discussion
Conclusions & Future Work
Comparison of FIR and IIR Filter Designs
• FIR: Equiripple
• IIR: Butterworth, Chebychev I, Chebychev II, Elliptic
Butterworth
Equiripple
0
-10
0
-20
-10
-20
-30
-40
Magnitude (dB)
-60
Magnitude (dB)
Magnitude (dB)
0
-40
-20
-80
-100
-120
-160
-60
-30
-40
-50
-140
-50
0
Elliptic
-60
-180
0.5
1
1.5
2
2.5
3
Frequency (kHz)
3.5
4
4.5
0
0.5
1
1.5
2
2.5
3
Frequency (kHz)
3.5
4
0
4.5
0.5
1
1.5
2
2.5
3
Frequency (kHz)
3.5
4
4.5
0
0
-10
-50
Magnitude (dB)
Chebychev I
Magnitude (dB)
-20
-100
-150
-30
-200
-50
-250
-60
0
0.5
1
1.5
2
2.5
3
Frequency (kHz)
3.5
4
4.5
Chebychev II
-40
-70
0
0.5
1
1.5
2
2.5
3
Frequency (kHz)
3.5
4
4.5
Motivation & Objectives
Methods
Results & Discussion
Conclusions & Future Work
Comparison of FIR and IIR Filter Designs
Motivation & Objectives
Methods
Results & Discussion
Conclusions & Future Work
Transient Response
x(n)
h(n)
Y(n) = Ytransient(n) +Ysteady-state(n)
Y(n)
0.3
0.2
Amplitude
• Duration & energy
dependent on filter
design & order
0.1
0
-0.1
-0.2
0
20
40
60
Sample Number
80
100
Motivation & Objectives
Methods
Results & Discussion
Conclusions & Future Work
Impact of Filter Parameters on Output
Motivation & Objectives
Methods
Results & Discussion
Conclusions & Future Work
Impact of Filter Parameters on Output
Case 2 (CFR = 0dB)
Case 5 (CFR = 20dB)
Motivation & Objectives
Methods
Results & Discussion
Conclusions & Future Work
Selecting the Optimal Filter Design
• From the FIR and IIR filter design comparison results:
Filter Design
Equiripple Butterworth
Chebychev I
Chebychev II
Elliptic
Passband Ripple
1.5
1.5
3.5
3.5
5
Stopband Ripple
Transition Band
Width
1
2
3.5
3.5
5
1
2
3.5
3.5
5
Transient Response
5
4
2
3
1
• From the impact of filter parameters on output power error results:
Passband Ripple
Stopband Ripple
Transition Band Width
Transient Response
Weighting Factor (WF)
Cases 1-3 Cases 4-6
3.38
3.38
1.00
1.00
-0.069
-0.069
0.050
-2.01
Assumed:
Motivation & Objectives
Methods
Results & Discussion
Conclusions & Future Work
Selecting the Optimal Filter Design
• Scalar multiplication of the performance results with the weighting
factors gives:
Equiripple
Butterworth
Chebychev I
Chebychev II
Elliptic
Final Tallies
Cases 1-3 Cases 4-6
5.75
-4.06
6.74
-1.12
15.0
11.1
14.9
9.05
21.5
19.5
• Elliptic filter is the best candidate to act as a clutter filter out of all
FIR and IIR filters considered
• Consistent for both high and low frequency power Doppler
Motivation & Objectives
Methods
Results & Discussion
Conclusions & Future Work
IIR Initialization Schemes
• Zero
– x(n) = 0 for n<0
Y(n) = 3x(n) + 2x(n-1) + …
• Step
– x(n) = x(0) for n<0
• Projection
– Predicts and subtracts transient response
• Mirroring of the Input Signal
– x(-n) = - x(n) for n = 0,1,…,L
• Mirroring & Step, Mirroring & Projection
Motivation & Objectives
Methods
Results & Discussion
Conclusions & Future Work
IIR Initialization Schemes
• No significant
improvement over
zero initialization
• Use projection
initialization
Motivation & Objectives
Methods
Results & Discussion
Conclusions & Future Work
Chebychev I vs. Elliptic vs. Regression
CFR = 0dB (research)
CFR = 20dB (clinical)
Regression filter design is always best
Motivation & Objectives
Methods
Results & Discussion
Conclusions & Future Work
Frequency Spectrum Comparison
Case
3 Simulated
Doppler
Signal
Case
3 Simulated
Doppler
Signal
33
Simulated Doppler Signal
Case 33 Simulated
Simulated Doppler
Doppler Signal
Signal
Case
2.52.5
33
33
2
2.5 2
2.5
1.51.5
22
1.51.5
22
11
1.5
1.5
11
1.5
1.5
0.510.5
1
0.5
10.5
1
00
Chebychev I (N=3)
ChebychevII (N=3)
(N=3)
Chebychev
2.52.5
33
2
2.5 2
2.5
00
0.5
0.5
Chebychev
I (N=3)
Chebychev
I (N=3)
500
500
1000
1000
1500
1500
2000
2000
2500
2500
3000
3000
500
500
1000
1000
1500
1500
2000
2000
2500
2500
3000
3000
00
0.5
0.5
00
500
500
1000
1000
1500
1500
2000
2000
2500
2500
3000
3000
500
500
1000
1000
1500
1500
2000
2000
2500
2500
3000
3000
Regression (D=2)
Regression
(D=2)
Regression
(D=2)
33
Regression (D=2)
Regression (D=2)
2.532.5
3
Elliptic (N=3)
2.5
22
2.5
2
1.51.5
2
2
1.51.5
2
1.5
11
1.5
1.5
11
1.5
1
0.50.5
1
1
0.50.5
1
0.5
00
0.5
0.5
00
0.5
1000
1500
2000
Elliptic (N=3), mirror & step init
Elliptic (N=3), mirror & step init
3
2.5
3
2.5
2.5
22
2.5
500
Elliptic
(N=3),
mirror
&&
step
initinit
Elliptic
(N=3),
mirror
step
33
2500
3000
500
1000
1500
2000
2500
3000
Motivation & Objectives
Methods
Results & Discussion
Conclusions & Future Work
Statistical Analysis
• Student’s T-test
– Two-sample, unequal variances, unpaired, single tail
– Microsoft Excel
CFR = 0dB (research)
CFR = 20dB (clinical)
DF
t critical
T observed
P(T<=t)
DF
t critical
T observed
P(T<=t)
3
2.353
5.335
0.006
Reject the null hypothesis. With 95% confidence:
3
2.353
3.778
0.016
Motivation & Objectives
Methods
Results & Discussion
Conclusions & Future Work
Qualitative Comparison to Benchmark
Commercial Scanner
(proprietary filter design)
Dr. Lacefield’s Lab
(3rd order Chebychev I)
Proposed Filtering Chain
(2nd degree Regression
then 3rd order Elliptic)
Commercial scanner post-filter image enhancement?
Motivation & Objectives
Methods
Results & Discussion
Conclusions & Future Work
WFSC Comparisons
Dr. Lacefield’s Lab
(3rd order Chebychev I)
Proposed Filtering Chain
(Cascade of 2nd degree Regression
with 3rd order Elliptic)
Motivation & Objectives
Methods
Results & Discussion
Conclusions & Future Work
Conclusions
• Novel power Doppler ultrasound signal simulation
• Regression is the optimal stand-alone filter design for both
research and clinical ultrasound frequencies
• With 95% confidence, the regression filter performance was
superior to the Chebychev I filter currently used in Dr. Lacefield’s
lab
• Novel approach to processing power Doppler signal
– Cascade regression filter with elliptic
– Can be used with automated tuning algorithm for Vc
• Qualitatively improved images over all Vc
Motivation & Objectives
Methods
Results & Discussion
Conclusions & Future Work
Future Work
• Use proposed filtering method in coordination with automated wall
filter cut-off selection algorithm in Dr. Lacefield’s lab
• Future fully automated, online implementation
• Possible for non-specialist or time-sensitive operators to produce
diagnostic quality Doppler images
• Apply WFSC principles to other user controls
Motivation & Objectives
Methods
Results & Discussion
Conclusions & Future Work
References
Goertz, David E., Joanne L. Yu, Robert S. Kerbel, Peter N. Burns, and F. Stuart Foster. "High-frequency Doppler
Ultrasound Monitors the Effects of Antivascular Therapy on Tumor Blood Flow." Cancer Research 62.22 (2002):
6371. Print.
Miller, Janet C., Homer H. Pien, Dushyant Sahani, Gregory Sorensen, and James H. Thrall. "Imaging Angeogenesis:
Applications and Potential for Drug Development." Journal of the National Cancer Institute 97.3 (2005): 172. Print.
Hoskins, Peter, Kevin Martin, and Abigain Thrush. Diagnostic Ultrasound: Physics and Equipment. 2nd ed. New York:
Cambridge UP, 2010. Print.
Bjaerum, Steinar, Hans Torp, and Kjell Kristoffersen. "Clutter Filter Design for Ultrasound Color Flow Imaging."
IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control 49.2 (2002): 204. Print.
Pinter, Stephen Z., and James C. Lacefield. "Objective Selection of High-Frequency Power Doppler Wall Filter
Cutoff Velocity for Regions of Interest Containing Multiple Small Vessels." IEEE Transactions on Medical
Imaging 29.5 (2010): 1124. Print.
Proakis, John G., and Dimitris G. Manolakis. Digital Signal Processing: Principles, Algorithms, and Applications. 4th ed.
Upper Saddle River, NJ: Prentice Hall, 2006. Print.
Winkler, P., K. Helmke, and M. Mahl. "Major Pitfalls in Doppler Investigations." Pediatric Radiology 20.5 (1990):
304. Print.
Motivation & Objectives
Methods
Results & Discussion
Conclusions & Future Work
Acknowledgements
• Thank you for your mentorship and guidance
Supervisor: Dr. James C. Lacefield
Ph.D. Candidate: Mai Elfarnawany
• Raw power Doppler data obtained via Vevo 770
Ultrasound System owned and operated by Robart’s
Research Institute