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Ultrasound Nakagami imaging and its medical applications
超音波Nakagami影像的發展與醫學應用
Po-Hsiang Tsui (崔博翔)
Department of Medical Imaging and Radiological Science, College of Medicine, Chang Gung University
長庚大學醫學院醫學影像暨放射科學系
X-ray imaging Optical imaging Ultrasound image
Medical imaging
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Acoustic waves with frequencies higher than 20 kHz
Need a medium to propagate
Longitudinal wave
Non-ionizing radiation
Ultrasound
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How to generate ultrasound?
Ultrasound transducer
Medical ultrasound system
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Ultrasonic imaging
Noninvasive
Soft tissues
Real time
Portable
Non-ionizing
Good resolution
Speckle due to scattering
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Demo: reflection and scattering
Reflection signal Scattering signal
Why is the sky blue?
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) cos
1
8 (
22 4
2 4
0
I R I
Rayleigh scattering
Rayleigh scattering intensity for a single particle
Clouds are white
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Scattering behavior of light depends
on particles properties in the air
Ultrasonic scattering
Incident wave
Scatterers
Tissue
Scattering behavior should depend on scatterer structures
Scattering signals
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What is the scattering behavior
of ultrasound in tissues?
Ultrasonic echo model
i r
j N
n
i
j
a e A A
Ae
i
1
A
The resolution cell has N scatterers, and then the complex ultrasonic echoes can be modeled as
Ultrasound transducer
Amplifier
If N is large, according to central limit theorem, Ar and Ai are Gaussian distributed random variables, and the joint distribution of Ar and Ai is
2 ) ( 2
2 2 2
2 ) 1
,
(
i r
i r
A A i
r A
A
A A e
p
Change from rectilinear to polar coordinate,
2 0 )
, (
) 2 ( 2
2 2
A e
A A
p
A A
So the pdf of envelope A is the marginal density
2 ) ( 2
2 2
) , ( )
(
A
AA
A e
d A
p A
p
2
,
2
i
r
A
A
A
Rayleigh distribution
A
p(A)
When the resolution cell has a large number of scatterers, the envelope statistics of echo would follow Rayleigh distribution
) 2 ( 2
2 2
)
(
A
A
A e
A p
Rayleigh distribution
Time-domain ultrasound signal Envelope histogram Envelope
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Pre-Rayleigh Rayleigh
Post-Rayleigh
Incident pulse
Rayleigh distribution is inadequate
Tissue Received echoes Envelope statistics
Rayleigh distribution
(Burckhardt 1978) for Rayleigh
Rician and generalized Rician distributions
(Joynt 1979;Wagner et al. 1987)
for Rayleigh and post-Rayleigh
K-distribution
(Weng et al. 1991; Shankar et al. 1993) for pre-Rayleigh and Rayleigh
Generalized K- and homodyned K-distributions
(Shankar1995; Dutt and Greenleaf 1994)
for pre-Rayleigh, Rayleigh, and post-Rayleigh
the complex nature of these models limited their practical applications
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History of developing general models
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Γ(.) is the Gamma function, U(.) is the step function, and r means envelope
The Nakagami parameter m and the scaling parameter Ω can be estimated by
) ( ) ) exp(
( ) 2
(
21 2
r U m r
m r r m
f
mm m
2 2 2
2 2
)]
( [
)]
( [
R E R
E
R m E
) ( R
2 E
Nakagami distribution
(Shankar 2000)Ultrasound transducer
Amplifier
m < 1
m = 1
m > 1
Nakagami parameter
- a predictor for tissue characterization
Signal
?
Unknown properties23 23 NOR-EM-060
Phantom (Tsui and Wang 2004)
Bone (Wang and Tsai 2001)
Blood (Huang et al. 2007)
Breast mass (Shankar et al. 2001)
Scatterer Concentration (mm-3)
0 5 10 15 20 25 30 35
m
0.2 0.4 0.6 0.8 1.2 1.4
1.0
Previous studies
Problems for clinical purpose
Not an image mode. Not convenient and friendly for clinical physicians.
Hard to locally characterize biological tissues
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Our strategy: Nakagami imaging
Envelope image Sliding
window
Nakagami image
mw Using a sliding window to construct a parameter map
How to determine the window size?
m
m
mw
m
wEnvelope signal
The appropriate size is determined when
m
w m
(sidelength = 3 times pulselength)
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How to display the Nakagami image?
Grayscale is not suitable for Nakagami image,
because Nakagami parameter has physical meanings associated with envelope distribution and scatterer properties.
We used blue for pre-Rayleigh, white for Rayleigh, and
red for post-Rayleigh.
B-mode image Nakagami image
B-scan and Nakagami images
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Simulations and experiments
Z H
signals
RF
Model of ultrasonic backscattered signals
For 1-D
consideration
Ultrasonic echo is obtained from the convolution of Gaussian pulse with 1-D scatterers
B-mode image is obtained from the convolution of Gaussian pulse with a cross-sectional scatterer distribution
=
=
1 1 0 1 0 0 1 1 0
For 2-D
consideration
Simulation model
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Nakagami imaging
Low scatterer concentration (4/mm2) Relative backscattering coefficient: 4
High scatterer concentration (32/mm2) Relative backscattering coefficient: 1
Pulser/
Receiver Diplexer Transducer
AD converter Data storage
Timer/
Counter
Motor
controller Motor driver Ultrasonic
motor Encoder
PC
Sync. trigger
60 MHz clock
Move transducer
35 MHz transducer
Image scanning stage
Cataract study
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Lens
Capsule Saline
Saline
Lens
Capsule
(mm)
(mm)
2 4 6 8 10 12
2 4 6 8
10 10
20 30 40
(mm)
(mm)
2 4 6 8 10 12
2
4
6
8
10
0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
Nuclear cataract
Nuclear cataract
Cortical cataract
Normal stage
Immersion time 40 mins
Immersion time 120 mins ROI
Normal stage
Immersion time 40 mins
Immersion time 120 mins ROI
Young's modulus (KPa)
0 20 40 60 80 100 120
IB (dB)
-170 -168 -166 -164 -162 -160 -158
Young's modulus (KPa)
0 20 40 60 80 100 120
0.0 0.2 0.4 0.6 0.8 1.0
mw
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Liver fibrosis in rats
Normal case Fibrosis (score<1)
Liver fibrosis assessment
Fibrosis in human
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Results as a function of fibrosis stage
3-D Nakagami imaging for fibrosis detection
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Tissue ablation
Before before (antenna) heating heating heating and stop stop (antenna) stop t t= 0 40 sec 70 sec 100 sec 280 sec 300 sec B-scan
Nakagami image
Sample: pork tenderloin
Microwave ablation (2.45GHz, 60 W)
Imaging by portable system (7.5 MHz)
(Terason 2000)
Breast mass classification
cyst
fat
tumor Results from breast phantom
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Breast tumor classification
Fibroadenomas Invasive ductal carcinoma
5 mm
Patients come from Taiwan University Hospital
In vivo scan by Terason 2000
1-Specificity
0.0 0.2 0.4 0.6 0.8 1.0
Sensitivity
0.0 0.2 0.4 0.6 0.8 1.0
At threshold = 0.64, Sensitivity: 88.6%
Specificity: 74.3%
Accuracy: 81.4%
Nakagami image
Pathology
Total Malignant Benign
0.64 31 (TP) 9 (FP) 40
0.64 4 (FN) 26 (TN) 30
Total 35 35 70
Vocal fold characterization
50 MHz results 60 MHz results 50 MHz Nakagami image 50 MHz B-mode image
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Blood flow estimation
Medium hardness assessment
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Medium hardness assessment
Temperature estimation
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Results of phantoms
Results of liver tissues
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Results of ablation (1)
Results of ablation (2)
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