A novel functional ultrasound image based on
generalized Rayleigh scattering distribution
for tissue characterization
以廣義雷利散射分佈為基礎之新世代功能性超音波影像
Po-Hsiang Tsui (崔博翔) and Chien-Cheng Chang (張建成)
Division of Mechanics, Research Center for Applied
Sciences, Academia Sinica
中央研究院應用科學研究中心 力學與工程科學專題中心
Ultrasonic imaging
Noninvasive
Soft tissues
Real time
Portable
Non-ionizing
Resolution: < 1 mm
Fundamental of imaging
Scatterers
Ultrasound
transducer
Reflection
Scattering
Backscattered echoes
speckle
B-mode image
Reflected echoes
Ultrasonic imaging system
Shortcomings of ultrasound image
Image process
Operator-dependent
Qualitative information
Morphology analysis
Hard to characterize
scatterers
Low gain
TGC
Gain
High gain
Imaging display settings
Shortcomings of ultrasound image
B-scan (the same gain)
Low scatterer
concentration
High scatterer
concentration
(but weak reflection
coefficient)
B-scan (the same gain)
High scatterer
concentration
Low scatterer
concentration
(but the same reflection coefficient)
How to characterize scatterers by
B-scan data?
Backscattering distribution
If the resolution cell has a large number of scatterers (N scatterers), the
complex ultrasonic echoes can be modeled as
N
A  Ae   ai e ji  Ar  Ai
j
(1)
n 1
According to central limit theorem, Ar and Ai are Gaussian distributed
random variables, the joint distribution of Ar and Ai is
p Ar Ai ( Ar , Ai ) 
(
1
2
2
Ar 2  Ai 2
e
2 2
)
(2)
Change from rectilinear to polar coordinate, eq. (2) can be
p A ( A,  ) 
(
A
2
2
e
A2
2 2
)
A  0 (3)
p(A)
Rayleigh distribution
So the pdf of envelope A is the marginal density

p A ( A)   p A ( A,  ) d 

A

2
(
e
A2
2 2
)
(4)
A
Different backscattering conditions
Ultrasound
transducer
Scatterers
Pre-Rayleigh
Rayleigh
Post-Rayleigh
Generalized Rayleigh scattering model
Nakagami distribution
2mm r 2 m1
m 2
f (r ) 
exp( r )U (r )
m
(m)

Γ(.): Gamma function
U(.): Step function
[ E ( R 2 )]2
m
E[ R 2  E ( R 2 )]2
  E( R2 )
R: Ultrasonic envelope
m : Nakagami parameter
Ω : Scaling parameter
E : Mean
m<1
m=1
m>1
Ultrasonic Nakagami imaging
- to visualize scatterer properties
m
m
mw
mw
Envelope signal
Envelope image
The appropriate size is determined when
(sidelength = 3 times pulselength)
Nakagami image
mw  m
(Local mean = global mean)
Simulation, animal model, and
clinical experiment
Nakagami imaging
Low scatterer concentration (4/mm2)
High scatterer concentration (32/mm2)
Lens cataract
Porcine lens
Formalin solution to induce cataract
In vitro scan by a 35 MHz probe
saline
PC
capsule
lens
Data storage
AD
converter
Pulser/
Receiver
Diplexer
Transducer
40 mins
Timer/
Counter
Motor
controller
Sync. trigger
Motor driver
Move transducer
Ultrasonic
motor
Encoder
120 mins
Liver fibrosis
Rat liver
IMN injection to induce fibrosis
In vitro scan by a 5 MHz probe
Fibrosis scoring by doctors
Normal case
Fibrosis (score<1)
Tissue ablation
Sample: pork tenderloin
Microwave ablation (2.45GHz, 60 W)
Imaging by portable system (7.5 MHz)
(Terason 2000)
B-scan
Nakagami image
Before
t
before (antenna)
t= 0
heating
40 sec
heating
70 sec
heating and stop stop (antenna)
100 sec
280 sec
stop
300 sec
Breast tumors
Sensitivity
Patients come from Taiwan
University Hospital
In vivo scan by Terason 2000
Nakagami
image
Pathology
Malignant
Benign
Total
0.64
31 (TP)
9 (FP)
40
1.0
0.64
4 (FN)
26 (TN)
30
0.8
Total
35
35
70
0.6
0.4
0.2
5 mm
0.0
0.0
0.2
0.4
0.6
0.8
1.0
1-Specificity
At threshold = 0.64,
Sensitivity: 88.6%
Specificity: 74.3%
Accuracy: 81.4%
Fibroadenomas
Invasive ductal carcinoma
3-D Nakagami image of rat liver
Potential:
Resolution improvement
Multi-directional information
Pathological model (e.g., fibrosis growth model)
Comparison between B-scan and Nakagami images
B-mode image
Nakagami image
Image pixel
Grayscale
Nakagami parameter
Image physical
meaning
Echo intensity
Envelope statistics
Image type
Qualitative
Quantitative
Resolution
Relatively better
Relatively poor
Medical
applications
Morphology analysis
Scatterer analysis
Summary and future works
 Nakagami imaging (2-D and 3-D modes) reflects scatterer
properties, having ability to characterize tissues and
discriminate benign and malignant tumors.
 Nakagami image can be complementary to the B-scan for
morphology analysis and scatterers characterization
 Potential for monitoring tissue treatment process
 Developing very high frequency system for small scale
analysis (e.g., cell)
Acknowledgements
中央大學數據分析方法研究中心: 黃鍔院士、張建中博士
台灣大學醫學院: 張金堅教授、 陳文翔醫師、郭文宏醫師、何明志醫師
南加州大學醫學工程系: 熊克平教授
台灣大學電機系: 李百祺教授
清華大學生醫工程與環境科學系: 葉秩光助理教授
輔仁大學電子工程系: 黃執中助理教授
Thank you for
your attention