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1 1 NOR-EM-060

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

(2)

X-ray imaging Optical imaging Ultrasound image

Medical imaging

(3)

3 3 NOR-EM-060

(4)

Acoustic waves with frequencies higher than 20 kHz

Need a medium to propagate

Longitudinal wave

Non-ionizing radiation

Ultrasound

(5)

5 5 NOR-EM-060

How to generate ultrasound?

Ultrasound transducer

(6)

Medical ultrasound system

(7)

7 7 NOR-EM-060

Ultrasonic imaging

Noninvasive

Soft tissues

Real time

Portable

Non-ionizing

Good resolution

(8)

Speckle due to scattering

(9)

9 9 NOR-EM-060

Demo: reflection and scattering

Reflection signal Scattering signal

(10)

Why is the sky blue?

(11)

11 11 NOR-EM-060

) cos

1

8 (

2

2 4

2 4

0

I R I

Rayleigh scattering

Rayleigh scattering intensity for a single particle

(12)

Clouds are white

(13)

13 13 NOR-EM-060

Scattering behavior of light depends

on particles properties in the air

(14)

Ultrasonic scattering

Incident wave

Scatterers

Tissue

Scattering behavior should depend on scatterer structures

Scattering signals

(15)

15 15 NOR-EM-060

What is the scattering behavior

of ultrasound in tissues?

(16)

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

(17)

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

  

A

A

A e

d A

p A

p

 

2

,

2

i

r

A

A

A  

(18)

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

(19)

19 19 NOR-EM-060

Pre-Rayleigh Rayleigh

Post-Rayleigh

Incident pulse

Rayleigh distribution is inadequate

Tissue Received echoes Envelope statistics

(20)

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

(Shankar

1995; Dutt and Greenleaf 1994)

for pre-Rayleigh, Rayleigh, and post-Rayleigh

the complex nature of these models limited their practical applications

5

History of developing general models

(21)

21 21 NOR-EM-060

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

(

2

1 2

r U m r

m r r m

f

m

m m

 

 

2 2 2

2 2

)]

( [

)]

( [

R E R

E

R m E

 

) ( R

2

E

Nakagami distribution

(Shankar 2000)

(22)

Ultrasound transducer

Amplifier

m < 1

m = 1

m > 1

Nakagami parameter

- a predictor for tissue characterization

Signal

?

Unknown properties

(23)

23 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

(24)

Problems for clinical purpose

Not an image mode. Not convenient and friendly for clinical physicians.

Hard to locally characterize biological tissues

(25)

25 25 NOR-EM-060

Our strategy: Nakagami imaging

Envelope image Sliding

window

Nakagami image

mw Using a sliding window to construct a parameter map

(26)

How to determine the window size?

m

m

mw

m

w

Envelope signal

The appropriate size is determined when

m

w

m

(sidelength = 3 times pulselength)

(27)

27 27 NOR-EM-060

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.

(28)

B-mode image Nakagami image

B-scan and Nakagami images

(29)

29 29 NOR-EM-060

Simulations and experiments

(30)

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

(31)

31 31 NOR-EM-060

Nakagami imaging

Low scatterer concentration (4/mm2) Relative backscattering coefficient: 4

High scatterer concentration (32/mm2) Relative backscattering coefficient: 1

(32)

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

(33)

33 33 NOR-EM-060

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

(34)

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

(35)

35 35 NOR-EM-060

Liver fibrosis in rats

Normal case Fibrosis (score<1)

(36)

Liver fibrosis assessment

Fibrosis in human

(37)

37 37 NOR-EM-060

Results as a function of fibrosis stage

(38)

3-D Nakagami imaging for fibrosis detection

(39)

39 39 NOR-EM-060

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)

(40)

Breast mass classification

cyst

fat

tumor Results from breast phantom

(41)

41 41 NOR-EM-060

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

(42)

Vocal fold characterization

50 MHz results 60 MHz results 50 MHz Nakagami image 50 MHz B-mode image

(43)

43 43 NOR-EM-060

Blood flow estimation

(44)

Medium hardness assessment

(45)

45 45 NOR-EM-060

Medium hardness assessment

(46)

Temperature estimation

(47)

47 47 NOR-EM-060

Results of phantoms

(48)

Results of liver tissues

(49)

49 49 NOR-EM-060

Results of ablation (1)

(50)

Results of ablation (2)

(51)

51 51 NOR-EM-060

Comparison

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 characterization

(52)

Thank you for

your attention

參考文獻

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