ultrasound doppler instrumentation and color flow...

Ultrasound Doppler Instrumentation

and

Color Flow Imaging

한림대학교

정보통신공학부

배무호

TABLE OF CONTENT

• Introduction

• Doppler Principle

• CW Doppler System

• PW Doppler System

• Color Flow Imaging

• Doppler Measurement Examples

• Other Doppler Imaging Methods

INTRODUCTION

Ultrasound Doppler Imaging for Medical Applications

• 초음파를 이용, 인체 내의 혈류를 계측, 또는 영상화심장, 주변 혈관계 질환 등의 진단Non-invasive, real-time : 편리하고 저비용의 효과적인 진단수단

• Spectral Doppler관심있는 지점의 혈류 정보 계측혈류의 시간에 따른 변화정량적 계측 : 속도, 방향 등.Doppler Spectrum과 Audio로 표현

• Color Doppler관심있는 평면의 혈류를 단층영상으로 표현정성적 영상화평균속도, 방향, 난류(Turbulence), Power 등을 색상으로 표현

INTRODUCTION

Image Example : Spectral Doppler

INTRODUCTION

Image Example : Color Flow Imaging

DOPPLER PRINCIPLE

General Doppler Effect

DOPPLER PRINCIPLE

Christian Andreas Doppler

Born: 29 Nov 1803 in Salzburg, AustriaDied: 17 March 1853 in Venice, Italy

DOPPLER PRINCIPLE

General Doppler Effect

Receiver A

Stationary source

Receiver CReceiver B

Moving source

• Frequency of transmitted wave

• Received wave frequency� by Receiver A

� by Receiver B

� by Receiver C

= f0

= f0

< f0

> f0

s

od vc

vcffff−+

=+= 001 dfc

ovsv

: Doppler shift frequency

: Sound Speed

: Speed of Sound Source

: Speed of Observer

DOPPLER PRINCIPLE

Ultrasound Doppler Effect in Flowing Blood Cells

θcos2 0

cvffd =

frequencyTransmit :speed flow :

speed ultrasound :

0fvc

v

θ

flow

f 0 (3M

Hz)f0+

fd

(3.00

3896

MHz)

Transducer

Doppler shift frequency:

where

Example : m/s1=vm/s1540=c 1cos =θ Hz3896=dfMHz30 =f

가청주파수 범위!

DOPPLER PRINCIPLE

General Doppler Effect : Formulation

거리 z

이동속도 vs

송신 수신

음속이 c인 경우, 출발~도착까지 걸린 시간 :

즉, 송신기에서 시각의 현상은 수신기에서 시각에 관측됨.

송신신호를 , 수신신호를 라 하면

Let Then

thus

If then where

ctvzt s−

=∆

0t ctvzt s 0

0−

+

)(ts )(tr

)( 00

0 tsc

tvztr s =⎟⎠⎞

⎜⎝⎛ −

+

cz

cvt

ctvztt ss +⎟

⎠⎞

⎜⎝⎛ −=

−+≡ 10

00 cv

cztts /1/

0 −−

=

⎟⎟⎠

⎞⎜⎜⎝

⎛−−

=cvcztstr

s /1/)(

)2cos()( ftts π= ( )112cos1

2cos)( φππ +=

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜

⎝

⎛

−

−= tf

cvczt

ftrs

fvc

c

cv

ffss −

=⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜

⎝

⎛

−=

11

DOPPLER PRINCIPLE


음속이 c인 경우, 출발~도착까지 걸린 시간 :

즉, 수신기에서 시각의 현상은 송신기에서 시각에 출발됨.

송신신호를 , 수신신호를 라 하면

If then

where

송/수신이 다 움직이면

거리 z

이동속도 vo

수신송신

ctvzt o−

=∆

0t ctvzt o 0

0−

−

)(ts )(tr

⎟⎟⎠

⎞⎜⎜⎝

⎛−⎟⎠⎞

⎜⎝⎛ +=⎟

⎠⎞

⎜⎝⎛ −

−=cz

cvts

ctvztstr oo 1)( 0

000

)2cos()( ftts π= ( )112cos12cos)( φππ +=⎥⎦

⎤⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛−⎟⎠⎞

⎜⎝⎛ += tf

cz

cvtftr o

fcvcf

cvf oo +

=⎟⎠⎞

⎜⎝⎛ += 11

s

od vc

vcffff−+

=+= 001

DOPPLER PRINCIPLE


거리 z

이동속도 v

수신

송신

반사

즉, 초음파진단기에서는 송/수신기가서로 마주보고 같은 속도로 다가가는(멀어지는) 상황과 같음. 즉

동일한 상황

cvff

vcvcffff d

00001

2+≈

−+

=+=

cvffd

02≈

프로브 적혈구

적혈구

프로브 따라서

거리 z

이동속도 v

수신

송신 수신

그대로 재송신

DOPPLER PRINCIPLE

Ultrasound Doppler Signal Modelling

Doppler Signal

• 주로 적혈구에서 반사

• fd : 가청주파수대역

Clutter

• 혈관벽, 연조직 등 거의 정지해 있는 target으로부터의 신호

• fd : 낮음. (DC 부근)

• Doppler Signal에 비해 진폭이 매우 큼

CDR

• Clutter-to-Doppler Ratio

• 일반적으로 CDR > 40dB

PowergnalDoppler sipowergnalClutter siCDR

=

CW DOPPLER SYSTEM

CW Doppler Spectrum Example

CW DOPPLER SYSTEM

CW Doppler Spectrum Example : Real-Time

CW DOPPLER SYSTEM

Doppler Spectrum의 표현

0

10

20

30

40

50[cm/s]

-10

-20

시간

어느 한 순간

0

10

20

30

40

50

[cm/s]

-10

-20

크기

속도

일반적 초음파Doppler spectrum

표현순시 Spectrum

이 속도의 적혈구가 비교적 많음

이 속도의 적혈구는거의 없음

CW DOPPLER SYSTEM

Tx Beam

Rx Beam

Tx Beam

Rx Beam

Steering Type

• 일반적 phased array

• Aperture 절반은 Tx,

절반은 Rx로 사용

• 송수신 빔 이동 가능

• 2D image 위에서 조작 : 편리

Static CW Probe (Pencil Type)

• CW 전용 : 2-element

• 한 element는 Tx,

나머지는 Rx로 사용

• 빔 방향 및 교차점 고정

• 저가형

• 2D image 없이 감각적으로 혈류 찾아야 함.

CW Doppler Probe

CW DOPPLER SYSTEM

System Block Diagram

flow

CWOscillator

TxAmp.

RxAmp.

-90o LPF

LPF

HPF

HPF

i(t)

q(t)

Clutter filter

FFTSpectrumAnalysis

Transmit Probe Receive

ProbeTransmit Beam Pattern

Receive Beam Pattern

toDisplay

ADC

ADC

QuadratureDemodulator

-90o

+

+

+-

Audio Amp

Audio Speaker

Forward flow

Reverse flow

Hilbert Transform

i1(t)

q1(t)

r(t)

s(t)

af(t)

ar(t)

CW DOPPLER SYSTEM

CW : Frequency, Phase, Magnitude

Re

Re

t

=0o

=90o

=180o

AA

T

f=1/T

Im

θ

θ

θ

θ

)2cos( tfA π⋅

• 반지름 A인 원주를 등속으로 돌고 있는 점을 Re축상으로 투영한 길이 :

• A : 진폭 (amplitude), T : 주기 (period), f=1/T : 주파수, : instantaneous phaseθ

)2cos( tfA π⋅

CW DOPPLER SYSTEM

Re

Re

t

AA

T

f=1/T

기준 phasor

계속 변화

불변 (-45o)Im

Im

Re

Quadrature Base Band Signal

T

f=1/T

A

CW : Relative Phase, Quadrature Base Band Signal

• Quadrature base band signal : 기준phasor signal에 대한 상대적 위상과 진폭을복소수로 표시.

•Quadrature base band signal

• I : inphase, Q: Quadrature

)2cos( tfA π⋅

)452cos( O−⋅ tfA π

707.0707.0)45sin()45cos( oo jjQIjAA −=+=−⋅+−⋅=

CW DOPPLER SYSTEM

t

Quadrature Base Band Doppler Signal

)2cos( tfA

)(tI )(tQ

π⋅

( )tffA d )(2cos +⋅ π

• Doppler Signal : 기준 phasor signal(송신신호)과 주파수가 만큼 차이남.

• Quadrature base band Doppler signal :

• 이 신호의 주파수가 바로 Doppler shift 주파수임.

• 허수부의 역할 : 이동방향을 알려줌. (물체 접근 : , 멀어짐 : )

)2exp()2sin()2cos()()( tfjAtfjAtfAtjQtI ddd πππ ⋅=+⋅=+=

df

0>df 0<df

Forward Flow

t tReverse Flow

)(tI)(tI

)(tQ

)(tQ

CW DOPPLER SYSTEM

Quadrature Demodulator

-90o LPF

LPF


i(t)

q(t)

i0(t)

q0(t)

s(t)

r(t)

))()(2cos()()()2cos()(

0

0

ttfftAtstftr

d φππ

++==

))(2cos()(21))()2(2cos()(

21

)2cos())()(2cos()()(

0

000

ttftAttfftA

tfttfftAti

dd

d

φπφπ

πφπ

++++=

⋅++=

))(2sin()(21))()2(2sin()(

21

)2sin())()(2cos()()(

0

000

ttftAttfftA

tfttfftAtq

dd

d

φπφπ

πφπ

+−++=

⋅++=

))(2cos()(21)( ttftAti d φπ +=

))(2sin()(21)( ttftAtq d φπ +−=

CW DOPPLER SYSTEM

Clutter FIlter

frequency

0

Magnitude

Quadrarture demodulator output signal

i(t)+jq(t)

Clutter filterCharacteristics

frequency

0

Magnitude

Clutter Filter output signal

ic(t)+jqc(t)

Clutter filterCharacteristics

ClutterFiltering

PW DOPPLER SYSTEM

PW Doppler Principle

• CW Doppler : Almost no range information

• Range information 위해

송신 : burst

수신 : range-gating

• Frequency resolution 위해 일정주기 반복 송/수신

Discrete-time signal

• Transmitting Signal Example

T = PRI : Pulse Repetition Interval [s].PRF = Pulse Repetition frequency [Hz]

=1/T

0'th Tx 1'st Tx 2'nd Tx

t0 [s]Center Frequency f0 [Hz]

= 1/t0

T

PW DOPPLER SYSTEM

PW Doppler Principle : Range Information

tissuevessel

Transducer

Transmit Burst pulse

Range gate

Sampled signal

PW DOPPLER SYSTEM

PW Doppler Principle : Range Information

• Received Signal Example

Single Target

Constant velocity moving

toward probe

• Doppler 효과로 이해할 수도 있지만,

target의 위치 이동

초음파 왕복시간 변화

수신신호 위상 변화

로 이해할 수도 있음.

t

t

t

0

T

2T

Range gate

Moving

Sampled Data

T = 1/PRF

k

PW DOPPLER SYSTEM


flow

CWOscillator

TxAmp.

RxAmp.

-90o LPF

LPF

HPF

HPF

i(t)

q(t)

Clutter filter

FFTSpectrumAnalysis

toDisplay

ADC

ADC


-90o

+

+

+-

Audio Amp

Audio Speaker

Forward flow

Reverse flow

Hilbert Transform

i1(k)

q1(k)

r(t)

s(t)

af(k)

ar(k)

Probe

Burst

S/H

S/H

DAC

DAC

LPF

LPF

i2(k)

q2(k)

Range Gate

Aliasing Problem

t

t

Real

Imaginary

a

bc

d

ef

a

b

cd

e

f

t

t

Real

Imaginary

a

b

c

d

e

f

a

b

c

d

e

f

t

t

Real

Imaginary

a

b

c

d

e

f

a

b

c

de

f

Real

Imaginary

Counter-clockwise!

a

bc

def

ab

c

d

e

f

Imaginary

Real

Counter-clockwise!

Imaginary

Reala

b

c

d

e

f

??

??

PW DOPPLER SYSTEM

Doppler Signal Example : Liver

CDR =37[dB]

DNR = 21[dB]

*PRF

100

1000

10000

100000

1000000

-0.5 -0.25 0 0.25 0.5

0

500

1000

1500

2000

2500

3000

1 11 21 31 41 51 61 71 81 91 101 111 121

i(k)q(k)

k

Actual ImageSpectrum at an instance

i & q data

PW DOPPLER SYSTEM

PW DOPPLER SYSTEM

B-D Simultaneous Mode

• Live B-mode image와 동시에 Live Doppler Spectrum

•Scanline Sequence

Probe

01234567891011

12

Doppler Scan line

Scanline number

• 0 7 1 7 2 7 … 7 12 7 0 …

• 매 두 번의 송신에 하나의 Doppler data를 얻음

• PRF가 실질적으로 반으로 줄어듦.

PW DOPPLER SYSTEM

PW Doppler Real-Time Image Example

COLOR FLOW IMAGING

Spectrum Estimation

• Estimates mean and variance

of the Doppler spectrum

• in Every Pixel in the ROI

Display

• Mean velocity :

Towards : Red, Away : Blue

Fast : Light, Slow : Dark

• Turbulence : Add Yellow

Important Issues : Ensemble Number Limitation• Efficient clutter filtering

• Noise insensitive estimation

Velocity Only

Velocity + Turbulence

0

+Max

-Max

Velocity

0

+Max

-Max

Velocity

Turbulence0 Max

COLOR FLOW IMAGING

Image formation and Tx/Rx sequence

...............

................

12

M

1 2 L

................

... ...

...…

Scanline index

................

0 x

ZM

Pix

elin

dex

2-D ROI

vessel

혈류

한 scanline당 N회 반복 송/수신

1 2 3 N 1 2 3 N

to Scanline 1 to Scanline 2

Ensemble index

Transmit Burst

COLOR FLOW IMAGING


InputCornerturning

Auto-correlator

tan-1()i,qClutterFilter

velocity

Input Corner Turning

• Data 순서 재정돈, 각 pixel에 필요한 data끼리 모음

3,1 3,2 3,3 3,4 3,M

1,1 1,2 1,3 1,4 1,M

2,1 2,2 2,3 2,4 2,M

N,1 N,2 N,3 N,4 N,M

forpixel 1

forpixel 2

forpixel 3

forpixel 4

forpixel M

0'th Tx

1'st Tx

2'nd Tx

N'th Tx

COLOR FLOW IMAGING

Clutter FilteringProblem : Small Ensemble Number

N tap FIR Filter

• N transient output data : M-N output data available

• Large N needed for stiff transient band characteristics

IIR Filter

• Inherent transient response problem

Some ways of state variable initialization to minimize it.

Example : E.S. Chornoboy, “Initialization for improved IIR filter performance,”IEEE Transactions on Signal Processing, Vol. 40, No. 3, pp543-550, Mar. 1992.

Regression Filter

• Clutter를 ensemble data의 regression으로 추정, 제거.

• No loss of output data number : frequency estimation에 유리

Example : A. P. Kadi and T. Loupas, “On the performance of regression and step initialized IIR clitter filters for color Doppler systems in diagnostic medical ultrasound,” IEEE Transactions on UFFC, vol. 42, no. 5, pp. 927-937, Sept. 1995

COLOR FLOW IMAGING

Clutter Filtering

• Example : Regression Filter

1’st Order : Linear Regression

-500

0

500

1000

1500

20001 3 5 7 9

11

13

15

i

q

regression of i

regression of q

filtered i

filtered q

COLOR FLOW IMAGING

Velocity Estimator Block Diagram

Z-1

Z-1

i(k)

q(k)

i(k-1)

q(k-1)

+

-

+

+

Z-1

Z-1

A = Σ[i(k-1)q(k) - i(k)q(k-1)]

B = Σ[i(k)i(k-1) + q(k)q(k-1)]

tan-1(y,x) v

+

+

+

+

COLOR FLOW IMAGING

Overall System Block Diagram

Beam-former

Tx Amp.

Rx Amp.

BPF

LPF

LPF

DopplerProcessor

CFProcessor

i

q

EchoProcessor

B-modeimage

Doppler Spectrum

Color Flow Image

DigitalScan

Converter to Display

Array Transducer Quadrature

Demodulator

Audio

AudioSpeaker

COLOR FLOW IMAGING

Real-Time Image Examples

경동맥 Aliasing 발생한 경우

COLOR FLOW IMAGING

Real-Time Image Examples

심장, Regurgitation

DOPPLER MEASUREMENT EXAMPLES

Stroke Volume

velocityFlowCSArateFlow ×=

Flow velocity가 시간에 따라 변화하는 경우

timevelocityFlowCSAFlowofVolume ××=

∫ ⋅→× dtvlocityFlowtimevelocityFlow )(

Velocity-time integral (VTI) or Time-velocity integral (TVI)

한 주기동안 적분

따라서

TVICSAVolumeStroke ×=

CSA : Cross-sectional area

785.02

22

×=×⎟⎠⎞

⎜⎝⎛= DDCSA π

또

따라서

TVIDSV ××= 785.02

CSA

)(높이밑면적

timevelocityFlowCSAFlowofVolume

××=×=

timevelocityFlow ×

DOPPLER MEASUREMENT EXAMPLES

PISA (Proximal Isovelocity Surfce Area) Method (Color Doppler)

TVItRegurgitanEROVolumetRegurgitan ×=

ERO : Effective Regurgitant Orifice area

Flow rate conservation :

Flow rate at any shell surface

= flow rate at the orifice

계산의 편의상 surface는 isovelocity surface

특히, aliasing이 생기는 면

반구의 표면적이 이므로

Isovelocity surface

flowr

22 rπvelocityaliasingrrateFlow ××= 228.6

at OrificevelocitytregurgitanERO×=

at surface

velocityMRvelocityaliasingrERO ××= 228.6

TVIMRvelocityMR

velocityaliasingrTVIMREROvolumetregurgitan ×××=×= 228.6즉

Other Doppler Imaging Methods

• Power Doppler Imaging

•Color Doppler에서 평균속도, 분산 등을 계산하지 않고

Doppler signal의 power만을 계산

혈관 분포 등을 관찰

시간적으로 평균을 많이 취할 수 있으므로 SNR 유리.

• ‘Engio mode’ 등으로 부르기도.

• Tissue Doppler Imaging (TDI)

• 적혈구로부터의 신호 대신 wall로부터의 clutter를 이미징.

• PW, Color, Color M-mode 등으로 관찰

• Cardiac에서 valve 등의 motion관찰, 진단.

B-Flow Imaging

• B-Flow : B-Mode Blood Flow

• Conventional B-mode image :

Very small reflection from the RBC

Blood is almost black level

• To visualize the ‘dark’ blood in the B-mode,

Coded transmission to improve SNR

Ex; Golay Code : Long pulse(=high power)

but can be compressed (Good Resolution)

Tissue Equalization (similar to clutter filter)

Suppress Tissue brightness

Emphasize moving blood brightness

• Benefits : Fast, Intuitive Visualization of blood flow

• Drawback : poor penetration, poor sensitivity

Recent Researchs- SFP in HFUS

• VXD Yang (Toronto Univ) et al, 2004 Ultrasonic Symposium

• SFP : Speckle Flow Processing, HFUS : High Frequency Ultrasound

• Over 40MHz : Very high resolution (<100um),

very poor penetration (4~5mm)

RBC reflection coefficient dramatically increased

Speckle from RBC can be observed

Flow can be estimated by speckle variation at a pixel.

Angle independent!

• Experimental Results : Imaging of developing leg region of a tadpole

Thank You

ultrasound doppler instrumentation and color flow...

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