Ultrasound Doppler Instrumentation and Color Flow...
Transcript of 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
General Doppler Effect : Formulation
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
General Doppler Effect : Formulation
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
QuadratureDemodulator
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
System Block Diagram
flow
CWOscillator
TxAmp.
RxAmp.
-90o LPF
LPF
HPF
HPF
i(t)
q(t)
Clutter filter
FFTSpectrumAnalysis
toDisplay
ADC
ADC
QuadratureDemodulator
-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
System Block Diagram
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