What anatomy to know Fall 2019 - Stanford University · 2019. 11. 13. · urinary bladder gall...
Transcript of What anatomy to know Fall 2019 - Stanford University · 2019. 11. 13. · urinary bladder gall...
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Rad225/Bioe225
Ultrasound
Fall 2019What anatomy to knowliver
diaphragm
kidney
bag of fluid (vessel, cyst, bladder, gall bladder, uterus with amniotic fluid)
urinary bladder
gall bladder with gall stones
fetus
heart
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Rad225/Bioe225
Ultrasound
Fall 2019Class 13 - Doppler
CV System 101Doppler ShiftContinuous Wave DopplerPulsed DopplerColor FlowPower
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Rad225/Bioe225
Ultrasound
Fall 2019The Cardiovascular System 101
The aorta has the highest flow rates~ 100 cm/s
Flow rates decrease as you move more peripheraleg. femoral arteries ~15 cm/s
Flow is pulsatile in arteries, mostly constant in veins
Can be quite high in narrowings:stenoses or diseased valves ~4 m/s
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Rad225/Bioe225
Ultrasound
Fall 2019The Cardiovascular System 101
laminar flowparabolic flow
turbulent flow
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Rad225/Bioe225
Ultrasound
Fall 2019
Doppler Shift
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Rad225/Bioe225
Ultrasound
Fall 2019Doppler Shift
Transducer
Transducer
Transducer
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Rad225/Bioe225
Ultrasound
Fall 2019Sound Emission
Stationary Moving
SOS is the same
f 'λ 'fλ =
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Rad225/Bioe225
Ultrasound
Fall 2019Doppler Shift for moving sound emitter
f 'λ ' = fλ
If no angle, λ ' = λ − vTT = λ / cλ ' = λ − vλ / cλ ' = λ(1− v / c)
λλ '
= cc − v
λ ' = λ c − vc
f ' = fλλ '
Δf = f '− f = fλλ '
− f = f ( λλ '
−1)
Δf = f ( cc − v
−1) = f (c − c + vc − v
) ≈ f vc
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Rad225/Bioe225
Ultrasound
Fall 2019Doppler Shift for blood
Δf ≈ 2vfc
RBC is both receiver and transmitter: twice the shiftIf no angle,
where v is the velocity of the reflectorc is speed of soundfo is the transducer frequency
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Rad225/Bioe225
Ultrasound
Fall 2019Doppler Shift
The frequency shift is given by
whereθ is the angle of the velocity wrt/ the sound wave.
Example: If a 5 MHz transducer is used, what is the shift measured from blood moving at 20 cm/s at an angle of 60°?
f = 2 * (20 cm/s / 1540 m/s) * 5 MHz * cos (60°) = 650 Hz
θ
Δf = 2vf cos(θ )c
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Rad225/Bioe225
Ultrasound
Fall 2019Doppler Angle
completereflection
30°
60°
• Works best when transducer angle wrt bloodis 30-60°.
sensitive to angle errors±5° => 100% error
cos 85° = 0.087 cos 80° = 0.17100% error
cos 35° = 0.819cos 30° = 0.8665% error
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Rad225/Bioe225
Ultrasound
Fall 2019Angle Transducer
Is there a better/simpler way?
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Rad225/Bioe225
Ultrasound
Fall 2019Beam Steer to get the angle
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Rad225/Bioe225
Ultrasound
Fall 2019Frequency Tradeoffs
Imaging✦High frequency gives better resolution✦High frequency limits depth penetration
DopplerThe signal reflected from blood is ~ 2 orders of magnitude smaller than that reflected from tissue.
Doppler✦High frequency increases scattering from blood ~ f4✦High frequency limits depth penetration✦High frequency more likely to alias✦Generally use a lower frequency than B-mode
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Rad225/Bioe225
Ultrasound
Fall 2019Key Difference from B-Mode
In B-Mode, we look at the echo envelope
In Doppler, we will use the echo phase.
π2
Phase Shift
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Rad225/Bioe225
Ultrasound
Fall 2019
Doppler ModesSpectral Doppler Color Flow Imaging
✤Velocity/freq - time spectrogram✤Quantitative analysis
✤2D image of flow field✤Qualitative visualization
Continuous Wave
Pulsed Wave
Velocity Power
Very high velocities
No depth resolution
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Rad225/Bioe225
Ultrasound
Fall 2019CW Doppler Systems
• Simplest and least expensive• Pair of half circle transducers, angled in• “pencil probe”• sample volume is overlap of two beams
transmitter receiver
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Rad225/Bioe225
Ultrasound
Fall 2019Signal Demodulation
f0
f0+ δ-(f0+ δ)
2f0+ δ-(2f0+ δ) δ-δ
2f0+ δ-(2f0+ δ) δ-δ
A negative shift would look the same.Nondirectional Doppler devices cannot differentiate the direction of blood flow.
Time Frequency
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Rad225/Bioe225
Ultrasound
Fall 2019Signal Demodulation
f0 - δ-(f0 - δ)
f0
2f0- δ-(2f0- δ) δ-δ
- shift
Vb
f0+ δ-(f0+ δ)
f0
2f0+ δ-(2f0+ δ) δ-δ
+ shift
Vb
Va
f0+ δ-(f0+ δ)
f0
2f0+ δ-(2f0+ δ) δ-δ
vb has a 180° phase shift
cos sin
sin
-sin
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Rad225/Bioe225UltrasoundFall 2019
sinc( f )
A Few Fourier Transform Pairs
20
⇔
⇔
⇔
⇔
⇔⇔
Function(x) Fourier Transform(s)
sincrect(t)
comb(t)
sin(2π f0t)
cos(2π f0t)
f (t)g(t)ei2π f0t
comb( f )12
δ ( f + f0 )+δ ( f − f0 )⎡⎣ ⎤⎦
i 12
δ ( f + f0 )−δ ( f − f0 )⎡⎣ ⎤⎦
δ ( f − f0 )
F( f )∗G( f )
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Rad225/Bioe225
Ultrasound
Fall 2019+
Va
f0+ δ-(f0+ δ)
f0
2f0+ δ-(2f0+ δ) δ-δ
Va
f0+ δ-(f0+ δ)
f0
2f0+ δ-(2f0+ δ) δ-δ
+
+f0 - δ-(f0 - δ)
f0
2f0- δ-(2f0- δ) δ-δ
Vb
sin
f0+ δ-(f0+ δ)
f0
2f0+ δ-(2f0+ δ) δ-δ
Vb
-sin
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Rad225/Bioe225
Ultrasound
Fall 2019
Doppler - Continuous Wave (CW)
• lacks depth resolution - can pick up signal from multiple vessels
• measures high velocities without aliasing
• Obstetrics - fetal heart Doppler audio
• Cardiac - high velocity jets
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Rad225/Bioe225
Ultrasound
Fall 2019
Doppler ModesSpectral Doppler Color Flow Imaging
✤Velocity/freq - time spectrogram✤Quantitative analysis
✤2D image of flow field✤Qualitative visualization
Continuous Wave
Pulsed Wave
Velocity Power
Very high velocities
No depth resolution
Max velocity limit
Sample Gate Control
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Rad225/Bioe225
Ultrasound
Fall 2019Duplex Scanner
Duplex instruments are real-time B-mode scanners (imaging scanners) with built-in Doppler capabilities.
Duplex scanning, the instrument timeshares between “imaging” and Doppler.
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Rad225/Bioe225
Ultrasound
Fall 2019Pulsed Doppler
1. Position “Sample Gate”- selects echoes based on measurement time (depth)
2. Set the Doppler Angle along axis of the vessel
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Rad225/Bioe225
Ultrasound
Fall 2019Pulsed Doppler
• measure
• measure
• measure
...
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Rad225/Bioe225
Ultrasound
Fall 2019How far does it move?
v = 20 cm/sPRF = 5 kHzT=200 μsx = v*T = 20 cm/s*200 μsx = 40 μm
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Rad225/Bioe225
Ultrasound
Fall 2019Pulsed Doppler
• measure
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Rad225/Bioe225
Ultrasound
Fall 2019Challenge with Pulsed Ultrasound
If Δf=650 Hz, T=1.5 ms at 1 MHz, that’s 1500 cycles,
Measure a single phase difference from the reference with each pulse
π2
Phase Shift
but each pulse is 3 μs or 3 cycles, so not adequately sampling it with a single pulse.
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Rad225/Bioe225
Ultrasound
Fall 2019Pulsed Doppler
...
Multiple measurements of the Doppler freq shiftSample rate = PRF
• measure at φ1
• measure at φ2
• measure at φ3
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Rad225/Bioe225
Ultrasound
Fall 2019Doppler Spectrum Analysis
Single reflector
δ-δ
δ δ2δ3
Beam is wide enough to measure several reflections => intensity-modulated spectral line
vmax
vres
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Rad225/Bioe225
Ultrasound
Fall 2019Image Annotations
B-Mode:
Color Flow:
Pulsed Wave:vmax
vres
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Rad225/Bioe225
Ultrasound
Fall 2019Sensitive to Prescribed Flow Direction
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Rad225/Bioe225
Ultrasound
Fall 2019Pulse Doppler: Aliasing
Good
Aliased
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Rad225/Bioe225
Ultrasound
Fall 2019
fshift
PRF
Well Sampled
= 2 * (20 cm/s/1540 m/s) * 6 MHz
= 1558 Hz
= 1540m/s/(2*10cm)= 7700 Hz
You have a 6MHz transducer measuring the velocity in a vessel at a depth of 10 cm. If the velocity is 20 cm/s and the angle is 0°, will it alias?
= 2 * (v/c) * fo
= v/(2*depth)
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Rad225/Bioe225
Ultrasound
Fall 2019
fshift = 2 * (v/c) * fo
PRF = v/(2*depth)
Aliased
= 2 * (100 cm/s/1540 m/s) * 6 MHz
= 7792 Hz
= 1540m/s/(2*10cm)= 7700 Hz
You have a 6MHz transducer measuring the velocity in a vessel at a depth of 10 cm. If the velocity is 100 cm/s and the angle is 0°, will it alias?
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Rad225/Bioe225
Ultrasound
Fall 2019Pulsed Doppler - VmaxThe max Doppler shift we can detect is PRF/2
Higher velocities will “alias”
depth Tx freq.
2vf cos(θ )c
= PRF2
vmax =c2
8zf cos(θ )
vmax =PRFc
4 f cos(θ )
PRF = c2zSubstitute
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Rad225/Bioe225
Ultrasound
Fall 2019
vmax =c2
8zf cos(θ )
Reduce Aliasing
Increase PRF if possible
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Rad225/Bioe225
Ultrasound
Fall 2019Aliasing? Change the Scale. How?✦ Pulsed Wave PRF Changed
✦ MI changed, but TIs didn’t (?)
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Rad225/Bioe225
Ultrasound
Fall 2019
vmax =c2
8zf cos(θ )
Reduce Aliasing
Decrease Tx frequency
Increase PRF if possible
Decrease depth
Increase the angle
Apply Fourier Shift Theorem
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Rad225/Bioe225
Ultrasound
Fall 2019Aliasing? Baseline Shift. How?
✦ No parameters changed
✦ Apply a linear phase before FT
(Fourier Shift Theorem)
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Rad225/Bioe225UltrasoundFall 2019
sinc( f )
A Few Fourier Transform Pairs
42
⇔
⇔
⇔
⇔
⇔⇔
Function(x) Fourier Transform(s)
sincrect(t)
comb(t)
sin(2π f0t)
cos(2π f0t)
f (t)g(t)ei2π f0t
comb( f )12
δ ( f + f0 )+δ ( f − f0 )⎡⎣ ⎤⎦
i 12
δ ( f + f0 )−δ ( f − f0 )⎡⎣ ⎤⎦
δ ( f − f0 )
F( f )∗G( f )
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Rad225/Bioe225
Ultrasound
Fall 2019Aliasing? Baseline Shift. How?
✦ No parameters changed
✦ Apply a linear phase before FT
(Fourier Shift Theorem)
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Rad225/Bioe225
Ultrasound
Fall 2019
How do you interpret these images?
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Rad225/Bioe225
Ultrasound
Fall 2019
How do you interpret these images?
Reflectors at all different velocities => turbulent flow
Small range of velocities=> well behaved flow
negative measurements=> biphasic
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Rad225/Bioe225
Ultrasound
Fall 2019Spectral Broadening
62°
72°
More spectral
broadening, Velocities appear higher
Computer thinks there is one angle,
But a range of angles is present