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

Rad225/Bioe225

Ultrasound

Fall 2019Class 13 - Doppler

CV System 101Doppler ShiftContinuous Wave DopplerPulsed DopplerColor FlowPower

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

Rad225/Bioe225

Ultrasound

Fall 2019The Cardiovascular System 101

laminar flowparabolic flow

turbulent flow

Rad225/Bioe225

Ultrasound

Fall 2019

Doppler Shift

Rad225/Bioe225

Ultrasound

Fall 2019Doppler Shift

Transducer

Transducer

Transducer

Rad225/Bioe225

Ultrasound

Fall 2019Sound Emission

Stationary Moving

SOS is the same

f 'λ 'fλ =

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

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

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

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

Rad225/Bioe225

Ultrasound

Fall 2019Angle Transducer

Is there a better/simpler way?

Rad225/Bioe225

Ultrasound

Fall 2019Beam Steer to get the angle

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

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

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

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

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

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

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 )

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

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

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

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.

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

Rad225/Bioe225

Ultrasound

Fall 2019Pulsed Doppler

• measure

• measure

• measure

...

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

Rad225/Bioe225

Ultrasound

Fall 2019Pulsed Doppler

• measure

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.

Rad225/Bioe225

Ultrasound

Fall 2019Pulsed Doppler

...

Multiple measurements of the Doppler freq shiftSample rate = PRF

• measure at φ1

• measure at φ2

• measure at φ3

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

Rad225/Bioe225

Ultrasound

Fall 2019Image Annotations

B-Mode:

Color Flow:

Pulsed Wave:vmax

vres

Rad225/Bioe225

Ultrasound

Fall 2019Sensitive to Prescribed Flow Direction

Rad225/Bioe225

Ultrasound

Fall 2019Pulse Doppler: Aliasing

Good

Aliased

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)

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?

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

Rad225/Bioe225

Ultrasound

Fall 2019

vmax =c2

8zf cos(θ )

Reduce Aliasing

Increase PRF if possible

Rad225/Bioe225

Ultrasound

Fall 2019Aliasing? Change the Scale. How?✦ Pulsed Wave PRF Changed

✦ MI changed, but TIs didn’t (?)

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

Rad225/Bioe225

Ultrasound

Fall 2019Aliasing? Baseline Shift. How?

✦ No parameters changed

✦ Apply a linear phase before FT

(Fourier Shift Theorem)

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 )

Rad225/Bioe225

Ultrasound

Fall 2019Aliasing? Baseline Shift. How?

✦ No parameters changed

✦ Apply a linear phase before FT

(Fourier Shift Theorem)

Rad225/Bioe225

Ultrasound

Fall 2019

How do you interpret these images?

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

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