UltrasoundUltrasound

Sound wavesSound waves

Sounds are mechanical disturbances that propagate through the medium

Frequencies <15Hz Infrasound

15Hz<Frequencies <20KHz Audible sound

Frequencies>20Khz Ultrasound

Medical Ultrasound frequency 2 -20MHz

Some experimental devices at 50MHz

Velocity and frequencyVelocity and frequency

For sound waves the relationship between frequency/velocity and wavelength is

c = f x

Speed of sound depends on the material sound travels

Velocity is inversely proportional to compressibility

the less compressible a material is the greater the velocity

Average velocity in tissue 1540 m/sec (air 331m/sec, fat 1450 m/sec)

The difference in speed of sound at the boundaries determines the contrast in US

Wave SpeedWave Speed

cair= 331 m/s csalt water

= 1500 m/s

B = Bulk Modulus = density

Bulk modulus measures stiffness of a medium and its resistanceto being compressedSpeed of sound increases with stiffness of material

k = adiabatic bulk modulus = density

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c =B

ρ

Wave speed cntWave speed cnt

Changes in speed DO NOT affect the frequency so only the wavelength is dependent on the material.

What is the wavelength of a 2MHz beam traveling into tissue?

What is the wavelength of a 5MHz beam traveling into tissue?

Wave speed cntWave speed cnt

Changes in speed DO NOT affect the frequency so only the wavelength is dependent on the material.

What is the wavelength of a 2MHz beam traveling into tissue? 0.77mm

What is the wavelength of a 10MHz beam traveling into tissue? 0.15mm

The wavelength determines the image resolution

Higher frequency -> higher resolution

Penetration is higher at smaller frequencies.

Penetration and resolutionPenetration and resolution

Thick body parts (abdomen)

Low frequency ultrasound (3.5 - 5 Mhz)

Small body parts (thyroid, breat)

High frequency (7.5 - 10 Mhz)

InterferenceInterference

Waves can constructively and destructively interfere

Constructive interference -> Increase in amplitude (waves in phase)

Destructive interference -> Null amplitude (waves out of phase)

Acoustic ImpedanceAcoustic Impedance

Z= x c [kg/m2/sec] SI unit ([Rayl] =1 [kg/m2/sec])

Independent of frequency

Air -> Low Z

Bone -> High Z

Large difference in acoustic impedence in the body generate large reflections that translate in large US signals

Example going from soft tissue to air filled lunghs ->BIG REFLECTION

Sound and pressureSound and pressure

Sound waves cause a change in local pressure in the media

Pressure (Pascal)=N/m2

Atmospheric pressure 100KPa

US will deliver 1 Mpa

Intensity I (amount of energy per unit time and area) is proportional to P2

This is the energy associated with the sound beam

Temporal and Spatial intensity when dealing with time or space

Sound and pressureSound and pressure

Relative sound intensity (dB) (Bels => B, 1B=10dB)

Relative intensity dB= 10 log(I/Io) Io original intensity, and I measured intensity

Negative dB -> signal attenuation

-3dB -> signal attenuated of 50%

AttenuationAttenuation

Loss by scatter or absorption

High frequency are attenuated more than low frequencies

Attenuation in homegeneous tissue is exponential

A 1Mhz attenuation in soft tissue is 1 dB/cm, 5 MHz -> 5dB/cm

Bone media attenuation increases as frequency squared.

Absorbed sound ->heat

ReflectionReflection

Echo -> reflection of the sound beam

The percentage of US reflected depends on angle of incidence and ZSimilar to light

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R =Z2 − Z1

Z2 + Z1

⎡

⎣ ⎢

⎤

⎦ ⎥

2

€

T =4 Z1 ⋅Z2[ ]

Z1 + Z2[ ]2

ReflectionSnell’s LawReflectionSnell’s Law

i angle of incidence

t angle of transmittance

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sin θ i( )

sin θ t( )=

v1

v2

TransducerTransducer

Made of piezoelectric material

Crystals or ceramics

Stretching and compressing it generate V

Lead-zirconate-titanate (PZT)

• A high frequency voltage applied to PZT

generate high freq pressure waves

Are generators and detectorsAre generators and detectors

Q factor Q factor

• Q factor is the frequency response of the piezoelectric crystal

• Determines purity of sound and for how long it will persist

• High Q transducers generate pure frequency spectrum (1 frequency)

• Q=operating frequency/BW

– BW bandwidth

– High Q -> narrow BW

– Low Q->broad BW

Transducer backingTransducer backing

• Backing of transducer with impedance-matched, absorbing material reduces reflections from back damping of resonance

– Reduces efficiency

– Increases Bandwidth (lowers Q)

Axial beam profileAxial beam profile

• Piston source: Oscillations of axial pressure in near-field (e.g. z0= (1 mm)2/0.3mm = 3 mm)

• NF Variation in pressure and amplitude

• Caused by superposition of point wave sources across transducer (Huygens’ principle)

• Side lobes = small beams of reduced intensity at an angle to the main beam

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sin(θ ) = 1.22λ /(2r)

Near FieldFresnel Zone

Far FieldFraunhofer zone

US usually uses Fresnel Zone

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z0 =r2

4

Lateral beam profile Lateral beam profile

• Determined by Fraunhofer diffraction in the far field.

• Given by Fourier Transform of the aperture function

• Lateral resolution is defined by width of first lobe (angle of fist zero) in diffraction pattern

– For slit (width a):

– For disc (radius r, piston source):

sin 0.61 arcsin 0.61r r

⎛ ⎞= → = ⎜ ⎟⎝ ⎠

( ) 0

sin sinc

Minima at: sin

aI I

na

π θθ

λ

λθ

⎛ ⎞= ⎜ ⎟

⎝ ⎠

⇒ =

Focused transducersFocused transducers

• Reduce beam width

• Concentrate beam intensity, increasing penetration and image quality

• All diagnostic transducers are focused

• Focal zone – Region where beam is focused

• Focal length – distance from the transducer and center focal zone

Focusing of ultrasoundFocusing of ultrasound

• Increased spatial resolution at specific depth

• Self-focusing radiator or acoustic lens

Array typesArray types

a) Linear Sequential (switched) ~1 cm 10-15 cm, up to 512 elements

b) Curvilinearsimilar to (a), wider field of view

c) Linear Phasedup to 128 elements, small footprint cardiac imaging

d) 1.5D Array3-9 elements in elevation allow for focusing

e) 2D PhasedFocusing, steering in both dimensions

Array resolutionArray resolution

• Lateral resolution determined by width of main (w) lobe according to

Larger array dimension increased resolution

• Side lobes (“grating lobes”) reduce resolution and appear at

sinw

=

wa

g

sin 1, 2,3,...g

nn

g

= =

Ultrasound ImagingUltrasound Imaging

ImagingImaging

• Most ultrasound beam are brief pulses of 1 microsecond

• Wait time for returning echo

• Object must be large compared to wavelength

• Signal is amplified when returned (echo is small signal)

A-mode (amplitude mode) IA-mode (amplitude mode) I

• Oldest, simplest type

• Display of the envelope of pulse-echoes vs. time, depth d = ct/2• Pulse repetition rate ~ kHz

(limited by penetration depth, c 1.5 mm/s 20 cm 270 s, plus additional wait time for reverberation and echoes)

A-mode (amplitude mode) A-mode (amplitude mode)

• Or space! Also M mode!

depth

A-mode IIA-mode II

• Frequencies: 2-5 MHz for abdominal, cardiac, brain; 5-15 MHz for ophthalmology, pediatrics, peripheral blood vessels

• Applications: ophthalmology (eye length, tumors), localization of brain midline, liver cirrhosis, myocardium infarction

• Logarithmic compression of echo amplitude (dynamic range of 70-80 dB)

Logarithmic compression of signals

M mode or T-M modeM mode or T-M mode

• Time on horizontal axis and depth on vertical axis

• Time dependent motion

• Used to study rapid movement – cardiac valve motion

B-mode clinical exampleB-mode clinical example

Static image of section of tissue

Brighter means intensity of echo

B-mode (“brightness mode”)B-mode (“brightness mode”)

• Lateral scan across tissue surface

• Grayscale representation of echo amplitude

Add sense of direction to information-> where did echo come from

Real-time B scannersReal-time B scanners

• Frame rate Rf ~30 Hz:

• Mechanical scan: Rocking or rotating transducer + no side lobes - mechanical action, motion artifacts

• Linear switched array

12

2acq f

d ct N R t

c d N−= × ⇒ = = d: depth

N: no. of lines

Linear switchedLinear switched

CW DopplerCW Doppler

• Doppler shift in detected frequency

• Separate transmitter and receiver

• Bandpass- filtering of Doppler signal:

– Clutter (Doppler signal from slow-moving tissue, mainly vessel walls) @ f<1 kHz

– LF (1/f) noise

– Blood flow signal @f < 15 kHz

• CW Doppler bears no depth information

2 cosshift

vf f

c

=

v: blood flow velocityc: speed of sound: angle between direction of blood flow and US beam

Frequency Counter

SpectrumAnalyzer

CW Doppler clinical imagesCW Doppler clinical images

• CW ultrasonic flowmeter measurement (radial artery)

• Spectrasonogram:

Time-variation of Doppler Spectrum

t

f

t [0.2 s]

v [10cm/s]

CW Doppler exampleCW Doppler example

Duplex ImagingDuplex Imaging

• Combines real-time B-scan with US Doppler flowmetry

• B-Scan: linear or sector

• Doppler: C.W. or pulsed (fc = 2-5 MHz)

• Duplex Mode:

– Interlaced B-scan and color encoded Doppler images limits acquisition rate to 2 kHz (freezing of B-scan image possible)

– Variation of depth window (delay) allows 2D mapping (4-18 pulses per volume)

Duplex imaging example (c.w.)Duplex imaging example (c.w.)

www.medical.philips.com

Duplex imaging (Pulsed Doppler)Duplex imaging (Pulsed Doppler)

US imaging example (4D)US imaging example (4D)