01 Intro Easton-3Doppler effect: Change in frequency (and wavelength) due to motion of a sound...

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© 2006 Carlson Center for Imaging Science / RITImaging Science Fundamentals

Ultrasound Imaging

■ Imaging by sound waves● Just like SONAR

■ Many of same principles applied to RADAR● phased arrays●Doppler● synthetic apertures


Phased Arrays

■ Simulate large optic (antenna) by adjusting timing (“phase”) of small sources to steer beam

■ This is how “phase-array radar” is steered without rotating the antenna

If all sources emit wave atsame time, envelope travelsperpendicular to line of sources

If source at bottom emits wavefirst, and others at proportionaltimes later, the envelope of wavestravels at an angle


Resolution of Imaging System

■ Ability of system to “resolve” (i.e., distinguish) point sources that are close together

■ Measured as the ANGLE Δθbetween two point objects that can “just” be distinguished

■ Larger diameter optic ⇒ smaller ΔθΔθ

Δθ λ≈

D

2


Resolution Δθ

■ Want smallest possible Δθ to be able to “resolve” the most detail

⇒ largest possible diameter D and/or shortest wavelength λ

■ Limit is due to diffraction of light (“spreading” due to wave nature)

Δθ λ≈

D


Synthetic Aperture Imaging

■ “Active” Imaging●Source carried by platform (e.g., plane)

■ Large area of object is “illuminated”by source at one time

■ Reflected signals are recorded and tracked during motion of platform

■ Image is “constructed” by subsequent computation


Synthetic Aperture Radar/Sonar

■ Make one small antenna (“aperture”) do the work of large antenna

■ Used for aircraft-borne radar and “side-scan” sonar

“Patch” Illuminatedon Ground

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SAR Images

http://www.sandia.gov/RADAR/images/capitol1.jpg

http://www.higp.hawaii.edu/~hamilton/Images/venus_sm.gif


Shuttle SAR Images

http://southport.jpl.nasa.gov/


Sidebar: Synthetic Aperture (“Side Scan”) Sonar

■ Developed by Jacques Cousteau and “the”Harold Edgerton (“Doc”)

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Synthetic Aperture (“Side Scan”) Sonar

http://www.abc.se/~pa/mar/sidescan.htm

Shadows (characteristic of side-scan imaging)


Resolution can be VERY GOOD because antenna size D is VERY LARGE


Shadow from Masted Shipwreck

http://www.abc.se/~pa/mar/img/sture/mastvra2.jpg

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Pulse interacts with tissue

Echoes return from tissue, providing anatomic information used for imaging

Ultrasound

Transducer(transmitter and receiver)


Ultrasound Imaging

■Sound is due to traveling variations of air pressure● involves mechanical motion in medium● Pressure variation causes particles in medium to

vibrate due to variation in medium density

■Oscillation frequency of “ultrasound” is higher than humans can hear


Sound Waves

■ “Coordinated disturbance moving at a fixed speed through a medium”

■ Generally do not produce visible changes■ Result of TWO Forces

● Force of motion: Inertia● Restoring Force: Pressure of Medium

■ Conveys energy by motion of particles in medium ■ Generally travel as longitudinal waves

● motion of particles in medium is (more or less) parallel to direction of travel of wave

■ Transverse waves also can be propagated● motion of particles is transverse (perpendicular) to

direction of travel● Transverse waves do not travel well through soft tissue

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Longitudinal Sound Wave

Motion of Air Molecules

Propagation Direction of Wave


Graph of Air Pressure vs. Time

time

period

pres

sure

High Pressure = Compression

Low Pressure = Rarefaction


Frequency and Period■ Frequency ν (“nu”): Number of cycles per second

● measured in Hertz (Hz) (1 Hz = 1 cycle per second)● Human hearing: 20 Hz d ν d 20 000 Hz = 20 KHz

■ Ultrasound: ν > 20 KHz● Specific frequency is important because it determines

the resolution and penetration of the images

■ Period T: Time for one cycle to occur● Reciprocal of frequency ⇒period decreases if frequency increases ● Period is important concept for pulsed ultrasound

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■ Wavelength: Distance over which one cycle occurs● Usually expressed in millimeters for sound● Important in describing resolution of images

■ Propagation speed: Speed of wave through medium● Measured in meters per second or millimeters per microsecond

► 1 microsecond = 1 millionth of a second = 10-6 seconds

► Wavelength depends on the frequency and propagation speed:

● (Check units!)

Wavelength and Velocity

)()/()(

MHzfrequencysmmspeednpropagatiommwavelength μ

=


■ Depends on medium● In soft tissue, v ≈ 1540 m/s = 1.54 mm/ms

■ Determined by Density and Stiffness ■ Density = concentration of matter

● (mass per unit volume: kg/m3 )

■ Stiffness: resistance of material to compression ● (inverse of compressibility)● usually the dominant factor on propagation speed

Gas ⇒ low propagation speedLiquid ⇒ higher propagation speed

Solid ⇒ highest propagation speed

Propagation speed v


1600Muscle1560Blood1555Liver1460Fat600Lung1480Water330Air

v (m/s)Material

Propagation speed v

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Used to position echoes on display

A-line

Propagation speed v


Position determined from direction of pulse entering patient and time delay until echo returns to transducer

0 1 2 3 4 5 6 7 8 9 10

13 μs

39 μs

130 μs

cm

td2v =

Range Equation

Range equation


Pulsed ultrasound

Pulse Pulse repetition period

■ Frequency, period, wavelength and propagation speed describe continuous-wave (cw)ultrasound● Cycles repeat indefinitely

■ Sonography uses pulsed ultrasound, i.e., a few cycles of ultrasound separated by gaps of no signal

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Pulsed Ultrasound Parameters

Pulse duration Pulse repetition period

■ pulse duration (measured in μs) ■ pulse-repetition frequency (PRF): number

of pulses in 1 s (measured in kHz)● equivalent to pulse-repetition period (PRP):

Time between beginnings of adjacent pulses (measured in μs)


Attenuation■ Weakening of sound as it propagates

● Attenuation measured in decibels (dB)►3 dB ⇒ Energy has decreased by half

● Attenuation coefficient α: amount of attenuation per cm

■ Limits imaging depth● Attenuation must be compensated by amplifying echo

■ Includes:● Absorption (conversion of sound energy to heat)● Reflection● Scattering of sound at tissue interfaces

■ Absorption dominates■ Echoes from reflection and scattering are essential

to create images but contribute little to attenuation


Attenuation

attenuation coefficient α ↑ ⇒ attenuation ↑path length ↑ ⇒ attenuation ↑

Attenuation increase with increasing frequency:

Attenuation (dB) = ½ × frequency (MHz) × path length (cm)

Attenuation limits the depth of images (penetration).frequency ↑ ⇒ penetration ↓

Frequencies in diagnostic ultrasound range from 2 to 15 MHzLower frequencies for deeper penetration

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Transducer■ Converts one form of energy to another

● e.g., electric to mechanical and vice versa

■ Piezoelectric materials generate voltage when deformed by pressure and deform when voltage applied (PZT)

■ Single-element transducers are disks (piston transducer)■ Several rectangular elements in linear-array transducer■ Transducers are driven by one to three cycles of

alternating voltage● 5-15 cycles are used for Doppler

■ Frequency of ultrasound equal to frequency of driving voltage● approximately resonance frequency of element


■ Each element is about one wavelength wide■ Voltage applied to sequential groups of elements■ Individual element too small to transmit “well-defined beam”■ Groups of elements are driven simultaneously as one (phased

array)■ Central axis of resulting scan line corresponds to central

element in group■ Same principle used in “Phased-Array Radar”

Linear Arrays

beam

beam

beam

beam


Focusing

1. Curved transducer elements2. Lenses3. Phasing■ Improves resolution■ Moves end of near field towards transducer and narrows

beam■ Focusing can take place only in near field

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Doppler

■ Used in medical ultrasound to quantify and image blood flow and to detect fetal heart motion

■ Must understand principles of flow to understand system

■ Circulatory system consists of heart, arteries, arterioles, capillaries, venules, and veins● 5 L of blood

■ Heart is pump that keeps blood flowing

■ Circulation is a closed loop of tubes that run in continuous figure "8" centered on heart


Circulation

Vena cava aorta

■ One loop carries blood to lungs in pulmonary arteries, returns in pulmonary veins

■ Other loop supplies blood at high pressure to head and body, blood returns to heart in vena cava

http://www.emc.maricopa.edu


Doppler

■ Characteristics of fluids and their behavior when they flow through tubes (e.g., blood vessels), in steady and pulsing flows

■ Doppler effect: Change in frequency (and wavelength) due to motion of a sound source, receiver, or reflector● If source moving towards receiver, received wave has higher

frequency than without motion● If receiver is moving toward source, received wave has higher

frequency than without motion

■ If reflector is moving toward source and receiver, wave has higher frequency than would be experienced without motion

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Doppler■ Relative motion between source and receiver ⇒ frequency heard

by receiver differs from that of source■ Perceived frequency is either higher or lower

● depends on whether source and receiver are moving toward or away from each other

■ Moving receiver approaching bstationary source ⇒ more cycles of wave encountered in 1 sec● Speed of receiver motion divided by wavelength yields increase in

number of cycles/sec

Stationary source:Hear same frequency as source

Source Approaching Observer:hear MORE waves per second

S S


Doppler Equation

Quantitative description of Doppler effect

Three situations: moving source, moving receiver, moving reflector

Moving reflector: relevant to diagnostic Doppler ultrasound ⇒ Doppler shifts in echos from moving reflectors

Stationary reflector

Reflector moving TOWARD receiver

Reflector moving AWAY FROM receiver


Doppler shiftDoppler shift = received frequency – source frequency

■ Approaching reflector ⇒ Doppler shift is positive ⇒ received frequency > source frequency

■ Receding reflector ⇒ Doppler shift is negative ⇒ received frequency < source frequency

● fd is Doppler frequency (shift)● ν0 = frequency of source● v = speed of reflector● c = speed of sound in medium

cfD

θν cosv2 0=

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Doppler instrumentsFlow information provided by Doppler ultrasound:■ Presence of flow

● Yes● No

■ Direction of flow (by color)● →● ←

■ Speed of flow● Fast● Slow

■ Character of flow● Laminar● Turbulent


Color-Doppler imaging

■ Information presented in audible, color-Doppler, spectral-Doppler forms

■ Color-Doppler imaging displays 2-dimensional, cross-sectional, real-time blood flow or tissue motion information together with a 2-dimensional, cross-sectional, gray-scale anatomic image


++

--

Color-Doppler Imaging

Frequency of received echoes

Corresponding pixels

Stack-up lines of data to create a 2-D image

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Ultrasound Equipment

Philips, EnVisor


Ultrasound Images

http://www.mayoclinic.org/breastimagingservices-jax/breastultrasound.htmlhttp://www.danheller.com/jack-ultrasound.html

01 Intro Easton-3Doppler effect: Change in frequency (and wavelength) due to motion of a sound...

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