Lecture Ultrasound Beams

8/22/2019 Lecture Ultrasound Beams

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Transducers



Ultrasound is produced and detectedwith a transducer, composed of one or

more ceramic elements withelectromechanical (piezoelectric)properties.• The ceramic element converts electrical

energy into mechanical energy to produceultrasound and mechanical energy intoelectrical energy for ultrasound detection.



Over the past several decades, the transducer assembly has evolved considerably in design,function, and capability, from a single-elementresonance crystal to a broadband transducer

array of hundreds of individual elements.• A simple single-element, plane-piston source

transducer has major components including the• piezoelectric material,

• marching layer,

• backing block,• acoustic absorber,

• insulating cover,

• sensor electrodes, and

• transducer housing.





Piezoelectric Materials

A piezoelectric material (often a crystal

or ceramic) is the functional component

of the transducer.• It converts electrical energy into mechanical

(sound) energy by physical deformation of the

crystal structure.



ConverseIy, mechanical pressure

applied to its surface creates electrical

energy.• Piezoelectric materials are characterized by a

well-defined molecular arrangement of

electrical dipoles (Fig. 16-9).



An electrical dipole is a molecular entity

containing positive and negative electric

charges that has no net charge.• When mechanically compressed by an

externally applied pressure, the alignment of

the dipoles is disturbed from the equilibrium

position to cause an imbalance of the chargedistribution.



A potential difference (voltage) is created

across the element with one surface

maintaining a net positive charge andone surface a net negative charge.

• Surface electrodes measure the voltage,

which is proportional to the incident

mechanical pressure amplitude.



Conversely, application of an external

voltage through conductors attached to

the surface electrodes induces themechanical expansion and contraction of

the transducer element.



There are natural and syntheticpiezoelectric materials.

• An example of a natural piezoelectric materialis quartz crystal, commonly used in watchesand other time pieces to provide a mechanicalvibration source at 32.768 kHz for intervaltiming.

• This is one of several oscillation frequencies of quartz, determined by the crystal cut andmachining properties.



Ultrasound transducers for medical imagingapplications employ a synthetic piezoelectricceramic, most often lead-zirconate-titanate

(PZT).• The piezoelectric attributes are attained after aprocess of • Molecular synthesis,

• Heating,

• Orientation of internal dipole structures with an appliedexternal voltage,

• Cooling to permanently maintain the dipole orientation,and

• Cutting into a specific shape.



For PZT in its natural state, no piezoelectric

properties are exhibited; however, heating the

material past its “Curie temperature” (i.e., 3280

C to 3650 C ) and applying an external voltage

causes the dipoles to align in the ceramic.

• The external voltage is maintained until the material

has cooled to below its Curie temperature.

• Once the material has cooled, the dipoles retain their

alignment.



At equilibrium, there is no net charge on

ceramic surfaces.

• When compressed, an imbalance of chargeproduces a voltage between the surfaces.

• Similarly, when a voltage is applied between

electrodes attached to both surfaces, mechanical

deformation occurs.



The piezoelectric element is composed

of aligned molecular dipoles.



Under the influence of mechanicalpressure from an adjacent medium(e.g., an ultrasound echo), the element

thickness• Contracts (at the peak pressure amplitude),

• Achieves equilibrium (with no pressure) or

• Expands (at the peak rarefactional pressure),

• This causes realignment of the electrical dipoles toproduce positive and negative surface charge.





Surface electrodes (not shown)

measure the voltage as a function of

time.



An external voltage source applied to the

element surfaces causes compression or

expansion from equilibrium byrealignment of the dipoles in response to

the electrical attraction or repulsion

force.





Resonance Transducers

Resonance transducers for pulse echoultrasound imaging are manufactured tooperate in a “resonance” mode, whereby a

voItage (commonly 150 V) of very shortduration (a voltage spike of 1 msec) is applied,causing the piezoelectric material to initiallycontract, and subsequently vibrate at a natural

resonance frequency.• This frequency is selected by the “thickness cut,” dueto the preferential emission of ultrasound waveswhose wavelength is twice the thickness of thepiezoelectric material.



The operating frequency is determined

from the speed of sound in, and the

thickness of, the piezoelectric material.• For example, a 5-MHz transducer will have a

wavelength in PZT (speed of sound in PZT is

4,000 m/sec) of

mmmetersm

f

c80.0108

sec/105

sec/4000 4

6



A short duration

voltage spike causes

the resonance

piezoelectric elementto vibrate at its

natural frequency, f o,

which is determined

by the thickness of the transducer equal

to 1/A.



To achieve the 5-MHz resonance

frequency, a transducer element

thickness of ½ X 0.8 mm = 0.4 mm isrequired.

• Higher frequencies are achieved with thinner

elements, and lower frequencies with thicker

elements.• Resonance transducers transmit and receive

preferentially at a single “center frequency.”



Damping Block

The damping block, layered on the back of the

piezoelectric element, absorbs the backward

directed ultrasound energy and attenuates

stray ultrasound signals from the housing.

• This component also dampens he transducer vibration

in create an ultrasound pulse width a short spatial

pulse length, which is necessary to preserve detail

along he beam axis (axial resolution).









Dampening of the vibration (also knownas “ring-down”) lessens the purity of theresonance frequency and introduces abroadband frequency spectrum.• With ring-down, an increase in he bandwidth

(range of frequencies) of he ultrasound pulseoccurs by introducing higher and lower frequencies above and below the center (resonance) frequency.



The “Q factor” describes the bandwidth of the

sound emanating from a transducer as

where f o is the center frequency and the

bandwidth is the width of the frequencydistribution.

Bandwidth

f Q o



A “high Q” transducer has a narrow

bandwidth (i.e., very little damping) and

a corresponding long spatial pulselength.

• A “low Q” transducer has a wide bandwidth

and short spatial pulse length.



Imaging applications require a broadbandwidth transducer in order to achievehigh spatial resolution along the directionof beam travel.• Blood velocity measurements by Doppler

instrumentation require a relatively narrow-band transducer response in order topreserve velocity information encoded bychanges in the echo frequency relative to theincident frequency.



Continuous-wave ultrasound transducers

have a very high Q characteristic.

• While the Q factor is derived from the termquality factor, a transducer with a low Q does

not imply poor quality in the signal.



Matching Layer

The matching layer provides the interfacebetween the transducer element and the tissueand minimizes the acoustic impedance

differences between the transducer and thepatient.• It consists of layers of materials with acoustic

impedances that are intermediate to those of softtissue and the transducer material.

• The thickness of each layer is equal to one-fourth thewavelength, determined from the center operatingfrequency of the transducer and speed of sound in thematching layer.



For example, the wavelength of sound ina matching layer with a speed of soundof 2,000 m/sec for a 5-MHz ultrasoundbeam is 0.4 mm.• The optimal matching layer thickness is equal

to ¼ = ¼ x 0.4 mm = 0. 1 mm.• In addition to the matching layers, acoustic

coupling gel (with acoustic impedance similar tosoft tissue) is used between the transducer and theskin of the patient to eliminate air pockets thatcould attenuate and reflect the ultrasound beam.



Nonresonance (Broad-Bandwidth)

“Multifrequency” Transducers

Modern transducer design coupled with digital

signal processing enables “multifrequency or

“multihertz” transducer operation, whereby rhe

center frequency can be adjusted in he

transmit mode.

• Unlike the resonance transducer design, the

piezoelectric element is intricately machined into a

large number of small “rods,” and then filled with anepoxy resin to create a smooth surface.







The acoustic properties are closer to

issue than a pure PZT material, and thus

provide a greater transmission efficiencyof the ultrasound beam without resorting

to multiple matching layers.

• Multifrequency transducers have bandwidths

that exceed 80% of the center frequency.



Excitation of the multifrequencytransducer is accomplished with a short

square wave burst of 150 V with one tothree cycles, unlike the voltage spikeused for resonance transducers.

• This allows the center frequency to be

selected within the limits of the transducer bandwidth.



Likewise, the broad bandwidth responsepermits the reception of echoes within a

wide range of frequencies.• For instance, ultrasound pulses can beproduced at a low frequency, and the echoesreceived at higher frequency.



“Harmonic imaging” is a recentlyintroduced technique that uses this

ability;• lower frequency ultrasound is transmitted intothe patient, and the higher frequencyharmonics (e.g., two times the transmittedcenter frequency) created from the interactionwith contrast agents and tissues, are receivedas echoes.



Native tissue harmonic imaging has

certain advantages including greater

depth of penetration, noise and clutter removal, and improved lateral spatial

resolution.



Transducer Arrays

The majority of ultrasound systems

employ transducers with many individual

rectangular piezoelectric elementsarranged in linear or curvilinear arrays.

• Typically, 128 to 512 individual rectangular

elements compose the transducer assembly.

• Each element has a width typically less than half the wavelength and a length of several millimeters.



Two modes of

activation are used

to produce a beam.

• These are the “linear”(sequential) and

“phased”

activation/receive

modes.



Linear Arrays

Linear array transducers typically contain

256 to 512 elements; physically these

are the largest transducer assemblies.



In operation, the simultaneous firing of’ a

small group of 20 adjacent elements

produces the ultrasound beam.• The simultaneous activation produces a

synthetic aperture (effetive transducer width)

defined by the number of active elements.



Echoes are detected in the receive mode

by acquiring signals from most of the

transducer elements.• Subsequent “A-line” acquisition occurs by

firing another group of transducer elements

displaced by one or two elements.



A rectangular field of view is produced

with this transducer arrangement.

• For a curvilinear array, a trapezoidal field of view is produced.



Phased Arrays

A phased-array transducer is usually

composed of 64 to 128 individual

elements in a smaller package than alinear array transducer.

• All transducer elements are activated nearly

(but not exactly) simultaneously to produce a

single ultrasound beam.



By using time delays in the electrical activarion

of the discrete elements across the face of the

transducer, the ultrasound beam can be

steered and focused electronically withoutmoving the transducer.

• During ultrasound signal reception, all of the

transducer elements detect the returning echoes from

the beam path, and sophisticated algorithmssynthesize the image from the detected data.



BEAM PROPERTIES

The ultrasound beam propagates as alongitudinal wave from the transducer surface into the propagation medium,and exhibits two distinct beam patterns:• a slightly converging beam out to a distance

specified by the geometry and frequency of the transducer (the near field), and

• a diverging beam beyond that point (the far field).



For an unfocused,

single-element

transducer, the

length of the near

field is determined

by the transducer

diameter and thefrequency of the

transmitted sound.



For multiple transducer element arrays,an “effective” transducer diameter isdetermined by the excitation of a group

of’ transducer elements.• Because of the interactions of each of the

individual beams and the ability to focus and steer the overall beam, the formulasfor a single-element, unfocused transducer are not directly applicable.



The Near Field

The near field, also known as theFresnel zone, is adjacent to thetransducer face and has a converging

beam profile.• Beam convergence in the near field occurs

because of multiple constructive anddestructive interference patterns of the

ultrasound waves from the transducer surface.



Huygen’s principle describes a large

transducer surface as an infinite

number of point sources of soundenergy where each point is

characterized as a radial emitter.

• By analogy, a pebble dropped in a quiet pond

creates a radial wave pattern.



As individual wave

patterns interact, the

peaks and troughs from

adjacent sourcesconstructively and

destructively interfere,

causing the beam profile

to be tightly collimated in

the near field.



The ultrasound beam path is thus largely

confined to the dimensions of the active

portion of the transducer surface, withthe beam diameter converging to

approximately half the transducer

diameter at the end of the near field.



The near field length is dependent on the

transducer frequency and diameter:

• where d is the transducer diameter, r is the

transducer radius, and is the wavelength of

ultrasound in the propagation medium.

22

4

r d length field Near



In soft tissue, = 1.54mm/f(MHz), and

the near field length can be expressed

as a function of frequency:

mm

MHz mmd length field Near

22

54.14



A higher transducer

frequency (shorter

wavelength) will

result in a longer near field, as will a

larger diameter

element.



For a 10-mm-diameter transducer, the

near field extends 5.7 cm at 3.5 MHz

and 16.2 cm at 10 MHz in soft tissue.• For a 15-mm-diameter transducer, the

corresponding near field lengths are 12.8 and

36.4 cm, respectively.



Lateral resolution (the ability of the

system to resolve objects in a direction

perpendicular to the beam direction) isdependent on the beam diameter and is

best at the end of the near field for a

single-element transducer.

• Lateral resolution is worst in areas close to

and far from the transducer surface.



Pressure amplitude characteristics in thenear field are very complex, caused bythe constructive and destructive

interference wave patterns of theultrasound beam.• Peak ultrasound pressure occurs at the end of

the near field, corresponding to the minimumbeam diameter for a single-elementtransducer.



Pressures vary rapidly from peak

compression to peak rarefaction several

times during transit through the near field.

• Only when the far field is reached do the

ultrasound pressure variations decrease

continuously.



The far field is also known as theFraunhofer zone, and is where the beamdiverges.

• For a large-area single-element transducer,the angle of ultrasound beam divergence, 0,for the far field is given by

• where d is the effective diameter of thetransducer and is the wavelength; both musthave the same units of distance.

d

22.1sin



Less beam divergence occurs with high-

frequency, large-diameter transducers.

• Unlike the near field, where beam intensityvaries from maximum to minimum to

maximum in a converging beam, ultrasound

intensity in the far field decreases

monotonically with distance.



Focused Transducers

Single-element transducers are focused

by using a curved piezoelectric element

or a curved acoustic lens to reduce thebeam profile.

• The focal distance, the length from the

transducer to the narrowest beam width, is

shorter than the focal length of a non-focusedtransducer and is fixed.



The focal zone is defined as the region

over which the width of the beam is less

than two times the width at the focaldistance;

• Thus, the transducer frequency and

dimensions should be chosen to match the

depth requirements of the clinical situation.



Transducer Array Beam

Formation and Focusing

In a transducer array, the narrowpiezoelectric element width (typicallyless than one wavelength) produces a

diverging beam at a distance very closeto the transducer face.• Formation and convergence of the ultrasound

beam occurs with the operation of several or

all of the transducer elements at the sametime.



Transducer elements in a linear array that are

fired simultaneously produce an effective

transducer width equal to the sum of the widths

of the individual elements.• Individual beams interact via constructive and

destructive interference to produce a collimated

beam that has properties similar to the properties

of a single transducer of the same size.



With a phased-array transducer, thebeam is formed by interaction of theindividual wave fronts from each

transducer, each with a slight differencein excitation time.• Minor phase differences of adjacent beams

form constructive and destructive wave

summations that steer or focus the beamprofile.



Transmit Focus

For a single transducer or group of simultaneously fired elements in a linear array,

• The focal distance is a function of thetransducer diameter (or the width of the groupof simultaneously fired elements),

• The center operating frequency, and

• The presence of any acoustic lenses attachedto the element surface.



Phased array transducers and many

linear array transducers allow a

selectable focal distance by applyingspecific timing delays between

transducer elements that cause the

beam to converge at a specified

distance.



A shallow focal zone

(close to the

transducer surface)

is produced by firingouter transducers in

the array before the

inner transducers in

a symmetricalpattern.



Greater focal distances are achieved byreducing the delay time differencesamong the transducer elements,

resulting in more distal beamconvergence.• Multiple transmit focal zones are created by

repeatedly acquiring data over the same

volume, but with different phase timing of thetransducer array elements.



Receive Focus

In a phased array transducer, theechoes received by all of the individualtransducer elements are summed

together to create the ultrasound signalfrom a given depth.• Echoes received at the edge of the element

array travel a slightly longer distance than

those received at the center of the array,particularly at shallow depths.



Signals from individual transducer elements therefore must be rephased toavoid a loss of resolution when the

individual signals are synthesized into animage.• Dynamic receive focusing is a method to

rephase the signals by dynamically

introducing electronic delays as a function of depth (time).



At shallow depths, rephasing delays

between adjacent transducer elements

are greatest.



With greater depth,

there is less phase

shift, so the phase

delay circuitry for the

receiver varies as a

function of echo

listening time.



In addition to phased array transducers,

many linear array transducers permit

dynamic receive focusing among the

active element group.



Dynamic Aperture

The lateral spatial resolution of the linear array beam varies with depth, dependenton the total width of the simultaneously

fired elements (aperture).• A process termed dynamic aperture increases

the number of active receiving elements in thearray with reflector depth so that the lateral

resolution does not degrade with depth of propagation.



Side Lobes and Grating

Lobes



Side lobes are unwanted emissions of

ultrasound energy directed away from the main

pulse, caused by the radial expansion and

contraction of the transducer element duringthickness contraction and expansion.

• In the receive mode of transducer operation,

echoes generated from the side lobes are

unavoidably remapped along the main beam,which can introduce artifacts in the image.



In continuous mode operation, thenarrow frequency bandwidth of thetransducer (high Q) causes the side lobe

energy to be a significant fraction of thetotal beam.• In pulsed mode operation. the low Q

broadband ultrasound beam produces a

spectrum of acoustic wavelengths chatreduces the emission of side lobe energy.



For multielement

arrays, side lobe

emission occurs in a

forward directionalong the main

beam.



By keeping the individual transducer element widths small (less than half thewavelength) the side lobe emissions are

reduced.• Another method to minimize side lobes with

array transducers is to reduce the amplitudeof the peripheral transducer element

excitations relative to the central elementexcitations.



Grating lobes result when ultrasound energy is

emitted far off-axis by multielement arrays, and

are a consequence of the noncontinuous

transducer surface of the discrete elements.• The grating lobe effect is equivalent to placing a

grating in front of a continuous transducer

element, producing coherent waves directed at a

large angle away from the main beam.



This misdirected energy of relatively low

amplitude results in the appearance of

highly reflective, off-axis objects in the

main beam.



Spatial Resolution



In ultrasound, the major factor that limits

the spatial resolution and visibility of

detail is the volume of the acoustic

pulse.



The axial, lateral,

and elevational (slice

thickness)

dimensionsdetermine the

minimal volume

element.



Each dimension has an effect on the

resolvability of objects in the image.



Axial Resolution

Axial resolution (also known as linear,

range, longitudinal, or depth resolution)

refers to the ability to discern two closely

spaced objects in the direction of the

beam.

• Achieving good axial resolution requires that

the returning echoes be distinct withoutoverlap.



The minimal required separation

distance between two reflectors is one-

half of the spatial pulse length (SPL) to

avoid the overlap of returning echoes, as

the distance traveled between two

reflectors is twice the separation

distance.



Objects spaced

closer than ½ SPL

will not be resolved.



The SPL is the number of cycles emitted

per pulse by the transducer multiplied by

the wavelength.

• Shorter pulses, producing better axial

resolution, can be achieved with greater

damping of the transducer element (to reduce

the pulse duration and number of cycles) or with higher frequency (to reduce wavelength).



For imaging applications, the ultrasound

pulse typically consists of three cycles.

• At 5 MHz (wavelength of 0.31 mm), the SPL

is about 3 x 0.31 0.93 mm, which provides an

axial resolution of /2(0.93 mm) = 0.47 mm.



At a given frequency, shorter pulse

lengths require heavy damping and low

Q, broad-bandwidth operation.

• For a constant damping factor, higher

frequencies (shorter wavelengths) give better

axial resolution, but the imaging depth is

reduced.• Axial resolution remains constant with depth.



Lateral Resolution

Lateral resolution, also known as

azimuthal resolution, refers to the ability

to discern as separate two closely

spaced objects perpendicular to the

beam direction.



For both single

element transducers

and multielement

array transducers,the beam diameter

determines the

lateral resolution.



Since the beam diameter varies with the

distance from the transducer in the near

and far field, the lateral resolution is

depth dependent.

• The best lateral resolution occurs at the near

field—far field face.



At this depth, the effective beam

diameter is approximately equal to half

the transducer diameter.

• In the far field, the beam diverges and

substantially reduces the lateral resolution.



The typical lateral resolution for an

unfocused transducer is approximately 2

to 5 mm.

• A focused transducer uses an acoustic lens (a

curved acoustic material analogous to an

optical lens) to decrease the beam diameter

at a specified distance from the transducer.



With an acoustic lens, lateral resolution

at the near field-far field interface is

traded for better lateral resolution at a

shorter depth, but the far field beam

divergence is substantially increased.

• The lateral resolution of linear and curvilinear

array transducers can be varied.



The number of elements simultaneously

activated in a group defines an

“effective” transducer width that has

similar behavior to a single transducer

element of the same width.

• Transmit and receive focusing can produce

focal at varying depths along each line.



For the phased array transducer,

focusing to a specific depth is achieved

by both beam steering and

transmit/receive focusing to reduce the

effective beam width and improve lateral

resolution, especially in the near field.



Multiple transmit/receive

focal zones can be

implemented to maintain

Iateral resolution as afunction of depth.



Each focal zone requires separate pulse

echo sequences to acquire data.



One way to accomplish this is to acquire dataalong one beam line multiple times (dependingon the number of transmit focal zones), and

accept only the echoes within each focal zone,building up a single line of in-focus zones.

• Increasing the number of focal zones improvesoverall lateral resolution, but the amount of timerequired to produce an image increases andreduces the frame rate and/or number of scanlines per image.



Elevational Resolution

The elevational or slice-thickness

dimension of the ultrasound beam is

perpendicular to the image plane.

• Slice thickness plays a significant part in

image resolution, particularly with respect to

volume averaging of acoustic details in the

regions dose to the transducer and in the far

field beyond the focal zone.



Elevationalresolution isdependent on the

transducer elementheight in much thesame way that thelateral resolution isdependent on thetransducer elementwidth.



Slice thickness is typically the worst

measure of resolution for array

transducers.

• Use of a fixed focaI length lens across the

entire surface of the array provides improved

elevational resolution at the focal distance.



Unfortunately, this compromises

resolution due to partial volume

averaging before and after the

elevational focal zone (elevational

resolution quality control phantom image

shows the effects of variable resolution

with depth.



Multiple linear array transducers with fiveto seven rows, known as 1.5-dimensional (1.5-D) transducer arrays,

have the ability to steer and focus thebeam in the elevational dimension.



Elevational focusing is implemented withphased excitation of the outer to inner arrays to minimize the slice thickness

dimension at a given depth (Fig. 16-25).



By using subsequent excitations withdifferent focusing distances, multipletransmit focusing can produce smaller

slice thickness over a range of tissuedepths.

• A disadvantage of elevational focusing is aframe rate reduction penalty required for multiple excitations to build one image.



The increased width of the transducer array also limits positioning flexibility.

• Extension to full 2D transducer arrays with

enhancements in computational power willallow 3D imaging with uniform resolutionthroughout the image volume.



IMAGE DATA ACQUISITION

Understanding ultrasonic image

formation requires knowledge of

ultrasound production, propagation, and

interactions.

• Images are created using a pulse echo

method of ultrasound production and

detection.



• Each pulse transmits directionally into the

patient, and then experiences partial

reflections from tissue interfaces that create

echoes, which return to the transducer.



Image formation using

the pulse echo approach

requires a number of

hardware components:

• the beam former,

• pulser,

• receiver,

• amplifier,

• scan converter/imagememory, and

• display system.



Ultrasound equipment is

rapidly evolving toward

digital electronics and

processing, and current

state-of-the-art systems

use various combin-

ations of analog and

digital electronics.



Beam Formers

The beam former is responsible for generating

the electronic delays for individual transducer

elements in an array to achieve transmit and

receive focusing and, in phased arrays, beamsteering.

• Most modern, high-end ultrasound equipment

incorporates a digital beam former and digital

electronics for both transmit and receivefunctions.



A digital beam former controls application-

specific integrated circuits (ASICs) that

provide transmit/receive switches, digital-to-

analog and analog-to-digital converters, andpreamplification and time gain compensation

circuitry for each of the transducer elements

in the array.



Major advantages of digital acquisition

and processing include the flexibility to

introduce new ultrasound capabilities by

programmable software algorithms and

to enhance control of the acoustic beam.



Pulser

The pulser (also known as the transmitter)

provides the electrical voltage for exciting the

piezoelectric transducer elcnwnts, and controls

the output transmit power by adjustment of theapplied voltage.

• In digital beam-former systems, a digital-to analog-

converter determines the amplitude of the voltage. An

increase in transmit amplitude creates higher intensitysound and improves echo detection from weaker

reflectors.



A direct consequence is higher signal-to-noiseratio in the images, but also higher power deposition to the patient. User controls of theoutput power are labeled “output,” “power,”

“dB,” or “transmit” by the manufacturer. Insome systems, a low power setting for obstetric imaging is available to reduce power deposition to the fetus. A method for indicatingoutput power in terms of a thermal index (TI)

and mechanical index (MI) is usually provided(see section 16.1 1).

Documents

Lecture Ultrasound Beams