Saudi Board of Radiology: Physics Refresher CourseKostas Chantziantoniou, MSc2, DABRHead, Imaging Physics SectionKing Faisal Specialist Hospital & Research CentreBiomedical Physics DepartmentRiyadh, Kingdom of Saudi ArabiaUltrasound Transducers

Ultrasound Pulse Production and ReceptionA transducer is a device that can convert one form of energy into another. Ultrasoundtransducers are used to convert an electrical signal into ultrasonic energy that can betransmitted into tissue, and to convert ultrasonic energy reflected back from the tissueinto an electrical signal.The general composition of an ultrasound transducer is shown below: the most important component is a thin

piezoelectric (crystal) element located near the face of the transducer the front and back face of the element is coated

with a thin conducting film to ensure good contact with the two electrodes the outside electrode is grounded to protect the

patient from electrical shock an insulated cover is used to make the device

watertight an acoustic insulator made of cork or rubber is

used to prevent the passing of sound into the housing (i.e.: reduces transducer vibrations) the inside electrode is against a thick backing block that absorbs sound waves

transmitted back into the transducer

Matching LayerA matching layer of material is placed on the front surface of the transducer to improvethe efficiency of energy transmission into the patient. The material used has animpedance in between that of the transducer and tissue; and it has a thickness one forththe wavelength of sound in the transducer crystal material (quarter wave matching).

Creating a sound wave from an electrical pulse

When a positive voltage (A) is applied across the surface of the crystal, it creates an electric field across the crystal surface which cause the molecules (dipoles) in the crystal to realign and thus changing the shape (width) of the crystal.When the voltage polarity is changed from positive to negative, there is a point in timewhen the electric field across the crystal is zero (at voltage equal to zero) and the crystalrelaxes (B). When the voltage polarity is reversed (i.e.: negative) the crystal realigns once again and changes its width once again (C). ABCPositiveNegativeVoltage PulseTime

The net effect the alternating voltage pulse has on the crystal is to make it oscillate backand forth about its width. This change in shape of the crystal increases and decreasesthe pressure in front of the transducer, thus producing ultrasound waves. Ultrasound wave directionUltrasound wave directionCompression region created when crystalsurface is expanding (more pressure on surface)Rarefaction region created when crystalsurface is contracting (less pressure on surface)wavefront diagram

Creating an electrical signal from a sound wave

When the compression region (A) of the ultrasound wave is incident on the front surface of the crystal, it induces a high pressure region on the surface which in turn compresses the crystal. This cause the molecules in the crystal to re-align and induce an electric field across the crystal which generates an electrical voltage signal that is proportional to the intensity of the compression region.ABWhen the rarefaction region (B) of the ultrasound wave is incident on the frontsurface of the crystal, it induces a low pressure region on the surface which in turnrelaxes the crystal. Compression region compresses crystalsurface (more pressure on surface)Rarefaction region relaxes crystal surface(less pressure on surface)wavefront diagram

The net effect the ultrasonic wave has on the crystal is to make it oscillate backand forth about its width. This change in shape of the crystal induces a voltage signalthat also varies in time and in amplitude. NOTEA transducer can function both as a transmitter and a receiver of ultrasound energy, butit can not transmit and receive at the same time.Transmitter ModeReceiver Mode

Transducer CharacteristicsTransducer Thickness

A transducer can be made to emit sound of any frequency by driving it (in continuousmode) with an alternating voltage of that frequency. However, a transducer vibratesmost violently and produces the largest output (pressure amplitude) of sound when = 2 twhere the is wavelength of sound and t is the thickness of the piezoelectric crystal.The frequency of the emitted sound waves is then given by

frequency = v = v 2 t

where v is the speed of sound in the piezoelectric crystal. operating frequency crystal thickness

Why should the transducer thickness be equal to 1/2 of the desired wavelength?When the piezoelectric element is driven by a alternating voltage the crystalvibrates (i.e.: the width of the crystal moves back and forth). The front face of the crystal emits sound both in the forward and backward directions as does the back surface.Front surfaceBack surfaceThickness (t)ABCD wave front (A) will get absorbed by the transducers backing material wave front (D) will enter into the patient the wave front (C) is reflected at the back face of the disk, and by the time it joins

wave front (D), it has traveled an extra distance 2t. If this distance equals a wavelength the wave fronts (D) and (C) reinforce for they are in phase, and constructive interference or resonance occurs. if wave fronts (D) and (C) are not in phase, then there will be some destructive

interference same reasoning applies to wave front (B)

PatientBacking Block

Constructive Interference(waves A & B add to form a new wave of amplitude A + B)Destructive Interference(waves A & B add to form a new wave of amplitude A + B = 0)If wave B is wave front (C) and wave F is wave front (D) then we see that when transducer thickness is one half the wavelength, both wave fronts are in phase and constructive interference (ie: their individual amplitudes add) occurs.

changing the thickness of the crystal changes the frequency but not the ultrasound

amplitude (determined by applied voltage waveform) or speed (determined by piezoelectric crystal) high frequency transducers are thin and low frequency transducers are thicker to change the frequency one has to change the transducer

Resonant Frequency

The frequency at which the transducer is the most efficient as a transmitter of soundis also the frequency at which it is most sensitive as a receiver of sound. Thisfrequency is called the natural or resonant frequency of the transducer.

the thickness and the material (i.e.: speed of sound in the crystal) of the piezoelectric

crystal determines the resonant frequency of the transducer transducers crystals are normally manufactured so that their thickness (t) is equal to

one-half of the wavelength () of the ultrasound produced by the transducerBandwidth

The range of frequencies in the emitted ultrasound wave is called the bandwidth and is defined to be the full width of the frequency distribution at half maximum (FWHM).Resonant Frequency bandwidth SPL

Continuous voltage waveform Pulsed voltage waveformContinuous waveformcan be represented bya single sine wave (onefrequency), thus frequencydistribution is very narrowPulsed waveformcan be represented bythe sum of many sinewaves each of differentfrequency, thus frequencydistribution is wide Frequency distribution of emitted ultrasound wave

Q-factorThe Q-factor of a transducer system describes the shape of the frequency distribution(response curve) and is defined as where f0 is the resonance frequency, f1 is the frequency below resonance at whichintensity is reduced by half and f2 is the frequency above resonance at whichintensity is reduced by half high Q transducers produce relatively

pure frequency spectrums and low Q transducers produce a wider range of frequencies short pulses correspond to reduce Q

values and vice versa bandwidth Q-factor

Pulse Ultrasound ModeBecause a transducer can be a transmitter and a receiver of ultrasonic energy, it clearly stands to reason that a continuous voltage waveform can not be used. If such a waveform was used, the transducer would always function as a transmitter. Since the internally generated sound waves are stronger than the returning echoes, the returning signal is lost in the noise of the system. To over come this problem, most transducers are used in a pulse mode where the voltage waveform consists of many pulses each separated by a fixed distance and time. The transducer functions as a transmitter during pulse excitation and as a receiver during the time interval between pulses.Voltage waveformUltrasound pulses produced by transducerNOTE most transducers are designed to have short pulses (improved resolution) with low

Q values (broad bandwidth - desirable in order to receive echoes of many different frequencies)

Blocks of damping material, usually tungsten/rubber in a epoxy resin, are placed behindtransducers to reduce (or dampen) the vibrations and to shorten pulses. the exponential decay of the pressure wave over time is called damping if damping is heavy the transducer has a short ring down time and is said to have a

low Q value a transducers with lighter damping is said to have a high Q value

Pulse Repetition Frequency (PRF) Pulse Repetition Period (PRP) PRF is the number of pulses occurring in 1 second

PRP is the time from the beginning of one pulse to the beginning of the next pulse

Spatial Pulse Length (SPL)SPL is the length of space over which a single pulse occurs, and is defined as SPL = n where n is the number of cycles in the pulse and is the wavelength. NOTEAn important parameter when considering axial resolution

Pulse Duration (PD)PD is the time it takes for a single pulse to occur and is defined asPD = n Twhere n is the number of cycles in the pulse and T is the period. Duty Factor (DF)DF is the fraction of time that ultrasound generation (in the form of pulses) is ON, andis defined as:DF = PD PRP

Ultrasound Beam CharacteristicsIn order to understand the beam characteristics of ultrasound we have to revisit ourview of wave front (compression region) generation. A piezoelectric crystal surfaceactually behaves more like a series of vibrating points and not as the piston-likesurface that we have implied previously.simplified modelmore accurate model the compression waves are not uniform (at least not close to the crystal surface) each vibrating point produces multiple concentric rings or waves that eventually form

a continuous front as they reinforce each other along a line parallel to the surface of the crystal the distance at which the waves become synchronous depends on their wavelength,

the shorter the wavelength the close the front forms to the surface of the transducer

Fresnel Zone (Near Field)The length of the Fresnel zone is given by: d2 4 where d is the diameter of the transducer and is the wavelength. the Fresnel zone increases with transducer size and frequency (lower wavelength) ultrasound imaging normally uses the Fresnel zone but not the Fraunhofer zone in

which resolution is poor beam intensity falls off because of attenuation

Fraunhofer Zone (Far Field)The angle of divergence of the Fraunhofer zone is given by:

sin(q) = 1.22 dwhere d is the diameter of the transducer and is the wavelength.q beam intensity falls of due to attenuation and beam divergence angle of divergence increases with decreasing transducer diameter and frequency no useful imaging can be made in this region

Side LobesSide lobes are small beams of greatly reduced intensity that are emitted at angles tothe primary beam and they often cause image artifacts.

the origin of these lobes are due from radial vibrations from the edges of the

transducer

Grating LobesGrating lobes result when ultrasound energy is emitted far off-axis by multi-element arrays, and are a consequence of the non-continuous transducer surface of the discrete elements.

this misdirected energy of relatively low amplitude results in the appearance of

highly, off-axis objects in the main beam

Axial (Linear, Range, Longitudinal, Depth) ResolutionAxial resolution is the ability to separate two objects lying along the axis of the beamand is determined by the spatial pulse length (SPL).Case: SPL < XObjects a and b separate by distance XObjects resolvableObjects not resolvableCase: SPL = 2Xlimiting resolution = SPL = n where n is the number of cycles and 2 2 is the wavelength

because axial resolution is depended to the SPL then it is also depended on pulse

frequency and duration (PD) with a typical wavelength of 0.3 mm and three cycles per pulse, the axial resolution

is approximately 0.5 mm axial resolution deteriorates with increasing pulse length, decreasing frequency and

increasing wavelength the use of damping transducers (low Q) produces short pulses that improves axial

resolution frequency axial resolution (improved)cycle/pulse axial resolution SPL axial resolution (worsened)

Lateral (Azimuthal) ResolutionLateral resolution is the ability to separate two adjacent objects and is determined bythe width of the beam and line density. lateral resolution is equal to beam width in the scan plane lateral resolution is best in the Fresnel zone where ultrasound waves are parallel lateral resolution is generally a few millimeters

Object separation wider than beam widthObject separation narrower than beam width beam width lateral resolution (improved)

Elevation Resolution (Slice Thickness)Elevation resolution is the dimensions of the ultrasound beam perpendicular to theimage plane and depends on the transducer element height in much the same way that the lateral resolution is dependent on the transducer element width.

Focused TransducersHigh frequency beams have two advantages over low-frequency beams: (1) axial resolution is superior; and (2) the Fresnel zone is longer

It would seem logical to use high frequencies for all imaging. High frequencies however, have a major drawback related to penetration. Tissue absorption increaseswith increasing frequency, so a relatively low frequency beam is required to penetrate thick parts.

It would then seem logical to use low frequency transducers and to increase the size of the transducer to keep the beam coherent for sufficient depth to reach the point of interest (longer Fresnel zone). Although larger transducers improve coherence they deteriorate lateral resolution. The dilemma is at least partially resolved with the use focused transducers.

NOTE focused transducers reduce beam width which improves lateral resolution they also concentrate beam intensity thereby increasing penetration and echo

intensity thus improving image quality

the focal zone is the region over which the beam is focused the focal length is the distance from the transducer to the centre of the focal zone the depth of focus is the distance over which the beam is in a reasonable focus a small diameter transducer has a shorter focal zone and spreads more rapidly in

the far zone most diagnostic transducers are focused, which is achieved using a either a curved

piezoelectric crystal, an acoustic lens or electronics (phased arrays)

A focused transducer produces a narrower beam at the focal zone and, therefore, hasbetter lateral resolution than an unfocused transducer of the same size.

In reality we have:It is important to realize, that even for flat, unfocused transducer elements, there issome beam narrowing or focusing.

Curved Piezoelectric CrystalAcoustic LensElectronic Focusing (Phased Array)