Đầu dò Siêu âm Transducers Lecture ultrasound beams

BEAM PROPERTIES The ultrasound beam propagates as a longitudinal wave from the transducer surface into the propagation medium, and exhibits two distinct beam patterns: • a slightly conv

Transducers

 Ultrasound is produced and detected with a transducer, composed of one or more ceramic elements with

electromechanical (piezoelectric)

properties

• The ceramic element converts electrical

energy into mechanical energy to produce ultrasound and mechanical energy into

electrical energy for ultrasound detection

 Over the past several decades, the transducer assembly has evolved considerably in design, function, and capability, from a single-element resonance crystal to a broadband transducer array of hundreds of individual elements

transducer has major components including the

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 charge distribution

 A potential difference (voltage) is created across the element with one surface

maintaining a net positive charge and

one 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 the

mechanical expansion and contraction of the transducer element

 There are natural and synthetic

piezoelectric materials

• An example of a natural piezoelectric material

is quartz crystal, commonly used in watches and other time pieces to provide a mechanical vibration source at 32.768 kHz for interval

timing

quartz, determined by the crystal cut and machining properties.

 Ultrasound transducers for medical imaging applications employ a synthetic piezoelectric ceramic, most often lead-zirconate-titanate

 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

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 charge produces a voltage between the surfaces

electrodes attached to both surfaces, mechanical deformation occurs.

 The piezoelectric element is composed

of aligned molecular dipoles

 Under the influence of mechanical

pressure 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),

produce 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 by

realignment of the dipoles in response to the electrical attraction or repulsion

force

Resonance Transducers

 Resonance transducers for pulse echo

ultrasound imaging are manufactured to

operate in a “resonance” mode, whereby a

voItage (commonly 150 V) of very short

duration (a voltage spike of ≈ 1 µ sec) is

applied, causing the piezoelectric material to initially contract, and subsequently vibrate at a natural resonance frequency

to the preferential emission of ultrasound waves

whose wavelength is twice the thickness of the

 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

mm meters

m f

c

80 0 10

8 sec

/ 10 5

sec /

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 is

required

• Higher frequencies are achieved with thinner elements, and lower frequencies with thicker elements

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

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 known

as “ring-down”) lessens the purity of the resonance frequency and introduces a broadband frequency spectrum

• With ring-down, an increase in he bandwidth (range of frequencies) of he ultrasound pulse occurs 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 frequency

distribution.

Bandwidth

f

 A “high Q” transducer has a narrow

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

a corresponding long spatial pulse

length

• A “low Q” transducer has a wide bandwidth and short spatial pulse length

 Imaging applications require a broad

bandwidth transducer in order to achieve high spatial resolution along the direction

of beam travel

• Blood velocity measurements by Doppler

instrumentation require a relatively

narrow-band transducer response in order to

preserve velocity information encoded by

changes in the echo frequency relative to the incident frequency.

 Continuous-wave ultrasound transducers have a very high Q characteristic

• While the Q factor is derived from the term

quality factor, a transducer with a low Q does

not imply poor quality in the signal.

Matching Layer

 The matching layer provides the interface

between the transducer element and the tissue and minimizes the acoustic impedance

differences between the transducer and the

patient

impedances that are intermediate to those of soft

tissue and the transducer material

• The thickness of each layer is equal to one-fourth the wavelength, determined from the center operating frequency of the transducer and speed of sound in the matching layer

 For example, the wavelength of sound in

a matching layer with a speed of sound

of 2,000 m/sec for a 5-MHz ultrasound beam is 0.4 mm

• The optimal matching layer thickness is equal

to ¼ λ = ¼ x 0.4 mm = 0 1 mm

coupling gel (with acoustic impedance similar to soft tissue) is used between the transducer and the skin of the patient to eliminate air pockets that

could attenuate and reflect the ultrasound beam.

piezoelectric element is intricately machined into a

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

 The acoustic properties are closer to

issue than a pure PZT material, and thus

provide a greater transmission efficiency

of the ultrasound beam without resorting

to multiple matching layers

• Multifrequency transducers have bandwidths that exceed 80% of the center frequency.

 Excitation of the multifrequency

transducer is accomplished with a short square wave burst of 150 V with one to three cycles, unlike the voltage spike

used for resonance transducers

• This allows the center frequency to be

selected within the limits of the transducer bandwidth

 Likewise, the broad bandwidth response permits the reception of echoes within a wide range of frequencies

• For instance, ultrasound pulses can be

produced at a low frequency, and the echoes received at higher frequency

 “Harmonic imaging” is a recently

introduced technique that uses this

ability;

• lower frequency ultrasound is transmitted into the patient, and the higher frequency

harmonics (e.g., two times the transmitted

center frequency) created from the interaction with contrast agents and tissues, are received

as 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 elements

arranged in linear or curvilinear arrays

• Typically, 128 to 512 individual rectangular

elements compose the transducer assembly

the wavelength and a length of several millimeters

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.

 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 without

moving the transducer

transducer elements detect the returning echoes from the beam path, and sophisticated algorithms

synthesize the image from the detected data.

BEAM PROPERTIES

 The ultrasound beam propagates as a longitudinal 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 the frequency of the transmitted sound

 For multiple transducer element arrays,

an “effective” transducer diameter is

determined 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 formulas for a single-element, unfocused transducer are not directly applicable.

The Near Field

 The near field, also known as the

Fresnel zone, is adjacent to the

transducer face and has a converging beam profile

• Beam convergence in the near field occurs because of multiple constructive and

destructive 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 sound

energy 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 sources

constructively 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, with

the 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 λ is the wavelength of ultrasound in the propagation medium

λ λ

2 2

4

r

d length

field

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

the near field length can be expressed

as a function of frequency:

( ) ( )

( )mm

MHz mm

d length

field Near

2 2

54 1

4 ×

=

 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) is dependent 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 the near field are very complex, caused by the constructive and destructive

interference wave patterns of the

ultrasound beam

• Peak ultrasound pressure occurs at the end of the near field, corresponding to the minimum beam diameter for a single-element

transducer

 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 the

Fraunhofer zone, and is where the beam diverges

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

d

λ

θ 1 22 sin =

 Less beam divergence occurs with frequency, large-diameter transducers

high-• Unlike the near field, where beam intensity varies 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 the beam profile

• The focal distance, the length from the

transducer to the narrowest beam width, is

shorter than the focal length of a non-focused transducer 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 focal

distance;

• 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 narrow

piezoelectric element width (typically less than one wavelength) produces a

diverging beam at a distance very close

to the transducer face

• Formation and convergence of the ultrasound beam occurs with the operation of several or all of the transducer elements at the same

time

 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

destructive interference to produce a collimated beam that has properties similar to the properties

of a single transducer of the same size