Piezoelectric Effect  Sound waves striking a PZ material produce an electrical signal  Can be used to detect sound (and echoes)! Pierre Curie 1880.

Piezoelectric Effect  Sound waves striking a PZ material produce an electrical signal  Can be used to detect sound (and echoes)!

Reverse Piezoelectric Effect  Applying an electrical signal causes the PZ element to vibrate  Produces a sound wave

Transducer  Device that converts signals, or energy, from one form to another  Many types of transducers exist –Pressure transducers –Air flow transducers, etc.  Ultrasound transducers convert electrical signals to sound waves, and vice versa.

Ultrasound Transducer Materials  Quartz (naturally piezoelectric) –First used as a stable resonator in time measurement devices –Used in some laboratory ultrasound applications  Most current applications use piezoelectric ceramics (ie, lead zirconate titanate; barium titanate) –Lower “Q” (good for short pulses) –Good sensitivity –Many shapes are possible Miniature quartz tuning fork; 32,768 Hz.

Polarizing a Piezoelectric Element  Most ultrasound transducer materials are not ‘naturally’ piezoelectric –Lead zirconate titanate –Microscopic crystals, randomly oriented  Must be polarized –Heat to ~350 o C (Curie Temperature) –Apply strong voltage across crystal –Cool while voltage is still applied

Polarization

Single Element Transducers  Uses –Simple A-mode machines –Mechanical scanning transducers  The design serves as a useful example of general construction methods

Single element transducer construction

Ultrasound Transducers Piezoelectric (PZT) ceramic elements Matching layers, lens Backing layer

½ wavelength resonance  Resonance frequency corresponds to the thickness = ½ wavelength  Speed of sound in Piezoelectric material ~ 4,620 m/s  What thickness is required for a 3 MHz frequency transducer? d

½ wavelength resonance  Resonance frequency corresponds to the thickness = ½ wavelength  Speed of sound in Piezoelectric material ~ 4,620 m/s  What thickness is required for a 3 MHz frequency transducer? d

½ wavelength resonance  Resonance frequency corresponds to the thickness = ½ wavelength  Speed of sound in Piezoelectric material ~ 4,620 m/s  What thickness is required for a 5 MHz frequency transducer? d

Resonance Frequency

Backing (Damping) Layer  Need short duration pulses for decent axial resolution (we will discuss this later)  Backing layer helps to reduce vibrations of the element following excitation –Like placing your hand on a bell to stop the ringing!

Pulse Bandwidth A pulse of sound contains many frequencies (analogous to white light consisting of many colors) Range of frequencies quantified by the frequency “bandwidth” of the pulse Short pulses, very broad bandwidths Longer pulses, narrower bandwidths

Multi Herz

Matching Layers  Thin layer of material –¼ wavelength thick –Impedance is between that of the element (quite high) and that of tissue  Provides better sound transmission from the transducer-patient-transducer  Improves sensitivity

Broadband Transducers STI-Ultrasound.com Multiple matching layers (analogous to coatings on optical lenses) Center Freq: - 8 MHz Bandwidth: MHz - 82%

Pulsed Spectra vs transducer bandwidth Multi-herz The transducer design enables operation at various frequencies. Each pulse is associated with a range of frequencies.

Multi-frequency operation  Modern transducers can operate over a range of frequencies (sort of like the speakers of a stereo sound system)  By changing the frequency of the signal applied to the transducer, and by tuning the receiver, the center frequency can be changed

Spatial Detail in Ultrasound - depends on beam width, focus (lens); - depends on pulse duration (axially); - depends on slice thickness.

Axial Resolution

 Defined as the minimum distance between 2 reflectors along the beam direction, such that the reflectors can be distinguished on the display. Beam Direction

Axial Resolution Beam Direction

Axial resolution depends on the “pulse duration”  Pulse duration is the amount of time the transducer oscillates during each transmit pulse  The shorter the pulse duration, the better the axial resolution

Axial Resolution 2

Axial vs Freq

GE Logiq 700 Horizontal spacing: 2 mm, 1 mm, 0.5 mm, 0.25 mm Vertical Spacing: 2 mm, 1 mm, 0.5 mm, 0.25 mm 4 MHz 12 MHz

27.Axial resolution is determined by: A. pulse duration B. beam width C. beam diameter D. pulse repetition period

28. Axial resolution is most affected by changes in: A. beam frequency and beam diameter B. beam intensity and beam focusing C. beam frequency and pulse damping D. beam focusing and beam diameter

29. A decrease in pulse duration results in ________ frequency bandwidth. A. a wider B. a narrower C. an equivalent D. elimination of

Lateral Resolution and Beam Width Linear Array Poor

Lateral Resolution and Beam Width Linear Array Excellent

Lateral resolution depends on the “beam width”  Lateral resolution is how closely spaced 2 reflectors can be, along a line perpendicular to the ultrasound beam, and still be distinguished on the display  It depends of the beam width at depth considered  The narrower the beam, the better the lateral resolution

Christian Huygens ( ) Dutch Physicist Beam Physics  Huygen’s Principle –“All points on a propagating sound wave serve as the source of spherical wavelets; the total wave at any location (and time) is the sum of these wavelets.” “Point sources”

Interference  2 sources: –Final signal can be large or small, depending on the relative phase of the waves.  Many sources –Final signal can be large or small, depending on relative phases of all waves.

Huygens's Principle: all points on a propagating wavefront serve as the source of spherical secondary wavelets, such that the total wave at any location (and time) is the sum of these wavelets. 1 point source; spherical wave “Point sources”

Huygens's Principle: all points on a propagating wavefront serve as the source of spherical secondary wavelets, such that the total wave at any location (and time) is the sum of these wavelets. 2 point sources; wave interference Interference creates minima and maxima

Unfocused Transducer Beam

Beam properties depend on width of aperture and the wavelength (frequency); NFL 2.5 MHz 10 mm 5.0 MHz

Unfocused Transducer Beam a= transducer radius d=2a=transducer diameter

Unfocused Transducer Beam

NFL=D_squared over 4 lambda

NFL for 2 MHz ( =0.77 mm) If the diameter doubles, NFL increases by 4. NFL for 2 MHz ( =0.77 mm) DiameterNFL 1 cm3.2 cm 2 cm13 cm 4 cm52 cm Assume D = 1 cm=10mm

NFL for 2 MHz ( =0.77 mm) DiameterNFL 1 cm3.2 cm 2 cm13 cm 4 cm52 cm NFL for 4 MHz ( =0.385 mm) DiameterNFL 1 cm6.4 cm 2 cm26 cm 4 cm104 cm If the diameter doubles, NFL increases by 4. If the frequency doubles, NFL doubles. If the diameter doubles, NFL increases by 4.

Divergence in far field  (The ‘sin’ is a function of the angle)  Larger diameter diverges less  Higher frequency (smaller wavelength) diverges less

What is the divergence angle for a 2 cm diameter, 3 MHz transducer?

What is the divergence angle for a 2 cm diameter, 6 MHz transducer?

Dependence on frequency

Dependence on diameter

Focusing, Methods  Focusing reduces the beam width in the focal zone  Methods –Lens –Curved element –Electronic

Focal Definitions

2.5 MHz 20 mm 5.0 MHz In Most Applications, Beams Are Focused - curved element - lens - electronic (arrays) Improves lateral resolution near the focal distance Higher frequencies produce narrower beams

2.5 MHz 10 mm 20 mm 5.0 MHz - Previous diagrams exhibit sidelobes - Must be eliminated for good image quality - Pulsing reduces (or even eliminates) side lobes 5.0 MHz CW Short pulse (50% bw)

d F

24. In order to focus a sound beam relatively far away from the transducer, it is advantageous to ______ of the element. A. increase the thickness B. increase the diameter C. increase the temperature D. decrease the diameter

25. Lateral resolution is determined by: A. beam length B. pulse duration C. pulse length D. beam width

Array Transducer  “Scanhead” containing many small PZT elements  Element, along with a transmit-receive circuit in the machine is a channel.  128 channels are common.

Beam Forming (Transmit) Group also permits electronic beam steering and electronic focusing.

Curvilinear

Phased Array

Linear-Phased ( “Virtual Convex”)  Linear array –Rectangular FOV, defined by transducer footprint  VC adds beam steering to expand imaged region at edges

Annular

Multiple Tx Focus

4 Tx focal zones 12 Hz frame rate

Focus During Reception

Dynamic Receive Focusing Focusing delays change in real time. (Not adjusted by the sonographer.)

Dynamic Aperture

Side Lobes, Grating Lobes - Both are forms of off axis sound transmission - Both lead to undesirable effects  Side Lobes: part of the beam pattern from any transducer (single element, array) –Reduce using short duration, broad band pulses –Reduce using apodization  Grating Lobes: result from having the transducer surface cut into small elements (think of grating cheese) –Reduce using very closely spaced elements

Spatial Resolution Typical values  Axial: 0.1 to 1 mm  Lateral: 0.2mm to 10mm

Spatial Pulse Length

Transducer “Q”  Q stands for “quality factor”  A high Q system is one that rings at a pure tone  A low Q system is well damped  Low Q is needed for short duration pulses Miniature quartz tuning fork; 32,768 Hz.

Slice Thickness (Conventional)

 2 and 4 mm diameter spherical targets;  Low scatter level;  Target centers are co - planar. Spherical Lesion Phantom

Conventional Transducer

Annular Image-plane beam width = slice thickness Electronic focusing applies to both dimensions. Conventional Phased and linear Electronic focusing applies to lateral only.

1 ½ D Probe (matrix probe) 100 – 200 elements in lateral direction 5 – 7 rows

Matrix Transducer

1 ½ D (Matrix) Transducer Matrix Conventional

Use of “Matrix” or “1 ½ D” Arrays  Advantages: –Better control of slice thickness  Disadvantages –Size (older models) –Cost –Complexity

2-D Array One of the transducer types used in 3-D imaging

Volumetrics - Image Formats “Traditional” “C-scans” (constant depth)

Use in 2-D arrays (Phillips) 2400 element 2-D array Possible Scan Planes

Use in 2-D arrays (Phillips) 2400 element 2-D array

Applications of 3-D  Visualization of coronal planes  Volume calculations  OB Imaging –facial and other anatomical anomalies –detailed information on orientation  Improved visualization of vasculature with 3-D color flow

Important features of arrays  Enable electronic scanning –Time delays between elements (phased arrays) –Electronic switching groups of elements (linear and curvilinear)  Enable electronic focusing

Type of transducer Method used for beam focusing Method used for scanning Linear arrayElectronic Curvilinear arrayElectronic Phased arrayElectronic Annular arrayElectronicMechanical Single elementMechanical lensMechanical

Homework  Calculate the NFL for a 3 cm diameter transducer operating at 5 MHz. Assume c=1540 m/s.  Calculate the resonance frequency of a piezoelectric ceramic material whose thickness is 0.25mm.