PZT and ultrasound arrays

what must an ultrasound probe be able to do and how does it do it?

1. generate sound waves: converts electric signal → sound waves

2. detect incoming sound waves: converts sound wave → electrical signal

uses piezoelectric material

when was PZT effect discovered

1880

types of PZ effects

1. direct piezoelectric effect: when a substance is subjected to mechanical stress it produces an electric charge → 10nM deformation = 100mV charge

2. converse piezoelectric effect: applying a potential difference over a material results in compression of extension of the material depending on polarity

→ 100mV = 10nM

what makes a material PZE

when a material is relaxed the crystal structure has a perfectly balanced charge of 0

when the structure is deformed:

• crystal structure changes to have more -ve charge carriers closer to one side and +ve charge carriers on the other (net amount of +ve and -ve particle changes)

• produces a dipole moment (separation of charges)

• results in a PD

types of PSE materials

• Quartz: is naturally occurring but is weakly piezoelectric

• Piezoelectric ceramics: requires poling to become piezoelectric → made from ferroelectric materials

  • Ex: PZT, PZT5A, PZT4

• Piezoelectric polymers (PVDF): is a thin film material with an acoustic impedance that closely matches that of tissue

• Piezocomposites: are comprised of pieces of PZT embedded into a polymer material in order to have improved impedance match to tissue

what are the properties of PZE materials

1. transmission/strain constant (D)

2. receiving/voltage constant (G)

3. electromechanical coupling factor (k)

what is the transmission/strain constant

units?

it is a measure of how good the material is at generating US

• quantifies the resulting mechanical strain a material undergoes when an electric field is applied

• measured in m/v

what is the receiver/voltage constant

units?

it is a measure of how efficient a material is at receiving US and producing a resulting voltage change/image

• measured in electric field per unit applied stress (V.m/N)

what is the electromechanical coupling factor

measure of effectiveness in converting electrical energy ←→ mechanical energy

PZT vs PVDF

PZT:

• high d → good producer of US

• low g → not as good of a receiver

• high k → good conversion efficiency

• large impedance missmatch to water → narrow bandwidths/high q (Q = 500)

PVDF:

• LOW D → poor US transmitter (rarely used as such)

• high g → good US receiver

• low k: poor conversion efficiency

• good impedance matching to water → broad bandwidth/low q (Q = 3)

what are ferroelectric materials

materials with a permanent electric polarisation which can be reversed by applying an external electric field

difference between PZE materials and ferroelectric materials

PZ does not have a permanent pole but ferroelectric materials do

what is poling

• naturally occurring PZE materials have a weak piezoelectric effect due to disorderes polycrystaline structure

• crystal structure contains several domains with a net dipole moment in different directions → dipole moments cancel each other → weak PZE effect

poling:

1. heat to 200c (for PZT) or above curie temperatures

2. apply an electric field whilst material is still hot (2000v/m DC voltage)

3. material cooled whilst voltage is still being applied

result → each unit orients in the same direction as the electric field

only applied to ferroelectric materials as they retain the changes

what special considerations are there when poling piezoelectric polymers

piezoelectric polymers have molecular dipoles that are antiparallel at room temp causing them to cancel each other out

1. the material is first stretched in 1 or 2 directions to 5 times the original length

2. this changes the molecular conformation → all -ve charges on one side +ve charges the other

3. material can then be poled to force it to retain this conformation

types of PZE elements

1. width expander

2. length expander

3. thickness expander

4. linear array transducers

5. piezocomposites

what are ultrasound arrays

• solid block of PZT (piezoelectric ceramic) that is cut to form a grid of elements (usually 128)

• elements share a matching layer and ground electrodes

• usually used in diagnostic imaging

what are the dimensions of an US array

1. pitch: distance between the center of adjacent element

2. element width

3. kerth width: distance between adjacent elements

4. elevation height: height of element

what mode allows for the maximum amount of information in an array

full matrix capture:

• one element of the array fires a pulse (red)

• rest of the elements act as a receiver/detector (blue)

• process repeats for every element

what are the drawbacks of FMC

extremely time consuming causing frame rate to drop a lot + computationally intensive

what is usually used instead of FMC

elements are fired in groups → groups are then fired sequentially

how does aperture size affect image

increasing the number of element firing increases aperture size → increased nearfield strength and length → beam is more directional

remember that aperture: \frac{\left(4a^2-\lambda\right)}{4\lambda}=\frac{a^2}{\lambda}-\frac{\lambda}{4}

in this case a=\frac{group~length}{2}

what is electronic focusing → advantages?

firing the elements in the periphery first and the other elements with a time/phase delay producing a converging pulse

• can control the time/phase delay → alter focal length at different points along the scan line → optimise lateral resolution at different depths

how is electronic focusing time shift calculated

\delta t_{i}=\frac{\delta x_{i}}{c_{o}}=\frac{1}{c_{o}}\left(\sqrt{\left(id\right)^2+F^2}-F\right)

where:

• x_i: distance from element to focus

• F: focal length

• d: pitch

• i:element number

what are the planes of a transducer

1. azimuth plane → US produces a slice in this plane → lateral resolution

2. elevation plane → thickness of the slice defined by the length of the element

elevation plane field dimensions with no focusing

1. near field: thickness is defined by the length of the elements (S = b)

2. far field: thickness is is defined by the divergence angle

how is focusing done in the elevation plane → how are the focuses dimensions defined

• done using a lens on the transducer

focus thickness: S = 1.41\lambda \frac{F}{b}

focal zone length: D=9.7\lambda(\frac{F}{b})^{2}

what is electronic beam steering

follows the same principles as electronic focusing where a time delay is used to fire some elements first causing the beam to go to one direction

difference between a rectangular and circular element field

1. focus and far field are the same

2. near field is different

what are grating lobes?

bi-product of using any sort of phase delay element firing, produces:

• main lobe: projects in the intended direction

• grafting lobe: beam that goes in an unwanted direction

occurs when:

• path length difference between adjacent elements = wavelength

• due to the finite pitch distance

if we take the main lobe direction as the x line:

dsin(\theta)=n\lambda

how do we reduce grating lobes?

• reducing pitch → does not remove the grating lobe completely but just steers it in a direction that doesn’t interfere with the main lobe

  • if pitch is small enough the path length difference will be smaller than the wavelength

  • d<\frac{\lambda}{2} is required to prevent grating lobes even is the beam is steered

• reducing kerf width → reduces energy in the grating lobe

types of transducers

1. linear arrays

2. curvilinear arrays

3. sector arrays

4. endoscopic/endocavity

5. intravascular

6. 3d imaging probes

7. cable free probes

linear arrays:

1. elements are in a straight line and are fired as a group

2. beam electronically focused

3. used in musculoskeletal and vascular imaging

curvilinear array

1. elements are arranges in a curve

2. fired in groups + electronically focused

3. used in abdominal and obstetrics

sector array

1. all elements are fired simultaneously

2. beam is electronically focused and steered

3. used in cardiac and brain imaging

endocavity/endoscopic

can be linear, curvilinear or sector

intravascular

1. multi or single element transducer

2. transducers can rotate or use an acoustic mirror

3D probe

can be made of:

1. 2d sector probe where all elements are fired together

2. moving 1D array

beam is electronically focused and steered

used in cardiac and obstetric imaging