Chapter 9 : Ultrasound fields

Question 1

Near field

Answer 1

The near field region begins at the transducer surface and extends outwards in the shape of a cylinder approximately the same diameter as the source.

Question 2

Far field

Answer 2

The far field region is characterised by the smooth decay of the pressure amplitude in both the axial and radial directions. In this region, the path length difference between the plane waves and edge waves is small and the waves are almost in phase, particularly close to the beam axis. The field diverges gradually, and the pressure amplitude falls off smoothly due to geometrical spreading with increasing z without any rapid fluctuations.

Question 3

The structure of the beam emitted by a circular piston can be explained using _______’s principle

Answer 3

Huygens

Question 4

The acoustic pressure at any point in front of a transducer (on-axis) can be calculated from knowledge of the normal particle velocity on the transducer surface using the _______

Answer 4

Rayleigh integral

Question 5

Where are the maxima and minima of this on-axis pressure signal? They will occur when the sin term is a minima or maxima, i.e., when

Answer 5

Question 6

Using r = sqrt(a^2+z^2)

and lambda=co/f

and the equations shown in the image

write an equation for the positions that the minima and maxima and last axial maximum occur,

and what the last axial maximum would be if the transducer surface is large

Answer 6

Question 7

At what distance does the near field end and the far field begin?

Answer 7

the same as the position of the last axial maximum!

Question 8

What equation is this?

Answer 8

The far field directivity function - which is the approximate variation of the pressure amplitude as a function of the angle.

Question 9

What is the angle that the pressure first falls to zero in the far field?

Answer 9

Question 10

three ways to produce a curved wavefront?

Answer 10

Curved elements

Lenses

Electronically

Question 11

What is the ratio of the pressure at the focus to the pressure at the surface of the transducer called and the equation of it?

Answer 11

The focusing gain

g=kh where h is the height of the bowl

Question 12

What is the width of the focal zone given by?

Answer 12

Question 13

The length of the focal zone (also called the depth of focus or depth of field ) is given by

Answer 13

Question 14

What is the positive and negative sides of a highly focused transducer?

Answer 14

It will have good lateral resolution but poor depth of field.

Question 15

what is a major advantage of using an array transducer with multiple elements?

Answer 15

the acoustic waves emitted from the transducer can be controlled by changing the electronic signal used to drive each individual element.

Question 16

For a linear (plane wave) array transducer if the individual elements are used in groups the time delays for the ith element relative to the central element can be calculated how?

Answer 16

Question 17

For an element pitch of d, the angle of the grating lobes will be given by ?

Answer 17

Question 18

what is dynamic receive focusing

Answer 18

When the ultrasound waves are transmitted, a single value for the time delay for each element is used to focus or steer the beam to a particular location. However in recieve the entire waveform for each element is digitised and thus the signals can be summed in different ways. In dynamic receive focusing, the time delays for each element are updated dynamically so the focus depth matches the depth where the echoes originated from. The time delays where the focal distance is set dynamically to F = 0.5 * c* t.

Question 19

aperture expansion

Answer 19

the beam width for a given aperture is proportional to the focal depth, thus when using dynamic receive focusing, the image resolution will degrade at larger depths. To counteract this, the receive aperture can be expanded as the focus depth is increased to maintain a constant beamwidth.

Question 20

Multi-zone transmit

Answer 20

While dynamic receive focusing and aperture expansion can improve focusing on receive, the focusing on transmit is still fixed (the waves can only physically focus in one position). To improve image resolution, multiple transmit pulses can be used, each focused at a different imaging depth, and the resulting scan lines (or images) later combined. However, this also has the effect of reducing the imaging frame rate, as a larger number of transmit-receive events are needed to form the image.

Question 21

co-processed transmit focusing

Answer 21

One way to improve the frame rate is by using different sub-sets of the transducer array to acquire scan lines at the same time. While this can improve the frame rate, it requires more advanced electronics to process multiple A-mode scan lines at the same time.

Question 22

Apodisation

Answer 22

To reduce side lobes, the signals from the individual elements can be weighted such that the elements in the middle contribute more to the summation. This makes the summation less sensitive to waves arriving from outside the main lobe of the receive beam, at the expense of slightly increasing the main lobe width.

Question 23

What is frequency filtering?

Answer 23

The scan lines are filtered using a band-pass filter centered around the transmit frequency or the second harmonic. This reduces the effects of noise outside the transmit frequency range, or in the latter case, obtains the harmonic signal for tissue harmonic imaging.

Question 24

Envelope detection

Answer 24

Before display, the high frequency variations in the scan lines (which depend on both of the reflected waves and the transmitted ultrasound pulse) are removed in a demodulation process known as envelope detection. This removes the oscillations at the transmit frequency, leaving only information about the amplitude of reflections.

Question 25

Log compression

Answer 25

The strenght of reflections from different tissue interfaces typically cover a wide dynamic range, on the order of 60dB for soft tissue imaging. This exceeds the gray scale range that can be displayed by a computer monitor which is generally only 20 dB. To improve the differentiation of weaker signals, a nonlinear amplifier is used, where the output is proportional to the log of the input signal. One way to perform the log compression is via

where senv is the A-mode scan line after envelope detection, reject sets the zero value, and dynamic range sets the maximum value displayed in dB.

Question 26

Scan conversion

Answer 26

After the individual A-mode scan lines have been acquired, they are combined together and converted to the correct resolution for display on screen. For steered beams, this includes converting from polar coordinates to cartesian coordinates using interpolation.

Question 27

Speckle Reduction

Answer 27

Modern commercial ultrasound machines also include a range of other image acquisition and signal processing techniques, including parallel and adaptive receive beamforming, synthetic aperture imaging, denoising, and edge detection. These are often done using proprietary algorithms (ie. they are not made public), and often don’t change the ultrasound image drastically, so they are not discussed here. However, one common processing technique that is worth briefly discussing is image compounding. This is used to reduce the effect of speckle and noise on the image by averaging several ultrasound images taken under different conditions.

Question 28

Three methods of speckle reduction?

Answer 28

There are three main flavors:

1. Temporal compounding or persistence where several subsequent image frames are averaged. Something must change between the images - perhaps a slight movement of the imaging probe or tissue - or the speckle, which is deterministic, will be the same.
2. Spatial compounding where images from different scan directions are averaged.
3. Frequency compounding where images at different frequencies are averaged, either by using several band-pass filters on receive or using several images with different transmit frequencies.

Question 29

Frame rate

Answer 29

(a B-mode ultrasound image is composed of a series of A-mode scan lines taken at different positions in the tissue)

FR = PRF/N = C₀/2NL_max

If an image consists of N vertical (or radial) scan lines, the rate at which an ultrasound image can be formed, called the frame rate (FR), is given by the PRF divided by N.

Question 30

What is the far field beam divergence angle?

Answer 30

The angle at which the pressure first falls to zero in the far field.

Question 31

as the frequency or the aperture size are increased what happens to the main lobe and the side lobes?

Answer 31

The beam becomes increasingly directional with a smaller main lobe and a larger number of side lobes. The length and width of the near field region also increases.

Question 32

What is the PRF?

Answer 32

The rate at which scan lines can be acquired is called the pulse repetition frequency. (_{It is limited by the time required for the ultrasound pulse to travel to the desired maximum imaging depth Lmax and return to the transducer.)}

PRF = 1/round-trip time = C₀ / 2L_max

Question 33

Types of spatial resolution

Answer 33

Axial resolution

Lateral resolution

Question 34

Axial resolution

Answer 34

corresponds to the ability to distinguish between two objects at di↵erent depths in the image. Reflected pulses can be distinguished provided their separation in time is greater than the full-width at half maximum (FWHM) of the pulse envelope tp. Accounting for two way propagation, this means the axial resolution is given by

Question 35

• Lateral resolution ?

Answer 35

corresponds to the ability to distinguish between two objects at the same depth but different lateral positions within the imaging plane. it is = the beam width.

Question 36

Types of Image artefacts?

Answer 36

Reverberation

Acoustic shadowing and enhancement

Target misregistration

Mirror image artefacts

Question 37

Why are the elements of an imaging transducer array normally used in groups and not one at a time?

Answer 37

As the elements are very narrow in the in-plane direction, they are typically pulsed in groups to increase the size of the near field zone and allow electronic steering and focusing.

Question 38

what element pitch should be used to avoid grating lobes?

Answer 38

d < half a wavelength

Question 39

can you remember off by heart (need to remember for the exam perhaps) the equation for calculating the time delay between the central and outside elements?

Answer 39

Question 40

Explain the main differences between a linear phased array and a sector transducer

Answer 40

A sector transducer is curved physically so that the elements are placed offset to eachother wilst the linear phased array does this offset by triggering them at different times so they provide a curved wave.

Question 41

demodulation?

Answer 41

The process of removing the transmit frequency, f, from the measured signal so that the doppler frequency can be estimated.

Question 42

In general, lateral resolution for focused beams is highly spatially variant, and can be improved by ____ _____ _____ .

Answer 42

In general, lateral resolution for focused beams is highly spatially variant, and can be improved by multi-zone focusing.