Ultrasound Physics & Instrumentation
4 th Edition
Volume I
Companion Presentation
Frank R. Miele
Pegasus Lectures, Inc.
Pegasus Lectures, Inc.
COPYRIGHT 2006

This presentation is the sole property of
Pegasus Lectures, Inc.
No part of this presentation may be copied or used for any purpose other than as part of the partnership program as described in the license agreement.
Materials within this presentation may not be used in any part or form outside of the partnership program. Failure to follow the license agreement is a violation of Federal Copyright Law.
All Copyright Laws Apply.
Pegasus Lectures, Inc.
COPYRIGHT 2006

 Chapter 1: Mathematics
 Chapter 2: Waves
 Chapter 3: Attenuation
 Chapter 4: Pulsed Wave
 Chapter 5: Transducers
 Level 1
 Level 2
 Chapter 6: System Operation
Pegasus Lectures, Inc.
COPYRIGHT 2006

Level 2 focuses on the evolution of transducers, specific types of transducers, advantages and disadvantages of each type of transducer, and a review of resolution.
Pegasus Lectures, Inc.
COPYRIGHT 2006

The natural focal depth (also referred to as the Near Zone Length (NZL)) can be calculated using the following equation:
NZL

D 2
4

By substituting for the wavelength and assuming the propagation velocity of 1540 m/sec, this expression is approximated as:
( )

2 D mm )
 f MHz
0
( )
6
Pegasus Lectures, Inc.
COPYRIGHT 2006

By the approximated equation, it is now possible to calculate in your head the approximate natural focal depth.
Fresnel Zone Fraunhoefer Zone
Natural Focus
D/2 D
NZL = D 2 • f
0
6
2 • Near Zone Length
Fig. 18: (Pg 252)
Pegasus Lectures, Inc.
COPYRIGHT 2006

In this example we see that doubling the diameter increases the focal depth by a factor of four.
D
1
=2 •D
2
NZL
1
=2 2 •NZL
2
=4 •NZL
2
D
1
D
2
/2 D
2
D
1
/2
NZL
2
NZL
1
Fig. 19: (Pg 254)
Pegasus Lectures, Inc.
COPYRIGHT 2006

As suggested by the equation, a higher frequency produces a deeper focus; however, by design the focus is usually controlled by the diameter since higher frequency attenuates much faster.
NZL
D/2 D
Transmit Frequency = 2 • f
0
D/2 D
NZL Transmit Frequency = 2 • f
0
Fig. 20: (Pg 254)
Pegasus Lectures, Inc.
COPYRIGHT 2006

When a beam converges and diverges quickly, it has a very shallow depth of field. This yields a very good focus at one depth but poor focus in the relative near field and far field.
Shallow
Depth of
Field
Broad
Depth of
Field
Fig. 3: (Pg 236)
Pegasus Lectures, Inc.
COPYRIGHT 2006

There are many different names used for the axial and lateral dimensions of the image, as listed below.
 axial, depth, range, longitudinal
 lateral, azimuthal, side-by-side, transverse
 elevation
Fig. 22: (Pg 258)
Pegasus Lectures, Inc.
COPYRIGHT 2006

The pedof transducer is still in use today in both cardiac and vascular studies. The clear disadvantage is the inability to produce an image.
The unexpected advantage is that these transducers usually are the most sensitive for Doppler.
Fig. 23: (Pg 259)
Pegasus Lectures, Inc.
COPYRIGHT 2006

The transducer on the left is a 5 MHz transducer used for vascular applications. The transducer on the right is a 1.9 MHz transducer used for cardiac applications.
(Pg 259)
Pegasus Lectures, Inc.
COPYRIGHT 2006

Limitation of Pencil Probes: No Image
The greatest limitation to the pencil probe is the inability to create an image. The desire to create images lead to two parallel development paths:
 sequencing: used to produce vascular images
 mechanical steering: used to produce cardiac images
Pegasus Lectures, Inc.
COPYRIGHT 2006

Sequencing was performed with large arrays in a linear format (multiple elements in a straight line). By turning on and off switches, groups of elements were activated over time (in a sequence) to scan across the patient (as visualized in the animation on the next slide).
Fig. 24: (Pg 261)
Pegasus Lectures, Inc.
COPYRIGHT 2006

(Pg 261)
Pegasus Lectures, Inc.
COPYRIGHT 2006

Linear switched arrays are now obsolete, but the fundamental principle of sequencing is still used today in phased array linear transducers.
Fig. 25: (Pg 261)
Pegasus Lectures, Inc.
COPYRIGHT 2006

Mechanical steering was produced by mounting a single crystal on a motor. By
“wobbling” the motor, the crystal was pointed in different directions over time, creating the ability to produce an image. (as visualized by the animation of the next slide)
Fig. 26: (Pg 263)
Pegasus Lectures, Inc.
COPYRIGHT 2006

(Pg 263)
Pegasus Lectures, Inc.
COPYRIGHT 2006

Sector images were produced for cardiac scans so as to provide rib access.
Fig. 27: (Pg 264)
Pegasus Lectures, Inc.
COPYRIGHT 2006

Examples of Mechanical Transducers
Although the original design of mechanical transducers facilitated cardiac imaging, mechanical transducers were also designed for other applications, taking on a variety of form factors such as the endovaginal transducer shown below.
Pegasus Lectures, Inc.
COPYRIGHT 2006

Limitation of Mechanical Transducers
Although there are many limitations to mechanical transducers, one of the largest issues was the fact that there was a “fixed” focus. In other words, there was no ability to vary the focus. This limitation lead to the design of the mechanically steered annular array transducer.
Pegasus Lectures, Inc.
COPYRIGHT 2006

Activate All Rings
Activate Inner Rings Activate Center Disc Annular arrays allow for a variable focus in both the lateral and elevation planes.
As the name suggests, by creating an array of concentric element rings, the transducer diameter can be varied, varying the focal depth (as visualized in the animation of the next slide).
Fig. 28: (Pg 265)
Pegasus Lectures, Inc.
COPYRIGHT 2006

Mechanical Annular Array (Animation)
(Pg 265)
Pegasus Lectures, Inc.
COPYRIGHT 2006

Annular array transducers still were steered mechanically, and as such, did not appear significantly different than other mechanical transducers.
However, the manufacturing of annular arrays was much more difficult and expensive.
Furthermore, the complexity of the system increased to allow for control of multiple elements and to receive signals from more than one channel.
(Pg 266)
Pegasus Lectures, Inc.
COPYRIGHT 2006

Limitations of Mechanical Transducers
Even with variable focus from annular arrays, the limitations to mechanical steering were significant and motivated the design of a new family of transducers which used electronic steering.
Pegasus Lectures, Inc.
COPYRIGHT 2006

Electronic Control of Array Transducers
To overcome the many limitations of mechanical steering and fixed focus, electronic steering and focusing with arrays of elements was created.
Electronic control is produced by using small time delays (phase delays) between the excitation pulses which drive each element. By changing the delay profile (pattern of delays to a group of elements) different transmit steering angles and varying transmit focuses can be achieved.
By also applying varying delay profiles for the received signals, receive steering and receive focus can be achieved.
Pegasus Lectures, Inc.
COPYRIGHT 2006

By using tiny time delay between the excitation pulses to each of the transducer elements, electronic beam steering can be achieved.
Fig. 30: (Pg 268)
Pegasus Lectures, Inc.
COPYRIGHT 2006

(Pg 269)
Pegasus Lectures, Inc.
COPYRIGHT 2006

1 2 3 4 5 6 7 8
Notice that the distance is different from the
“red dot” labeled “X” to each of the elements labeled 1 through 8. As a result of the varying distances, the signal from the red dot arrives a little earlier at element 8 than element 7, which is earlier than element 6, etc. Therefore, for the signal to add up correctly from each of the individual elements, a delay must be applied with the greatest delay applied to element 8 and the least delay applied to element 1.
X
Fig. 31: (Pg 270)
Pegasus Lectures, Inc.
COPYRIGHT 2006

Compare the two delay profiles and resulting wavelets from each transducer element.
No Focusing or Steering
Fig. 32: (Pg 270)
Electronic Focusing
Fig. 33: (Pg 271)
Pegasus Lectures, Inc.
COPYRIGHT 2006

(Pg 271)
Pegasus Lectures, Inc.
COPYRIGHT 2006

Simultaneous Steering and Focusing
Focus Profile Steer Profile
Steering and focusing simultaneously is obviously greatly desired. Quite simply, the steering delay profile is added to the focusing delay profile to achieve a steered and focused beam. This approach works for both the transmitted and receive beams.
Fig. 34: (Pg 272)
Pegasus Lectures, Inc.
COPYRIGHT 2006

Electronic Steering and Focusing (Animation)
(Pg 272)
Pegasus Lectures, Inc.
COPYRIGHT 2006

A sector scan is produced by phasing. For each beam, a new phase delay profile is applied to steer both the transmitted and receive beam in a different direction. The sector format is acquired over time.
(Sector functionality is further explained and demonstrated in a few later slides and through an animation.)
Fig. 35: (Pg 273)
Pegasus Lectures, Inc.
COPYRIGHT 2006

Pegasus Lectures, Inc.
COPYRIGHT 2006
(Pg 273)

The most often recognized form of a sector transducer format is the transducer designed primarily for cardiac imaging, The sector format is very useful for access through the ribs. The
“fanning” out of the beams produces a broader far-field while the narrow near-field if the direct consequence of having to get between the ribs which would otherwise produce significant shadowing.
(Pg 273)
Pegasus Lectures, Inc.
COPYRIGHT 2006

A transesophageal transducer also produces a sector formatted image.
(Pg 273)
Pegasus Lectures, Inc.
COPYRIGHT 2006

Time 1
Time 2 Time 3
A sector scan is created by phasing. A phase delay profile is produced to steer the beam in the desired direction and receive the resulting echoes. The delay profile is then changed to steer in a different direction, and the process repeated until the desired region is scanned (as visualized in the animation of the next slide).
Time mid Time n
Fig. 36: (Pg 274)
Pegasus Lectures, Inc.
COPYRIGHT 2006

(Pg 274)
Pegasus Lectures, Inc.
COPYRIGHT 2006

Notice that for a “straight” vessel, the angle formed between the steered beam and the flow direction varies across the entire sector image. In this example, the angle on the left side of the image is less than 90 degrees. In the middle of the image, the angle equals 90 degrees. On the left side of the image, the angle is greater than 90 degrees.
Fig. 37: (Pg 275)
Pegasus Lectures, Inc.
COPYRIGHT 2006

For vascular applications, sector transducers are clearly suboptimal since there is such a narrow near field image. To overcome this drawback, phased array linear transducers were produced. These transducers can be used by sequencing alone (like the earlier switched linear arrays) or can in a more complex manner using both sequencing and phasing.
Fig. 38: (Pg 276)
Pegasus Lectures, Inc.
COPYRIGHT 2006

(Pg 276)
Pegasus Lectures, Inc.
COPYRIGHT 2006

There are many different forms of linear transducers (including dimensions, number of elements, handle design, and operating frequency range) depending on the specific application. The transducer pictured here is an example of an intra-operative linear array.
These transducers typically have significantly fewer elements than the larger arrays used for more “conventional” vascular imaging and tend to be relatively high frequency.
(Pg 276)
Pegasus Lectures, Inc.
COPYRIGHT 2006

These two transducers are of the form most commonly seen for vascular applications such as cerebrovascular, arterial, and venous scans. Usually these transducers are designed to span a range of frequencies (broad bandwidth) for both easier and more challenging patients.
(Pg 276)
Pegasus Lectures, Inc.
COPYRIGHT 2006

Unsteered linear images are produced by sequencing. As shown earlier, sequencing is a method by which a group of elements are activated with a flat delay profile, producing a beam that transmits straight ahead. Once the echoes are received, another group of elements laterally displaced are activated, producing a parallel beam. This process repeats until the desired scan region is complete (as visualized in the animation of the next slide).
Fig. 39: (Pg 277)
Pegasus Lectures, Inc.
COPYRIGHT 2006

(Pg 277)
Pegasus Lectures, Inc.
COPYRIGHT 2006

Steered linear images are produced by sequencing and phasing simultaneously.
The phasing is used to steer each beam to the desired angle and the sequencing is used to “traverse” across the patient. Notice that the delay profiles applied to each group of elements during the time intervals, T
1
, T
2
, T
3
, etc. is always the same. The result is that all of the beams of the image are parallel (as visualized in the animation on the slide after the next slide).
Fig. 40: (Pg 278)
Pegasus Lectures, Inc.
COPYRIGHT 2006

This image is actually comprised of two images. The black and white portion (the 2D or B-mode image) is not steered and was produced by sequencing alone.
The color image is steered by setting the color box, and was produced by both phasing and sequencing.
(Color is applied – refer to picture in book.)
Fig. 40: (Pg 278)
Pegasus Lectures, Inc.
COPYRIGHT 2006

(Pg 278)
Pegasus Lectures, Inc.
COPYRIGHT 2006

In order to produce a larger field of view, trapezoidal scanning was created. To create the trapezoid format, a group of elements are phased as if a sector transducer to produce the
“wings”. Sequencing is then used to produce the unsteered middle part of the image (as visualized in the animation on the next slide).
Fig. 41: (Pg 279)
Pegasus Lectures, Inc.
COPYRIGHT 2006

(Pg 279)
Pegasus Lectures, Inc.
COPYRIGHT 2006

* Color is applied – refer to picture in book.
(Pg 279)
Pegasus Lectures, Inc.
COPYRIGHT 2006

Fig. 42: (Pg 280)
Pegasus Lectures, Inc.
COPYRIGHT 2006

(Pg 280)
Pegasus Lectures, Inc.
COPYRIGHT 2006

Pegasus Lectures, Inc.
COPYRIGHT 2006
(Pg 280)

As with all phased array format types, curved linear arrays take many different forms as best suits the application. Transducers used on the abdomen are generally “relatively” large whereas probes that are more invasive are for obvious reasons physically much smaller.
(Pgs 280 - 281)
Pegasus Lectures, Inc.
COPYRIGHT 2006

For a conventional 2-D image using a curved linear array, the scan is produced by sequencing only. Phasing can be used to affect the focus within the image or for Doppler and color Doppler steering. The curvature of the transducer face determines the curvature of the image.
(Pg 281)
Pegasus Lectures, Inc.
COPYRIGHT 2006

The 1.5-D array was the first electronic step towards controlling the focus in the elevation direction. Either the center elements alone could be used (shallower elevation focus) or both the center and outer set of elements could be used to make the elevation focus deeper. These were the precursor to the 2-D arrays.
Fig 43: (Pg 281)
Pegasus Lectures, Inc.
COPYRIGHT 2006

Two-dimensional arrays have multiple elements in both the lateral and elevation directions (2 dimensions). By electronically phasing these elements both steering and focusing can be achieved in both the lateral and elevation planes. The ability to steer electronically in the elevational direction allows for 3-D scanning.
Fig 44: (Pg 282)
Pegasus Lectures, Inc.
COPYRIGHT 2006

This image shows how small the crystals are for the new matrix arrays that are being developed. The arrows in this picture indicate a human hair which is overlaid on the matrix. Notice that there are elements in two directions, giving control in both the elevation and lateral directions.
Fig 45: (Pg 282)
Pegasus Lectures, Inc.
COPYRIGHT 2006

This image shows how piezocomposite materials are constructed. These materials are a composite of PZT posts and a polymer. The polymer results in lower acoustic impedances which results in a better efficiency both into and out of the patient.
Fig. 46: (Pg 283)
Pegasus Lectures, Inc.
COPYRIGHT 2006

The lateral resolution of an image is determined by the lateral dimension of the beam. The beam must fit between two structures so as to not result in a combined echo.
Therefore, the lateral resolution equals the beamwidth. Since the beamwidth changes with depth, the lateral resolution varies with the beam changes over depth.
Fig. 47: (Pg 284)
Lateral Resolution

Lateral Beamwidth
Pegasus Lectures, Inc.
COPYRIGHT 2006

Resolution in the elevation direction is determined by the beam dimension elevationally. Like the lateral resolution, the elevation resolution is different at different depths and is best at the elevation focus.
Fig. 48: (Pg 284)
Elevation Resolution

Elevation Beamwidth
Pegasus Lectures, Inc.
COPYRIGHT 2006

Resolution in the axial direction is determined by the spatial pulse length. Because of the roundtrip effect, the resolution is actually better than the pulse length by a factor of 2. Recall that smaller numbers are always better for resolution.
Fig. 49: (Pg 285)
Axial Resolution

S.P.L.
2
Pegasus Lectures, Inc.
COPYRIGHT 2006

Pegasus Lectures, Inc.
COPYRIGHT 2006