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

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

Pegasus Lectures, Inc. COPYRIGHT 2006 Chapter 4: Pulsed Wave - Level 1

Pegasus Lectures, Inc. COPYRIGHT 2006 Chapter 4: Pulsed Wave The motivation for using pulsed wave is to generate some ability to resolve structures in depth (range resolution). Continuous wave offers no range specificity, whereas pulsed wave offers good range resolution. The animations of the next pages demonstrate how continuous wave results in complete range ambiguity, and how the spatial pulse length (SPL) relates to the range resolution.

Pegasus Lectures, Inc. COPYRIGHT 2006 Chapter 4: Pulsed Wave  The ability to resolve structures is paramount in diagnostic ultrasound.  In chapter 2 we discussed waves, with a tacit assumption that the wave is continuous.  Continuous waves offer no “depth” or “range” resolution.  The desire for range resolution is the motivation for pulsed wave imaging and Doppler.

Pegasus Lectures, Inc. COPYRIGHT 2006 Imagine these wavefronts moving in time, with a continuous stream of new wavefronts traveling from left to right. With a continuous transmit, notice how the echoes form all three mountains connect together and become indistinguishable. (no range resolution) Continuous Wave 1 2 3

Pegasus Lectures, Inc. COPYRIGHT 2006 Continuous Wave Animation Fig. 1: (Pg 194)

Pegasus Lectures, Inc. COPYRIGHT 2006 Pulsed Wave Now imagine these short bursts of wavefronts moving in time traveling from left to right. Imagine these wavefronts moving in time, with a continuous stream of new wavefronts traveling from left to right. 12 3

Pegasus Lectures, Inc. COPYRIGHT 2006 Range Specificity and a Very Short Pulse Fig. 2: (Pg 194) Notice that the echoes from each of the three mountains return at distinct times such that each mountain is resolved (range resolution).

Pegasus Lectures, Inc. COPYRIGHT 2006 Longer Pulse but Still Resolved Fig. 3: (Pg 195) Notice that in this case, the pulse length is longer than in the previous case but that the echoes from each of the three mountains are still separated in time. Therefore, the three mountains are still adequately resolved although there is less separation between the echoes.

Pegasus Lectures, Inc. COPYRIGHT 2006 Range Ambiguity Fig. 4: (Pg 195) In this case, the pulse length is so long that the echoes from mountain 1 and mountain 2 overlap, making it impossible to distinguish mountain 1 from mountain 2. The echo from mountain 3 is still distinct since the separation between mountain 2 and mountain 3 is greater than the separation between mountain 2 and mountain 1.

Pegasus Lectures, Inc. COPYRIGHT 2006 Pulsed Wave Four points made obvious by our mountain analogy:  Continuous wave did not have any range resolution  Pulsed wave did allow for range resolution  Shorter pulses result in better resolution  The roundtrip effect separates the echoes by a factor of twice the distance between the objects. This roundtrip affect improves our resolution by a factor of 2.

Pegasus Lectures, Inc. COPYRIGHT 2006 Pulsed Wave Definitions Many new definitions are required to specify the pulsed wave characteristics such as:  The time the pulse lasts (Pulse Duration)  How often the pulse repeats (Pulse Repetition Period)  The percentage of time the transmit is on versus off (Duty Factor)  The physical length of the pulse (Spatial Pulse Length) The following slides define each of these parameters.

Pegasus Lectures, Inc. COPYRIGHT 2006 Pulse Duration Fig. 5: (Pg 196) The Pulse Duration (PD) is a time measure of how long the transmit pulse lasts.

Pegasus Lectures, Inc. COPYRIGHT 2006 The PRP Fig. 6: (Pg 196) The Pulse Repetition Period (PRP) is the time between repeating transmit pulses.

Pegasus Lectures, Inc. COPYRIGHT 2006 The PRF Fig. 6: (Pg 196) Notice that the PRP and the PRF are really the same information, just in reciprocal form. The Pulse Repetition Frequency (PRF) is simply calculated as the reciprocal of the PRP.

Pegasus Lectures, Inc. COPYRIGHT 2006 The Duty Factor Fig. 7: Work Week Duty Factor Example (Pg 197)

Pegasus Lectures, Inc. COPYRIGHT 2006 The Duty Factor and the PD Fig. 8: Longer Pulse Duration (PD) Increases the Duty Factor (Pg 198)

Pegasus Lectures, Inc. COPYRIGHT 2006 The Duty Factor and the PRP Fig. 9: Shorter Pulse Repetition Period (PRP) Increases the Duty Factor (Pg 198)

Pegasus Lectures, Inc. COPYRIGHT 2006 Duty Factor (Example) Fig. 10: (Pg 199)

Pegasus Lectures, Inc. COPYRIGHT 2006 Spatial Pulse Length (SPL) Fig. 11: (Pg 199) The Spatial Pulse Length refers to the physical dimension the pulse occupies in space. As was seen from the mountain analogy and animations, a longer spatial pulse length results in worse range resolution.

Pegasus Lectures, Inc. COPYRIGHT 2006 The Meaning of Resolution The word “resolution” signifies the ability or inability to distinguish between two structures or to visualize an activity. There are many important points about resolution such as:  For resolution, smaller numbers are always better (it is better to able to resolve structures 1 mm apart than 7 mm apart)  Resolution is a general term which can refer to many different aspects of ultrasound.  The limiting factor which ultimately determines the resolution can be as a result of many factors such as:  Limits based on physics of the situation  Limits based on equipment  Limits based on display device (such as monitor)  Limits based on human perception (eyesight, hearing, etc.)

Pegasus Lectures, Inc. COPYRIGHT 2006 SPL and Range Resolution Fig. 12: (Pg 200) This diagram depicts why the range resolution smaller than the SPL by a factor of 2. Notice that the echoes between mountains 2 and 3 are twice as far apart (2x) as the separation between mountains 2 and 3 (x).

Pegasus Lectures, Inc. COPYRIGHT 2006 Range Resolution Animation

Pegasus Lectures, Inc. COPYRIGHT 2006 Other Names for Range Resolution There are at least three other names often used interchangeable in reference to the Range resolution. These terms are:  Depth Resolution  Longitudinal Resolution  Axial Resolution

Pegasus Lectures, Inc. COPYRIGHT 2006 Relating Wave Parameters and PW Parameters Fig. 13: Calculating the Pulse Duration (Pg 201)

Pegasus Lectures, Inc. COPYRIGHT 2006 Numerical Example Fig. 14: (Pg 202)

Notice that although both transmit pulses have 2 cycles per pulse and the same PRP, the duty cycle is higher for the wave with the longer period. Since a longer period corresponds to a lower frequency, leaving all things equal except lowering the transmit frequency, increases the duty factor. Effect of Period on Duty Factor Fig. 15: (Pg 203)

Pegasus Lectures, Inc. COPYRIGHT 2006 SPL and Wavelength Fig. 16: (Pg 203)

Pegasus Lectures, Inc. COPYRIGHT 2006 Foundational Drawing For PW Fig. 17: (Pg 204)

Pegasus Lectures, Inc. COPYRIGHT 2006 Notes: