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

2. Pegasus Lectures, Inc. COPYRIGHT 2006 License Agreement 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.

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

4. Pegasus Lectures, Inc. COPYRIGHT 2006 Chapter 2: Waves - Level 2

5. Pegasus Lectures, Inc. COPYRIGHT 2006 Classification of Sound Fig. 26: Linear and Logarithmic Scale (Pg 112) Notice how the same data is presented on both a linear and a logarithmic scale. Because of the large dynamic range, notice that the logarithmic scale is a more “useful” way of presenting the data.

6. Pegasus Lectures, Inc. COPYRIGHT 2006 Sound Ranges Note that:  “infra” means below  “ultra” means above  “audible” refers to human hearing 0.02 0.2 20 20 K 20 M 2 200 2 K 200 K 2 M Infrasound Audible Range Diagnostic Ultrasound Ultrasound

7. Pegasus Lectures, Inc. COPYRIGHT 2006 Typical Ultrasound Periods The frequency and the period give the same information. You should be able to convert back and forth between the period and the frequency.  Frequency = 2 MHz  Period = 1/(2 MHz) = 0.5  sec  Frequency = 10 MHz  Period = 1/(10 MHz) = 0.1  sec

8. Pegasus Lectures, Inc. COPYRIGHT 2006 Diagnostic Ultrasound and Higher Frequencies Fig. 27: Intravascular Ultrasound (IVUS) Image of a Coronary Artery (Pg 113)

9. Pegasus Lectures, Inc. COPYRIGHT 2006 Propagation Velocity (c) In Level 1, we discussed the fact that sound was determined strictly by the properties of the medium. It is now important to discuss which properties of the medium affect the propagation velocity and how.  The propagation velocity is related to the square root of the bulk modulus of the medium.  The propagation velocity is inversely related to the density of the medium.

10. Pegasus Lectures, Inc. COPYRIGHT 2006 Bulk Modulus Fig. 28: Changing Volume with Pressure (Pg115)

11. Pegasus Lectures, Inc. COPYRIGHT 2006 Bulk Modulus and Stiffness High Bulk Modulus results when the material is stiff (incompressible or inelastic). Therefore, materials that are stiff tend to have high propagation speeds. Propagation Speed (c) is related to stiffness. (stiffer mediums have higher propagation speeds)

12. Pegasus Lectures, Inc. COPYRIGHT 2006 Propagation Velocity Analogy Fig. 29: (Pg 116)

13. Pegasus Lectures, Inc. COPYRIGHT 2006 Stiffness and Propagation Velocity Fig. 30: (Pg 117) Slower Wave Propagation (More Compressible) Faster Wave Propagation (Stiffer)

14. Pegasus Lectures, Inc. COPYRIGHT 2006 Compressibility and Propagation Velocity (Animation) (Pg. 118 A)

15. Pegasus Lectures, Inc. COPYRIGHT 2006 Density and Propagation Velocity Fig. 31: (Pg 117) Slower Wave Propagation (Higher Density) Faster Wave Propagation (Lower Density)

16. Pegasus Lectures, Inc. COPYRIGHT 2006 Density and Propagation Velocity (Animation) (Pg. 118 B)

17. Pegasus Lectures, Inc. COPYRIGHT 2006 Wave Velocity versus Train Velocity Fig. 32: (Pg 118) Notice that the “wave” moves 30 m in the time that the train only moved 3 m. (See animation of next slide)

18. Pegasus Lectures, Inc. COPYRIGHT 2006 Wave vs. Train Velocity (Animation) (Pg. 118 C)

19. Pegasus Lectures, Inc. COPYRIGHT 2006 Don’t Oversimplify This last fact becomes apparent by looking at the table of propagation velocities.  At first glance, it appears that higher density materials would have lower propagation velocities because of the inverse relationship.  This contradicts what we see in reality in the body.  The reason is that the bulk modulus is generally higher for more dense materials (it is harder to compress a dense material than a less dense material).  A higher bulk modulus results in a higher propagation velocity.  Therefore, more dense materials in the body tend to have higher not lower propagation velocities.

20. Pegasus Lectures, Inc. COPYRIGHT 2006 Propagation Velocities in the Body Table 5: (Pg 121) MediumPropagation Velocity Air (25 degrees C)347 m/sec Lung500 m/sec Fat1440 m/sec Water (25 degrees C)1495 m/sec Brain1510 m/sec “Soft Tissue”Average 1540 m/sec Liver1560 m/sec Kidney1560 m/sec Blood1560 m/sec Muscle1570 m/sec Bone4080 m/sec

21. Pegasus Lectures, Inc. COPYRIGHT 2006 Propagation Speed (c) Summary The propagation speed of sound is determined by two properties of the medium:  density (  )  (Bulk Modulus) stiffness As the density increases, the propagation speed decreases. (assumes no change in stiffness – which is not very realistic) As the stiffness increases the propagation speed increases. Important point: For most materials, as the density increases, the stiffness increases much faster. This non-linear relationship results in more dense materials typically having much higher propagation velocities.

22. Pegasus Lectures, Inc. COPYRIGHT 2006 Density, Stiffness and Propagation Velocity (Animation) (Pg. 119)

23. Pegasus Lectures, Inc. COPYRIGHT 2006 Calculating the Wavelength You must be able to calculate the wavelength. (Pages 123 - 124) Example: If the transmit frequency is 5 MHz, what is the wavelength in water?

24. Pegasus Lectures, Inc. COPYRIGHT 2006 Power Power is a measure of how much work or energy is expended per time. Power has units of Watts. So what happens to the power if you double the transmit voltage (amplitude)?

25. Pegasus Lectures, Inc. COPYRIGHT 2006 Intensity The intensity is the distribution of power over area. So what happens to the intensity if you double the transmit voltage (amplitude)? Intensity has units of Watts per area:

26. Pegasus Lectures, Inc. COPYRIGHT 2006 Relationship of intensity with Amplitude So if the amplitude is doubled, the power increases by a factor of four, resulting in an increase in intensity by a factor of four. Recall that voltage is a measure of amplitude.

27. Pegasus Lectures, Inc. COPYRIGHT 2006 Decibels Decibels is a logarithmic power ratio: Note: the extra factor of 2 in the amplitude form converts the amplitude ratio into a power ratio.

28. Pegasus Lectures, Inc. COPYRIGHT 2006 Amplitude versus Frequency Amplitude and frequency are measures of completely different parameters. In terms of sound:  Amplitude corresponds to volume  Frequency corresponds to pitch

29. Pegasus Lectures, Inc. COPYRIGHT 2006 Same Frequency – Different Amplitude Fig. 33: (Pg 135)

30. Pegasus Lectures, Inc. COPYRIGHT 2006 Same Amplitude – Different Frequency Fig. 34: (Pg 136)

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