# ECE 472

## ECE 472 - Biomedical Ultrasound Imaging

### Spring 2021

### Official Description

### Subject Area

### Course Director

### Description

### Notes

Grading: 26% - Homework; 44% - Exam I, II; 30% - Final Exam. Homework will consist of 4 to 6 problems a week.

### Topics

- Acoustic wave propagation
- Attenuation in ultrasound
- Ultrasonic Sources
- Fields

Anatomical Imaging:

- Conventional ultrasonic imaging
- Arrays
- Ultrasound Contrast Agents (UCAs)
- Harmonic Imaging

Functional Imaging:

- Doppler (theory)
- Continuous wave Doppler
- Pulsed wave Doppler
- Color Flow Imaging
- Doppler with ultrasound contrast agents

Advanced ultrasonic imaging:

- Coded excitation
- Elastography
- Quantitative ultrasound imaging

Ultrasound computed tomography

### Detailed Description and Outline

Topics:

- Acoustic wave propagation
- Attenuation in ultrasound
- Ultrasonic Sources
- Fields

Anatomical Imaging:

- Conventional ultrasonic imaging
- Arrays
- Ultrasound Contrast Agents (UCAs)
- Harmonic Imaging

Functional Imaging:

- Doppler (theory)
- Continuous wave Doppler
- Pulsed wave Doppler
- Color Flow Imaging
- Doppler with ultrasound contrast agents

Advanced ultrasonic imaging:

- Coded excitation
- Elastography
- Quantitative ultrasound imaging

Ultrasound computed tomography

Grading: 26% - Homework; 44% - Exam I, II; 30% - Final Exam. Homework will consist of 4 to 6 problems a week.

### Texts

Lecture Notes, Select literature

R. Cobbold, *Fundamentals of Biomedical Ultrasound*

### Course Goals

The overall objective of this course is to familiarize students with most of the theoretical and engineering foundations of ultrasonic imaging for medical diagnostics. Conventional, Doppler, and advanced ultrasonic imaging techniques will be described. Students will be introduced to important medical applications of different ultrasonic imaging techniques. Engineering problems related to characterization of ultrasonic sources and arrays, image production, image quality, the role of contrast agents in ultrasonic imaging, and system design will be examined.

### Instructional Objectives

**A. ****by the time of exam number one (after 12 lectures), the student should be able to do the following:**

1. Derive the classical acoustic wave equation assuming linear wave propagation (1).

2. Determine the acoustic pressure, condensation, particle velocity, particle displacement, intensity, or acoustic density given anyone of these parameters (1).

3. Determine the frequency, wavelength, period, wave number, attenuation, and direction of propagation of acoustic waves given an acoustic wave function (1).

4. Find the attenuation of an ultrasonic wave given measurements of the ultrasonic wave at two different locations (1).

5. Convert pressure, attenuation and intensity to a decibel scale from the amplitude and vice versa (1).

6. Calculate the time average intensity of a given ultrasonic waveform (1).

7. Apply the boundary conditions at an interface between two media to determine the general form of the pressure reflection and transmission coefficients (1).

8. Calculate the pressure reflection and transmission coefficients from the impedance values of two media (1).

9. Determine the sound speed of the material media given signals reflected from the front and back surfaces of the material (1).

10. Identify the trade-offs between axial resolution and acoustic energy (1).

11. Identify the relationship between pulse length and axial resolution in ultrasonic imaging (1).

12. Determine the thickness of a piezoelectric crystal required to produce a particular frequency of ultrasound (1).

13. Write the expression for simple acoustic source (1).

14. Apply the principle of superposition in the field from a simple acoustic source to construct fields from more complicated apertures (1).

15. Determine the beam pattern of a circular piston transducer and determine the beam width from the beam pattern function (1).

16. Identify the trade-offs between lateral resolution, aperture diameter, ultrasonic frequency, and apodization (1), (6), (7).

17. Apply the spectral source method to determine the far field pattern of ultrasonic sources (1).

18. Find the far field beam pattern given an arbitrary aperture function (1).

**B. By the time of exam number two (after 24 lectures), the student should be able to the following:**

19. Identify three methods for focusing single-element ultrasonic sources (1).

20. Determine the beam width for a focused ultrasonic source in terms of the f-number and wavelength (1).

21. Determine the depth of field for focused ultrasound source in terms of the f-number and wavelength (1).

22. Identify the trade-off between spatial resolution, ultrasonic energy, and depth of field for focused ultrasound sources (1).

23. Determine the focal gain for a given ultrasonic source with particular focal properties (1).

24. Identify the differences in beam fields between monochromatic waves and higher bandwidth waveforms from a focused source (1).

25. Calculate the shift in center frequency of a pulse due to frequency dependent attenuation and bandwidth (1).

26. Construct an ultrasonic B-mode image from raw RF data (1).

27. Detect the envelope of an RF waveform using the Hilbert transform (1).

28. Identify B-mode, M-mode, C-mode, and A-mode ultrasonic images and how each are constructed (1), (4).

29. Quantify the axial resolution in terms of the envelope of the pulse, bandwidth of the pulse, Rayleigh criteria, and the modulation transfer function (1),(6).

30. Quantify the contrast resolution in terms of the contrast ratio and the contrast to noise ratio (1), (6).

31. Identify the trade-offs between contrast resolution and signal-to-noise ratio, spatial resolution, presence of side lobes, and the dynamic range of the system (1), (6).

32. Calculate the field due to an array of ultrasonic elements including the effects of the elements factor, steering, focusing, minimizing grating lobes, and apodization (1).

33. Design an ideal array system for ultrasonic imaging including synthetic aperture imaging techniques (1), (2), (6).

34. Apply beamforming principles to achieve dynamic focusing of arrays (1).

35. Determine the reduction in grating lobe levels due to pulsing of ultrasound (1).

36. Determine the scattered field due to ultrasound contrast agent and how this affects image contrast (1).

37. Derive the nonlinear acoustic wave equation based on first principles (1).

38. Determine the shock distance, Goldberg number, and mock number for different tissues given their nonlinear coefficients (1).

39. Identify the trade-offs between fundamental imaging and harmonic imaging based on nonlinear ultrasonic propagation (1), (4).

40. Identify the trade-offs between methods for processing harmonic images including: a band pass filter technique, pulse inversion, and pulse to pulse amplitude modulation (1).

**B. By the time of exam number three (after 40 lectures), the student should be able to the following:**

41. Write the expression for the Doppler shift frequency in terms of the interrogating frequency and the speed of a moving object (1).

42. Calculate the Doppler shift from blood moving in a particular velocity when exposed to ultrasound field (1).

43. Identify the trade-offs between CW Doppler and PW Doppler in ultrasonic imaging (1).

44. Find the Doppler signal through heterodyning and filtering of the RF ultrasound signal (1), (6).

45. Calculate the Doppler shift using PW Doppler and a multi-pulse sampling technique (1), (4).

46. Identify the trade-offs between low PRF and high PRF PW Doppler imaging (1).

47. Obtain direction of blood flow using quadrature sampling and PW Doppler (1).

48. Obtain blood flow velocity using time domain techniques (1).

49. Identify trade-offs between power Doppler and color flow imaging and how each of these images are constructed (1), (4).

50. Determine the gain in signal-to-noise ratio, side lobe levels, and spatial resolution using coded excitation and pulse compression in ultrasonic imaging (1).

51. Obtain the normalized backscatter coefficient from ultrasound signals backscattered from tissues (1).

52. Relate the spectral content of backscattered signals from ultrasound to underline scatterer properties (1), (7).

53. Obtain attenuation estimates from insertion loss data (1).

54. Construct a strain image from ultrasound signals from compressed tissues using cross correlation techniques (1).