1. EE 5340/7340, SMU Electrical Engineering Department, © 2004 1 Carlos E. Davila, Electrical Engineering Dept. Southern Methodist University slides can be viewed at: http:// www.seas.smu.edu/~cd/ee5340.html EE 5340/7340 Introduction to Biomedical Engineering Ultrasound Flowprobes

2. EE 5340/7340, SMU Electrical Engineering Department, © 20042 Ultrasound-Based Flow Measurement n Basic Ultrasound Transducer Principles n Ultrasound Attennuation, Transmission, and Backscatter n Transit Time Flowprobes n Doppler Flowprobes n Pulsed Doppler

3. EE 5340/7340, SMU Electrical Engineering Department, © 20043 Definition of Ultrasound n Sound consists of traveling pressure waves n Speed of sound waves is about 1500 m/s in tissue n Frequency range: 2 MHz < f < 10 MHz n Ultrasound is produced using piezo-electric transducers n Applications of Medical Ultrasound n Imaging n Measurement of Blood Flow (Doppler and transit- time flowmeters) n Lythotripsy

4. EE 5340/7340, SMU Electrical Engineering Department, © 20044 Transducer Properties n Piezo-electric material (lead-zirconate), formed into disks: D = transducer diameter ~ Application of a voltage causes crystal to vibrate at 2-10 MHz.

5. EE 5340/7340, SMU Electrical Engineering Department, © 20045 Transducer Properties (cont.) d nf  d nf = near-field distance =  = divergence angle: wave fronts transducer D

6. EE 5340/7340, SMU Electrical Engineering Department, © 20046 Transducer Properties (cont.) ~ n crystal will vibrate at same frequency, f, as that of the applied voltage. c: speed of sound in tissue: about 1500 m/s : wavelength of sound c = f E = Acos(2  f t)

7. EE 5340/7340, SMU Electrical Engineering Department, © 20047 Transducer Properties (cont.) n S = change in crystal thickness/original crystal thickness = gE E: applied electric field g: constant

8. EE 5340/7340, SMU Electrical Engineering Department, © 20048 Transducer Properties (cont.) n If crystal undergoes mechanical compression, a voltage is generated proportional to the compression. n In flowmetry, the piezoelectric crystal is used to generate ultrasound, which is transmitted into the tissue. n Some of the ultrasound is reflected by the tissue. n Voltage is turned off and the crystal is then used to convert the reflected pressure waves to a voltage. n The information in the reflected pressure waves can be used to image tissue.

9. EE 5340/7340, SMU Electrical Engineering Department, © 20049 Ultrasound Attennuation in Tissue due to: n Divergence of wavefronts in the far-field. n Conversion of wave energy to heat (exponential with distance): n p(z): sound pressure at distance z from transducer face  : attenuation coefficient n p 0 : sound pressure at transducer face

10. EE 5340/7340, SMU Electrical Engineering Department, © 200410 Attenuation Coefficients at 1MHz source: Medical Imaging Systems, A. Macovsky, Prentice Hall

11. EE 5340/7340, SMU Electrical Engineering Department, © 200411 Ultrasound Attennuation in Tissue due to: n Rayleigh scattering: due to acoustic impedance irregularities (i.e. red blood cells) n Specular reflection at planar interfaces: n tissue characterized by acoustic impedance Z.  : density n c: speed of sound in tissue n sound waves encountering tissue boundary having different acoustic impedances is partially reflected at the interface.

12. EE 5340/7340, SMU Electrical Engineering Department, © 200412 Propagation Velocity source: Medical Imaging Systems, A. Macovsky, Prentice Hall

13. EE 5340/7340, SMU Electrical Engineering Department, © 200413 Models for Ultrasounic Backscatter (Reflection) n Specular reflection: tissue interface incident reflected transmitted Z1Z1 Z2Z2 z

14. EE 5340/7340, SMU Electrical Engineering Department, © 200414 Specular Reflection (cont.) R: reflectivity = source: Medical Imaging Systems, A. Macovsky, Prentice Hall

15. EE 5340/7340, SMU Electrical Engineering Department, © 200415 Models for Ultrasonic Backscatter (cont.) n Isotropic scattering 1-D model assumptions: n transmitted ultrasound assumed to consist of planar waves (no diffraction). n sound propagates with uniform velocity c. attennuation coefficient  is uniform throught body. n body is modeled as an array of isotropic (invariant with respect to direction) scatterers.

16. EE 5340/7340, SMU Electrical Engineering Department, © 200416 Isotropic scattering 1-D model (cont.): n : reflected ultrasound pressure wave : transmitted ultrasound pressure wave : reflectivity profile :attennuation due to heat loss :attennuation due to reflected wave divergence (diffraction spreading) Reflected ultrasound has convolution property:

17. EE 5340/7340, SMU Electrical Engineering Department, © 200417 Comparison of Backscatter Models n Note that if Z(z) is a step function, n Isotropic scattering model is more general, it considers gradual changes in reflectivity. n Attennuation is compensated for by electronics. z Z1Z1 Z2Z2 h(z) is an impulse function and corresponds to specular reflection.

18. EE 5340/7340, SMU Electrical Engineering Department, © 200418 Specular reflection tissue interface incident reflected transmitted Z1Z1 Z2Z2 z

19. EE 5340/7340, SMU Electrical Engineering Department, © 200419 Wave Equation p: pressure, f(x, t) x: spatial variable t: time variable K: compressibility of medium along which wave is traveling (1)

20. EE 5340/7340, SMU Electrical Engineering Department, © 200420 Wave Equation Solutions trivial solutions: p = 0 and p = constant these can be verified by substituting into (1). Another solution: A: wave amplitude  : angular frequency of wave k: propagation constant > 0 (2)

21. EE 5340/7340, SMU Electrical Engineering Department, © 200421 Dispersion Equation Other possible solutions: Equation (2) is a solution to (1) provided that: is satisfied. Equation (3) is called the dispersion equation. (3) In fact, any function having the form is a solution provided (3) is satisfied.

22. EE 5340/7340, SMU Electrical Engineering Department, © 200422 Pressure Wave Propagation: x p x = 0 t = 0 phase = 0 phase = -2  phase = -4  phase = -6  x p x =  x t =  t phase = 0 phase = -2  phase = -4  phase = -6  xx phase

23. EE 5340/7340, SMU Electrical Engineering Department, © 200423 Wavelength and Phase Velocity wavelength, distance between two successive phase fronts: or phase at t =  t and x =  x : (4) (5)

24. EE 5340/7340, SMU Electrical Engineering Department, © 200424 Temporal Variation of Pressure Wave Observer located at x = x o, pressure is given by: t p temporal frequency: (6)

25. EE 5340/7340, SMU Electrical Engineering Department, © 200425 Frequency, Wavelength, and Phase Velocity combining (4), (5), and (6): dispersion equation, (3), can be expressed as: using (5): (7)

26. EE 5340/7340, SMU Electrical Engineering Department, © 200426 Phase Velocity of Sound in Water compressibility, density, from (7): we have looked at 1-D waves, if wave amplitude is constant along 2 spatial dimensions (x and y), then waves are called plane waves.

27. EE 5340/7340, SMU Electrical Engineering Department, © 200427 Doppler Ultrasound Flowprobes n Sound is transmitted “downstream” at frequency f t using an ultrasound transducer-transmitter. n Sound strikes red blood cell (RBC) and is reflected (specular reflection), travels “upstream” against blood flow current and strikes the transducer which has been put in receive mode. n frequency of reflected ultrasound, f r, has undergone a Doppler shift: proportional to velocity of RBC reflector

28. EE 5340/7340, SMU Electrical Engineering Department, © 200428 Geometry for Doppler Ultrasound Pressure displacement ctct P1P1 P2P2 x = 0 x = - u t = 0 c t m/s traveling wave striking a reflector moving at u m/s reflector boundary red blood cell (RBC)

29. EE 5340/7340, SMU Electrical Engineering Department, © 200429 Geometry for Doppler Ultrasound (cont.) n P 2 and P 1 : successive peaks of ultrasound wave, P 2 strikes reflector at time t = 0. n u: velocity of reflector (red blood cell), same direction as sound direction. n T: time between peak P 1 and P 2 striking the RBC. f t,  t, c t : frequency, wavelength, and velocity of transmitted ultrasound, c t = c + u f r,  r, c r : frequency, wavelength, and velocity of reflected ultrasound, c r = c - u n c: velocity of sound in stationary medium. (8) (9)

30. EE 5340/7340, SMU Electrical Engineering Department, © 200430 First Frequency Shift displacement equation:  x: displacement, since t = 0 x 0 : displacement at t = 0 v: velocity T found by solving: P 1 displacement starting at t = 0 = RBC displacement or (10)

31. EE 5340/7340, SMU Electrical Engineering Department, © 200431 First Frequency Shift (cont.) frequency of ultrasound if a listener were at the RBC = 1/T Hz or But ultrasound detector is stationary and is located upstream from RBC so frequency of reflected ultrasound (f r ) at detector is different from f m. Note also that f m < f t.

32. EE 5340/7340, SMU Electrical Engineering Department, © 200432 Second Frequency Shift wavelength of reflected ultrasound: this requires some thought, imagine moving in a vehicle at u m/s, facing the rear of the vehicle, and throwing a ball once every T seconds at a velocity of c r m/s (w.r.t. a stationary object). Distance between successive balls is r : u crcr crcr r (11)

33. EE 5340/7340, SMU Electrical Engineering Department, © 200433 Second Frequency Shift (cont.) from (9): substitute (11): subst. (10) for  : subst. for t using(8): (12) use c t = c + u, c r = c - u:

34. EE 5340/7340, SMU Electrical Engineering Department, © 200434 Total Doppler Frequency Shift Assume c >> u: (13)

35. EE 5340/7340, SMU Electrical Engineering Department, © 200435 A More Realistic Geometry x = 0 u red blood cell (RBC) transmitted ultrasound reflected ultrasound tt rr

36. EE 5340/7340, SMU Electrical Engineering Department, © 200436 A More Realistic Geometry (cont.) (12) becomes: (13) becomes: (see HW problems)