Ultrasound Physics

1. Ultrasound Physics Reflections & Attenuation ‘97

2. Perpendicular Incidence • Sound beam travels perpendicular to boundary between two media 90o Incident Angle 1 2 Boundary between media

3. Oblique Incidence • Sound beam travel not perpendicular to boundary Oblique Incident Angle (not equal to 90o) 1 2 Boundary between media

4. Perpendicular Incidence • What happens to sound at boundary? • reflected • sound returns toward source • transmitted • sound continues in same direction 1 2

5. Perpendicular Incidence 1 2 • Fraction of intensity reflected depends on acoustic impedances of two media Acoustic Impedance = Density X Speed of Sound

6. Intensity Reflection Coefficient (IRC)&Intensity Transmission Coefficient (ITC) • IRC • Fraction of sound intensity reflected at interface • <1 • ITC • Fraction of sound intensity transmitted through interface • <1 Medium 1 IRC + ITC = 1 Medium 2

7. IRC Equation 2 For perpendicular incidence • reflected intensity z2 - z1 • IRC = ------------------------ = ---------- • incident intensity z2 + z1 • Z1 is acoustic impedance of medium #1 • Z2 is acoustic impedance of medium #2 Medium 1 Medium 2

8. Reflections 2 • reflected intensity z2 - z1 • Fraction Reflected = ------------------------ = ---------- • incident intensity z2 + z1 • Impedances equal • no reflection • Impedances similar • little reflected • Impedances very different • virtually all reflected

9. Why Use Gel? 2 • reflected intensity z2 - z1 • IRC = ------------------------ = ---------- • incident intensity z2 + z1 • Acoustic Impedance of air & soft tissue very different • Without gel virtually no sound penetrates skin Fraction Reflected: 0.9995

10. Rayleigh Scattering • redirection of sound in many directions • caused by rough surface with respect to wavelength of sound

11. Diffuse Scattering & Rough Surfaces • heterogeneous media • cellular tissue • particle suspension • blood, for example

12. Scattering • Occurs if • boundary not smooth • Roughness related to frequency • frequency changes wavelength • higher frequency shortens wavelength • shorter wavelength “roughens” surface

13. Specular Reflections • Un-scattered sound • occurs with smooth boundaries • similar to light reflection from mirror • opposite of scatter from rough surface • wall is example of rough surface

14. Backscatter • sound scattered back in the direction of source

15. Backscatter Comments • Caused by • rough surfaces • heterogeneous media • Depends on scatterer’s • size • roughness • shape • orientation • Depends on sound frequency • affects wavelength

16. Backscatter Intensity • normally << than specular reflections • angle dependance • specular reflection very angle dependent • backscatter not angle dependent • echo reception not dependent on incident angle • increasing frequency effectively roughens surface • higher frequency results in more backscatter

17. PZT is Most Common Piezoelectric Material • Lead Zirconate Titanate • Advantages • Efficient • More electrical energy transferred to sound & vice-versa • High natural resonance frequency • Repeatable characteristics • Stable design • Disadvantages • High acoustic impedance • Can cause poor acoustic coupling • Requires matching layer to compensate

18. Resonant Frequency • Frequency of Highest Sustained Intensity • Transducer’s “preferred” or resonant frequency • Examples • Guitar String • Bell

19. Operating Frequency • Determined by • propagation speed of transducer material • typically 4-6 mm/msec • thickness of element • prop. speed of element (mm / msec)oper. freq. (MHz) = ------------------------------------------------ 2 X thickness (mm)

20. Pulse Mode Ultrasound • transducer driven by short voltage pulses • short sound pulses produced • Like plucking guitar string • Pulse repetition frequency same as frequency of applied voltage pulses • determined by the instrument (scanner)

21. Pulse Duration Review Pulse Duration = Period X Cycles / Pulse • typically 2-3 cycles per pulse • Transducer tends to continue ringing • minimized by dampening transducer element

22. Damping Material • Goal: • reduce cycles / pulse • Method: • dampen out vibrations after voltage pulse • Construction • mixture of powder & plastic or epoxy • attached to near face of piezoelectric element (away from patient) Damping Material Piezoelectric Element

23. Disadvantages of Damping • reduces beam intensity • produces less pure frequency (tone)

24. Bandwidth • Damping shortens pulses • the shorter the pulse, the higher the range of frequencies • Range of frequencies produced called bandwidth

25. Bandwidth Actual Intensity Bandwidth Frequency • range of frequencies present in an ultrasound pulse Ideal OperatingFrequency Intensity Frequency

26. Quality Factor (“Q”) Actual Intensity Frequency operating frequencyQuality Factor = ----------------------------- bandwidth • Unitless • Quantitative Measure of “Spectral Purity” Bandwidth

27. Damping • More damping results in • shorter pulses • more frequencies • higher bandwidth • lower quality factor • lower intensity • Rule of thumb • for short pulses (2 - 3 cycles) quality factor ~ number of cycles per pulse

28. Transducer Matching Layer Transducer – skin interface • Transducer element has different acoustic impedance than skin • Matching layer reduces reflections at surface of piezoelectric element • Increases sound energy transmitted into body

29. Transducer Matching Layer 2 • reflected intensity z2 - z1 • IRC = ------------------------ = ---------- • incident intensity z2 + z1 ) ( • placed on face of transducer • impedance between that of transducer & tissue • reduces reflections at surface of piezoelectric element • Creates several small transitions in acoustic impedance rather than one large one Matching Layer

30. Transducer Arrays • Virtually all commercial transducers are arrays • Multiple small elements in single housing • Allows sound beam to be electronically • Focused • Steered • Shaped

31. Electronic Scanning • Transducer Arrays • Multiple small transducers • Activated in groups

32. Electrical Scanning • Performed with transducer arrays • multiple elements inside transducer assembly arranged in either • a line (linear array) • concentric circles (annular array) Curvilinear Array Linear Array

33. Linear Array Scanning • Two techniques for activating groups of linear transducers • Switched Arrays • activate all elements in group at same time • Phased Arrays • Activate group elements at slightly different times • impose timing delays between activations of elements in group

34. Linear Switched Arrays • Elements energized as groups • group acts like one large transducer • Groups moved up & down through elements • same effect as manually translating • very fast scanning possible (several times per second) • results in real time image

35. Linear Switched Arrays

36. Linear Phased Array • Groups of elements energized • same as with switched arrays • voltage pulse applied to all elements of a groupBUT • elements not all pulsed at same time 1 2

37. Linear Phased Array • timing variations allow beam to be • shaped • steered • focused Above arrows indicate timing variations. By activating bottom element first & top last, beam directed upward Beam steered upward

38. Linear Phased Array Above arrows indicate timing variations. By activating top element first & bottom last, beam directed downward Beam steered downward By changing timing variations between pulses, beam can be scanned from top to bottom

39. Linear Phased Array Focus Above arrows indicate timing variations. By activating top & bottom elements earlier than center ones, beam is focused Beam is focused

40. Linear Phased Array Focus Focal point can be moved toward or away from transducer by altering timing variations between outer elements & center

41. Linear Phased Array Focus • Multiple focal zones accomplished by changing timing variations between pulses • Multiple pulses required • slows frame rate

42. Listening Mode • Listening direction can be steered & focused similarly to beam generation • appropriate timing variations applied to echoes received by various elements of a group • Dynamic Focusing • listening focus depth can be changed electronically between pulses by applying timing variations as above 2

43. 1.5 Transducer • ~3 elements in elevation direction • All 3 elements can be combined for thick slice • 1 element can be selected for thin slice Elevation Direction

44. 1.5 & 2D Transducers • Multiple elements in 2 directions • Can be steered & focused anywhere in 3D volume