Primary Snippet – Doppler Effect and properties of transducers

Dr Swapnil Pawar March 11, 2023 197

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    Primary Snippet – Doppler Effect and properties of transducers
    Dr Swapnil Pawar

The principles of ultrasound:

  • US is sound whose frequency is above the range of human hearing
  • US waves are generated from multiple small piezoelectric crystals within the transducer; alternating current applied to crystals  crystals deform and vibrate at high speeds  electrical energy converted into sound waves
  • These waves can be represented graphically as a sine wave
    • Wavelength = distance between one peak of the wave and the next peak
    • A cycle = time it takes for a complete wave
    • Amplitude = maximal excursion of the wave in the positive or negative direction from baseline.
  • For most modes of ultrasound, the transducer emits a limited number of wave cycles termed a pulse  sent out at regular intervals = pulse repetition frequency
  • The high frequency sound waves generated by transducer do not travel well through air  requires gel to conduct it
  • Pulses travel through different tissues and lose energy = attenuation. Deeper structures undergo more attenuation  more difficult to image. Four processes cause attenuation:
    • Absorption: some of the sound wave is absorbed by tissues  converted into heat. Higher frequency sound waves absorbed more than lower frequency
    • Reflection: sound wave bounces back to the probe
      • Generally more reflection = more hyperechoic (brighter) image
      • Interfaces between soft tissues will have a different percentage of energy reflected depending on the difference in acoustic impedance between the tissues (acoustic mismatch)
        • If small difference than very little energy reflected e.g. kidney and liver
        • If very large difference there may be complete reflection e.g. soft tissue and bone  acoustic shadowing (area behind the structure is completely black as virtually all sound waves are reflected)
      • Refraction: sound wave meets interface between two tissues at an angle other than 90 degrees  part of wave is reflected and part transmitted into neighbouring tissue  direction of wave is changed (can cause errors in location of reflected objects)
        • Optimal is when sound wave meets tissue of interest at 90 degrees
      • Scattering
        • Propagation of sound waves in oblique directions  occurs when tissue being examined is not heterogeneous or is irregular
      • Pulses return to transducer as reflected echoes  converted back into electrical impulses by crystals  amplified and processed to form an ultrasound image on the screen. The transducer acts as a receiver of these echoes (as opposed to sending signals), more than 99% of the time.

Transducer properties and image resolution:

  • Different types of transducers exist – operate over range of frequencies depending on the type of transducer
    • Lower frequency sounds penetrate more deeply but lower resolution image
    • Higher frequency sound waves can not image as deep but provide higher resolution
  • Image resolution can be spatial or temporal
    • Spatial: ability to distinguish correct location of an object relative to another object  three types are axial, lateral, elevational
      • Axial: ability to differentiate distinct objects parallel to the ultrasound beam  determined by sound wave frequency  higher frequencies = better axial resolution
      • Lateral: ability to differentiate objects perpendicular to the beam – side by side structures  determined by width of beam which depends on diameter and frequency of piezoelectric crystals
        • Small diameter crystals producing high frequency pulses  narrow ultrasound beams  increase lateral resolution. Narrowest part of US beam = focal zone – has greatest lateral resolution
          • Depth of focal zone can be adjusted to area of target structures to maximise lateral resolution
          • Decreasing gain (gain is amplification of returning ultrasound signal)  decreases beam width  improves lateral resolution
        • Elevational: ability to distinguish two structures perpendicular to the plane formed by ultrasound beam’s path and the lateral axis of the path
          • Governed by beam height  decreased beam height improves elevational resolution
        • Temporal: ability to correctly determine position of object at a particular moment which depends on how much the imaged object moves and the frame rate
          • Decreased imaging depth increases the time the transducer has to wait for return echoes  increases frame rate  improves temporal resolution
          • Narrowing sector to area of interest also improves temporal resolution.
  • Common probes we use
    • Linear array: multiple small crystals arranged in a straight line across the rectangular probe face
      • Beams generated travel at 90 degrees to transducer face therefore the line of sight is parallel and the image view is rectangular
      • High frequency  good for superficial structures but lower penetration
    • Curved array or curvilinear: face of transducer is convex
      • Beam travels at 90 degrees  due to convex transducer field of view is wider at bottom of image and narrower at top of image (near field)  can image an area larger than the footprint of the transducer,
      • Good for deeper structures as it is lower frequency (although image resolution decreases with depth) but worse lateral resolution
    • Phased array: generally used for echocardiography
      • Narrow beam which expands depending on applied frequency  triangle beam shape, poor near field resolution
      • Small footprint, lower frequency, higher penetration depth

The Doppler Effect:

  • Observed change in frequency of a sound wave due to relative movement between emitting sound source and observer:
    • Sound waves emitted by an object travelling towards an observer are compressed resulting in higher frequency
    • Sound waves moving away are stretched  lower frequency
    • Doppler effect does not occur if both sound source and observer are moving in same direction at the same speed OR if source is at 90 degrees to the receiver
  • With ultrasound can be used to detect and measure blood flow (can use to check the presence or absence of flow, the direction of flow and the velocity of flow)
    • If blood is moving towards transducer  higher frequency  positive Doppler frequency shift (generally seen as RED in colour Doppler)
    • If blood is moving away from transducer  lower frequency  negative Doppler frequency shift (generally seen as BLUE in colour Doppler)

fDop : Doppler shift – refers to the difference between the transmitted and received frequencies (n the case of blood flow, occurring due to movement of red blood cells relative to the transducer)
f0: transmitted frequency from US probe
v: velocity of moving reflector (blood in Doppler US)
c: velocity of sound in tissue
Ѳ: angle between the US beam and the axis of flow

  • cos0° = 1  to improve Doppler technique when scanning try and ensure the movement of what you’re measuring is as close to parallel as possible to the probe
  • higher Doppler shift is obtained if the velocity of blood is higher and if higher frequency ultrasound signal is sent
  • equation can be re-arranged to calculate the velocity of blood flow
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