9 Ultrasound Imaging

Introduction

  • Pros of ultrasound imaging
      * Inexpensive
      * Simple
      * Fast
      * Portable
      * Non-ionizing
        * True: True or false, ultrasound imaging is non-ionizing.
      * Excellent depth resolution
      * Anatomical & functional info
        * True: True or false, ultrasound imaging shows anatomical and functional info.
        * Blood flow is the best example of the functional information that an ultrasound can show.
  • Cons of ultrasound imaging
      * Poor angular resolution
        * Fan beams from ultrasounds don’t help show the angular rays, because it uses mostly parallel beams.
      * Depth limited
        * Some beams are immediately reflected at the skin, so beams that pass through are already low energy and then they still have to travel back to the receptor
      * Material specific limitations
        * False: True or false, ultrasounds can handle a big difference in density (i.e. between bone and air) and can see beyond bone.
        * Think, why would ultrasound imaging be bad for looking at the lungs? Because it has to pass through the ribcage and you have to deal with air reflection

Common Imaging Modes

  • A-mode: An imaging mode of ultrasound, where the amplitude of returning signal is returned and plotted; measures one line at a time
      * X axis is time and y axis is amplitude
      * A mode is a 1-D plot
  • B-mode: An imaging mode of ultrasound, where A-line the a line plot of amplitude is shown as brightness over a certain distance
      * B mode is a 2-D plot
  • M-mode: An imaging mode of ultrasound where a plot of A-line, converted to brightness, and then repeated over time; shows motion; the plot is position vs time
      * M mode is a 2-D plot
  • Doppler: An imaging mode of ultrasound; if the object is moving then the returning wave will change, and that change in frequency is measured as velocity; color overlays are used to show velocity of flow and direction
      * Continuous doppler requires two transducers
      * Pulse doppler works like a speed trap meter
      * Doppler mode is a 2-D plot with an overlay

Ultrasound Physics

What is Sound?

  • Sound is a mechanical pressure wave
  • Audible waves have a frequency of 20 Hz to 20 kHz
  • Ultrasound waves operate with frequencies greater than 20 kHz
  • Speed of sound = frequency * wavelength

Ultrasound Physics

  • Sound needs a medium to travel through
  • Sound is a longitudinal mechanical wave, which means the wave goes out and comes back along the same line
      * Transverse waves can scatter, but aren’t used by ultrasounds
      * Particles vibrate back-and-forth with a “zero” net movement in ultrasound
  • Represent compression (particles bump down the line like a spring) and rarefaction (particles move away from each other) of travel medium particles

Wave Propagation

  • Particle velocity: How fast a particle is moving back and forth, not wave speed
      * u = 𝝏𝒛/𝝏𝒛

Wave Equations

 

  • Exponential sinosoid decay in pressure variation
  • ρ is the average material density (kg/m^3)
  • K is the compressibility constant of the material (ms^2 / kg)
  • Pm is the maximum pressure intensity and amplitude (kPa)
  • α is the linear attenuation coefficient (1/cm)
  • ω is the frequency (rad/s) or 2pif where f is frequency (Hz)
  • k is the wave number or the propagation constant (1/m)
  • The average speed of sound through soft tissue is 1540 m/s
  • Intensity is the square of the pressure
      * Pressure vs time (a) and intensity vs time (b)

Ultrasound Imaging

  • The gel that goes on the skin where the transducer applies decreases the amount of air between transducer and skin, so you get less uneccessary reflection
  • Note: The black x axis is time and the red x axis is distance
  • A-Mode
      * Distance = c * ∆t * 1/2
  • Smaller peaks in the [V] vs time mean that the wave has less energy when it reaches the transducer
  • B-mode imaging is formed by combining multiple A-mode lines to form a frame
      * Frame time = number of lines x (time of a line + time of a pulse) *for individually pulsed
      * Frame time = time of line + time of pulse *for simultaneously pulsed
      * Frame time determines the maximum depth of return echos in ultrasound.
      * Refresh rate: Numbe of frames drawn per second (1/time of frame)
        * Refresh rate being higher means it’s closer to real-time

Transducers

  • Sector: Ultrasound probe best for large structures that are deep in the tissue
      * Sector transducers allow imaging through a narrow sonographic window in ultrasounds
      * Sector transducers have an image shaped like a pie slice
  • Linear: Ultrasound probe best for imaging small structures that works best for structures just beneath the skin
  • Curved: An array ultrasound probe that combines sector and linear formats, best for a broad sonographic window

Acoustic Impedance

  • Acoustic impedance is denoted by the letter Z
  • Z = 𝜌0 c = 𝜌0 x (𝜌0 * k)^-1/2 = (𝜌0 / k)^1/2
      * Z of soft tissue is 1.63 x 10^6 kg / m^2 *s
      * Z of water is 1.52 x 10^6 kg / m^2 *s
      * Z of the skull is 7.8 x 10^6 kg / m^2 *s
  • Units of acoustic impedance are kg / m^2 *s

Material & Wave Interaction

  • There are two types of acoustic interaction, which is at interfaces between different materials (boundaries & transmission) and within the material itself (attenuation)
  • At a new interface, some energy is reflected back and some is transmitted (refracted)
      * The reflecting and refracting at a new interface during ultrasound is due to the acoustic impedance
  • Snell’s Law
      *
  • At the critical angle, we will have total reflection of the incident wave and no transmission into second medium
  • A negative value for R indicates a 180 degree phase shift (flip over x-axis); this affects phase shift, but not amplitude or anything else
  • ==Reflectivity is zero when the acoustic impendences are equal to one another==
  • Transmittivity (T) is transmitted pressure over initial presssure
      * Transmittivity is between zero and positive 2
        * 2 occurs when the reflected energy is the same as the initial, so it doubles (reflects on the same path)
      * Transmission = 1 + R
        * 1 + (Z2 - Z1) / (Z2 + Z1)
  • At interface
      * At interface, there is no particle movement.
      * At interface, pressure must be continuous
  • The linear attenuation coefficient in ultrasound imaging is a linear function of frequency
      * As frequency increases in an ultrasound, the linear attenuation also increases
  • Pressure vs Intensity
      * Acoustic wave intensity is used to measure the power in the wave
      * I = Pressure^2 / Z
  • P = Pm e ^ - 1 alpha *** frequency * distance
      * Alpha needs to be in the inverse unit of the distance
      * To increase distance, you need to decrease the energy
  • Combined effects of interaction through multiple materials are multiplicative
      *
      *