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

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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

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• 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

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• At the critical angle, we will have total reflection of the incident wave and no transmission into second medium

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• 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

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