Principles of Ultrasound

Describe the physical principles of ultrasound and the Doppler Effect.

Ultrasound is an imaging technique where high-frequency sound waves (2-15MHz) are used to generate an image. An ultrasound wave is produced by a probe using the piezoelectric effect:

• Certain crystalline structures will vibrate at a particular frequency when a certain voltage is applied across them
  The conversion of electrical energy to kinetic energy is how the ultrasound probe creates an ultrasound wave.
• Similarly, they can generate a voltage when a vibration is induced in them
  This is how the probe interprets reflected waves.

Basic Principles

• Spatial resolution
  How close two separate objects can be to each other and still be distinguishable. It is divided into:
  • Axial resolution, how far apart two objects can be when one is above the other (in the direction of the beam)
  • Lateral resolution, how far apart two objects can be when side side-by-side

• Contrast resolution is how similar two objects can appear (in echogenic appearance) and still be distinguishable

• Higher frequency settings offer greater spatial resolution but decreased penetration

• Lower frequency settings offer reduced spatial resolution but increased penetration
  They are used for visualising deep structures.

Affect of Tissues on Ultrasound

At tissue interfaces, the wave may be:

• Absorbed
  Sound is lost as heat, and increases with decreased water content of tissues.
• Reflected
  Sound bounces back from the tissue interface, and returns to the probe.
  • Reflection is dependent on the:
    • Difference in sound conduction between the two tissues
    • Angle of incidence (close to 90° improves reflection)
    • Smoothness of the tissue plane
  • The amplitude of sound returning to the probe determines echogenicity, or how white the object will be displayed
  • The time taken for the sound to return determines depth
    • The time taken for a wave to return is proportional to twice the distance of the object from the probe
    • Depth can be calculated using $d = vt$, where:
      • $d$ is Depth
      • $v$ is the speed of sound in tissue, and is assumed to be 1540 ms^-1
      • t is Time
• Transmitted
  Sound passes through the tissue, and may be reflected or absorbed at deeper tissues.
• Scattered
  Sound is reflected from tissue but is not received by the probe.

• Attenuated
  Attenuation describes the loss of sound wave with increasing depth, and is a function of the above factors.
  • Attenuation is managed by increasing the gain
    Gain refers to amplification of returned signal.
  • Time-gain compensation refers to amplification of signals which have taken longer to return, which amplifies signals returned from deep tissues

Modes

Ultrasound modes include:

• B-Mode (brightness mode)
  The standard 2D ultrasound mode, and plots the measured amplitude of reflected ultrasound waves by the calculated depth from which they were reflected.
• M-Mode (movement mode)
  Selects a single vertical section of the image and displays changes over time (i.e. depth on the y-axis, and time on the x-axis).

Doppler Effect

The doppler effect is the change in observed frequency when a wave is reflected off (or emitted from) a moving object, relative to the position of the receiver. In medical ultrasound, this is the change in frequency of sound reflected from a moving tissue (e.g. an erythrocyte). It is given by the equation:

$V = { \Delta Fs \over 2F_0cos\theta}$ where:

$V$ = Velocity of object
$F$ = Frequency shift
$s$ = Speed of sound (in blood)
$F_0$ = Frequency of the emitted sound
$\theta$ = Angle between the sound wave and the object

Reflected frequencies are higher towards the probe and lower away.

Calculation of Cardiac Output

Remember, $CO = HR \times SV$.

• Heart rate is measured
• Stroke volume is calculated by:
  • Measuring the cross-sectional area of the left ventricular outflow tract
    Obtained by measuring the diameter using ultrasound.
  • Measuring the stroke distance
    Obtained via integrating the velocity-time waveform for time across the left ventricular outflow tract (LVOT VTI).
    • The integral of flow (m.s^-1 and time (s)) for time (s), produces a distance (m)
  • Multiplying the LVOT cross-sectional area (m²) by the stroke distance (m), produces a volume (m³)
    This is the stroke volume.

References

1. Cross ME, Plunkett EVE. Physics, Pharmacology, and Physiology for Anaesthetists: Key Concepts for the FRCA. 2nd Ed. Cambridge University Press. 2014.
2. CICM July/September 2007.