Ultrasound Physics Summary

1. Introduction to Ultrasound

• Definition: Ultrasound refers to sound waves with frequencies higher than the upper audible limit of human hearing. This limit is typically considered to be 20,000 Hertz (20 kHz).

• Frequency Range: Medical diagnostic ultrasound typically uses frequencies ranging from 2 MHz to 18 MHz (or higher).

• Applications: Used in various medical fields for imaging, diagnosis, and therapeutic purposes due to its non-invasive nature and real-time imaging capabilities.

2. Sound Wave Properties

• Nature of Sound Waves: Ultrasound waves are mechanical, longitudinal waves, meaning they require a medium for propagation and molecular particles oscillate parallel to the direction of wave propagation.

• Key Parameters:

  • Frequency ($f$): The number of cycles per second, measured in Hertz (Hz). Determines penetration and resolution.

  • Wavelength ($\lambda$): The spatial length of one complete cycle of a wave, measured in meters (m). Inversely related to frequency: $\lambda = c/f$

  • Period ($T$): The time it takes for one complete cycle to occur, measured in seconds (s). $\text{Period} = 1/ ext{Frequency}$.

  • Amplitude: The maximum displacement or distance moved by a point on a vibrating body or wave measured from its equilibrium position. Related to the strength or intensity of the sound wave.

  • Power ($P$): The rate at which energy is transferred, measured in Watts (W). Proportional to amplitude squared.

  • Intensity ($I$): The power per unit area, measured in $W/cm^2$. Proportional to power: $I = P/A$. Related to the strength of the sound wave.

• Propagation Speed ($c$): The speed at which sound travels through a medium, determined by the medium's density and stiffness.

  • Formula: $c = f \lambda$

  • Average speed in soft tissue: approximately $1540 \text{ m/s}$ ($1.54 \text{ mm/}\mu s$).

3. Interaction of Ultrasound with Tissue

• Attenuation: The gradual reduction in intensity (and amplitude) of the ultrasound beam as it travels through a medium due to absorption, reflection, and scattering.

  • Absorption: Conversion of acoustic energy into heat (primary mechanism)

  • Reflection: Occurs when the sound wave encounters an interface between two media with different acoustic impedances.

  • Scattering: Redirection of the sound wave in multiple directions by small, irregular interfaces (e.g., red blood cells).

  • Attenuation Coefficient: The rate at which sound is attenuated per unit distance ($dB/cm$). Generally, higher frequencies attenuate more rapidly.

• Acoustic Impedance ($Z$): The resistance a medium offers to the passage of sound waves. It is the product of the density ($\rho$) of the medium and the speed of sound ($c$) in that medium: $Z = \rho c$, measured in Rayls.

• Reflection: The bouncing back of sound waves when they hit a boundary.

  • Specular Reflection: Occurs at large, smooth interfaces, where the angle of incidence equals the angle of reflection (e.g., organ capsules).

  • Diffuse Scattering: Occurs at rough or irregular interfaces where the sound is scattered in many directions (e.g., parenchyma of organs).

• Refraction: The change in direction of an ultrasound beam as it crosses an interface between two media where the speed of sound is different and the incidence is oblique. Described by Snell's Law.