Physics of Ultrasound Energy

This course explores the physics of ultrasound energy, including wave propagation, intensity, and attenuation with relevant calculations.

Module 1: Basics of Sound Waves

Ultrasound waves are mechanical sound waves that propagate through a medium by compressions and rarefactions.

Formula:
Speed of Sound (c):
c = λ * f
where
c = speed of sound in the medium (m/s)
λ = wavelength (m)
f = frequency (Hz)

Example Calculation:
Given an ultrasound frequency of 2 MHz (2 × 10⁶ Hz) in soft tissue where c = 1540 m/s, calculate the wavelength.
Solution:
λ = c / f = 1540 m/s / 2 × 10⁶ Hz = 0.00077 m or 0.77 mm

Module 2: Ultrasound Intensity

Ultrasound intensity represents the power per unit area and is crucial in medical imaging for assessing energy delivered to tissue.

Formula:
Intensity (I):
I = P / A
where
I = intensity (W/m²)
P = power (W)
A = area over which power is distributed (m²)

Example Calculation:
If an ultrasound transducer delivers 0.5 W of power over an area of 0.001 m², calculate the intensity.
Solution:
I = P / A = 0.5 W / 0.001 m² = 500 W/m²

Module 3: Attenuation of Ultrasound in Tissue

As ultrasound travels through tissue, its intensity decreases due to absorption, scattering, and reflection.

Formula:
Attenuation (I):
I = I₀ * e^-μx
where
I = final intensity
I₀ = initial intensity
μ = attenuation coefficient (m^-1)
x = depth (m)

Example Calculation:
Given an initial intensity of 600 W/m² and a depth of 0.05 m with an attenuation coefficient of 1.5 m^-1, calculate the final intensity.
Solution:
I = 600 * e^{-1.5 * 0.05} ≈ 600 * e^-0.075 ≈ 555.2 W/m²

Note: The attenuation coefficient varies by tissue type and frequency, and understanding this is critical in diagnostic imaging.