Formulae Flashcards
Describe the relationship between propagation speed, wavelength and frequency
c = f x λ
Define intensity
intensity = power/area
Show the formula for attenuation
Attenuation = 10 x log(I1/I2) dB
Attenuation = (α x L x f) dB
Coefficient for soft tissue is approximately 0.5dB/cm/MHz
Show the formula for the reflection coefficient
R = (z1 - z2)^2 / (z1 + z2)^2
This is a measure of the fraction of ultrasound energy that is reflected
When the impedance is similar, the fraction is close to 0
When the impedance is very different, the fraction is close to 1
Show the formula for Snell’s law
(sin θi)/c1 = (sin θt)/c2
Show the formula for calculation of the critical angle
θc = sin-1(c1/c2)
Solving Snell’s law for θt = 90 degrees
How does the ultrasound machine determine the depth of an object?
d = (c x t) / 2
round path = 2d
propagation speed assumed at 1540m/s
Calculate the timing of the last detectable echo
tp = 2P/c
P = depth of maximum penetration
Show the relationship between PRF max and timing of the last detectable echo
How does the ultrasound machine use this information
1/tp = PRF
Given that tp = 2P/c
PRF = c/2P
Show the relationship between frame rate and PRF
PRF = FR x N
N = number of pulses required to form an image
Show the relationship between FR max, depth of penetration and propagation speed
FR max = c/2 x P x N
FR max x P x N = c/2
Given c is a physical constant, to increase any of the left side, we must decrease the others
Define the formula to calculate the nearzone length
NZL = A^2 / 4 x wavelength
Define the formula for calculation of the diffraction limit divergence angle
theta = sin-1 (1.22 x wavelength) / A
A = aperture
Define the formula for beam width at focus
(2.44 x wavelength x F) / A
F = depth of focus
A = aperture diameter
Define the formula for axial resolution
propagation speed x transmit pulse duration / 2
(c x t) / 2
