Ultrasound 1 Flashcards
what is acoustic pressure?
also called excess pressure
Pressure_Tube = pressure from the ambient level + acoustic pressure
When is there an increase in pressure in a longitudinal wave?
compression (positive pressure)
When is there a decrease in pressure in a longitudinal wave?
rarefaction (negative pressure)
When is the acoustic pressure at a maximum?
When the particles are moving towards to each other
How are pressure and particle velocity related?
related by the bulk speed of sound value and the ambient value of density
pressure of the particle in a plane wave = pressure of the ambient * bulk sound speed value * particle velocity
For waves with a small amplitude, how are pressure and density related?
By the sound speed:
p = c^2 * density
what is the equation that describes the wave with a small amplitude, in time and space?
p(x,t) = p_0 * sin(kx + wt)
What does the constant k represent in the equation describing the wave in time and space?
2*pi/ wavelength also known as the wavenumber (i.e number of waves that fit in one full oscillation)
what does the constant w represent in the equation of a small amplitude wave?
w = 2*pi * frequency of the wave
How is angular frequency and wavenumber related?
w = c* k
given that k = 2pi/ wavelength
and w = 2pif
where c = fwavelength
so that f = c/wavelength
substituting into the equation for angular frequency
w = 2* pi* c/wavelength
wavelength = k/2*pi
substituting again
w = ck
what is the constant c equal to in the equation describing the wave in space and time w = ck
c = sqrt (K/density)
What is the constant K in the equation of wave speed derived from the wave in time and space equation?
The Bulk modulus
What does the bulk modulus describe?
The stiffness of the medium
The relative change in density of a material induced by an applied pressure (the higher the change, the lower the resistance)
density, applied pressure are inversely proportional
What is the density of water?
1000kg/m^3
How can the transfer of energy through the medium in acoustic waves be described?
Acoustic energy density
Kinetic energy
Kinetic energy density
Potential energy density
What is the word definition of acoustic energy
The sum of time averaged kinetic and potential energy density
What is the mathematical definition of kinetic energy?
1/2 * m* v^2
What is the mathematic definition of kinetic energy density?
1/2 * density * speed of particle^2
What is the mathematical definition of potential energy density?
1/2 * (pressure ^2) * (1/ambient pressure * speed of sound ^2)
How to describe the energy flow of acoustic waves?
Energy/energy density, intensity, Power
What is the word definition of intensity?
the energy flowing through unit area per second.
What is the definition of power?
The rate of energy production by a source, or the rate at which energy flows across a surface- the sum or integral of intensity over a surface
Mathematical definition of instantaneous intensity (a function of space and time)
I(x,t) = pu
pressure of the wave * speed of the wave
Mathematical definition of the time averaged intensity (a function of space)
I(x) = <pu>
The pressure and particle velocity are averaged over a whole number of wave cycles</pu>
How are echoes created?
By reflections and scattering from objects, structures or small scatterers in the tissues of the body.
What must there be for an echo to be generated?
A difference in the sound speed and/or the density of the structure for this to happen - i.e the acoustic impedance must vary
What does the impedance describe?
How particles in a medium respond to a pressure wave.
What type of quantity is specifci acoustic impedance?
A local quantity
How to mathematically define the specific acoustic impedance?
The ratio of pressure to the particle velocity z = p/u
What does the impedance depend on?
The density and stiffness of the medium (i.e the bulk modulus)
What kind of quantity is charactersitic acoustic impedance?
A bulk property
for a plane wave, what is the characteristic acoustic impedance equal to?
z = ambient density * speed of sound = ambient density * sqrt( bulk modulus/density of the material )
What happens to a wave incident on a boundary?
It will be partly reflected and partly transmitted
What do the amplitudes of the reflected and transmitted waves relative to the amplitude of the incident wave depend on?
The impedance of the materials on either side of the boundary
What constant defines the factor that affects the amplitude of the reflected and transmitted waves relative to the incident wave? (reflection)
The factor that affects the amplitude of the reflected and transmitted waves relative to the incident wave is the amplitude reflection coefficient
What constant defines the factor that affects the amplitude of the reflected and transmitted waves relative to the incident wave? (transmission)
The factor that affects the amplitude of the reflected and transmitted waves relative to the incident wave is the amplitude transmission coefficient
what is the amplitude reflection coefficient equal to?
the ratio between the reflection pressure amplitude/ incident pressure amplitude
what is the amplitude transmission coefficient equal to?
the ratio between the transmission pressure amplitude and the incident pressure amplitude
How can the ratio of reflected pressure amplitude and incident pressure amplitude be calculated?
From the properties (impedances) of the 2 materials on either sides of the boundary
i.e
amplitude reflection coefficient = (z_2 - z_1)/(z_2 + z_1)
How can the ratio of transmission pressure amplitude and incident pressure amplitude be calculated?
From the properties (impedances) of the 2 materials on either sides of the boundary
i.e
2*z_2 / (z_2 + z_1)
How to derive the expression describing the reflection amplitude coefficient in terms of impedances? (1)
at the boundary: pressure must be continuous, so pressure at one side of the boundary = pressure at other side
incident pressure + reflected pressure = transmitted pressure
How to derive the expression describing the reflection amplitude coefficient in terms of impedances? (2)
The particle velocity at either side of the boundary must also be continuous - particles at one side are moving at the same velocity as particles on the other side
u_i + u_r = u_t
(incident particle velocity+ reflected particle velocity = transmitted particle velocity)
How to derive the expression describing the reflection amplitude coefficient in terms of impedances? (3)
The specific impedances of the 2 materials are given by the ratio of the pressure to the particle velocity
How to derive the expression describing the reflection amplitude coefficient in terms of impedances? (4)
The specific impedances for the incident, reflected and transmitted waves are:
- u_i = P_i / z_1
- u_r = -P_r /z_1
- u_t = P_t / z_2
substitue these into the equation for velocities and rearrange for the form p_r / p_i = amplitude reflection coefficient
How are the intensity reflection and transmission coefficient sderived?
There must be conservation of energy at the boundary so the intensity reflection coefficient + intensity transmission reflection coefficient = 1
what is the intensity of the wave proportional to ?
the square of the pressure
how can the intensity reflection coefficient be rewritten?
the ratio of the reflected intensity coefficient / incident intensity coefficient = pressure of the reflected wave ^ 2/ pressure of the incident wave ^ 2 = amplitude reflection coefficient ^ 2
How can the intensity transmission coefficient be written as?
1 - intensity reflection coefficient = 1 - ratio of intensity reflected coefficient / intensity incident coefficient = 1 - amplitude reflection coefficient ^ 2
T_1 = 4z_1z_2 / (z_2 + z_1)^2
What is snell’s law in terms of velocity of the wave in medium 1/2?
sintheta 1/ c_1 = sintheta 2 / c_2
When does TIR occur?
when the velocity of the wave in the first material < wave in the second material (i.e impedance of first is higher than impedance of second material)
what is the equation for the critical angle?
sin(critical angle) = c_1/ c_2
On what types of boundaries does specular reflection occur?
At large, flat and smooth boundaries
What is the dependency of power and frequency of sound during specular reflection?
NO dependency
How does the type of interaction with structures on a range of scales depend on in specular reflection?
depends on the size of the structure relative to the wavelength of sound
When does Rayleigh scattering occur?
When the size a of the scatterer is much less than the wavelength a«_space;wavelength
What is the dependency of power of the scattered sound, W, on the frequency of the sound?
W is proportional to the a^6 * f^4
When the sound is scattered over a large angle in Rayleigh scattering, what will be the appearance on an ultrasound image?
The same when imaged from different angles
When does diffraction occur?
when the size of the scatterer is similar to the wavelength
What happens to sound as it passes through a medium?
Some of the energy is lost, and the wave amplitude decreases with distance
What are the mechanism of energy loss of a wave as it travels?
absorption, scattering and diffraction
What is the overall loss in energy from a beam called?
attenuation
Absorption, scattering and diffraction(divergence of the beam)
How does pressure decay with distance?
Exponentially
p(z) = ambient pressure * e^(-attenuation coefficient * specific acoustic impedance)
In exponential form, what are the units of the attenuation coefficient?
Nepers/m or m^-1. Nepers is dimensionless
How to convert from nepers/m to dB/m
20log10((p_0 * e^-a)/p_0) = -a20log10(e) = -8.686a
How can the attenuation over some distance be calculated for a graph in the units of db/m vs m?
Adding together the reduction over each cm
In tissues, how does the attenuation coefficient change with frequency?
It increases with frequency
for many tissues, the value of the attenuation coefficient doesn’t vary linearly with frequency so what is the actual equation?
a = a_0 * f^y
What is the equation for attenuation?
the sum of the absorption attenuation coefficient and scattering attenuation coefficient
What forces resist the movement of the particles in the medium (oscillation)?
Viscous drag
What are the main forms of energy loss in oscillating wave?
viscous drag (friction)
processes on the molecular level
What is the energy transfer from being removed from the oscillation of the wave and the molecular level energy?
absorbed by the medium and turned into thermal energy
What does the energy transfer due to attenuation effects lead to?
A temperature rise as it is turned into thermal energy
