### Ultrasound

```Outline
• What is ultrasound
• Ultrasonic signal generation
• Diagnostic Ultrasound
–
–
–
–
Ultrasound imaging
Array systems, Co-Arrays, K-space
Beamformers
Biosensors
• Theraupatic Ultrasound
– Effect of US->Heating, vibrating,etc.
– US power transmission and the applications
• Doppler effect and the applications
• Microfluidics applications
What is Ultrasonic wave?
• Wave, a wave is a disturbance or oscillation that travels
through space and matter, accompanied by a transfer
of energy. Wave motion transfers energy from one
point to another, often with no permanent
displacement of the particles of the medium.
• There are two main types of waves:
– Mechanical Waves: Propagate through a medium, and the
substance of this medium is deformed.
– Electromagnetic Waves: do not require a medium. Instead,
they consist of periodic oscillations of electrical and
magnetic fields generated by charged particles
Mechanical Waves
• Longitudinal Wave: wave particles vibrate back
and forth along the path that the wave travels.
• Compressions: The close together part of the
wave
• Rarefactions: The spread-out parts of a wave
Mechanical Waves
• Transverse Wave: wave particles vibrate
in an up-and-down motion.
• Crests: Highest part of a wave
• Troughs: The low points of the wave
Wave Properties
• In liquids and gases, US propagates as
longitudinal waves.
• In solids, US propagates also as transversal
waves.
• Amplitude: is the maximum distance the
particles in a wave vibrate from their rest
positions.
• Frequency : the number of waves produced in
a given time
Wave Properties
Frequency= #ofwaves/time
• Wavelength: The length of a single wave.
• #ofwaves = (Total displacement in a given
time) / (The length of a single wave)
• => Frequency = Total
displacement/wavelength*Time)
• Wave Velocity - is the speed with which a wave
crest passes by a particular point in space. (wave
velocity=Total displacement/time). It is measured
in meters/second.
• Result: Wave Velocity = Frequency Wavelength
Speed of Sound
• Medium
air (20 C)
air (0 C)
water (25 C)
sea water
diamond
iron
copper
glass
velocity m/sec
343
331
1493
1533
12000
5130
3560
5640
Speed of Sound Waves
In gas and liquids:
v
In solids:
B
v

Y

Y… Young’s modulus
B… Bulk modulus of medium
…density of material
Bulk modules
determines the
volume change of
an object due to an
applied pressure P.
volumestress F / A
P
B


volumestrain V / Vi V / Vi
Young’s modules
determines the length
change of an object
due to an applied force
F.
tensilestress F / A
Y

tensilestrain L / Li
Ultrasound
sound waves with frequencies above the
normal human range of hearing.
Sounds in the range from 20-100kHz
-
Infrasound
- sounds with frequencies below the
normal human range of hearing.
Sounds in the 20-200 Hz range
Types of US Waves
• Bulk Waves: 3 Dimensional propagation
• Guided waves: Propagates at surfaces,
interfaces and edges. (Surface Acoustic
Waves). Reigleigh wave. Lowe Wave Shear
Horizontal Wave etc.
Interference
• the result of two or more sound
• waves overlapping
Diffraction
• No-one has ever been able to define the
difference between interference and diffraction
satisfactorily. It is just a question of usage, and
there is no specific, important physical difference
between them.
Richard Feynman
Interactions of US with Tissue
 Reflection (smooth homogeneous interfaces of size
greater than beam width, e.g. organ outlines)
 Rayleigh Scatter (small reflector sizes, e.g. blood cells,
dominates in non-homogeneous media)
 Refraction (away from normal from less dense to denser
medium, note opposite to light, sometimes produces
distortion)
 Absorption (sound to heat)
– absorption increases with f, note opposite to X-rays
– absorption high in lungs, less in bone, least in soft
tissue, again note opposite to x-rays
15
Acoustic parameters of medium:
• Interaction of US with medium – reflection and backscattering, refraction, attenuation (scattering and
absorption)
16
Acoustic parameters of medium
Speed of US c depends on elasticity and density r of
the medium:
K - modulus of compression
in water and soft tissues c = 1500 - 1600 m.s-1, in
17
Acoustic parameters of medium
Attenuation of US expresses decrease of wave amplitude along its
trajectory. It depends on frequency
Ix = Io e-2ax
a = a´.f2
Ix – final intensity, Io – initial intensity, 2x – medium layer thickness
(reflected wave travels „to and fro“), a - linear attenuation
coefficient (increases with frequency).
Since
a = log10(I0/IX)/2x
we can express a in units dB/cm. At 1 MHz: muscle 1.2, liver 0.5,
brain 0.9, connective tissue 2.5, bone 8.0
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Acoustic parameters of medium
Attenuation of
ultrasound
When expressing intensity
of ultrasound in decibels,
i.e. as a logarithm of Ix/I0,
we can see the amplitudes
of echoes to decrease
linearly.
I or P
[dB]
attenuation
depth [cm]
19
Acoustic parameters of medium
Acoustic impedance: product of US speed c and
medium density 
Z= .c
(Pa.s/m)
Z.10-6: muscles 1.7, liver 1.65 brain 1.56, bone
6.1, water 1.48
20
Acoustic parameters of medium: US reflection
and transmission on interfaces
We suppose perpendicular incidence of US on an interface between two
media with different Z - a portion of waves will pass through and a portion
will be reflected (the larger the difference in Z, the higher reflection).
P1
Z2 - Z1
R = ------- = --------------P
Z2 + Z1
P2
2 Z1
D = ------- = --------------P
Z2 + Z1
Coefficient of reflection R – ratio of acoustic pressures of reflected and
incident waves
Coefficient of transmission D – ratio of acoustic pressures of transmitted and
incident waves
21
Acoustic parameters of medium: Near field and
far field
 Near field (Fresnel area) – this part of US beam is cylindrical –
there are big pressure differences in beam axis
 Far field (Fraunhofer area) – US beam is divergent – pressure
distribution is more homogeneous
 Increase of frequency of US or smaller probe diameter cause
shortening of near field - divergence of far field increases
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pressures effect each
other. This effect is less
in far field.
• Feynman derives the wave equation that
describes the behaviour of sound in matter in
one dimension (position x) as:
• Provided that the speed c is a constant, not
dependent on frequency (the dispersionless
case), then the most general solution is:
• where f and g are any two twice-differentiable
functions. This may be pictured as the
superposition of two waveforms of arbitrary
profile, one (f) travelling up the x-axis and the
other (g) down the x-axis at the speed c. The
particular case of a sinusoidal wave travelling in
one direction is obtained by choosing either f or g
to be a sinusoid, and the other to be zero, giving:
• Where omega is the angular frequency of the
wave and k is its wave number.
3D Wave Eq.
• Solution in cartesian coordinates:
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