1. Ultrasound Physics Saudi Board of Radiology: Physics Refresher Course
Kostas Chantziantoniou, MSc2, DABR
Head, Imaging Physics Section
King Faisal Specialist Hospital & Research Centre
Biomedical Physics Department
Riyadh, Kingdom of Saudi Arabia

2. What is Ultrasound?
Ultrasound literally means “above or beyond sound”, that is, it is the sound above the
human audible (hearing) range.
Although ultrasound was first used on a large scale practical basis in World War I in
order to detect the position and depth of submarines and was referred to as Sonar, it
was not until 20 years later that it was first applied to medicine (sonography).
ASIDE
the frequency of sound that is in the human audible range is between
15 Hz to 20 kHz (Note: 1 Hz = 1 Hertz = 1 cycle/second, 1 kHz = 1,000 Hz)
ultrasound frequencies are higher than that of audible sound and thus comprises of
sounds with frequencies greater than 20 kHz (similarly, sound under 20 kHz is
called infrasound “below sound”)
the range of sound that is commonly used in Radiology (Diagnostic Ultrasound) is
between 1 MHz and 20 MHz (Note: 1 MHz = 1,000 kHz = 1,000,000 Hz)

3. Characteristics of Sound
A sound beam is similar to an x-ray ray beam in that both are waves transmitting
energy. A more important difference is that x-rays pass readily through a vacuum while
sound requires a medium for its transmission. The velocity of sound depends on the
nature of the medium.

4. How does sound travel through a medium?
each sphere represents an atom or a molecule
springs between spheres represent atomic interactions or molecular bonds
when the first particle is pushed, it moves and compresses the attached
spring, thus exerting a force on the adjacent particle (sphere)
this sets up a chain reaction, but each subsequent particle moves a little less than
its neighbor
the tension or pressure (piston device above) applied to the spring is greatest
between the first two particles and less between any two down the line
if the driving force reverses its direction, the particles also reverse their direction
if the force vibrates to and fro like a cymbal that has been struck, the particles
respond by oscillating back and forth
the particles in a sound beam behave in the same manner: that is, they oscillate
back and forth, but over a short distance of only a few microns in liquids and even
less in solids

5. although the individual particles move only a few microns, we can see that the effect
of their motion is transmitted through their neighbors over a much longer distance
during the same time that the first particle moves through a distance “a”, the effect
of the motion is transmitted over a distance “b”
the velocity of sound is determined by the rate at which the force is transmitted from
one molecule to another
NOTE
In summary then, sound waves are a mechanical disturbance that propagate through a medium.

6. Longitudinal Waves
Ultrasound waves are transmitted through tissue as longitudinal waves of alternating
compression and rarefaction regions.
The term “longitudinal wave” means that the motion of the particles in the medium is
parallel to the direction of wave propagation. The molecules of the conducting liquid
move back and forth, producing bands of compression and rarefaction.
the wave front starts at time 1 when the vibrating piston compresses the adjacent
material
a band of rarefaction is produced at time 2, when the piston reverses its direction
each repetition of this back-and-forth motion is called a cycle, and each cycle produces
a new wave

7. Wavelength
The length of the wave (or wavelength) is the distance between two bands of
compression or rarefaction and is represented by the symbol  (has unit of millimeters).
ASIDE
The wavelength of a wave can also be represented using the following illustration
Compression region Rarefaction region

8. Frequency
The motion of the vibrating piston, plotted against time, forms the sinusoidal curve
shown along the left side of the diagram below
The frequency is the number of compressions (or rarefactions) bands that pass any
given point in space per unit time and is measured in Hertz which is defined as:
1 Hertz = 1 cycle per second
frequency has the units of Hz (or 1/second or sec-1 or s-1)

9. frequency  period  Period
The period is the time between compression or rarefaction (oscillations) bands and has
the units of time (seconds). In other words, the period is the time that it takes for one
cycle to occur.
ASIDE
The period of a wave can be represented using the following illustration
The relationship between period and frequency is:
frequency (Hz) =
period (s)
frequency  period 

10. Propagation Speed of Sound
Propagation speed is the speed with which a sound wave moves (travels) through a
medium and for sound waves the velocity is given by:
velocity (m/sec) = wavelength (m) • frequency (Hz)
= wavelength (m)
period (sec)
For body tissues in the diagnostic ultrasound range, the speed of sound is
(approximately) independent of frequency and depends primarily on the physical
makeup of the material through which the sound is being transmitted. Because of the
above observation, that means:
frequency  wavelength 
and the speed of sound in soft tissue is a constant.
NOTE
the average speed of sound in soft tissue (excluding in bone) is 1,540 m/s
all ultrasound scanners use this value for the speed of sound to compute tissue depth

11. NOTE
1 s = 1 x 10-6 s

12. The physical properties of a material that directly affects the speed of sound are:
(1) Physical Density (concentration of mater, mass per unit volume)
(2) Stiffness
Physical Density
Dense material tend to be composed of massive molecules, and these molecules have a great deal of inertia. They are difficult to move or to stop once they are moving.
Because the propagation of sound involves the rhythmic starting and stopping of
particulate motion, we would not expect a material made up of large molecules (i.e.:
large in mass) such as mercury to transmit sound at as great a speed as a material
composed of smaller molecules, such as water.
the speed of sound in a material decreases if the density is increased, assuming
constant stiffness

13. Stiffness
Stiffness is the resistance of a material to compression. It is the opposite of
compressibility, and in fact the less compressible a material is the more rapidly it will transmit sound. We have,
speed of sound   stiffness
compressibility
the speed of sound in a material increases if the stiffness is increased
sound travels slower in gases because the molecules are far apart [i.e.: they are held
by loose “springs” (bonds) and a particle must move relatively a long distance before
it can affect a nearest neighbor]
liquids and solids are less compressible because their molecules are closer together
Combined Effects of Density and Stiffness
It is generally true that media with higher densities also have higher stiffness.
Because stiffness differences between materials generally dominate the effect of
density differences, higher-density materials usually have higher sound speeds than
lower-density materials.

14. in general speed of sounds are lower through gases, higher through liquids and
highest through solids
this increasing sequence is due to the fact that the stiffness differences between gases,
liquids and solids are greater than the density differences
mercury is a special case: mercury has a density 13.9 times greater than water and
water has a compressibility that is 13.4 times greater than that of mercury (both effects
balance out)

15. Acoustic Impedance Acoustic impedance (Z) of a material is given by:
impedance (Rayl) = speed of sound (m/s) • density of material (kg/m3)
in material
the acoustic impedance unit is called the Rayl (kg/m2/s)
acoustic impedance can be considered to be a measure of a material’s ability to
transmit acoustic energy (air and lung media have low values, and bone and metal
have high values)
acoustic impedance is determined by the density and stiffness of a medium
since the speed of sound is independent of frequency in the diagnostic ultrasound
range, acoustic impedance is also independent of frequency
acoustic impedance determines the amount of energy reflected at an interface
since the speed of sound in tissue is relatively constant in the diagnostic ultrasound
range, then the acoustic impedance of most tissues is also a constant, they typically
have values around 1.6 x 106 kg/m2/s (Rayls)
impedance  density 
impedance  speed of sound 

16. unit conversion: g/cm2/sec = kg/m2/s (Rayls)10

17. Intensity
The intensity (or loudness) of sound is determined by the length of oscillation of the
particles (vibration amplitude) conducting the waves.
the harder the piston is struck, the more energy it receives and the wider its vibration
amplitude
these wider excursions are transmitted to the adjacent conducting media and produce
a more intense beam
in time the vibrations diminish in intensity although not in frequency, and the sound
intensity decreases, producing a lower intensity beam
ultrasound intensities are expressed in power per unit area, where power (mW)
is the rate at which acoustic energy is transferred and the area (cm2) is the area of the
the ultrasound beam at some distance from the transducer surface, thus:
intensity (mW/cm2) = power (mW)
area (cm2)

18. The amplitude of a wave is the size of the wave displacement or pressure.
larger amplitudes of vibration produce denser compression bands and, hence, higher
intensities of sound (i.e.: the greater the amplitude of oscillation the more intense the
sound).
ultrasound beam intensity is a measure of the energy associated with the beam and is
proportional to the square of the amplitude, that is:
intensity  (amplitude)2

19. Relative Sound Intensity and Pressure (Decibels)
In diagnostic ultrasound it is not uncommon to receive ultrasound intensities (I) from
the patient that are 1,000,000 to 1,000,000,000 times smaller than the original
intensity (I0). In fact depending on the depth of the I intensity source, we can have a
wide variation of the ratio of these two intensities. In order to reduce the ‘dynamic’
range of these ratio’s we introduce the following numerical scale:
1 B = 10 dB
where B is called
the ‘bel’ and dB the
‘decibel’
relative intensity (B) = log10( I/I0) or
relative intensity (dB) = • log10( I/I0)
where I0 is the original intensity and I is the measured (received) intensity.
ASIDE
The logarithmic scale is used in mathematics to remap a very large number scale, like the ratio (I/I0), with a new much smaller number scale
Since intensity is proportional to the square of the pressure amplitude (i.e.: I  P2) then:
relative pressure (dB) = • log10( P/P0)

20. - decibels may have either positive or negative values
a positive value corresponds to signal amplification (I > I0)
a negative value corresponds to signal attenuation (I < I0)
Example
An intensity reduction of 50% corresponds to - 3 dB (that is I = 0.5 I0). On the same note, a + 3dB change corresponds to a twofold increase in intensity (that is I = 2 I0).

21. Interaction of Ultrasound with Matter
Attenuation
Detector
Tissue
Refracted
(Scattered)
Reflected (Scattered)
Absorbed
With an unfocused beam in any medium, such as tissue, amplitude and intensity will
decrease as the sound travels through the medium. This reduction in amplitude (and
thus intensity) is called attenuation. It encompasses absorption, reflection and scattering.
NOTE
the absorbed sound wave energy is converted into heat
absorption is normally the dominate contribution to attenuation in soft tissue

22. I1 I2
path length
attenuation = log intensity at second point (I2)
intensity at first point (I1)
(in dB)
Note
The minus sign is often ignored in most textbooks
attenuation coefficient = attenuation (dB)
path length (cm)
(in dB/cm)
Note
Path length is the distance between the first and second point
attenuation coefficient  attenuation 
attenuation  path length 

23. the attenuation of ultrasound in a homogeneous medium is exponential with
penetration depth
3 dB/cm
1 dB/cm
10 dB/cm

24. the attenuation coefficient increases with frequency
for soft tissue, there is a linear relationship between the frequency and attenuation
average attenuation coefficient = 0.5 dB/cm (for 1 MHz)
= 2.5 dB/cm (for 5 MHz)
for water and bone, attenuation increases approximately as frequency2

25. since the attenuation for soft tissue is on the average 0
since the attenuation for soft tissue is on the average 0.5 dB per centimeter for each
MHz of frequency (i.e.: 0.5 dB/cm/MHz), then
attenuation (dB) = • frequency (MHz) • path length (cm)
attenuation coefficient  frequency 
attenuation  frequency 
attenuation is higher in lung than in other soft tissues, and it is higher in bone than in
soft tissues (explains for poor US imaging of this tissue)
the practical consequence of attenuation is that it limits the depth at which images
can be obtained
the imaging depth decreases as frequency increases
frequency 
image depth 

26. Absorption
The term “absorption” refers to the conversion of ultrasonic energy to thermal energy,
and is the dominate contribution to attenuation in soft tissue.
The mechanisms involved in absorption are rather complex (and thus will not be
discussed in detail); the three primary factors that determine the amount of absorption
are:
(1) the viscosity of the conducting medium
(2) the “relaxation time” of the medium; and
(3) the frequency of the sound wave
Viscosity
viscosity is an internal friction (or a frictional force) that opposes the motion of the
particles in the medium
particle freedom decreases and internal friction increases with increasing viscosity
this internal friction absorbs the sound, or decreases its intensity, by converting sound
into heat
in liquids, which have low viscosity, very little absorption takes place, in soft tissue
viscosity is higher and a medium amount of absorption occurs, while bone shows high
absorption of ultrasound

27. Relaxation Time
the relaxation time is the time that it takes for a molecule to return to its original
position after it has been displaced
when a molecule with short relaxation time is pushed by a longitudinal compression
wave, the molecule has time to return to its resting state before the next compression
wave arrives
a molecule with a longer relaxation time may not be able to return completely before
a second compression wave arrives, when this happens, the compression wave is
moving in one direction and the molecule in the opposite direction. Since more
energy is required to reverse the direction of the molecule (in phase with compression
wave) in order to transmit the sound wave further, more acoustic energy is used used
up and is converted to heat
Frequency of Sound Wave
since the frequency of sounds effects both of the above processes it also affects the
amount of absorption produced by a medium
the higher the frequency (ie: the more often a particle moves back and forth in a
given time), the more the particle motion is affected by the drag of a viscous
material and its relaxation time

28. Reflection
A portion of the ultrasound beam is reflected at tissue interfaces as shown below. The
sound reflected back towards the source is called a echo and is used to generate the
ultrasound image. qi qr
Like in the optical properties of light, in ultrasound we also have:
Angle of incidence (qi) = Angle of reflection (qr)

29. the percentage of ultrasound intensity reflected depends, in part, on the angle of
incidence
as the angle of incidence increases, reflected sound is less likely to reach the
transducer and thus no acoustic signal is received to image
no reflection is generally detected by the transducer, if the angle of incidence is
greater than 3°
specular (smooth) reflection occurs from large, smooth surfaces (major contributor to
ultrasound images)
non-specular (diffuse) reflections is scatter from “rough” surfaces where the
irregular contours are bigger than the ultrasound wavelength

30. specular reflections

31. Intensity Coefficients
The percentage of ultrasound reflected at a tissue interface is also dependent on the
acoustic impedance of the two tissues.
impedance difference  IRC 
For normal incidence (incident angle = reflected angle = 90°)
intensity reflection coefficient (IRC) = reflected intensity (mW/cm2)
incident intensity (mW/cm2)
= (Z2 - Z1)2
(Z2 + Z1)2
where Z1 and Z2 is the impedance of tissue 1 and tissue 2

32. intensity transmission coefficient (ITC) = transmitted intensity (mW/cm2)
incident intensity (mW/cm2)
= IRC
= 4Z1Z2
(Z2 + Z1)2
IRC  ITC 
NOTE
IRC is the fraction of the incident ultrasound intensity that is reflected, and ITC is the
fraction transmitted at a interface of two different material (or tissues)

33. Common Interface Reflection Factors
air/tissue interfaces reflect virtually all (99.9%) of the incident ultrasound beam, thus
imaging through lungs (air) is generally not possible
gel is applied between the transducer (PZT) and the skin to displace the air and
minimize large reflections (80%) that would interfere with ultrasound transmission
into the patient
bone/tissue interfaces also reflect substantial fractions (30%) of the incident intensity
the lack of transmissions beyond these interfaces results in an area void of echoes
called shadowing
in imaging the abdomen, the strongest echoes are likely to arise from gas bubbles
organs such as the kidney, pancreas, spleen and liver are composed of sub-regions
that contain many scattering sites, which results in a speckled texture on ultrasound
images
organs that contain fluids such as the bladder, cysts, and blood vessels have no
internal structure and almost no echoes (i.e.: show black on images)

34. Refraction
Refraction is the change in direction of an ultrasound beam when passing through one
medium to another.
When ultrasound passes from one medium to another, the frequency remains the
same but the wavelength changes to accommodate the new velocity of sound in the
second medium (for diagnostic ultrasound, the speed of sound is independent of
frequency).

35. qi qt NOTE If the speed of sound in media 2 is less than that of
media 1, then the wavelength of the sound beam in media 2 must be shortened in order to maintain a constant beam frequency. qi
Media 1
Media 2 qt
Snell’s Law:
sin(qi) = velocity of sound in media 1
sin(qt) velocity of sound in media 2
the transmitted angle (qt) is determined by the speed of sound in both media’s and the
incident angle (qi) of the beam