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Файл:Ординатура / Хирургия / Библиотека им академика М.И. Перельмана / Книга_5189_Библиотеки_им_академика_М_И_Перельмана.pdf
Physics ofUltrasound
Thespeed of sound wavelength frequency=×
ZiadS.Shaman andFaisalS.Qadir
I chose to pursue a career in physics because there the truth isn’t so easily bent.
Angela Merkel
1
Learning Objectives
1. Understand the basic physical principles of
sound waves
2. Demonstrate how an ultrasound image is
formed
3. Review the different types of ultrasound
4. Describe the various types of tissue interac-
tion with the ultrasound beam
Sound Waves
Sound, and ultrasound, waves are forms of
mechanical energy propagatedfrom one point to
another by the effect of moving or vibrating the
medium that transmits the sound. Sound is an
example of a longitudinal wave oscillating back
and forth in the direction of wave travel, and
hence comprises areas of compressions alternating with areas of decompressions (rarefactions).
If the sound wave strikes an object and cannot
penetrate it (e.g., a wall), it may go around it by
diffraction. If the beam encounters an object
larger than the width of the beam (e.g., a mountain), it will be unable to go around it. The beam
will bounce off (or reect), creating an echo [1].
Z. S. Shaman (*)
Case Western Reserve University, MetroHealth
Medical Center, Cleveland, OH, USA
e-mail: zss@case.edu
F. S. Qadir
Summa Health Medical Group, Akron, OH, USA
Although sound is a longitudinal wave with
energy traveling in the same direction as the
propagation, it is usually represented graphically
as a transverse wave. In this layout, the energy is
depicted as waves drawn perpendicular to the
direction of propagation (Fig.1.1).
With this scheme in mind, a wave goes through
a peak (compression) and a trough (rarefaction) to
complete one cycle. A wave has a length that represents the distance the wave occupies in space or
on the horizontal axis, called the wavelength. The
time it takes the wave to complete onecycle is
called the period. Each cycle has a frequency,
which is the number of times the wave completes
a cycle in 1 second. The product of the wavelength and the frequency determines the propagation speed of sound in a medium as in Fig.1.1.
Since the speed of sound depends on the
medium it travels through, for a constant propagation speed the frequency and the wavelength of
the ultrasound beam are inversely related.
On the vertical axis of the graphical representation of an ultrasound beam (Fig. 1.1), the
strength of the compression/decompression is
represented by the height of the wave and is
referred to as the amplitude. While the strength of
the sound wave is measured in units of sound
energy, decibels, the effects of sound energy on
the medium it travels through are described in
terms of mechanical and thermal energy and will
be addressed later.
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2025
M. J. Lanspa, A. T. Levinson (eds.), Echocardiography and Ultrasonography in the ICU,
Respiratory Medicine, https://doi.org/10.1007/978-3-031-80038-2_1
3
4
Trough
Peak
Wavelength
Amplitude
Z. S. Shaman and F. S. Qadir
Fig. 1.1 Graphical depiction of a longitudinal wave such
as sound traveling througha medium (upper panel), and a
transverse wave representation of the longitudinal wave
Therefore, because the speed of sound in soft
tissue is approximately 1540 m/s, in a typical cardiac transducer that generates an ultrasound
beam of 3MHz frequency, the period will be 0.33
μs and the wavelength of the beam will be
approximately0.513mm.
However, a typical vascular transducer that
generates an ultrasound beam of 10 MHz frequency will have a period of 0.1 μs. The beam
wavelength will be 0.154mm when traveling in
soft tissue.
In both cases, the amplitude of the wave is
determined by the transducer imaging modality
and by other settings that allow tissue penetration
to the desired depth of interrogation.
Ultrasound
Ultrasound waves are similar to audible sounds
but have frequencies that are higher than audible
sounds. The range of sound frequencies that
humans can hear is 20 Hz–20 kHz. Therefore,
frequencies >20 kHz are called ultrasound.
Diagnostic ultrasound tends to be in the range of
2–12MHz.
(lower panel) showing the locations of the peak (compression) and trough (rarefaction), in addition to the wavelength and the amplitude
In diagnostic ultrasound transducers, ultrasound waveforms are generated by transforming
electrical energy to pressure waves using crystals
with piezoelectric properties. When thesecrystals are subjected to a high-voltage alternating
current, they vibrate, and the vibration is translated into pressure waves [2] (Table1.1).
The piezoelectric effect is known to naturally
occur in quartz and in other materials such as leadzirconate-titanate crystals which are currently in
use in many commercial ultrasound transducers.
New technologies use capacitive micromachined
drums or use epoxy resin instead of piezoelectric
crystals to perform similar conversions between
electrical and mechanical energies. This allows
lower production costs and may also reduce the
electrical voltages required to operate transducers.
At appropriately high electrical frequencies,
ultrasound waves are created through a series of
compressions and rarefactions in the medium
surrounding the vibrating elements. The same
crystals that generate the ultrasound beam can act
as receivers of reected ultrasound energy, which
results in the generation of electrical voltage that
can be captured, processed, and presented on a
screen as an image (Fig.1.2).
1 Physics ofUltrasound
5
Table 1.1
Characteristic Denition Examples
Period (p) Time required to complete one cycle
Frequency (f) Number of cycles per second, which
Propagation velocity (C) Velocity of sound
Wavelength (λ)
Amplitude The strength or intensity of the
Characteristics, denitions, and examples of sound wave properties
Unit: any unit of time, usually in μs
is also the inverse of the period
f=cycles/s=1/p
Unit: per second, Hertz
C=frequency (f)×wavelength (λ)
Unit: m/s
Length of a single longitudinal wave
Unit: any unit of length, usually mm
sound beam
Unit: dB
Acoustic Matching Layer
Determined by the sound source
Typically 0.5–0.083μs
Determined by the sound source
Medical ultrasound frequency is typically
2–12MHz
Property of the medium varies according to the
density and stiffness of the medium
Velocity of sound in soft tissue is about
1540m/s
Determined by the sound source and medium
Image resolution is inversely related to the
wavelength
Determined by the sound source
Decreases with propagation through the
medium
A wide range of amplitudes can be displayed on
a gray-scale display for ultrasound imaging
Acoustic Lens
Fig. 1.2 A schematic depiction of the components of an
ultrasound transducer. The piezoelectric elements are
housed between a backing material on one side and an
acoustic matching layer and lens on the other. The back-
Velocity ofSound
The velocity of sound, in general terms, refers to
the speed of sound through air in a particular
direction. It is important to note that the speed of
sound through a given medium is constant (ata
certain temperature) and that the speed of sound
varies across differentmedia, depending on the
density and stiffness of the medium (Table1.2).
Backing Element
Piezoelectic Elements
(Transducer)
ing material dampens the vibrations. The acoustic matching layer allows ultrasound waves to travel to the face of
the transducer. The acoustic lens focuses the beam coming out of the transducer
Table 1.2
Medium Sound velocity (m/s)
Lung 600
Adipose tissue 1450
Muscle 1580
Blood 1584
Liver 1590
Bone 2100–3500
Duck FA (1990) Acoustic properties of tissue at ultrasonic
frequencies. Physical Properties of Tissues 73–135
The speed of sound in different tissue media
6
S
Pulse Duration or Spatial Pulse Length
Z. S. Shaman and F. S. Qadir
In liquids, the velocity of sound is given by the
Newton–Laplace equation:
ound velocity
=
stiffness
density
The velocity of sound through various media
is shown in the table below.
For diagnostic medical sonography, the speed of
sound is assumed to be constant at 1540 m/s,
regardless of the tissue type being examined, ignoring the effect of sound on the tissue temperature.
Pulsed Ultrasound
For most applications of ultrasound, other than
continuous wave ultrasound, the transducer sends
signals as a collection of cycles separated by
quiet, listening periods. Each set of cycles is
called a pulse. The time the transducer is active,
sending a pulse, is called the pulse duration, and
the length of space that the pulse occupies is
called the spatial pulse length (usually measured
in mm) (Fig.1.3). The time between the start of
two pulses is called the pulse period (usually
measured in ms), and the rate at which the pulse
is repeated in 1s is called the pulse repetition frequency (which is usually measured in kHz).
Finally, the pulse duration relative to the pulse
period, or the fraction of time that the transducer
spends transmitting is called the duty factor (a
unitless number), andit is usually <1%.
While the operator cannot change most of the
pulse characteristics in two-dimensional imaging, as the operator attempts to examine deeper
structures, the transducer will decrease the pulse
repetition frequency, resulting in a lower duty
factor, to allow for longer listening periods for
returned echoes from deeper structures.
Not all modalities of ultrasound are pulsed
(Table 1.3). A notable exception is continuous
wave Doppler where some of the transducer
vibrating elements generate a continuous beam (a
duty factor of 100%) and other elements are used
to continuously receive echoes (a duty factor of
0%). This imaging modality allows very accurate
detection of signals at the expense of location
(see Chap. 2).
Fig. 1.3 Schematic showing the difference between pulse duration (which equals the spatial pulse length) and the pulse
period
Table 1.3
Ultrasound beam characteristic Pulsed beam characteristic
Period (p)
Frequency
(f)
Wavelength
(λ)
Characteristics and denitions of the ultrasound beam and the pulsed nature of beam generation
Time required to complete
one cycle, usually in μs
Number of cycles per
second, usually in MHz
Length of a single wave,
usually in mm
Pulse Period
Pulse duration Time from the start to the end of a pulse,
Pulse period or pulse
repetition period (PRP)
Duty factor Pulse duration/pulse period, presented
Pulse repetition
frequency (PRF)
Spatial pulse length
(SPL)
usually in μs
Time from the start of one pulse to the
start of the next pulse, usually in μs
as a fraction
Number of pulses per second, usually
in kHz (of note PRF = 1/PRP)
Distance from the start to the end of a
pulse, usually in mm
Distance to reflecting
//
()
1 Physics ofUltrasound
7
The Range Equation
In diagnostic ultrasound, we can estimate the
depth of a structure reecting sound to generate
two-dimensional images. Using the assumption
that the velocity of sound is constant through
various soft tissues, ultrasound systems measure
the time it takes for an ultrasound pulse to travel
from the transducer to the reecting structure and
back to the transducer. This transit time depends
onboth the velocity of the sound wave and on the
depth of the reecting structure. The “range
equation” is used to calculate the depth:
structuremm=Transit time
× speed mm
() ()
So, for a structure that is 30mm in depth, it
would take the ultrasound beam 39 μs to travel
from the transducer to the structure and back.
And here, the distance = (39 × 1.54)/2 = 30mm.
However, if the ultrasound beam has a 130 μs
transit time, the structure reecting the beam
must be (130 × 1.54)/2 = 100mm away from the
transducer.
A simplied “Rule of 13” states that for every
1cm depth, the ultrasound beam takes 13 μs of
round-trip travel time. Try the math on this. It
works.
µs
2µs
Interaction Between Ultrasound
andTissue
As ultrasound travels through the tissue, it is redirected through reection, refraction, and scatter.
Also, as ultrasound beams interact with the tissue, energy is lost as it converts into heat through
a process called absorption. This loss of energy,
called attenuation, results in dampening of the
wave or reduction in its amplitude.
Reection, refraction, and scatter occur
because of differences in the acoustic properties
of different tissues. This property is called acous-
tic impedance. Acoustic impedance depends on
the density of the medium and the speed of sound.
The bigger the difference in acoustic impedance
of adjacent structures, the stronger the reection,
refraction, and scatter (Table1.4).
Reection and refraction occur when the ultrasound beam strikes a tissue boundary with a lateral dimension that is larger than the wavelength
of the ultrasound beam. This happens, for example, when the ultrasound beam interacts with the
diaphragm, with heart valves, or with vessel walls.
These interfaces are referred to as “specular”
reectors. Reection is the rebound of the beam
fromthe interface. Refraction is the redirection
of the transmitted beam at the interface. Both
reection and refraction increase as the angle of
incidence deviates from 90° (Fig.1.4).
Table 1.4 A summary of the terms, denitions, and examples of the effect of tissue interaction with the ultrasound
beam
Term Denition Examples
Acoustic
impedance
(Z)
Reection Return of ultrasound beam to the transducer from a
Scatter Widespread redirection of the ultrasound beam due
Absorption Loss of energy of an ultrasound beam=tissue
Tissue impedance=tissue density(ρ) ×velocity of
sound (c)
boundary of media with different acoustic
impedances of large width compared to the
wavelength of the beam
to interaction with a boundary of small width
compared to the wavelength of the beam
absorption coefcient (a)×distance×frequency (f)
The boundaries between air and soft tissue
and between soft tissue and bone make
strong reectors
Reections are maximized when the
incident ultrasound beam is perpendicular
to the surface of the reector
Red blood cells ll the blood in cardiac
chambers, but the chambers appear empty
because the beam scatters when the beam
hits the surface of the red blood cells
Higher frequency ultrasound beam loses
more energy than lower frequency beam
for the same examination distance
8
AttenuationCoefficientdistance
=×
Fig. 1.4 Schematic
showing reection,
refraction, and scatter as
an ultrasound beam
interacts with tissue
boundaries
Z. S. Shaman and F. S. Qadir
Reflection
Scatter
Refraction
When the lateral dimension of the reector is
smaller than the wavelength of the ultrasound
beam, the beam is scattered in all directions. This
is called Rayleigh scattering. Scattering occurs,
for example, at the surface of gas bubbles within
the bowel lumen, at the edges of small granularities within tissues, or by red blood cell membranes within the blood. Scatter is used to detect
ow when using the Doppler imaging modality,
which is described later.
Signals returned to the transducer through
reection and scatter are used by ultrasound systems to generate two-dimensional images.
Unlike reection that takes place only at the
interfaces of two media with different properties,
absorption occurs continuously throughout beam
travel distance in any medium. Absorption
depends on a tissue property, indicated by the
Attenuation Coefcient (Table1.5), and on the
frequency of the ultrasound beam. The higher
the coefcient, the more energy the tissue
absorbs per unit of beam travel distance, and the
higher the frequency, the greaterthe absorption
of energy.
frequency
×
As you can see from Table1.5, water, or liquid
media in general, is considered “ultrasoundfriendly” where very little absorption occurs and
the beam can travel generous distances with little
attenuation, while air and bone are considered
ultrasound-unfriendly because of signicant degradation of signal in a very short travel distance.
For a clinical example, a 3MHz cardiac ultrasound beam will lose 18 dB by absorption after
traveling to a 6cm deep reector in soft tissue.
Here, absorption = 0.5 dB/cm/MHz × 12cm ×
3MHz = 18 dB.Of note, an 18 dB reduction in
sound level corresponds to 63 times reduction in
signal intensity because dBs are represented on a
logarithmic scale.
However, setting the transducer to a frequency
of 5MHz will cause the beam to lose more energy
examining the same structure. In this case,
absorption = 0.5 dB/cm/MHz × 12cm × 5MHz
= 30 dB. Here, a 30 dB reduction in sound
level corresponds to 1000 times reduction in
1 Physics ofUltrasound
9
Table 1.5
Medium Attenuation (absorption) coefcient (dB/cm/MHz)
Water 0.002
Blood 0.2
Spleen 0.45
Soft tissue 0.5 (on average)
Muscle 1.1
Fat 1.5
Bone 16
Lung 30
Duck FA (1990) Acoustic properties of tissue at ultrasonic frequencies. Physical Properties of Tissues 73–135
Fig. 1.5 An ultrasound
image showing multiple
scan paths. Each scan
line detects reections
along its scan path
The attenuation coefcient of sound in different tissue media
signal intensity due to the logarithmic nature of
the sound intensity scale.
Ultrasound Image Formation
For diagnostic ultrasound, the differences in
acoustic impedance within and between tissues
cause echoes to return to the transducer allowing
image formation [3]. The bigger the difference in
acoustic impedance between two tissues, the
larger the proportion of sound reected, and the
brighter the representation of the reector on the
ultrasound screen (Fig.1.4). For each ultrasound
beam (called “Scan Line”), multiple brightness
signals can be represented on the screen vertically
and this creates a single line on the screen. As
multiple beams are transmitted through a swathe
of tissue, and as multiple scan lines are presented
on the screen, a two-dimensional image is formed
(Fig.1.5). After a two- dimensional image is created, the process is then repeated multiple times
per second, each time creating a “frame.” With
multiple frames per second still images come to
life, and a view of the underlying structures is created on the screen [4] (Fig.1.6).
10
Fig. 1.6 A 2- dimensionalultrasound image is formed by running multiple scan lines through the width of the sector
Z. S. Shaman and F. S. Qadir
Time Gain Compensation
Because attenuation weakens ultrasound beams
as they travel through the tissue, the deterioration
of echo signal strength returning from deeper
structures needs to be taken into account to allow
a homogeneous presentation of the reectors on
the screen. This post-processing is called “Time
Gain Compensation” or Correction, or simply
“Gain.” Unfortunately, absorption will eventually make the signals returning from deeper
structures too weak to be detected, and imaging
depth is limited. This is particularly a problem
with high-frequency beams because of the direct
relationship between absorption and beam
frequency.
Gaining an area can occur inappropriately,
leading to acoustic enhancement artifacts
(more in the artifact section). These artifacts
occur when the beam traverses tissues with a
higher or lower attenuation coefcient than
expected by the machine algorithm. This
anomaly causes the machine to inappropriately display reections from deeper areas
asdimmeror brighter than adjacent structures,
leading to a misrepresentation of the tissue
image on the screen.
Resolution
Resolution is dened as the smallest distance
between two structures that can be distinguished
using an ultrasound beam. The greater the resolution, the greater the detail of the image obtained.
The resolution of an ultrasound image can be
described in terms of space and time as
• Spatial Resolution: Resolution relative to the
ultrasound image plane, usually measured in
mm, indicating the smallest distance between
two structures that would still be recognizable
as separate structures, therefore, a smaller
number indicates better resolution (Fig.1.7).
– Axial: Resolution along/parallel to the
ultrasound beam’s main axis
– Lateral: Resolution perpendicular to the
ultrasound beam’s main axis
– Elevational: Resolution along the ultra-
sound image slice thickness
• Temporal Resolution: The ability to accu-
rately locate moving structures over time, usually measured in milliseconds. A smaller
number indicates more real-time imaging,
where movement appears more smooth and
less choppy.
Acoustic Lens Focal Zone
Axial resolutioninmm SPLinmm= /2
1 Physics ofUltrasound
Fig. 1.7 Spatial
resolution components
are the axial resolution
along the axis of the
beam (blue arrows);
lateral resolution
perpendicular to the axis
of the beam (red
arrows); and elevational
resolution (along the
thickness of the imaging
slice (yellow arrows))
11
Fig. 1.8 Schematic showing multiple ultrasound beams.
Beam A has an pulse of a particular length, the SPL,
which determines the axial resolution of the beam.
BeamB has a shorter SPL because the wave has a higher
There are multiple factors that affect each type
of resolution. Some are modiable by the operator, while others depend on the transducer type
usedand are not modiableby the operator.
Axial Resolution
Of all resolution types, axial resolution is the
most precise. This means that measurements are
best obtained along the axis of the ultrasound
beam (Fig.1.8). Axial resolution is dependent on
the length of the ultrasound pulse (the spatial
pulse length—SPL).
The two factors that determine the SPL are the
number of cycles per pulse and the wavelength
(or frequency) of the beam. Therefore, axial resolution can be improved by using higher frequency
beams (if modiable by the operator). However,
the number of cycles per pulse is intrinsic to each
transducer and is not modiable.
Of note, an ultrasound beam that is continuous
and does not pulse, such as in continuous wave
Doppler imaging, has no axial resolution at all.
frequency although it has the same number of cycles per
pulse. Beam Chas a shorter SPL than beam A,as well,
because it has fewercycles in eachpulse although it has
the same frequency as beamA
Fig. 1.9 The acoustic lens of the transducer lengthens the
focused area of the beam, resulting in a focal zone that has
higher lateral resolution than the zones proximal and distal to it
Lateral Resolution
Lateral resolution depends on the diameter of the
ultrasound beam. Ultrasound beams tend to be
more wide than long; therefore, lateral resolution
is usually inferior to axial resolution. As the
ultrasound beam exits the face of the transducer,
the beam reaches a focal point and then widens
(through divergence). The focal point is the narrowest area of the beam and has the best lateral
resolution (Fig. 1.9). The focal point can be
increased in length by focusing the beam, using
an acoustic lens, and by electronic focusing of
the beam, to create a focal zone. This improves
the lateral resolution along more of the beam
depth, rather than at just the focal point. The
depth of the electronic focusing of the beam can
12
Z. S. Shaman and F. S. Qadir
be adjusted by the operator on some machines,
however focusing that is achieved through the
acoustic lens is not modiable for each transducer. Of note, divergence is dependent on the
beam frequency. The higher the frequency, the
smaller the divergence angle and the better the
lateral resolution in the area distal to the focal
point or the focal zone.
Elevational Resolution
Elevational resolution is affected by the image
slice thickness. A mechanical acoustic lens determines the slice thickness and is not modiable by
the user. So, similar to lateral resolution, elevational resolution is best at the acoustic focal point
or focal zone for each transducer. While the
acoustic lens is not modiable by the user; divergence still depends on the beam frequency which
is, in some machines, modiable by the user.
Here, the higher the frequency, the smaller the
divergence angle, and the better the elevational
resolution at the depth ofthe focal point.
Temporal Resolution
The ability of ultrasound images to track moving
structures depends on the time it takes the system
to generate a two-dimensional image. The time it
takes an image to be formed depends on the
image depth and the sector width. Both depth and
widthcan be changed by the operator. Shallower
imaging depth results in decreased transit time
and less time is needed between ultrasound
pulses. A narrow imaging sector requires a fewer
number of scan lines per frame. In both cases,
more frames can be generated per second resulting in a higher frame rate and better temporal
resolution [5].
Certain imaging modalities, such as cardiac
imaging, require high frame rates, while other
modalities, such as abdominal imaging, do not.
Therefore, frame rate ranges are usually set for
each transducer for optimal performance for the
area of predicted clinical use.
The Resolution—Penetration Interplay
Ultrasound beam frequency seems to play an
important role in determining resolution
(Table 1.6). A higher frequency improves both
axial and lateral resolution. However, using highfrequency ultrasound leads to higher attenuation
of ultrasound energy and the inability to examine
deeper structures. As ultrasound waves undergo
attenuation in soft tissue with each wave cycle,
attenuation becomes the limiting factor for the
penetration of an ultrasound beam. Therefore,
using lower frequency ultrasound transducers,
and hence longer wavelengths, will undergo less
attenuation. However, with the use of lower frequency, resolution suffers (for probe selection,
see Chap. 2).
High frequency—shallow images with better
overall resolution
Low frequency—deeper images with lower over-
all resolution
Table 1.6 Comparing different resolutions and the factors inuencing each kindof resolution
Resolution Factors Adjustability Resolution improves with
Axial Frequency Sometimes Higher frequency
Cycles per pulse No Fewercycles per pulse
Lateral Frequency Sometimes Higher frequency (less divergence)
Focal zone Sometimes Scanning within the focal zone depth
Elevational Frequency Sometimes Higher frequency (less divergence)
Focal zone (xed) No Scanning within the focal zone depth
Temporal Image depth Yes Shallower scanning
Sector width Yes Narrower sectors