This document provides an overview of ultrasound imaging presented by Dr. Ahmed Ehab Mahmoud. It discusses the basic idea of ultrasound imaging which is to send waves into the body that are reflected at tissue interfaces. It then covers the history of ultrasound, principles including B-mode imaging, physics of ultrasound including acoustic pressure and wave equations, reflection and scattering, refraction, attenuation, and ultrasound wave interference. The document is intended to teach medical instrumentation students about ultrasound imaging.

1. SBE 405 Medical Instrumentation IV:
Ultrasound Imaging
Ahmed M. Ehab Mahmoud, PhD
Department of Biomedical Engineering and Systems, Cairo University, Giza,
Egypt.
Office: Medical Equipment Calibration Laboratory, 2nd floor, Architecture
building, Faculty of Engineering.
Email: a.ehab.Mahmoud@gmail.com
a.e.mahmoud@ieee.org
Ultrasound Imaging 1
Department of Systems and
Biomedical Engineering
Cairo University

2. Ultrasound Imaging
Dr. A.M. Ehab Mahmoud
Basic Idea
➢ Send waves into body which are reflected at the
interfaces between tissue.
➢ Return time of the waves tells us of the depth of the
reflecting surface.
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3. Ultrasound Imaging
Dr. A.M. Ehab Mahmoud
History
➢ The potential of ultrasound as an imaging modality was
realized as early as the late 1940s when utilizing sonar and
radar technology developed during World War II. Several
groups of investigators around the world started exploring
diagnostic capabilities of ultrasound
➢ WW II brought massive military research - SONAR
(Sound Navigation And Ranging)
➢ Mid-century used for non-destructive testing of materials
➢ 1950’s 2D gray scale images
➢ 1965 or so real-time imaging
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4. Ultrasound Imaging
Dr. A.M. Ehab Mahmoud
Principles of Ultrasound
4
An example of a B-mode image showing
reflections from organ and blood vessel
boundaries and scattering from tissues.
➢ It is constructed from echoes,
and scattering from small
irregularities within tissues.
➢ A brightness mode (B-mode)
image is a cross-sectional
image representing tissues
and organ boundaries within
the body.

5. Ultrasound Imaging
Dr. A.M. Ehab Mahmoud
Principles of Ultrasound
5
An example of a B-mode image showing
Reflections from organ and blood vessel
boundaries and scattering from tissues.
➢ Each echo is displayed at a
point in the image, which
corresponds to the relative
position of its origin within the
body cross section, resulting in
a scaled map of echo-
producing features.
➢ The brightness of the image
at each point is related to the
strength or amplitude of the
echo, giving rise to the term B-
mode (brightness mode).

6. Ultrasound Imaging
Dr. A.M. Ehab Mahmoud
Physics of Ultrasound
6
➢ Ultrasound are mechanical
longitudinal waves that require a
physical medium to propagate
through.
➢ “Ultrasound” refers to
frequencies greater than 20 kHz,
the limit for human hearing.
➢ The frequency range used for
medical imaging is about 100 times
higher than human audible. Typically 2-20 MHz.
➢ Particles of the medium oscillate backwards and forwards along
the direction of propagation.

7. Ultrasound Imaging
Dr. A.M. Ehab Mahmoud
Physics of Ultrasound
7
➢ When particles move towards each other, a region of
compression results, but where particles moves apart, a region of
rarefaction results.
➢ There is no net movement of the medium. Only the disturbance
and its associated energy are transported

8. Ultrasound Imaging
Dr. A.M. Ehab Mahmoud
Physics of Ultrasound
8
➢The frequency (f) of the wave is the number of oscillations or
wave crests passing a stationary observer per second and is
determined by the source of the sound wave. (1 Hz = 1 cycle per
second)
➢The wavelength (λ) is the distance between consecutive wave
crests or other similar points on the wave.
➢ The speed/velocity (c) is determined by the medium in which it
is travelling. Examples are the speed of sound in air (330 m s −1 )
and water (1480 m s −1 ).
c=λf

9. Ultrasound Imaging
Dr. A.M. Ehab Mahmoud
Physics of Ultrasound
9
➢ Sound speed is determined by the medium it is travelling in.
➢ The material properties which determine the speed of sound are
density (ρ) and stiffness (K).

10. Ultrasound Imaging
Dr. A.M. Ehab Mahmoud
Physics of Ultrasound
10
➢ As a sound wave passes
through a medium, the particles
are displaced backwards and
forwards from their rest positions
in a repeating cycle like a paddle.
➢The pattern of particle
displacement with time can be
described by a sine wave.
➢ The phase (θ) of the pedal is
its position within such a cycle of
rotation and is measured in
degrees.

11. Ultrasound Imaging
Dr. A.M. Ehab Mahmoud
Acoustic Pressure
➢ The difference between this actual
pressure and the normal rest pressure
in the medium is called the excess
pressure, p , which is measured in
pascals (Pa).
➢ For longitudinal waves, the acoustic
pressure can be related to the
underlying particle velocity (u) as
follows:
where Z is called the characteristic impedance
This is a like V=IR,
Note that u ≠ c
p =uZ
11

12. Ultrasound Imaging
Dr. A.M. Ehab Mahmoud
Wave Equation
The acoustic pressure p satisfies the three-dimensional wave
Equation:
Or
It is a linear equation. When no shear stress is presented and only
compression (longitudinal) wave in z direction is considered, this
can be reduced to:
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13. Ultrasound Imaging
Dr. A.M. Ehab Mahmoud
Wave Equation
Solution form f(z±ct)
where the negative sign indicates a wave traveling in the +z
direction and the positive sign indicates a wave traveling in the –z
direction.
The sinusoidal solution for this equation is
(pressure) (displacement)
Note that ω=2πf (angular frequency), and k= ω/c (wave number)
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14. Ultrasound Imaging
Dr. A.M. Ehab Mahmoud
Acoustic Impedance
The acoustic impedance of a medium is determined by its
density (ρ) and stiffness (K).
or
14
kg m−2 s−1 ,

15. Ultrasound Imaging
Dr. A.M. Ehab Mahmoud
Reflection and Scattering
➢ Specular echoes originate from relatively large, regularly
shaped objects with smooth surfaces. These echoes are relatively
intense and angle dependent. (i.e. valves)
➢ Scattered echoes originate from relatively small, weakly
reflective, irregularly shaped objects are less angle dependant and
less intense. (i.e.. blood cells)
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16. Ultrasound Imaging
Dr. A.M. Ehab Mahmoud
Reflection and Scattering
➢ When sound wave travels through the interface between two
tissues of different z, part of the wave is transmitted and the other
part is reflected.
➢ The amplitudes of the transmitted and reflected waves depend
on the change in z.
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Pi + Pr = Pt
vt + vr = vi
v here is particle velocity to be
consistent with the book
Continuity of P and normal component of V

17. Ultrasound Imaging
Dr. A.M. Ehab Mahmoud
Scattering
17
➢The total ultrasound power scattered by a very small target
is much less than that for a large interface.
➢ For small targets ( d << λ ), scattered power is proportional
to the sixth power of the size d and inversely proportional to
the fourth power of the wavelength λ:
This frequency dependence is often
referred to as Rayleigh scattering .Diffuse Reflection

18. Ultrasound Imaging
Dr. A.M. Ehab Mahmoud
Refraction
18
Snell’a law

19. Ultrasound Imaging
Dr. A.M. Ehab Mahmoud
Acoustic Intensity
19
➢ The energy transported in an ultrasound wave is usually
characterized by an acoustic intensity I.
➢ The acoustic intensity can be calculated in terms of the sound
pressure as follows:
(W·cm−2)
Ti = 1- Ri Intensity transmission coefficient
Intensity reflection
coefficient+
Normal Incidence
Z
P
I
2
=

20. Ultrasound Imaging
Dr. A.M. Ehab Mahmoud
For Incidence Angle ≠ 90o
20
http://books.google.com.eg/books?id=Hwb5D60vb5IC&pg=PA54&dq=reflection+coefficient+u
ltrasound+cos&hl=en&sa=X&ei=TIeDUrClBMS80QWNuoH4DA&ved=0CCsQ6AEwAA#v=onepag
e&q=reflection%20coefficient%20ultrasound%20cos&f=true

21. Ultrasound Imaging
Dr. A.M. Ehab Mahmoud
Attenuation
21
➢ Attenuation means the loss of the signal's amplitude with
increasing propagation distance.
➢ There are two major causes of attenuation
1- Absorption: the conversion of acoustic energy into heat
via viscosity, relaxation, heat conduction, etc.
2- Scattering: the conversion of the energy of the coherent,
collimated beam into incoherent, divergent waves as a
result of wave interaction with inhomogeneities in the
material.
Absorption is the dominant mechanism for ultrasonic attenuation
in biological tissues.

22. Ultrasound Imaging
Dr. A.M. Ehab Mahmoud
Attenuation
22
➢ Where P(z=0) is the pressure at
z=0 and α is the pressure
attenuation coefficient.
➢The attenuation coefficient has a unit of nepers per centimeter
and is expressed in units of decibels per centimeter
dB ~ 20logP2/P1 in terms of pressure or 10logI2/I1 in terms of intensity

23. Ultrasound Imaging
Dr. A.M. Ehab Mahmoud
Attenuation
23
The attenuation coefficient
of tissues, when expressed
in dB cm-1 , increases
approximately linearly with
frequency.
Common unit for α is
dB cm −1 MHz −1

24. Ultrasound Imaging
Dr. A.M. Ehab Mahmoud
Ultrasound Wave Interference
24