Estimation of Blood Velocities Using
A Signal Processing Approach
Jørgen Arendt Jensen,
Cambridge University Press, New York, 1996,
Please note that the book currently (January 2005)
is sold out from the publisher. Laser printed color copies can, however,
be obtained from me by sending an e-mail to
The price is 90 US$ plus shipping.
The use of ultrasound for diagnosing the human circulatory system
dates back more than 30 years and has in the recent decade matured
to the level of routine use in hospitals. Real-time B-mode scanners
are used for acquiring anatomical gray scale images for investigating
nearly all soft tissue structures in the human body. Some of the many
advantages of the technique is its rapid image formation, its non-invasiveness,
and that non-ionizing radiation is employed. Ultrasound is, thus, painless
and safe for the patient, and can give a rapid diagnosis. The systems used
are transportable and can be moved to the patient, rather than the reverse,
and they are also used in the operating theater.
One of the most exciting new developments within medical imaging in recent
years is the appearance of Doppler ultrasound scanners that display an
estimate of blood velocity in the body in real-time.
Several different velocity estimation systems exist. The
continuous wave system displays the velocity distribution within the ultrasound
beam by determining the Doppler shift of the emitted sinusoid. Pulsed wave systems
interrogate a single volume, and display the velocity distribution as a function
of time. They use the shift in position of the red blood cells to find the
velocity. Color flow mapping systems interrogate a whole region of the body,
and show a real-time image of velocity. The technique has already established
its success in, e.g., diagnosing heart valve problems, stenosis of veins
and arteries, and other hemodynamic problems.
The all-embracing term for these systems has been "Doppler ultrasound scanners"
implying that the velocity is detected by finding the Doppler shift of the
emitted ultrasound pulse. This book goes to great length to explain that
this is not possible for the pulsed systems, and the Doppler shift is actually
not used in these systems. It is the shift of position of the signals between
pulses that is employed, and the classical Doppler effect plays a minor role.
Unfortunately many publications, and even very recent reviews, fail to make
this distinction resulting in quite erroneous system descriptions and fallacious
interpretations of the influence from various physical effects such as attenuation.
Several books have appeared in recent years, which are dedicated to the
interpretation of the acquired images in a clinical setting. Fewer
books go into detail concerning the function of the system, but they
lack explanations of the intricacies of the different techniques.
This book is an attempt to make a coherent and thorough description
of the fairly advanced digital signal processing schemes that are used
for estimating blood velocity from the received ultrasound signal.
The emphasis is put on analyzing
the signal processing used for extracting the velocity information and
how the resulting estimates are influenced by the physical circumstances.
Examples are given throughout the book about how different operational
parameters are chosen, and how to design the different parts of theses
systems. This also includes a description of how the processing can be
performed by the currently available electronics. The book does not
include chapters on the clinical aspects of velocity estimation, nor
does it include advise on transducers, fabrication, phantoms, or security
issues. All of these topics have been dealt with in other books, that
can be consulted for advice.
The book evolved from a graduate course given by the author at Duke
University, Department of Biomedical Engineering in the spring of 1992
and at University of Illinois at Urbana-Champaign, Bioacoustics Research
Laboratory in 1993. The courses were taught by going through the
chapters consecutively, and the intent is that the book is read in
the same fashion. The treatment is expanded through the chapters, and
many results derived in one chapter are used or implied to be known in
The approach taken is to analyze
and quantify the behavior of the algorithms based on signal theory.
This often entails deriving rather complicated formulas, and it can
be difficult to gain the full understanding of the function of all
parts of the algorithms. Since this book is a monograph, it does not
include exercises, but a useful approach to enhance understanding is
to implement the different algorithms in software. This was
also the method of attack taken by this author and in the courses given.
Nearly all the graphs shown are generated from small Matlab programs.
Making such programs gives insight into the function of the algorithms
and is a very efficient learning tool. Any high level signal processing
program like Matlab, Mathematica, or even C can be used
in such a learning process. Enough information is found throughout
the book to implement all the commercially available algorithms
using realistic physical parameters.
The book consists of 9 chapters. A brief introduction to and historical
account of medical ultrasound systems are given in Chapter 1.
The function of the various systems is explained, and some clinical images
are shown. The next chapter covers ultrasound in general with special
emphasis on concepts important to medical systems. The scattering of
ultrasound fields by tissue, attenuation of the pulses by the tissue, and
characterization of pulsed pressure fields generated by medical transducers
The topic of Chapter 3 is flow physics. The purpose of the
chapter is to serve as a short introduction to basic flow physics. After
a brief description of the human circulatory system, the concepts of
steady flow, viscosity, and Poiseuille flow are given. The treatment
then focuses on pulsatile flow, and how it can be decomposed into
sinusoidal flow components. Flow profiles, Reynolds numbers, and
entrance effects are also covered.
Chapter 4 introduces a simple model for the interaction of ultrasound
with blood. Models are derived for just one scatterer and for a distribution
of scatterers. The important difference between Doppler and displacement
effects is pointed out. The chapter is central to the treatment of the
different velocity estimators and should be studied carefully. A few notes
are given on scattering from blood and on the stochastic nature of the
Chapter 5 describes continuous wave systems. How the systems
work in detail and various ways of presenting the result to the physician
are explained. The consequence of doing this signal processing in terms of
velocity resolution and amplitude accuracy is elucidated.
Then the treatment moves on to the more advanced systems in which specific
parts of the body can be investigated. The pulsed wave
system described in Chapter 6
can estimate blood velocity in one or more locations along one imaging
direction. Different ways of doing so are examined and limitations and
performances are assessed.
The most recent systems display a color image of the blood velocity in
the body. Two conceptually different techniques have been suggested.
The first estimates the phase shift between two consecutively received
lines and is investigated in Chapter 7. A number of algorithms
can be devised to make a phase shift estimation, but an autocorrelation
approach seems to be particularly successful. The second principle,
described in Chapter 8, estimates the time displacement
between two consecutive lines. This system is still in its infancy,
although one scanner has been marketed based on it. The chapter
investigates the accuracy of the technique, what influence echo signals
from vessel walls have, and why one, in some cases, might get erroneous
velocities out from this estimator.
The final chapter investigates experimental and research systems.
The treatment is less rigorous, because these systems are still in
development or under clinical evaluation. The particular approaches
treated are different attempts to solve some of the problems and
limitations encountered in commercial systems, and outlines the
direction for current and further research.
Each chapter concludes with a commented bibliography
in order to credit, at least partly, the many researchers involved
in developing and researching these systems. The references given
in the back are not exhaustive, since this book does not and cannot
cover all aspects of and algorithms for velocity estimation. The
main technical publications that play important roles in the development
of the systems are presented here. Not all incarnations of the
presentations of results are given; often, only the most accessible
papers from journals are included.
The book was prepared for a graduate course in biomedical engineering.
With the diversity of that group in mind, the course notes were
written so that a student with a B.Sc. in engineering could read them
without needing to consult other literature. Thus, a basic knowledge
of simple digital signal processing like Fourier and Z-transforms
and correlation functions is assumed, which is included in the
curriculum of nearly all science and engineering bachelor's degrees.
The intended readership is, thus, graduate students in physics and
engineering, and researchers working in medical ultrasound.
Technically inclined physicians should also be able to follow
many of the derivations and examples, and gain insight into
the artifacts of these systems. A primary
group is people new to medical ultrasound either in research or in
medical companies, as an attempt has been made to make the
Jørgen Arendt Jensen