Estimation of Blood Velocities Using Ultrasound

A Signal Processing Approach

Jørgen Arendt Jensen,
Cambridge University Press, New York, 1996,
ISBN 0-521-46484-6

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 jaj@elektro.dtu.dk. The price is 90 US$ plus shipping.

Preface

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.

Organization

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 subsequent chapters.

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 are described.

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 received signal.

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.

Intended readership

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 book self-contained

Jørgen Arendt Jensen

Lyngby, Denmark
December 1994