MRI Physics for Radiologists

Alfred L. Horowitz

MRI Physics for Radiologists

A Visual Approach

Second Edition

Springer-Verlag

New York Berlin Heidelberg London Paris Tokyo Hong Kong Barcelona Budapest

Alfred L. Horowitz, M.D.

Director, Magnetic Resonance Imaging, Resurrection Hospital, Chicago, IL and

Clinical Assistant Professor of Radiology,

University of Illinois Hospital at Chicago, Chicago, IL USA

Library of Congress Cataloging-in-Publication Data Horowitz, Alfred L.

MRI physics for radiologists: a visual approach I Alfred L. Horowitz. - 2nd ed.

p. cm.

Includes bibliographical references and index. ISBN-13: 978-0-387-97717-1

1. Magnetic resonance imaging.

[DNLM: 1. Magnetic Resonance Imaging. 2. Physics. OC 762 H816mj RC78.7.N83H45 1991

538'.36:-dc20 DNLMIDLC

for Library of Congress 91-5134

Printed on acid-free paper.

© 1989, 1992 Springer-Verlag New York, Inc. Originally published under the title MRI Physics for Physicians.

All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer-Verlag New York, Inc., 175 Fifth Avenue, New York, NY 10010, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereaf-ter developed is forbidden.

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Production managed by Henry Krell; manufacturing supervised by Jacqui Ashri. Camera ready copy provided by author.

987654321

ISBN-13: 978-0-387-97717-1 e-ISBN-13: 978-1-4684-0428-9 DOl: 10.1007/978-1-4684-0428-9

PREFACE

When this book was initially published three years ago, it was my goal to delineate the principles of magnetic resonance imaging in a format that could be understood without a sophisticated physics or mathematics back-ground. That is still my goal. However, in the interim, it has become clear to me that many magnetic resonance techniques that we now routinely use are inadequately understood by many of us. Therefore, I have re-structured and expanded the book in the following way. There are now three main sections: sections one and two deal with the contrast and spatial characteristics of the image, as they did in the original text; and an additional section deals with various peripheral but significant magnetic resonance topics. Sections one and two still provide the "meat" of the material through the guise of the spin-echo pulse sequence; but section three goes beyond by explaining other pulse cycles and devices that are commonly used in today's imaging centers.

To begin with, since fast scanning has now become a widely used tech-nique, that chapter has been significantly expanded, and now includes a complete but non-mathematical explanation of what a gradient echo is and how fast scan images differ in principle from spin-echo images. Also, the applications of 3DFT and "half-Fourier" imaging are graphically covered without mathematical intervention.

A large chapter is devoted to motion, including the considerations of motion artifacts and the devices used to control them, as well as the subjects of blood flow, and magnetic resonance angiography.

A separate little chapter on aliasing is provided to explain the mystery of the "wrap-around" artifact - both in the phase and frequency encoding di-rections.

The last of the new chapters in section three deals with the interaction of water and fat on the MR image, which includes discussions of chemical shift artifacts as well as chemical shift imaging.

The mathematical appendix, which appeared in the first addition, has been replaced by a separate chapter that reveals how a scanner receives and processes a signal to form an image (once again ignoring the "queen of sciences"). This chapter forms the conclusion of the section on the forma-tion of the image, and is placed immediately following the detailed explana-tions of the frequency and phase encoding processes.

The change in the title of the book, which now refers to a ''visual ap-proach," was undertaken because of the way in which the book was written: nearly every topic was based on a visual graphic conception. The image came first, and then the text was constructed to fit the picture. Certainly, my basic philosophy for this text remains hinged around my belief that the book can be understood by anybody with a knowledge of basic algebra.

In conclusion, I again hope that I have achieved my goal of providing

understandable explanations of the principles we use in our daily magnetic resonance imaging activities.

I again wish to thank the residents and other physicians in the Depart-ment of Radiology at the University of Illinois Hospital in Chicago for their helpful comments and questions, which were especially useful in the prepa-ration of sections one and two in the book.

I also wish to acknowledge and thank Pradip M. Pattany, MSc., Director of Research and Development MRI of Colorado, and Norbert J. Pelc, Sc.D., Associate Professor Department of Radiology Stanford University Medical School for their physics expertise, which helped me to understand some of the more difficult concepts.

CONTENTS

Preface

Section 1-Image Contrast

Overview ... . Magnetic Field ... . Fields ... . vii 3 4 4

Basic 'JYpes of Magnets ... - 4

Permanent Magnet ... 5

Superconducting Magnet ... 6

Vectors... 8 Paramagnetic, Diamagnetic, Ferromagnetic ... . Angular Momentum-Nuclear Spin ... . Magnetic Dipole Moment ... . Resultant M Vector ... . Precession and the Larmor Equation ... . Radiofrequency Pulse ... . Electromagnetic Waves ... . Periodic Functions ... . Axis Conventions ... . Perturbance of the M Vector ... . Rotating Frame of Reference ... . Resonance ... . M vs the Component MDM Vectors ... . The Signal and the Mx Vector ... . Controlling the Flip of M ... . Motion of M in the X-Y Plane ... . Relaxation ... . T1 and T2 Components of Relaxation ... . Tl Curves ... . Pulse Cycles, Pulse Sequences and Tissue Contrast ... . TRand TE ... . T1 and T2 Weighting ... . Balanced (Spin Density) Scans ... . T2 and the Spin-echo Pulse Cycle ... .

ix 9 9 10 10 12 15 15 17 19

20

29

29

35

35

Graph of MR Signal-free Induction Decay (FID) ... , 41

Envelopes of the Signal ... 42

T2* ... 42

Concept of Phase ... 43

Phase and the MR Signal .. . . .. 44

Dephasing and the MR Signal . . . .. 45

Rephasing the MR Signal-180D Refocusing Pulse... 45

The Spin-echo Pulse Cycle ... 47

The ltue T2 Curve ... 49

T2 Curves for Different Tissues for Long TR'S ... 51

Tl and T2 Constants ... 52

T2 Curves for Different Tissues for Short TR'S ... 53

Section 2-The Image in Space Gradients ... 57

The Slice Select Gradient ... 60

Changing Slice Thickness ... 61

Frequency Gradient ... 64

The Pixel Grid ... 64

Sine Functions for Each Pixel ... 66

Application of Frequency Gradient ... 68

The Fourier Transform ... 71

The Spectrum ... 71

The Fourier Series ... 72

Fourier Transform of Pixel Grid ... 74

Rotating Gradients-One Alternative. . . .. 76

The Phase Encoding Gradient . . . .. 77

Degrees of Phase Shift Per Row ... 78

Phase Shift in Sine Functions ... 80

Simple Summary of Phase Ideas. . . .. 81

Multiple Repetitions to Form the Image ... 82

Phase Encoding Repititions and the Pixel Grid ... 83

Phase Encoding Repetitions and the MDM . . . .. 87

Inside the "Black Box": From Signal to Image ... 94

(l)-Repetition-time Matrices ... 94

(2)-Phase-frequency Matrices ... 99

(3)-Transformation to Image-the 2DFT ... 100

Wrapping Up Basic Concepts ... 105

The Gradients in Perspective ... 105

Imaging in Other Planes ... 107

The Multislice Technique ... 110

Averages, Excitations ... 112

Exam Time ... 113

General Wrap-up ... 113

Section 3-Miscellaneous Topics Some Other Pulse Cycles and Procedures ... 117

Saturation Recovery and Partial Saturation ... 117

Inversion Recovery ... 118

Fast Scans ... 119

Pulse Cycle Summary . . . .. 128

Three Dimensional Fourier Imaging . . . .. 128

Half Fourier Imaging ... 130

Motion ... 133 General Considerations ... 133 Flowing Blood ... . . . .. 136 Time-of-flight Phenomena ... 136 Phase-related Phenomena ... 137 Thrbulence ... 139

Even and Odd Echo Effects ... 141

Flow-related Enhancement ... 141

Magnetic Resonance Angiography (MRA) ... 147

Maximum Intensity Projection Algorithm ... 147

Projection Acquisition ... 149

Methods to Combat Motion Artifacts ... 149

Pre-saturation ... 150

Cardiac Gating ... 151

Respiratory Ordered Phase Encoding ... 152

Gradient Moment Nulling ... 155

Aliasing ... 159

Aliasing in the Phase Encoding Axis ... 159

Aliasing in the Frequency Encoding Axis ... 163

Fat and Water ... 166

Chemical Shift Artifact ... 166

Method of Dixon ... 171

Selective Spectral Excitation ... 175

Stir Sequences ... 176

Coils ... 178

Receiver, Transmitter Coils ... 178

Gradient Coils ... 179

Shim Coils ... 180

User Parameter Summary ... ' 181 Bibliography ... 183 Index ... 185