Clinical MR imaging

P. Reimer · P. M. Parizel · F.-A. Stichnoth (Eds.)

Clinical MR Imaging
A Practical Approach


P. Reimer · P. M. Parizel · F.-A. Stichnoth (Eds.)

Clinical MR Imaging
A Practical Approach

Second, completely revised and updated edition
With 494 Figures and 141 Tables


Prof. Dr. Peter Reimer
Department of Radiology
Klinikum Karlsruhe
Moltkestr. 90
76133 Karlsruhe, Germany
e-mail:
Prof. Dr. Paul M. Parizel
Department of Radiology
Universitair Ziekenhuis Antwerpen
Wilrijkstraat 10
B-2650 Edegem, Belgium
e-mail:
Dr. Falko-A. Stichnoth
Radiologie München Ost
Wasserburger Landstr. 274–276

81827 München, Germany
e-mail:

2nd edition hardcover ISBN 3-540-43467-4 Springer Berlin Heidelberg New York

ISBN-10 3-540-31530-6 Springer Berlin Heidelberg New York
ISBN-13 978-3-540-31530-8 Springer Berlin Heidelberg New York
Library of Congress Control Number: 2005938673
Published in the medico-scientific book series of Schering as hardcover.
The book shop edition is published by Springer Berlin Heidelberg New York.
Where reference is made to the use of Schering products, the reader is advised to consult the latest
scientific information issued by the company.
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No part of this publication may be translated into other languages, reproduced or utilized in any
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© 1999, 2003, 2006 by Schering
Printed in Germany
Typesetting: K. Detzner, 67346 Speyer, Germany
Cover design: Erich Kirchner, Heidelberg, Germany
Printed on acid-free paper 21/3150 5 4 3 2 1 0


Foreword

Since the introduction of magnetic resonance imaging in the early 1980s, unprecedented
developments have taken place that have catapulted this imaging modality to the forefront of modern medical imaging. During this development, complex novel techniques
have been introduced, including diffusion imaging, perfusion imaging, functional MR
imaging, and basic innovations in pulse sequence design and system hardware. Despite

the myriad of publications and developments, it is frequently difficult for the practicing
radiologist to stay ahead of the game and translate advances into clinical protocols and
improvements.
The current book by Drs. Reimer, Parizel, and Stichnoth is an exercise in marrying
technological advances and clinical radiology. The book has 17 chapters: basic, contrast
agents, hemorrhage, head, ENT, spine, pelvis, abdomen, retroperitonium, vessels, joints,
soft tissue, chest breast, cardiac, pediatrics, and interventional imaging. All the chapters
have the same structure, including subchapters on coils, pulse sequences, imaging protocols, anatomy, and clinically relevant pathology. Each chapter also contains a succinct reference list. Overall there are over 500 pages with illustrations to highlight key concepts.
The authors have done a fine job and the current work certainly enriches the armamentarium for the clinical radiologist. The editors and contributors are to be commended for their efforts in achieving a clear synthesis of technological and clinical issues. This
volume clearly represents an important contribution to the field of medical imaging.

Ralph Weissleder, MD, PhD
Professor of Radiology
Massachusetts General Hospital, Boston, MA, USA


Preface

Magnetic resonance (MR) imaging has become the leading cross-sectional imaging method in clinical practice. Since the 1980s, continuous improvements in hardware and software have significantly broadened the scope of applications. At present, MR imaging is
not only the most important technique in neuroradiology and musculoskeletal radiology,
but has also become an invaluable diagnostic tool for abdominal, pelvic, cardiac, breast
and vascular imaging.
Due to ongoing technical developments, the complexity of MR imaging has increased
markedly. This often represents an obstacle not only to beginners (who find it difficult to
get started), but also to more experienced users (who find it hard to keep up). Information
about MR imaging can be found in many excellent textbooks and reference works, several of which have become encyclopaedic in scope and sheer volume. As editors and authors
of this book, we have endeavoured to use a different approach. As a starting point for the
first edition, we had taken into consideration that routine diagnostic questions account
for more than 90% of examinations. This implies that by adopting a practical protocolbased approach the workflow in a MR unit can be streamlined considerably, which is critical in today's economic environment. We have aimed to provide the reader with such
information, based on our combined experience.

The second edition of this book offers practical guidelines for performing efficient and
cost-effective MR imaging examinations in daily practice. The authors and editors have
reviewed all chapters, included new techniques, added new figures and replaced older
ones. As editors, we hope that this work will lead to a better practical understanding of
MR imaging and that new sequences and protocols will contribute to solving clinical
problems. As such, we believe this book will continue to help beginners to advance their
starting point in implementing the protocols and will aid more experienced users in
updating their knowledge.
The editors:
P. Reimer, P. M. Parizel, and F.-A. Stichnoth


Contents

1 Principles of Magnetic Resonance Imaging
and Magnetic Resonance Angiography
W. Nitz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1

2 Contrast Agents for Magnetic Resonance Imaging
T. Balzer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

53

3 Haemorrhage
T. Allkemper

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

65

4 Magnetic Resonance Imaging of the Brain
P. M. Parizel, H. Tanghe, and P. A. M. Hofman . . . . . . . . . . . . . . .

77

5 Magnetic Resonance Imaging of the Spine
J. W. M. Van Goethem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
6 Magnetic Resonance Imaging of the Head and Neck
L. van den Hauwe and J. W. Casselman . . . . . . . . . . . . . . . . . . . 173
7 Joints
H. Imhof, F. Kainberger, M. Breitenseher, S. Grampp, T. Rand,
and S. Trattnig . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211
8 Bone and Soft Tissues
J. van Gielen, A. Van der Stappen, and A. M. De Schepper

. . . . . . . 237

9 Upper Abdomen: Liver, Pancreas, Biliary System, and Spleen
P. Reimer and B. Tombach . . . . . . . . . . . . . . . . . . . . . . . . . . . . 271
10 Kidneys and Adrenal Glands
C. Catalano, G. Cardone, M. Castrucci, R. Brillo, F. Fraioli,
and F. Pediconi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 319
11 Pelvis
D. MacVicar and P. Revell . . . . . . . . . . . . . . . . . . . . . . . . . . . . 335


X

Contents

12 Heart
M. G. Lentschig

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 365

13 Large Vessels and Peripheral Vessels
M. Boos, J. Meaney . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 397
14 MRI of the Chest
H.-U. Kauczor, E. van Beek . . . . . . . . . . . . . . . . . . . . . . . . . . . 447
15 Magnetic Resonance of the Breast
C. Kuhl . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 469
16 Magnetic Resonance Imaging of Pediatric Patients
B. Kammer, T. Pfluger, M. I. Schubert, C. M. Keser,
and K. Schneider . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 489
17 Interventional Magnetic Resonance
C. Bremer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 571
Subject Index

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 581


List of Contributors

Dr. Thomas Allkemper
Institute of Clinical Radiology, Westfälische Wilhelms-Universität,
Albert-Schweitzer-Str. 33, 48129 Münster, Germany
Dr. Thomas Balzer
Schering AG, Clinical Department, Diagnostics, MR and Ultrasound Contrast Media,

Müllerstr. 178, 13353 Berlin, Germany
Dr. Matthias Boos
Institut für Radiologie und Nuklearmedizin, Krankenhausstr. 70,
85276 Pfaffenhofen, Germany
Dr. Martin Breitenseher
Osteologie und MR, Universitätsklinik für Radiodiagnostik,
Allgemeines Krankenhaus (AKH), Währinger Gürtel 18–20, 1090 Wien, Austria
Dr. Christoph Bremer
Institute of Clinical Radiology, Westfälische Wilhelms-Universität,
Albert-Schweitzer-Str. 33, 48129 Münster, Germany
Dr. Gianpiero Cardone
Department of Radiology University “La Sapienza”, Policlinico Umberto I,
Viale Regina Elena 324, 00161 Rome, Italy
Dr. Jan W. Casselman
Department of Radiology, A.Z. St. Jan, Ruddershove 10,
8000 Brugge, Belgium
Dr. Carlo Catalano
Department of Radiology, University “La Sapienza”, Policlinico Umberto I,
Viale Regina Elena 324, 00161 Rome, Italy
Prof. Dr. Arthur M. de Schepper
Universitair Ziekenhuis Antwerpen, Department of Radiology,
Wilrijkstraat 10, 2650 Edegem, Belgium
Dr. Francesco Fraioli
Department of Radiology, University “La Sapienza”, Policlinico Umberto I,
Viale Regina Elena 324, 00161 Rome, Italy


XII

List of Contributors

Prof. Dr. Stefan Grampp
Osteologie und MR, Universitätsklinik für Radiodiagnostik,
Allgemeines Krankenhaus (AKH), Währinger Gürtel 18–20, 1090 Wien, Austria
Dr. Paul A. M. Hofmann
Department of Radiology, University Hospital Maastricht, P.O. Box 5800,
6202 AZ Maastricht, The Netherlands
Prof. Dr. Herwig Imhof
Osteologie und MR, Universitätsklinik für Radiodiagnostik,
Allgemeines Krankenhaus (AKH), Währinger Gürtel 18–20,
1090 Wien, Austria
Prof. Dr. Franz Kainberger
Osteologie und MR, Universitätsklinik für Radiodiagnostik,
Allgemeines Krankenhaus (AKH), Währinger Gürtel 18–20,
1090 Wien, Austria
Dr. Birgit Kammer
Röntgenabteilung, Dr. von Haunersches Kinderspital, Klinikum Innenstadt,
LMU München, Lindwurmstr. 4, 80337 München, Germany
Prof. Dr. Hans-Ulrich Kauczor
Abt. für onkologische Diagnostik und Therapie,
Deutsches Krebsforschungszentrum, Im Neuenheimer Feld 280,
69120 Heidelberg, Germany
Dr. Claudia M. Keser
Institut für Anästhesiologie, Klinikum Großhadern und Klinikum Innenstadt,
LMU München, Nußbaumstr. 20, 80336 München, Germany
Priv.-Doz. Dr. Christiane Kuhl
Radiologische Universitätsklinik Bonn, Sigmund-Freud-Str. 25,
53105 Bonn, Germany
Dr. Markus G. Lentschig
Radiologische Praxis St. Jürgenstrasse, Prager Str. 11, 28211 Bremen, Germany

Dr. A. Laghi
Department of Radiology, University “La Sapienza”, Policlinico Umberto I,
Viale Regina Elena 324, 00161 Rome, Italy
Dr. David MacVicar, MA, MRCP, FRCP
The Royal Marsden NHS Trust, Department of Diagnostic Radiology,
Downs Road, Sutton, Surrey SM2 5PT, Great Britain
Dr. Jim Meaney
MRI Department, St. James’s Hospital, St. James’s Street, Dublin 8, Ireland


List of Contributors

Dr. A. Napoli
Department of Radiology, University “La Sapienza”, Policlinico Umberto I,
Viale Regina Elena 324, 00161 Rome, Italy
Dr. Wolfgang Nitz
Siemens A.G. Medical Solutions Magnetic Resonance Division, Henkestr. 127,
91052 Erlangen, Germany
Dr. Karsten Papke
Klinikum f. Radiologie und Neuroradiologie, Klinikum Duisburg,
Zu den Rehwiesen 9, 47055 Duisburg, Germany
Prof. Dr. Paul M. Parizel
Department of Radiology, Universitair Ziekenhuis Antwerpen,
Wilrijkstraat 10, 2650 Edegem, Belgium
Dr. Federica Pediconi
Department of Radiology University “La Sapienza”, Policlinico Umberto I,
Viale Regina Elena 324, 00161 Rome, Italy
Dr. Thomas Pfluger
Institut für Radiologische Diagnostik, Klinikum Innenstadt, LMU München,
Ziemssenstr. 1, 80336 München, Germany

Dr. Thomas Rand
Osteologie und MR, Universitätsklinik für Radiodiagnostik,
Allgemeines Krankenhaus (AKH), Währinger Gürtel 18–20, 1090 Wien, Austria
Prof. Dr. Peter Reimer
Klinikum Karlsruhe, Department of Radiology, Moltkestr. 90, 76133 Karlsruhe,
Germany
Dr. Patrick Revell, BSc, DCR
Siemens House, Oldbury, Bracknell, Berkshire RG12 8FZ, Great Britain
Prof. Dr. Karl Schneider
Röntgenabteilung, Dr. von Haunesches Kinderspital, Klinikum Innenstadt,
LMU München, Lindwurmstr. 4, 80337 München, Germany
Dr. Mirjam I. Schubert
Institut für Radiologische Diagnostik, Klinikum Innenstadt, LMU München,
Ziemssenstr. 1, 80336 München, Germany
Dr. Falko-A. Stichnoth
Radiologie München-Ost, Wasserburger Str. 274–276,
81827 München, Germany
Dr. Hervé Tanghe
Department of Radiology, Academisch Ziekenhuis Rotterdam,
Dr. Molewaterplein 40, 3015 GD Rotterdam, The Netherlands

XIII


XIV

List of Contributors

Dr. Bernd Tombach
Institute of Clinical Radiology, Westfälische Wilhelms-Universität,

Albert-Schweitzer-Str. 33, 48129 Münster, Germany
Dr. S. Trattnig
Osteologie und MR, Universitätsklinik für Radiodiagnostik,
Allgemeines Krankenhaus (AKH), Währinger Gürtel 18–20, 1090 Wien, Austria
Dr. Edwin van Beek
Section of Academic Radiology, Floor C, Royal Hallamshire Hospital,
Glossop Road, S1O 2JF Sheffield, Great Britain
Dr. Luc van den Hauwe
Dept. of Radiology, AZ KLINA, Augustijnslei 100, 2930 Brasschaat, Belgium
Dr. Jan van Gielen
Universitair Ziekenhuis Antwerpen, Department of Radiology,
Wilrijkstraat 10, 2650 Edegem, Belgium
Dr. Johan W. M. Van Goethem
Department of Radiology, Universitair Ziekenhuis Antwerpen,
Wilrijkstraat 10, 2650 Edegem, Belgium
Dr. Anja van der Stappen
Universitair Ziekenhuis Antwerpen, Department of Radiology,
Wilrijkstraat 10, 2650 Edegem, Belgium


Abbreviations

ADC
B0
B1
CE-T2-FFE
CE-FAST
CEMRA
CHESS
CISS

CNR
CSF
DESS
EPI
FAME
FAST
FFE
FISP
FLASH
fMRI
FOV
FSE
FSPGR
GMR
GRASE
GRASS
GRE
HASTE
HASTIRM
IR
IRM
MIN
MIP
MPGR
MPRAGE
MR
MRA
MT
MTC

analog to digital converter
main magnetic field strength in Tesla (T)
magnetic component of the RF field
contrast-enhanced T2-W FFE sequence
contrast-enhanced FAST sequence
contrast-enhanced magnetic resonance angiography
chemical shift selective pulse
constructive interference steady-state sequence
contrast-to-noise ratio
cerebrospinal fluid
double-echo steady-state sequence
echo planar imaging
fast-acquisition multi-echo sequence
Fourier acquired steady-state sequence
fast-field echo sequence
fast imaging with steady-state precession sequence
fast low-angle shot sequence
functional magnetic resonance imaging
field of view
fast spin-echo sequence
fast spoiled GRASS sequence
gradient motion rephasing
gradient and spin echo sequence
gradient recalled acquisition in the steady state sequence
gradient echo sequence
half Fourier acquired single-shot turbo spin-echo sequence
half Fourier acquired single-shot turbo spin-echo sequence using
inversion recovery and only the signal magnitude
inversion-recovery sequence
inversion-recovery sequence that utilizes only the magnitude

of the signal
minimum intensity projection
maximum intensity projection
multi-planar GRASS sequence
magnetization-prepared rapid acquired gradient echo sequence
magnetic resonance
magnetic resonance angiography
magnetization transfer
magnetization transfer contrast


XVI

Abbreviations

MTS
PC
PSIF
RAM-FAST
RARE
RF
SAR
SE
SNR
SPGR
SSFP
SSFSE
STIR
T1
T1-W

T2
T2*
T2-W
TE
TFE
TGSE
TIR
TIRM
TOF
TONE
TR
TSE

magnetization transfer saturation
phase contrast
a backwards-running FISP sequence
rapidly acquired magnetization-prepared FAST sequence
rapid acquisition with relaxation enhancement
radio frequency
specific absorption rate
conventional spin-echo sequence
signal-to-noise ratio
spoiled GRASS sequence
steady-state free-precession sequence
single-shot fast spin echo sequence
short tau inversion recovery sequence
tissue-specific spin-lattice relaxation time
contrast is weighted by the T1 relaxation time
tissue-specific spin-spin relaxation time
relaxation time T2 plus additional dephasing mechanism (signal decay)

due to local field inhomogeneities or chemical shift
contrast is weighted by the T2 relaxation time
echo time
turbo field echo sequence
turbo gradient and spin-echo sequence
turbo inversion recovery sequence
turbo inversion recovery sequence that utilizes only the magnitude
of the signal
time of flight
tilted optimized non-saturating excitation
repetition time
turbo spin-echo sequence


1

Principles of Magnetic Resonance Imaging
and Magnetic Resonance Angiography
W. Nitz

Contents
1.1
1.1.1
1.1.1.1
1.1.1.2
1.1.1.2.1
1.1.1.2.2
1.1.1.2.3
1.1.1.2.4
1.1.1.2.5

1.1.1.2.6
1.1.1.3
1.1.1.4
1.1.1.4.1
1.1.1.4.2
1.1.1.4.3
1.1.1.4.4
1.1.1.4.5
1.1.1.4.6
1.1.1.5
1.1.1.6
1.1.2
1.1.2.1
1.1.2.2
1.1.2.3
1.1.2.4
1.1.2.5
1.1.2.6
1.1.2.6.1
1.1.2.6.2
1.1.2.6.3
1.1.2.7
1.1.2.8
1.1.2.8.1

Basic Principles of Magnetic Resonance Imaging
Signal Source and Image Formation . . . . . . . .
Magnetic Resonance: What Is Resonating?
What Is Spin? . . . . . . . . . . . . . . . . . . . .
Relaxation and Tissue Differentiation . . . . . . .

Pd, T1 and T2 Relaxation Times . . . . . . . . . .
Chemical Shift . . . . . . . . . . . . . . . . . . . .
T2* Relaxation Time, BOLD and Perfusion . . . .
Diffusion . . . . . . . . . . . . . . . . . . . . . . .
Flow and Motion . . . . . . . . . . . . . . . . . .
Magnetization Transfer . . . . . . . . . . . . . . .
Image Formation and Image Contrast . . . . . .
Magnetization Preparation . . . . . . . . . . . . .
Spectral Suppression of Fat Signal . . . . . . . . .
Relaxation-Dependent Elimination of Fat Signal .
Relaxation-Dependent Elimination of CSF Signal
RF Inversion of the Magnetization
to Improve T1-Weighting . . . . . . . . . . . . . .
Magnetization Transfer . . . . . . . . . . . . . . .
Diffusion Weighting . . . . . . . . . . . . . . . . .
Imaging Protocols and Image Quality . . . . . . .
Basic Elements of a Magnetic Resonance Scanner
Imaging Sequences, Acronyms and Clinical
Applications . . . . . . . . . . . . . . . . . . . . .
Conventional Spin-Echo Imaging (CSE) . . . . .
Magnetization Prepared Spin-Echo Sequences,
the Inversion Recovery Techniques . . . . . . . .
Gradient-Echo Imaging (GRE) . . . . . . . . . . .
Steady-State Techniques . . . . . . . . . . . . . .
Magnetization-Prepared Gradient-Echo
Techniques . . . . . . . . . . . . . . . . . . . . . .
k-Space Interpolation and Half-Fourier Imaging
k-Space Interpolation . . . . . . . . . . . . . . . .
Half-Fourier Imaging . . . . . . . . . . . . . . . .
Echo Asymmetry . . . . . . . . . . . . . . . . . .

Parallel Acquisition Techniques . . . . . . . . . .
Fast Imaging . . . . . . . . . . . . . . . . . . . . .
Fast Imaging with Spin-Echo Sequences . . . . .

2
2
2
3
3
6
6
8
8
8
9
15
15
16
16
17
18
18
18
21
22
23
23
23
26
28

30
30
30
31
31
32
33

1.1.2.8.2 Fast Imaging with Gradient-Echo Sequences . . .
1.1.2.9
Magnetic Resonance Fluoroscopy . . . . . . . . .
1.2
1.2.1
1.2.2
1.2.3
1.2.4
1.2.5
1.2.6
1.3
1.3.1
1.3.2
1.3.3
1.3.4

Magnetic Resonance Angiography,
Techniques and Principles . . . . . . . .
3D Time-of-Flight Angiography . . . . .
2D Time-of-Flight Angiography . . . . .
3D PC Angiography . . . . . . . . . . . .
2D PC Angiography . . . . . . . . . . . .

Contrast-Enhanced Magnetic Resonance
Angiography . . . . . . . . . . . . . . . .
Flow Quantification . . . . . . . . . . . .
Techniques in Cardiac Imaging . . .
ECG Gating – Prospective Triggering
and Retrospective Cardiac Gating . .
Segmentation and Echo Sharing . . .
‘Dark Blood’ Preparation . . . . . . .
Coronary Artery Imaging
and the Navigator Technique . . . . .

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34
35

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36
37
38
39
39

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40
41

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41

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41
43
44

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44

1.4
1.4.1
1.4.1.1
1.4.1.2
1.4.1.3
1.4.1.4
1.4.2
1.4.2.1
1.4.2.2
1.4.2.3
1.4.3
1.4.3.1
1.4.3.2

Artifacts in Magnetic Resonance Imaging . . .
Unavoidable Artifacts . . . . . . . . . . . . . . .
Chemical Shift . . . . . . . . . . . . . . . . . . .
Flow and Motion . . . . . . . . . . . . . . . . .

Truncation Artifacts . . . . . . . . . . . . . . . .
Susceptibility Artifacts and RF Shielding Effects
Avoidable Artifacts . . . . . . . . . . . . . . . .
Flow and Motion . . . . . . . . . . . . . . . . .
Aliasing . . . . . . . . . . . . . . . . . . . . . .
Unexpected Software Features . . . . . . . . . .
System-Related Artifacts . . . . . . . . . . . . .
Parasitic Excitation (Third-Arm Artifact) . . .
Spikes . . . . . . . . . . . . . . . . . . . . . . . .

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45
45
45
45
46
47

49
49
49
50
51
51
51

1.5
1.5.1
1.5.2
1.5.3

MR Safety . . . . . . . . . . . . . . . . . . . . . .
Magnetic Force . . . . . . . . . . . . . . . . . . .
dB/dt – Fast Changes in Magnetic Field Gradient
SAR and Energy of the RF Pulses . . . . . . . . .

52
52
52
52

Further Reading . . . . . . . . . . . . . . . . . . . . . . . . .

52


2

W. Nitz

1.1
Basic Principles of Magnetic Resonance Imaging
This chapter is written as a practical approach to clinical magnetic resonance (MR) imaging. With most scanners available today, images can be generated without
knowledge of the basic principles, mostly by pushing
buttons and executing suggested imaging protocols.
However, in the event there is a need to change an imaging protocol or use another type of sequence, it is very
helpful to have a good understanding of the underlying
basic principles. This knowledge might also be very
helpful for improving the signal-to-noise ratio (SNR) of
an image or for the interpretation of potential artifacts.

1.1.1
Signal Source and Image Formation

Fig. 1.1. The macroscopic magnetization or ‘spin’: Exposed to an
external field, the magnetic moment of the spin causes a preferred
orientation, correlated with a consumption of energy if forced into
the less convenient position. Since the preferred position of a parallel alignment shows a higher population, a macroscopic magnetization builds up

1.1.1.1
Magnetic Resonance: What Is Resonating?
What Is Spin?
The quantum mechanical description of a subatomic
particle such as the proton implies that it has a quantized angular momentum, called a spin. Associated with
the spin is a magnetic moment. Because the hydrogen
atom has only one proton as a nucleus, this spin property can be observed by looking at hydrogen. Hydrogen is
an atom present in water and fat; since the human body
consists mostly of water and fat, we have a potential

medical application. This spin or, better, its magnetic
moment aligns itself to an external field B0. Another
possible position is alignment in the opposite direction,
although this is less convenient and causes energy consumption (Fig. 1.1). The energy difference between
these two possible positions can be written as the quantized energy of a photon
∆E = γ · –h · B0 = h · ν
with ν being the frequency of an electromagnetic field
and h Planck’s constant. Unfortunately, we are dealing at
this point with the inconvenient quantum uncertainties
of a single proton. Fortunately, we are not facing a single proton, but rather a large number of similar protons.
The term ‘spins’ is used to refer to these large groups,
also called a spin isochromat. The behavior of this spin
isochromat can be considered equivalent to a quantum
average or expectation and, fortunately, can be treated

Fig. 1.2. The ‘resonance’ phenomenon: A B1 field perpendicular to
the main field (z-direction) causes the macroscopic magnetization
to flip towards the x-y plane. Any attempt to turn the macroscopic magnetization away from the direction of the main magnetic
field will cause a rotation around the z-direction. If the B1 component of the electromagnetic field is rotating at the same frequency, the situation is called ‘on resonance’ and the B1 field will continue to turn the macroscopic magnetization

as a macroscopic magnetization M0 following the laws
of classical electrodynamics. As illustrated in Fig. 1.2,
hydrogen nuclei will provide a macroscopic magnetization when exposed to an external magnetic field,
aligned in the direction of the main static field, usually
referred to as the z-direction. This magnetization rotating is called longitudinal magnetization. Applying a


1 Principles of Magnetic Resonance Imaging and Magnetic Resonance Angiography

around any angle, depending on the amplitude and

duration of the B1 field. Such a process is called a radio
frequency (RF) excitation. With the B1 field switched
off, the macroscopic magnetization continues to rotate
with the specific frequency of 42.58 MHz/T and will
induce a signal in a nearby coil, as indicated in Fig. 1.3.
This is the basic source of the MR signal.
1.1.1.2
Relaxation and Tissue Differentiation

Fig. 1.3. The induction of the MR signal: If the macroscopic magnetization is not aligned with the direction of the main field, the
magnetization continues to rotate around the z-axis and will
induce a signal in a nearby coil

magnetic field perpendicular to the main static magnetic field will cause a rotation of the macroscopic magnetization. Any attempt to turn the macroscopic magnetization towards the x-y plane will cause the vector of
the magnetization to rotate around the main direction
with a frequency of 42.58 MHz/T, similar to a gyroscope. This frequency is also called the Larmor frequency. This magnetization rotating in the x-y plane is called
transverse magnetization.“ If the applied electromagnetic field uses the same frequency, one magnetic component of this field rotates with the macroscopic magnetization (being in resonance), mimicking a constant
so-called B1 field. For this so-called in-resonance situation, the macroscopic magnetization can be turned

Fig. 1.4. The dipole-dipole interaction as a main source for
relaxation: Intramolecular
dipole-dipole interactions are
the dominant factors for T1 and
T2 relaxation times. The spin of
a single hydrogen nuclei,
aligned parallel to an external
field B0, has a correlated magnetic moment indicated by the
field lines. That field is superimposed on the external field
experienced by the neighboring
hydrogen nuclei. Depending on

the orientation of the water
molecule within the external
field, the effective field is diminished or increased. This will
lead to significant differences in
resonance frequencies on the
molecular level

1.1.1.2.1
Pd, T1 and T2 Relaxation Times
The amplitude of the induced signal is proportional to
the number of protons involved in the excitation process (proton density). Usually, several excitations are
necessary to collect enough information to reconstruct
an image. Each time the actual longitudinal magnetization is flipped and thus converted to a signal inducing
rotating transverse magnetization. The amplitude of
the induced signal depends on the actual amount of
longitudinal magnetization ‘flipped’ into the transverse
plane. The actual longitudinal magnetization is a function of the tissue-specific relaxation rate, the time needed for the realignment of the magnetization with the
main magnetic field. That time is called the T1-relaxation time. The rotating transverse magnetization is the
result of a significant number of individual magnetic
moments of hydrogen nuclei, each pointing in the same
direction. The dipole-dipole interaction between all

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W. Nitz

these magnetic moments will cause a ‘dephasing’ of the

transverse magnetization. The slower the data are
acquired after the initial excitation, the lower the
induced signal detected. The relaxation rate assigned to
the phenomenon of this ‘dephasing’ is tissue-specific
and is called T2-relaxation. The simple dipole-dipole
interaction is illustrated in Fig. 1.4. Depending on the
orientation of the two protons relative to the main magnetic field B0, the field of the first proton may either
augment or oppose the main magnetic field at the location of the second proton. The difference in field
strength can be approximately as high as 2 mT. Such a
difference in field strength on a molecular level would
lead to a difference in resonance frequencies of approximately 85 kHz, and the transverse magnetization
would dephase within 12 µs. Current acquisition
schemes allow about 1 ms as a minimum time between
excitation and signal acquisition; thus, the signal of a
‘frozen’ arrangement of water molecules cannot be
observed. In the vicinity of macromolecules, the
attached immobile water molecules are not visible by
MR imaging and are often called ‘invisible water pool’.
Fortunately, the majority of water molecules in human
soft tissue are highly mobile, tumbling around, and the
averaging over the fluctuating fields leads to a slower
dephasing of the transverse magnetization. The time

for the dephasing process, the T2-relaxation time, is
also called the transverse relaxation or spin-spin relaxation time. As a rule, the higher the mobility of the
water molecules (the ‘squishier’ the tissue), the longer
the T2-relaxation time.
As described for the excitation process, in order to
‘flip’ or turn the magnetization, the generated B1-field
has to be ‘in resonance’ with the magnetization. The

same rule applies for the relaxation process aiming for
the realignment of the magnetization with the main
magnetic field B0, the ‘recovery’ of the longitudinal
magnetization. For tissue, where the ‘tumbling’ water
molecules causing field fluctuations close to the Larmor
frequency, the T1-relaxation time will be short. If the
molecules are very small and mobile (free water), the
tumbling frequency will be higher than the Larmor frequency, causing a slow T1-relaxation process. If the
water molecules are motion restricted, the tumbling
frequency may be below the Larmor frequency, and the
result will be the same, a slow T1-relaxation process.
The time for the recovery process, the T1-relaxation
time, is also called the longitudinal relaxation time or
spin-lattice relaxation time, since it depends on how
fast the stored energy (of the spin system) can be
returned to the surrounding environment (the ‘lattice’).
As a rule, the higher the mobility of the water molecules

Table 1.1. Relaxation parameters for various tissues
Region

Brain

Liver

Spleen
Pancreas
Kidney
Muscle

Longitudinal relaxation times
T1 (ms)

Gray matter (GM)
White matter (WM)
Cerebrospinal fluid (CSF)
Edema
Meningioma
Glioma
Astrocytoma
Misc. tumors
Normal tissue
Hepatomas
Misc. tumors
Normal tissue
Normal tissue
Misc. tumors
Normal tissue
Misc. tumors
Normal tissue
Misc. tumors

1,5 T

1,0 T

0,2 T

921
787

3000
1090
979
957
1109
1073
493
1077
905
782
513
1448
652
907
868
1083

813
683
2500
975
871
931
1055
963
423
951
857
683
455

1235
589
864
732
946

495
390
1200
627
549
832
864
629
229
580
692
400
283
658
395
713
372
554

Transverse relaxation times
T2 (ms)

101
92

1500
113
103
111
141
121
43
84
84
62

58
83
47
87


1 Principles of Magnetic Resonance Imaging and Magnetic Resonance Angiography

(the ‘squishier’ the tissue), the longer the T1-relaxation
time.
Since the Larmor frequency depends on field
strength whereas the ‘tumbling’ frequency of common
water molecules within human tissue remains the same,
T1-relaxation times are field strength dependent, as
listed in Table 1.1.
The majority of MR contrast agents utilize the paramagnetic properties of gadolinium (Gd). Gadolinium
has a powerful magnetic moment and is chelated to a
reasonably mobile ligand. The magnetic moment interacts with the resonating magnetizations of the hydrogen nuclei, allowing the magnetizations to relax more
rapidly – leading to a significant shortening of T1relaxation times.

Although the simple dipole-dipole interactions are
the most important processes for the T1- and T2-relaxation process, a variety of other mechanisms may be
important in certain tissues. Sophisticated theories
have been developed to explain the relaxation properties
of even simple solutions. Figure 1.5 illustrates a threecompartment model, and even this more complicated
perspective is only a crude approximation of ‘reality’.
In conventional spin-echo imaging, a 90° RF pulse is
used to convert the longitudinal magnetization Mz to
the transverse magnetization Mxy . This initial pulse is
also called the excitation pulse. The induced signal
amplitude depends on how much longitudinal magnetization there was, and how much had recovered since
the last excitation. The time between excitations is
called the repetition time TR. The T2-relaxation imme-

Fig. 1.5. A three-compartment model as an example
for approximation of T1and T2-relaxation times for
different tissue hydrogen
fractions

diately following the RF excitation will cause a dephasing of the transverse magnetization Mxy, leading to a
decreased signal the later the data are acquired. Leaving
ample room between excitations (long TR), the magnetizations of all tissues will be realigned with the main
magnetic field, and no differences in T1-relaxation will
be observed.
The time between the center of the excitation pulse
and the magnetization refocusing point within the
data-acquisition window is called the echo time TE. The
shorter the TE, the shorter the influence of the T2-related dephasing mechanism. A long TR, short TE generated image is called proton-density weighted (Pd-W),
since that is the main tissue parameter influencing the
contrast (Fig. 1.6). In conventional Pd-W spin-echo

imaging, CSF usually appears hypointense compared
with GM or WM, due to a TR of the order of 2.5 s. In fast
spin-echo imaging, the TR is usually longer than 3 s,
leading to a correct hyperintense appearance of CSF
following Pd-W imaging protocols. In order to differentiate tissues based on their T1-relaxation times, the TR
has to be reduced, with the TE kept short, to acquire T1weighted images. In that case, the contrast is strongly
influenced by the T1-relaxation time of the different tissues. CSF and ‘squishy’ tissues with long T1-relaxation
times will appear hypointense on T1-weighted (T1-W)
images (Fig. 1.7). A T2-weighted (T2-W) contrast is
achieved by using a long TR, similar to the Pd-W
approach, but instead of using a short TE, a long TE will
provide a stronger signal amplitude dependence on the
T2-relaxation time of the various tissues. CSF and

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W. Nitz

‘squishy’ tissues with long T2-relaxation times will
appear hyperintense on T2-weighted (T2-W) images
(Fig. 1.8).
1.1.1.2.2
Chemical Shift
The behavior of mobile fatty acids is slightly different
compared to the oxygen-bounded hydrogens previously discussed. For the water molecule, the oxygen
demands the single electron of the attached hydrogen,
thus ‘deshielding’ the proton. The carbon-bounded

hydrogen nuclei are more ‘shielded’ by the circulating
single electron, thus experiencing an effective lower
field than the water-bounded hydrogen nuclei. As a
result, the Larmor frequencies of mobile fatty acids are
below the water frequency. This phenomenon is called
chemical shift (Fig. 1.9). The difference in resonance
frequency scales with the strength of the main magnetic field and is approximately 3.5 ppm. Molecules containing aliphatic lipid protons are intermediate in size,
and their motions are close to the Larmor frequency,
causing short T1-relaxation times. Fat appears bright
on T1-W images. On the other hand, there are only a
few ‘static’ contributions in adipose tissue to allow a
rapid dephasing due to T2-relaxation. As a result, fat
also appears bright on T2-W images. Fat is the only tissue for which a long T2-relaxation time is not correlated with a prolonged T1-relaxation time.
1.1.1.2.3
T2* Relaxation Time, BOLD and Perfusion
As tissue is exposed to an external field, it becomes
‘magnetized’. The parameter indicating the ability to
Fig. 1.6. Proton densityweighting: The left graph
illustrates the recovery of the
longitudinal magnetization
(Mz) following excitation.
The right graph demonstrates the dephasing of the
generated transverse magnetization (Mx,y) due to the
T2-decay. Cerebrospinal fluid
(CSF) has a higher proton
density than gray (GM) or
white matter (WM) and
should appear hyperintense
on truly proton-density
weighted (Pd-W) images

become magnetized is called ‘(magnetic) susceptibility’. There is often a significant ‘susceptibility gradient’
across tissue boundaries, causing local inhomogeneities
of the magnetic field. Field inhomogeneities cause a
rapid dephasing of the transverse magnetization. The
relaxation time taking into account the dephasing due
to T2-relaxation as well as the local field inhomogeneities is called T2*:
1
1
p
c γ · ∆B
T 2* T2
γ is the magnetogyric ratio, ∆B represents the field
inhomogeneity across half a pixel
Local field inhomogeneities are usually fixed in location and consistent over time and are refocused in spinecho imaging. For all gradient-echo imaging, it is T2*
that is observed rather than T2.
Imaging of susceptibility differences is utilized in the
evaluation of hemorrhagic lesions and in functional
MR imaging based on the blood oxygenation leveldependent (BOLD) contrast. Deoxyhemoglobin is paramagnetic, while oxyhemoglobin demonstrates diamagnetic properties. A relative decrease of the deoxyhemoglobin level, as an ‘overcompensation’ reaction to
oxygen consumption, will lead to a diminished microscopic susceptibility effect and is measured as a small
increase in signal intensity – for imaging sequences
sensitive to susceptibility gradients.
The majority of MR contrast agents utilize paramagnetic properties which, along with a reduction in T1relaxation times, also create local field inhomogeneities
in perfused areas. The observable signal decay due to
shortened T2* relaxation times in those areas can also
be used to quantify tissue perfusion.


1 Principles of Magnetic Resonance Imaging and Magnetic Resonance Angiography
Fig. 1.7. T1-weighting: The

left graph illustrates the
recovery of the longitudinal
magnetization (Mz) following excitation. The right
graph demonstrates the
dephasing of the generated
transverse magnetization
(Mx,y) due to the T2-decay.
For a 1.5-T system, the optimum TR for gray matter–white matter differentiation is 800 ms. The selected
TE has to be sufficiently
short in order to minimize
the influence of the T2-relaxation

Fig. 1.8. T2-weighting: The
left graph illustrates the
recovery of the longitudinal
magnetization (Mz) following excitation. The right
graph demonstrates the
dephasing of the generated
transverse magnetization
(Mx,y) due to the T2-decay. A
long TR and long TE protocol will result in a T2-W
image. Image contrast is
dominated by the contribution of proton density and
T2-relaxation of the various
tissues

Fig. 1.9. Chemical shift: The electrons of oxygen-bounded hydrogen
atoms are more drawn towards the
oxygen atom than the electrons of
carbon-bounded hydrogen.

Hydrogen nuclei in adipose tissue
are more ‘shielded’, leading to a
lower resonance frequency than
free water. The term describing the
effect of an electronic environment
on the Larmor frequency is called
‘chemical shift’

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W. Nitz
Fig. 1.10. Diffusion weighting: The transverse magnetization can be prepared for diffusion-weighted
imaging using large bipolar gradients. Applying a
positive gradient after a negative gradient using the
same duration and the same amplitude has no
effect on stationary tissue. The transverse magnetization is refocused. If the macroscopic magnetization changed position due to motion, flow, perfusion, or diffusion, the refocusing will be unsuccessful. The unsuccessful rephasing will cause a signal
void in diffusion-weighted images for regions with
increased diffusion

1.1.1.2.4
Diffusion
The ability of water molecules to perform random
translational motion within a given tissue is described
by the diffusion coefficient. The application of a magnetic field gradient for a short duration will cause a
temporary change in resonance frequencies and a correlated dephasing of the transverse magnetization.
Applying the same gradient for the same duration but
of opposite polarity will result in a ‘rephasing’ of the

transverse magnetization – for stationary tissue. For
molecules which have changed position in the meantime, the rephasing of the transverse magnetization will
be incomplete (Fig. 1.10). Tissue or tissue areas with an
increased diffusion will appear as hypointense areas in
diffusion-weighted imaging. Diffusion weighting
involves the application of large magnetic field gradients in addition to the field gradients used for spatial
encoding. A diffusion-weighted image in which the signal attenuation does not depend on the directionality of
diffusion is also called trace-weighted image or isotropic diffusion-weighted image.
1.1.1.2.5
Flow and Motion
Flow and bulk motion can be considered an extreme
form of diffusion. Since magnetic field gradients are
used for the purpose of spatial encoding, as will be dis-

cussed in the next chapter, the positions of the transverse magnetizations, also referred to as ‘phase’, are
altered depending on the velocity or acceleration of the
moving tissue. The ‘phase’ information is actually utilized to measure velocities in MR flow quantification
and can also be used to visualize vasculature (also
called phase-contrast MR angiography, PC-MRA).
Special gradient arrangements can be applied to make
an imaging sequence insensitive to flow (and motion),
also called flow compensation or gradient motion
rephasing, GMR. One extreme form of flow is the
replacement of saturated blood (short TR sequences
causing a very low longitudinal magnetization of the
affected blood and the stationary tissue of the affected
slice) with unsaturated (fully relaxed longitudinal magnetization). This phenomenon is utilized in the so
called time-of-flight angiography (ToF-MRA). The ‘artificial shortening’ of the T1-relaxation time due to
replacement of ‘saturated’ spins with ‘unsaturated’ spins
can be bypassed by intravenous injection of T1-shortening contrast agents, as is done in the so-called contrast-enhanced MR angiography, ceMRA.

1.1.1.2.6
Magnetization Transfer
Macromolecules have a layer of ‘bound’ water. Since
static or slow changing magnetic fields are dominant in
the vicinity of macromolecules, the associated hydrogen pool has a very short T2. The correlated fast


1 Principles of Magnetic Resonance Imaging and Magnetic Resonance Angiography
Fig. 1.11. Magnetization transfer: Water molecules that are closely associated with proteins and
other macromolecules are restricted in motion.
The resulting static dephasing mechanism leads
to a very short T2, making these water molecules
‘invisible’. A short T2 is also synonymous for a
very broad range of resonance frequencies. In
contrast, the ‘visible’ water pool has a very narrow
frequency range. Mechanisms like cross-relaxation between protons within the ‘invisible’ water
pool and protons within the ‘visible’ water pool
are called ‘Magnetization Transfer’ (MT) mechanisms. Saturating the ‘invisible’ water pool will
result in a diminished signal within the ‘visible’
water pool as a consequence of this magnetization transfer

dephasing of the transverse magnetization causes this
pool of water to be ‘invisible’. However, the magnetization of that ‘invisible’ water pool is transferred to the
visible pool of ‘free’ water via various mechanisms like
chemical exchange or cross-relaxation (Fig. 1.11). The
term for these processes is called ‘magnetization
transfer’, MT. Cross-relaxation is a special form of
dipole-dipole interaction in which a proton on one
molecule transfers its spin orientation to that of
another molecule. A short T2 or fast dephasing is synonymous for a broad range of resonance frequencies,

whereas a long T2 is indicative of a narrow range. If
there are applicable magnetization transfer mechanisms within the tissue, a saturation of the ‘invisible’
water pool will affect the ‘visible’ water pool.

direction and applying a RF pulse covering a specific
frequency range, only the macroscopic magnetization
of that particular frequency will be affected, as illustrated in Fig. 1.12. This procedure is identical for small flipangle excitations, as well as the refocusing pulses that

1.1.1.3
Image Formation and Image Contrast
As mentioned at the very beginning, the macroscopic
magnetization will be affected if the RF field is ‘in
resonance’. Creating a small field gradient along one

Fig. 1.12. Slice selection gradient: Creating a magnetic field gradient along one direction and applying a RF pulse of a specific bandwidth will enable the rotation of the macroscopic magnetization
of a slice, where the resonance frequency of the macroscopic magnetization matches a frequency of the applied bandwidth

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W. Nitz

Fig. 1.13. The ‘sinc’ function: Summing up frequencies will result
in a so-called sinc-function, relevant for slice-selective excitation
and slice-selective refocusing and dictating the necessary length
of the RF duration

will be described later. Summing up the frequencies to

be covered will produce a so-called sinc envelope
around the center frequency, as illustrated in Fig. 1.13.
This sinc function is infinite, but the most important
information is contained within a relatively small time
frame, the center of the sinc envelope. There is a minor
practical aspect with respect to the duration of this RF
pulse. Fast imaging sequences are trying to be fast,
keeping everything as short as possible, including the
duration of the excitation pulse. In order to get the RF
duration as short as possible, there are two possibilities:
(1) either the sinc envelope has to shrink, or (2) it has to
be truncated. In order to shrink the sinc envelope, the
frequency range covered must be increased. For the
same slice thickness, this can be done by increasing the
gradient field. The latter requires a good strong gradient system. In order to turn the magnetization in less
time also requires a larger amplitude for the RF pulse.
Therefore, a robust RF system is also needed. An RF
pulse is capable of generating heat in tissues as a consequence of resistive losses. This exposure is quantified
with a specific absorption rate (SAR). With an increased
frequency range for excitation and with an increased
RF amplitude due to the short RF duration, the SAR for
the patient is increased as well and is, in fact, the limiting factor in faster imaging with a good slice profile.
The other solution is truncation of the sinc envelope. In
this case, reduction of the overall measurement time
happens at the expense of the slice profile. Truncating
the sinc envelope will lead to a compromised slice profile as illustrated in Fig. 1.14. A poor slice profile will
even lead to an improvement of the SNR since more tis-

Fig. 1.14. The slice ‘profile’: A slice-selection gradient (GS) is established in order to have a dependency of the resonance frequency
along the direction of slice selection. A RF pulse with no beginning and no end, containing all the frequencies of a desired slice,

would lead to a perfect slice profile. In reality, RF pulses have a
limited duration, leading to a compromised slice profile. This
knowledge is helpful in understanding the necessity of a gap
between slices for certain applications, and the limitation for fast,
slice-selective imaging

sue is contributing to the signal and the edges of the
slice will experience a low flip-angle excitation, with the
latter causing an increase in the signal contribution.
The effect of a low flip-angle excitation is discussed in
more detail in Sect. 1.1.2.2. Of course, a poor slice profile compromises the spatial resolution in the direction
of slice selection, with a potential increase of partial
volume artifacts.
The next step to be discussed after the concept of
slice-selective excitation is the concept of spatial encoding. As the local dependence of the resonance frequency in a magnetic field gradient is utilized for slice-selective excitation, the same phenomenon is used for spatial
encoding. A magnetic-field gradient is established, usually perpendicular to the direction of slice selection, in
order for the resonance frequencies to be different for
positions along the so-called read-out direction or frequency-encoding direction. A sampling of the signal at
that time will allow the identification of the spatial location of the signal sources in one direction, as illustrated
in Fig. 1.15. The frequency range for the selected field of
view (FoV) is called the bandwidth of the measurement.
In order to be able to display the information as pixel
intensity on a screen, the excited slice is split into a
number of voxels, where the pixel intensity on the
screen corresponds to the signal magnitude received
from each voxel. The magnetic field causes a frequency


1 Principles of Magnetic Resonance Imaging and Magnetic Resonance Angiography

Fig. 1.15. The ‘frequency’ encoding: All resonance frequencies
resulting from a magnetic field gradient being switched on during
data sampling are detected simultaneously. Sampling the signal
while a field gradient is switched on will provide information on
the location of the signal sources in one direction. The information will be later displayed as the signal intensity of a pixel on a
monitor, corresponding to the signal magnitude received from a
single voxel within the excited slice

range over the FoV, which is now split into columns of
voxels. Each voxel covers the same small frequency
range, also called pixel bandwidth or simply bandwidth.
The bandwidth of a sequence dictates the duration of
the sampling window and influences the SNR. A high
bandwidth will allow a short sampling window, but will
also give a poor SNR. A low bandwidth will dictate a
long sampling window, causing the sequence to be more
sensitive to artifacts such as chemical shift and local
susceptibility gradients or motion, but will provide a
better SNR. Since fat- and water-bounded hydrogen
atoms experience a different electronic environment,
their resonance frequencies differ by approximately
3.5 ppm, that is 217 Hz on a 1.5 T system. Since the frequency information is also used as spatial information,
the fat image and the water image have a slightly different position. For a sequence with a pixel bandwidth of
130 Hz, this chemical shift corresponds to a pixel shift
of less than two pixels. The missing overlap on one end
and the additional overlap on the other end cause hypointense and hyperintense lines at fat-water boundaries
and are called chemical-shift artifacts (see also Section
1.4.1.1 Chemical Shift).

The encoding of a second or third direction is

approaching the weak point of MR imaging. The only
tool available for encoding seems to be switching a gradient field to cause a difference in resonance frequencies. Encoding in the second dimension is actually carried out prior to frequency encoding. A gradient field is
switched on for a short duration in which the field
direction is perpendicular to the direction of frequency
encoding and the direction of slice selection. This gradient field will cause a phase shift, which is a shift in
position of the macroscopic magnetization within the
transverse plane as a function of location. In order to
differentiate between two adjacent voxel rows in the
direction of phase encoding, the amplitude and the
duration of the phase-encoding gradient must be high
enough to cause a phase difference of 180°, as illustrated in Fig. 1.16. Unfortunately, doing so will place the
macroscopic magnetization of every other voxel in the
same phase position. The signals from voxel ‘columns’ 1,
3, 5... all have the same phase position and cannot be
separated. In order to identify these voxel ‘columns’, the

Fig. 1.16. The ‘phase’ encoding: In order to be able to distinguish
the signal of two adjacent voxels, the gradient amplitude and
duration of a phase-encoding pulse has to be high enough for the
macroscopic magnetization of two adjacent voxels to have a phase
difference of 180°. Since the macroscopic magnetization of every
other voxel has the same orientation, the phase-encoding steps
have to be repeated with reduced phase-encoding amplitudes to
create n-equations for the calculation of the signal intensities
within n voxel rows.

11