The chemistry of contrast agents in medical magnetic resonance imaging

The Chemistry of Contrast Agents in
Medical Magnetic Resonance Imaging


The Chemistry of Contrast Agents in
Medical Magnetic Resonance Imaging
Second Edition

Edited by

ANDRE´ MERBACH
Ecole Polytechnique F´ed´erale de Lausanne, Lausanne, Switzerland

LOTHAR HELM
Ecole Polytechnique F´ed´erale de Lausanne, Lausanne, Switzerland

´
´
EVA
TOTH
CNRS, Orl´eans, France

A John Wiley & Sons, Ltd., Publication


This edition first published 2013
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Library of Congress Cataloging-in-Publication Data
´ T´oth.
The chemistry of contrast agents in medical magnetic resonance imaging. – Second edition / edited by Lothar Helm, Andr´e E. Merbach, Eva
pages cm
Includes bibliographical references and index.
ISBN 978-1-119-99176-2 (hardback)
1. Contrast-enhanced magnetic resonance imaging. 2. Magnetic resonance imaging. I. Helm, Lothar, editor of compilation. II. Merbach, Andr´e E.,
´

editor of compilation. III. T´oth, Eva,
editor of compilation.
RC78.7.C65C48 2013
616.07 548–dc23
2012037031
A catalogue record for this book is available from the British Library.
Print ISBN: 978-1-119-99176-2
Set in 10pt/12pt Times by Laserwords Private Limited, Chennai, India


Contents

List of Contributors
Preface
1
1.1
1.2

1.3
1.4

1.5

1.6

1.7

2
2.1
2.2

General Principles of MRI
Bich-Thuy Doan, Sandra Meme, and Jean-Claude Beloeil
Introduction
Theoretical basis of NMR
1.2.1
Short description of NMR
1.2.2
Relaxation times
1.2.3
Saturation transfer
1.2.4
Concept of localization by magnetic field gradients
Principles of magnetic resonance imaging
1.3.1
Spatial encoding
MRI pulse sequences
1.4.1
Definition
1.4.2
k -Space trajectory
1.4.3
Basic pulse sequences
Basic image contrast: Tissue characterization without injection of contrast agents
(main contrast of an MRI sequence: Proton density (P), T1 and T2 , T2∗ )
1.5.1
Proton density weighting
1.5.2
T1 weighting
1.5.3

T2 weighting
1.5.4
T2∗ weighting
Main contrast agents
1.6.1
Gadolinium (Gd) complex agents
1.6.2
Iron oxide (IO) agents
1.6.3
CEST agents
Examples of specialized MRI pulse sequences for angiography (MRA)
1.7.1
Time of flight angiography: No contrast agent
1.7.2
Angiography using intravascular contrast agent (Blood pool CA) injection
1.7.3
DSC DCE MRI
References
Relaxivity of Gadolinium(III) Complexes: Theory and Mechanism
´ T´oth, Lothar Helm, and Andr´e Merbach
Eva
Introduction
Inner-sphere proton relaxivity
2.2.1
Hydration number and hydration equilibria
2.2.2
Gd–H distance

xiii
xv

1
1
1
1
4
4
4
5
5
11
11
12
13
16
17
17
17
18
18
19
19
20
21
21
21
23
23
25
25
28

31
37


vi

2.3
2.4

2.5

3
3.1
3.2

3.3

3.4

3.5
3.6

4
4.1
4.2

4.3

Contents

2.2.3
Proton/water exchange
2.2.4
Rotation
Second- and outer-sphere relaxation
Relaxivity and NMRD profiles
2.4.1
Fitting of NMRD profiles
2.4.2
Relaxivity of low-molecular-weight Gd(III) complexes
2.4.3
Relaxivity of macromolecular MRI contrast agents
2.4.4
Contrast agents optimized for application at high magnetic field
Design of high relaxivity agents: Summary
References
Synthesis and Characterization of Ligands and their Gadolinium(III) Complexes
Jan Kotek, Vojtˇech Kub´ıcˇ ek, Petr Hermann, and Ivan Lukeˇs
Introduction – general requirements for the ligands and complexes
Contrast agents employing linear polyamine scaffold
3.2.1
Synthesis of linear polyamine backbone
3.2.2
N -functionalization of linear polyamine scaffold
Contrast agents employing cyclen scaffold
3.3.1
Synthesis of the macrocyclic skeleton
3.3.2
N -functionalization of macrocyclic scaffold
Other types of ligands

3.4.1
H4 TRITA and related ligands
3.4.2
H3 PCTA and related ligands
3.4.3
TACN derivatives
3.4.4
Ligands with HOPO coordinating arms and related groups
3.4.5
H4 AAZTA and related ligands
Bifunctional ligands and their conjugations
Synthesis and characterization of the Ln(III) complexes
3.6.1
General synthetic remarks
3.6.2
Characterization of the complexes
List of Abbreviations
References
Stability and Toxicity of Contrast Agents
Ern˜o Br¨ucher, Gyula Tircs´o, Zsolt Baranyai, Zolt´an Kov´acs, and A. Dean Sherry
Introduction
Equilibrium calculations
4.2.1
Constants that characterize metal ligand interactions (protonation constants
of the ligands, stability constants of the complexes, conditional stability
constants, ligand selectivity, and concentration of free Gd3+ : pM )
4.2.2
A brief overview of the programs used in equilibrium calculations (calculation
of protonation constants, stability constants, and equilibrium speciation diagrams)
Stability of metal–ligand complexes

4.3.1
Stability of complexes of open chain ligands (EDTA, DTPA, EGTA, and TTHA)
4.3.2
Stability of complexes of tripodal and AAZTA ligands
4.3.3
Stability of complexes of macrocyclic ligands

39
57
64
66
66
68
69
73
75
76
83
83
84
85
89
103
103
106
123
123
123
126
130

133
134
138
138
139
144
146
157
157
158

158
159
160
160
165
168


Contents

4.4

4.5

4.6

4.7

4.3.4

Ternary complexes formed between the Ln(L) complexes and various bio-ligands
4.3.5
Mn2+ -based contrast agents
Kinetics of M(L) complex formation
4.4.1
Formation kinetics of DOTA complexes
4.4.2
Formation kinetics of complexes of simple DOTA-tetraamides
Dissociation of M(L) complexes
4.5.1
Inertness of complexes of open chain ligands (EDTA, DTPA, and AAZTA)
4.5.2
Decomplexation of DOTA complexes
4.5.3
Decomplexation of DOTA-tetraamide complexes
Biodistribution and in vivo toxicity of Gd3+ -based MRI contrast agents
4.6.1
Osmolality and hydrophobicity of Gd3+ -based MRI contrast agents
4.6.2
Biodistribution
4.6.3
In vivo toxicity
4.6.4
Predicting in vivo toxicity of Gd3+ -based contrast agents using thermodynamic
conditional stability constants
4.6.5
The role of kinetic inertness in determining in vivo toxicity
4.6.6
Kinetic inertness combined with thermodynamic stability is the best predictor
of in vivo toxicity

4.6.7
Nephrogenic systemic fibrosis (NSF)
Concluding remarks
Acknowledgements
References

Structure, Dynamics, and Computational Studies of Lanthanide-Based
Contrast Agents
Joop A. Peters, Kristina Djanashvili, Carlos F.G.C. Geraldes, and Carlos Platas-Iglesias
5.1
Introduction
5.2
Computational methods
5.3
Lanthanide-induced NMR shifts
5.3.1
Bulk magnetic susceptibility shifts
5.3.2
Diamagnetic shifts
5.3.3
Contact shifts
5.3.4
Pseudocontact shifts
5.3.5
Evaluation of bound shifts
5.3.6
Separation of shift contributions
5.4
Lanthanide-induced relaxation rate enhancements
5.4.1

Evaluation of bound relaxation rates
5.4.2
Inner-sphere relaxation
5.4.3
Outer-sphere relaxation
5.5
Anisotropic hyperfine interactions on the first coordination sphere water molecules
5.6
Evaluation of geometries by fitting NMR parameters
5.7
Two-dimensional NMR
139
La and 89 Y NMR
5.8
5.9
Water hydration numbers
5.10 Chirality of lanthanide complexes of polyaminocarboxylates
5.11 Complexes of non-macrocyclic polyaminocarboxylates
5.11.1 DTPA and derivatives

vii

176
179
184
184
186
186
187
190

192
193
193
194
195
195
196
197
199
201
201
201

5

209
209
210
213
213
213
214
215
216
217
219
219
219
221
221

222
224
224
225
227
227
227


viii

5.12

5.13

Contents

5.11.2 TTHA
5.11.3 EGTA
5.11.4 DTTA
5.11.5 Tripodal complexes
Complexes of macrocyclic ligands
5.12.1 DOTA and derivatives
5.12.2 DO3A and derivatives
5.12.3 PCTA and derivatives
5.12.4 TETA
5.12.5 DOTP
5.12.6 Phosphinates and phosphonate esters
5.12.7 Cationic macrocyclic lanthanide complexes
5.12.8 AAZTA

Fullerenes
References

Electronic Spin Relaxation and Outer-Sphere Dynamics of Gadolinium-Based
Contrast Agents
Pascal H. Fries and Elie Belorizky
6.1
Introduction
6.2
Theory of electronic spin relaxation of Gd3+ ions
6.2.1
Classical approach: Bloch equations
6.2.2
Quantum approach: Electronic time correlation functions
6.2.3
The zero-field splitting Hamiltonian
6.2.4
The density matrix formalism
6.2.5
The Redfield approximation
6.2.6
The Swedish super-operator approaches
6.2.7
Monte-Carlo simulation of the Gd3+ electronic relaxation:
The Grenoble method
6.3
Outer-sphere dynamics
6.3.1
Standard theory neglecting the electronic relaxation
6.3.2

Analytical hard-sphere models
6.3.3
The general case of anisotropic polyatomic molecules
6.3.4
Experimental determination of the dipolar time correlation function
6.4
Relaxivity quenching by the electronic spin relaxation
6.4.1
The various field regimes
6.4.2
Outer-sphere relaxivity
6.4.3
Inner- and second-sphere relaxivities
6.4.4
Application to a cyclodecapeptide Gd3+ complex
6.5
Various experimental approaches of the electronic spin relaxation
6.5.1
Outer-sphere relaxivity profiles
6.5.2
EPR spectroscopy
6.6
Conclusion and perspectives
6.A Appendix: Similar evolutions of the macroscopic magnetization of the electronic spin and of
its correlation functions
References

236
238
239

240
244
244
250
252
253
254
257
260
264
265
267

6

277
277
279
279
281
281
284
285
287
288
289
289
291
292
292

295
295
295
297
299
301
301
302
306
307
308


Contents

7
7.1
7.2
7.3
7.4
7.5
7.6
7.7
7.8
7.9
7.10
7.11
7.12
7.13
7.14

7.15
7.16
7.17
7.18
7.19
7.20

8
8.1
8.2

8.3

9
9.1
9.2

Targeted MRI Contrast Agents
Peter Caravan and Zhaoda Zhang
Introduction
Serum albumin
Fibrin
Type I collagen
Elastin
Sialic acid
αV β3 integrin
Folate receptor
Matrix metalloproteinases (MMP)
E-selectin
Fibrin-fibronectin complex

Alanine aminopeptidase (CD13)
Carbonic anhydrase
Interleukin 6 receptor
Estrogen and progesterone receptors
Contrast agents based on natural products
Messenger RNA (mRNA)
Myelin
DNA
Conclusions
References

ix

311
311
313
319
325
326
327
328
329
330
331
332
332
333
334
335
336

337
338
338
340
340

Responsive Probes
´ T´oth
C´elia S. Bonnet, Lorenzo Tei, Mauro Botta, and Eva
Introduction
Probes responsive to physiological parameters
8.2.1
Temperature responsive probes
8.2.2
pH sensing
8.2.3
Redox responsive probes
8.2.4
Sensing of biologically relevant ions
8.2.5
Enzyme responsive probes
Conclusions
References

343

Paramagnetic CEST MRI Contrast Agents
Enzo Terreno, Daniela Delli Castelli, and Silvio Aime
Introduction
Theoretical and practical considerations on CEST response

9.2.1
NMR/chemical properties of CEST site(s)
9.2.2
NMR properties of the wat site
9.2.3
Instrumental variables
9.2.4
Variables dependent on the sample
9.2.5
Spectroscopic versus imaging detection of CEST response
9.2.6
Characterization of a CEST agent and its quantification

387

343
344
344
349
360
364
373
381
382

387
388
391
394
395

397
399
400


x

Contents

9.3
9.4

9.5
9.6

10
10.1
10.2

10.3

10.4
10.5
10.6

10.7

11
11.1
11.2

11.3

11.4

Diamagnetic versus paramagnetic CEST agents
Paramagnetic CEST agents
9.4.1
ParaCEST agents
9.4.2
SupraCEST agents
9.4.3
NanoCEST agents
Other exchange-mediated contrast modes accessible for paramagnetic CEST agents
Concluding remarks
References
Superparamagnetic Iron Oxide Nanoparticles for MRI
Sophie Laurent, Luce Vander Elst, and Robert N. Muller
Introduction
Synthesis of iron oxide nanoparticles
10.2.1 Coprecipitation in aqueous medium
10.2.2 Reverse micro-emulsions
10.2.3 Sol gel methods
10.2.4 Polyol methods
10.2.5 Hydrothermal methods
10.2.6 Sonochemistry methods
10.2.7 Pyrolytic methods
Stabilization
10.3.1 Steric stabilization: Natural or synthetic polymeric matrices
10.3.2 Electrostatical stabilization
Methods of vectorization for molecular imaging

Characterization
10.5.1 Relaxivity and NMRD profiles
Applications
10.6.1 Tissue labelling with iron oxide particles
10.6.2 Cellular and molecular labelling with iron oxide particles
10.6.3 Iron oxide nanoparticles as molecular MRI probes
Conclusions
Acknowledgements
References
Gd-Containing Nanoparticles as MRI Contrast Agents
Klaas Nicolay, Gustav Strijkers, and Holger Gr¨ull
Introduction
Length scales and excretion pathways
Preparation of Gd-containing nanoparticles
11.3.1 Lipid aggregates
11.3.2 Liposomes
11.3.3 Micelles
11.3.4 Other lipid-containing nanoparticles
11.3.5 Chemical structures of Gd-containing lipids
Methods for nanoparticle characterization
11.4.1 Morphology

400
401
402
411
413
419
421
421

427
427
428
429
430
430
430
430
431
431
431
431
432
432
436
436
440
441
442
442
444
444
444
449
449
452
454
455
456
457

458
458
460
461


Contents

11.5

11.6

11.7

Index

11.4.2 Particle composition
11.4.3 Magnetic properties
11.4.4 Chelate stability
11.4.5 Miscellaneous techniques
In vitro applications
11.5.1 Target specificity
11.5.2 Cellular interactions, internalization, and compartmentation
11.5.3 Biological effects
In vivo applications
11.6.1 Target-specific imaging
11.6.2 Image-guided drug delivery
Conclusions and future perspectives
Acknowledgements
References

xi

462
464
467
468
468
468
470
475
475
476
478
481
483
483
489


List of Contributors

Silvio Aime, Department of Molecular Biotechnologies and Health Sciences and Molecular & Preclinical
Imaging Centres, University of Turin, Turin, Italy
Zsolt Baranyai, Inorganic and Analytical Chemistry, University of Debrecen, Debrecen, Hungary
Jean-Claude Beloeil, Centre de Biophysique Mol´eculaire, CNRS, Orl´eans, France
Elie Belorizky, Universit´e Joseph Fourier, Grenoble, France
C´elia S. Bonnet, Centre de Biophysique Mol´eculaire, CNRS, Orl´eans, France
Mauro Botta, Dipartmento di Scienze e Innovazione Tecnologica, Universit`a del Piemonte Orientale
“Amedeo Avogadro”, Alessandria, Italy

Ern˝o Brucher,
Inorganic and Analytical Chemistry, University of Debrecen, Debrecen, Hungary
¨
Peter Caravan, Athinoula A. Martinos Center for Biomedical Imaging, Massachusetts General Hospital
and Harvard Medical School, Charlestown, MA, USA
Daniela Delli Castelli, Department of Molecular Biotechnologies and Health Sciences and Molecular &
Preclinical Imaging Centres, University of Turin, Turin, Italy
Kristina Djanashvili, Delft University of Technology, Delft, The Netherlands
Bich-Thuy Doan, CNRS, Chimie-Paristech, Universit´e Paris Descartes, Paris, France
Luce Vander Elst, Department of General, Organic and Biomedical Chemistry, NMR and Molecular
Imaging Laboratory, University of Mons, Mons, Belgium
Pascal H. Fries, Alternative Energies and Atomic Energy Commission (CEA), Grenoble, France
Carlos F.G.C. Geraldes, University of Coimbra, Coimbra, Portugal
Holger Grull,
¨ Biomedical NMR, Department of Biomedical Engineering, Eindhoven University of Technology, Eindhoven, The Netherlands and Department of Biomolecular Engineering, Philips Research
Eindhoven, Eindhoven, The Netherlands
Lothar Helm, Ecole Polytechnique F´ed´erale de Lausanne, Lausanne, Switzerland
Petr Hermann, Department of Inorganic Chemistry, Faculty of Science, Universita Karlova v Praze,
Prague, Czech Republic
Jan Kotek, Department of Inorganic Chemistry, Faculty of Science, Universita Karlova v Praze, Prague,
Czech Republic
Zolt´an Kov´acs, Advanced Imaging Research Center, University of Texas Southwestern Medical Center,
Dallas, TX, USA
Vojtˇech Kub´ıcˇ ek, Department of Inorganic Chemistry, Faculty of Science, Universita Karlova v Praze,
Prague, Czech Republic
Sophie Laurent, Department of General, Organic and Biomedical Chemistry, NMR and Molecular Imaging
Laboratory, University of Mons, Mons, Belgium
Ivan Lukeˇs, Department of Inorganic Chemistry, Faculty of Science, Universita Karlova v Praze, Prague,
Czech Republic
Sandra Meme, Centre de Biophysique Mol´eculaire, CNRS, Orl´eans, France

Andr´e Merbach, Ecole Polytechnique F´ed´erale de Lausanne, Lausanne, Switzerland


xiv

List of Contributors

Robert N. Muller, Department of General, Organic and Biomedical Chemistry, NMR and Molecular
Imaging Laboratory, University of Mons, Mons, Belgium
Klaas Nicolay, Biomedical NMR, Department of Biomedical Engineering, Eindhoven University of Technology, Eindhoven, The Netherlands
Joop A. Peters, Delft University of Technology, Delft, The Netherlands
Carlos Platas-Iglesias, University of A Coru˜na, A Coru˜na, Spain
A. Dean Sherry, Advanced Imaging Research Center, University of Texas Southwestern Medical Center,
Dallas, TX, USA and Chemistry Department, University of Texas at Dallas, Dallas, TX, USA
Gustav Strijkers, Biomedical NMR, Department of Biomedical Engineering, Eindhoven University of
Technology, Eindhoven, The Netherlands
Lorenzo Tei, Dipartmento di Scienze e Innovazione Tecnologica, Universit`a del Piemonte Orientale
“Amedeo Avogadro”, Alessandria, Italy
Enzo Terreno, Department of Molecular Biotechnologies and Health Sciences and Molecular & Preclinical
Imaging Centres, University of Turin, Turin, Italy
Gyula Tircs´o, Inorganic and Analytical Chemistry, University of Debrecen, Debrecen, Hungary
´
Eva
T´oth, Centre de Biophysique Mol´eculaire, CNRS, Orl´eans, France
Zhaoda Zhang, Athinoula A. Martinos Center for Biomedical Imaging, Massachusetts General Hospital
and Harvard Medical School, Charlestown, MA, USA


Preface

Magnetic Resonance Imaging is one of the most important tools in clinical diagnostics and biomedical
research. The estimated number of MRI scanners operating around the world is about 20 000. The development of contrast agents, currently used in about a third of the 50 million clinical MRI examinations
performed every year, has largely contributed to this important achievement. Today, the rapidly growing
field of molecular imaging which seeks non-invasive, in vivo, real-time monitoring of molecular events
occurring at the cellular level has the promise of a revolution in MRI. By nature, any molecular imaging
procedure requires a molecular imaging probe, thus chemistry plays a pivotal role in the development of
new applications. As a result, the chemistry of MRI agents has witnessed a spectacular evolution in the
last decade.
The second edition of The Chemistry of Contrast Agents in Medical Magnetic Resonance Imaging is
a comprehensive treatise. It has been completed with recent developments on “classical” Gd-based and
iron-oxide probes and includes chapters dedicated to the most significant advances in molecular imaging
probes. We also discuss Chemical Exchange Saturation Transfer which is a novel means of generating
MRI contrast. This treatise covers all aspects of production, use, operating mechanism, and theory of these
diagnostic agents used to produce high contrast images in MRI.
This book assembles a distinguished team of experts who have been largely involved in successive
COST (European Cooperation in the Field of Scientific and Technical Research) D1, D8, D18, D38 and
TD1004 Actions. These collaborations, as well as the annual COST meetings, largely contributed to the
development of our knowledge in the field of MRI contrast agents.
The first chapter discusses the general principles of MRI, explains the notion of relaxation time and
saturation transfer, spatial encoding and the pulse sequences related to the different type of contrast agents.
This chapter is followed by a detailed description of the theory and mechanism of relaxation of Gd(III)
complexes. Particular attention is paid to the water exchange rate and its effect on relaxation for a wide
variety of chelates, as assessed by 17 O NMR. Analysis of the NMRD profiles is also discussed. Simulations
that help optimize relaxivity as a function of water exchange rate, rotational correlation time, and magnetic
field strength, with a special attention to high field MRI, are presented.
Chapter 3 is dedicated to the synthesis and characterization of ligands and their gadolinium complexes.
The detailed procedures and reaction schemes will provide a useful guideline for the synthetic chemist.
The next chapter is dealing with safety requirements for Gd(III) complexes. The release of free Gd(III)
ion from a contrast agent, which can be source of toxicity, is related to the thermodynamic stability and
kinetic inertness of the chelate. The methods used to assess these properties are discussed, and stability

data from the literature are reported.
In Chapter 5, the authors review the structure, dynamics, and computational studies of linear and macrocyclic lanthanide chelates. This includes interpretation of solution lanthanide-induced NMR shifts and
relaxation rate enhancements, evaluation of geometries by fitting NMR parameters, two-dimensional NMR,
139
La and 89 Y NMR, hydration numbers, and the chirality of polyaminocarboxylate complexes. One chapter
is dealing with the theory of electron spin relaxation and outer-sphere dynamics of gadolinium-based
contrast agents.


xvi

Preface

The first contrast agents approved for human use were untargeted, discrete gadolinium complexes such
as [Gd(DTPA)(H2 O)]2− . Chapter 7 is dedicated to ongoing efforts to make contrast agents more specific
for a particular disease or molecular marker.
In contrast to nuclear imaging modalities, MRI is particularly well adapted to the design of smart,
activable, or responsive probes. These Gd(III)-, PARACEST or T2 -agents, reviewed in Chapter 8, could
allow assessment of tissue temperature, pH, redox state, cation and anion concentration, or enzyme activity.
Chapter 9 presents theoretical and practical considerations on Chemical Exchange Saturation Transfer
(CEST) and diamagnetic versus paramagnetic CEST agents. Small-sized, macromolecular, and nano-sized
CEST probes, as well as supraCEST and lipoCEST agents are discussed.
Due to the rapid advances in nanotechnology, a number of synthetic routes to obtain magnetic iron
oxide nanoparticles with control of their microstructures have been reported. Below a critical size, the
particles become single-domain and exhibit superparamagnetism. These particles are used as MRI contrast
agents because of their very large magnetic moment and also due to their surface for in vitro and in vivo
applications. Their properties are discussed in Chapter 10.
Given the low sensitivity of MRI, molecular imaging applications often require amplification strategies.
This explains the widespread use of nanoparticles, in particular those prepared from biocompatible phospholipids described in Chapter 11, which have a high loading capacity for Gd-containing entities by virtue
of their high surface-to-volume ratio. Recent years have seen rapid advances in the development of hybrid

imaging technologies, in which imaging signals from two different modalities are simultaneously acquired.
Nanoparticles also have much utility as hybrid imaging agents, since they can readily be equipped with
multiple imaging labels.
Twelve years after the first edition, we are convinced that the chemistry of MRI agents has a bright future.
By assembling all important information on the design principles and functioning of magnetic resonance
imaging probes, this book intends to be a useful tool for both experts and newcomers in the field. We
hope that it helps inspire further work in order to create more efficient and specific imaging probes that
will allow materializing the dream of seeing even deeper and better inside the living organisms.


1
General Principles of MRI
Bich-Thuy Doan,1 Sandra Meme,2 and Jean-Claude Beloeil2
1

1.1

CNRS, Chimie-Paristech, Universit´e Paris Descartes, Paris, France
2 Centre de Biophysique Mol´
eculaire, CNRS, Orl´eans, France

Introduction

Magnetic Resonance Imaging (MRI) derives directly from the phenomenon of Nuclear Magnetic Resonance
(NMR [1–4]), which is widely used by chemists to determine molecular structure. The word “nuclear” was
dropped in the switch to imaging to avoid alarming patients as NMR has nothing to do with radioactivity.
This book is intended mainly for chemists, who are generally familiar with the NMR spectra. After a brief
overview of the technique explaining the notion of relaxation time and saturation transfer used in MRI, we
will describe localization techniques, which are less well-known in chemistry. The purpose of this short
chapter is not to provide a complete theory of MRI [5–8], but to understand the rest of the book concerning

the action of contrast agents. We will not go into the theoretical background of the phenomena, and while
it is important to have some understanding of quantum mechanics, it is not our purpose to develop this
aspect. This is a “nuts and bolts” description of MRI. Whenever possible, we refer to chemists’ knowledge
of NMR (for example, “2D NMR”).

1.2
1.2.1

Theoretical basis of NMR
Short description of NMR

In most cases, MRI focuses on one type of atomic nucleus, that of hydrogen in H2 O. We will therefore
only use this nucleus, termed the “1 H proton.”
The physical phenomenon of NMR lies at the boundary between “conventional” and “quantum” treatment
due to the small transition energies involved. Traditionally, the 1 H proton can be considered as a charged
The Chemistry of Contrast Agents in Medical Magnetic Resonance Imaging, Second Edition.
´ T´oth.
Edited by Andr´e Merbach, Lothar Helm and Eva
c 2013 John Wiley & Sons, Ltd. Published 2013 by John Wiley & Sons, Ltd.


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The Chemistry of Contrast Agents in Medical Magnetic Resonance Imaging

sphere rotating with a magnetic moment and collinear angular momentum (in quantum mechanics, these
two entities are quantified as magnetic quantum number and spin quantum number (or spin)). Like a
spinning top precessing in the Earth’s gravitational field, the nucleus 1 H precesses in the static magnetic
field B0 of the spectrometer magnet. This precession will occur at a frequency (ν 0 ) dictated by the nature
of the nucleus and the strength of the magnetic field of the magnet (ν 0 = −(γ /2π )B0 ) (Larmor frequency).

There are two possible precessions (parallel and antiparallel to B0 ) corresponding to two energy states in
the presence of a strong magnetic field. According to the Boltzmann equation, there are more 1 H protons
in the lower level (parallel to B0 ) than in the upper level. There will be total magnetization (M0 ) of the
sample, parallel to B0 (by definition, the z axis) (Figure 1.1). The whole process of obtaining a spectrum
is summarized in Figure 1.1.
In an NMR experiment, the sample is subjected to the action of an oscillating electromagnetic field (B1 )
(frequency: ν 1 ) perpendicular to B0 (Figure 1.1); if we place ourselves within a rotating frame around the
z axis at frequency ν 1 (ν 1 close to ν 0 ), it is as if the magnetization M0 precesses around the magnetic field
!
z

z
M0

B0

1/
y

y

Radiofrequency pulse (B1)
B1
x

x
(a)

(b)

z
e (-t / T2)

y
x

v0

Receiver
Analog to digital converter
"F.I.D."

v

(c)

(d)

spectrum
F.T.
(e)

Figure 1.1 NMR experiment: (a) net magnetization M0 at equilibrium when the spins are placed in a permanent
magnetic field B0 ; (b) a radio frequency (RF) pulse, induced by a perpendicular B1 magnetic field created by an
RF coil, flips the magnetization into the xy plane; (c) the magnetization M precesses around the z axis and the
signal decreases in the xy plane; for example, the magnetization is recorded from the y axis and converted by an
analog-to-digital converter to an FID (Free Induction Decay); (d) FID: the recorded signal is a damped sinusoid;
(e) NMR spectrum produced by a Fourier transform.

General Principles of MRI

3

MZ

M0

z

M0 (1−e(−t /T1))

MZ

B0

(b)
y

Mxy

t

Mxy

M0

x

M0e (-t/T2)

(a)

(c)

t

Figure 1.2 (a) Return to equilibrium of the magnetization, (b) return to equilibrium on the z axis: (Mz = M0
(1-exp−t/T1 )), (c) return to equilibrium in the xy plane (My = M0 exp−t/T2 ).

B1 , which is stationary within this frame. The duration of the B1 field (pulse) is calculated for a M0 tilt of
90◦ , or, more generally, of a flip angle α. At the end of the RF pulse, the system then returns to equilibrium,
the magnetization in the xy plane decreases exponentially with time constant T2 , and the magnetization
rises exponentially on axis z with a time constant T1 (T2 < T1 ) (Figure 1.2). If we put a receiver coil in the
xy plane, an electric current is induced in the coil and a signal is obtained after analog/digital conversion
into a damped sinusoid called Free Induction Decay (FID).
This signal corresponds to a temporal frequency. The Fourier transform (FT) of this signal (Figure 1.1)
provides a spectrum of frequencies contained in the signal; in this case just one because we are only
interested in H2 O. The signal intensity is proportional to the quantity of 1 H protons and therefore the
amount of H2 O in the sample. In NMR, it is observed that we have a temporal frequency (FID) and that
the FID and spectrum are a Fourier pair (Scheme 1.1).

Spectrum

FID
FT or reverse FT

Scheme 1.1

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The Chemistry of Contrast Agents in Medical Magnetic Resonance Imaging

1.2.2

Relaxation times

Unlike other spectroscopic techniques, the energy difference between the excited state and steady state
is too low to allow spontaneous relaxation, and therefore relaxation needs to be stimulated. The longitudinal relaxation time T1 (Figure 1.2b) is characteristic of the return to equilibrium of the magnetization
(Figure 1.2a) along z (Mz = M0 (1−e−t/T1 )); this phenomenon corresponds to the enthalpic interaction of
the excited nucleus with its environment, and in particular with the magnetic active agents of this environment (1 H protons, unpaired electrons e− ). The movement of nuclear magnetic moments of other molecules
(or unpaired e− ) creates a distribution of frequencies within which one can find the resonance frequency
of the excited nucleus, and a stimulated relaxation may then occur. Therefore, for this mechanism to work,
there must be a movement of the molecules (Brownian motion). T1 relaxation time will depend on the
mobility of these entities and therefore on the viscosity of the environment.
The T2 transversal relaxation time is characteristic of the disappearance of the signal in the xy plane
(Figure 1.2c). It is an entropy phenomenon that corresponds to spin dephasing in the xy plane. T2 is
always below T1 . A parameter often used in MRI is the relaxation time T2 *, which contains both T2 and
the contribution of all magnetic field inhomogeneities and therefore those that are characteristic of the
sample. T2 * is thus linked to specific properties of the tissue under study and is very useful in medical
MRI.

1.2.3

Saturation transfer

The saturation phenomenon is used in NMR to identify hydrogens in conformational or chemical exchange.
It is easy to obtain saturation in NMR due to the low energy difference between the two energy levels of the
particles studied. We will see later that it can be utilized in the action mechanism of very typical contrast

agents (Chemical Exchange Saturation Transfer (CEST) [9] and PARACEST [10]). Assuming that one has
a chemical entity (X–H) carrying chemically exchangeable hydrogens (for example, with the hydrogens
of water, NH2 function), the 1 H protons of X–H are selectively saturated. This involves using a magnetic
field B1 pulse to send so much energy that the 1 H protons do not have time to return to equilibrium (the
relaxation process is not totally effective), leading to equalization of the populations of the two energy
levels (high and low), disappearance of M, and therefore loss of the X–H signal. For selective saturation,
we only need to apply a magnetic field B1 to X–H, without affecting H2 O. From a Fourier-type transform
relationship it can be shown that the application of B1 for a very short time (several microseconds of
“hard” pulse) acts on a broad spectrum, whereas B1 application for a long time (a few milliseconds of
“soft” pulse) acts on a narrow spectrum which may be limited to the signal to be saturated. Through
selective saturation and chemical exchange, and provided the exchange is fast enough, the 1 H protons take
their saturation on the H2 O molecules with them, leading to a reduction in signal intensity (Figure 1.3).

1.2.4

Concept of localization by magnetic field gradients

When we obtain the NMR spectrum of an organic chemical molecule, its protons resonate at different
frequencies, except in specific cases. We will now look at the concept of chemical shift, the resonance
frequency that is characteristic of a 1 H proton and which is determined by the electronic environment. The
molecular electron cloud creates a local magnetic field that opposes the magnetic field of the spectrometer
magnet (B0 ). This is called the “intramolecular magnetic field gradient.” This gradient allows the hydrogen
to be located in the intramolecular space. Following a principle known to chemists, the magnetic field varies
according to its position in space. Resonance frequency is proportional to the strength of the magnetic
field, it depends of the position in the “intramolecular” space. We will see later that the same principle
enables the position in space (imaging) to be coded.


General Principles of MRI

5

k1
X

H

H

O
H

k2

(a)

Selective saturation

(b)

Figure 1.3 Saturation transfer principle. (a) 1 H spectrum without selective saturation; (b) spectrum with selective
saturation of X–H. k1 , k2 , rate constants of the chemical reaction.

1.3

Principles of magnetic resonance imaging

MRI [5–8] can generate an image showing the spatial distribution of spin density of a specific type of
atom, usually the water protons. It can also display spin properties (T1 , T2 , etc.). In its 2D version this
technique allows virtual internal slices to be obtained. Three-dimensional images can also be obtained. For

clarity, we will focus on the 2D version. Localization in 3D space is obtained by using linear magnetic
field gradients.

1.3.1
1.3.1.1

Spatial encoding
Gradients

In our case, a gradient is a linear variation in the magnetic field with respect to position. These gradients
are superimposed on the static magnetic field B0 of the magnet. They are applied over very short times
(pulses) by gradient coils.
To obtain a 3D localization, we use three gradients: Gx , Gy , Gz . For a proton situated in position u(x,y,z),
Larmor frequency (ν) will be:
γ
−
→ →
B0 + G −
u
2π
γ
ν=
(B + Gx x + Gy y + Gz z )
2π 0
ν=

•

(1.1)

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The Chemistry of Contrast Agents in Medical Magnetic Resonance Imaging
z

Gz(z)
Gy (y )
y

Gx(x )

x

Figure 1.4 Magnetic field gradients used to localize spins in MRI (z axis is vertical in vertical magnets and
horizontal in horizontal magnets).

The localization of signal in 3D space is obtained by applying the three gradients (slice selection, phase
encoding, and frequency encoding) in three spatial directions.
For simplicity, we will focus on the distribution of H2 O in living tissue, knowing that the 1 H proton
NMR signal is proportional to the local quantity of H2 O. We need to localize the signal. Based on the
example cited here, we impose a spatial frequency encoding in one dimension, using a magnetic field
gradient produced by suitable coil geometry. It is of course possible to impose a linear gradient along
the three spatial axes (x, y, z), knowing that, by convention, the z axis is reserved for the axis of the
static magnetic field of the magnet (B0 ) (Figure 1.1). Note that x and y gradients correspond to a linear
variation of a magnetic field that is always parallel to B0 (z axis), and that only the variation of its
intensity depends on x or y (Figure 1.4).

1.3.1.2

Slice selection

The first step in signal localization is the selection of a slice to be imaged in the object. This version of MRI
is incorrectly called 2D MRI. In fact the slice has a third dimension – thickness. The slice is selected by
simultaneously combining a selective excitation pulse with a gradient pulse. The space frequency encoding
can be obtained from the gradient, and the selective excitation pulse selects the slice through a selected
bandwidth of frequencies.
Selective pulse: As in NMR spectroscopy, MRI uses selective pulses to excite frequency bands. They
are characterized by three parameters: the frequency bandwidth ( ν), the excitation profile, and the central frequency (ν i ) (Figure 1.5). Long duration pulses (milliseconds) are used to excite narrow frequency
bands corresponding to the thickness of the slice. In addition, the pulse shape defines the selective excitation profile corresponding to the spatial frequency profile of the slice. For example, pulse sinc shape


General Principles of MRI
B1(t)

M

x,y

( )

i

=2

7

i

1/ t 0

t

t0

t0
(a)

(b)

Figure 1.5 Selective RF pulse and corresponding magnetization excitation profile: (a) sinc pulse shape which
is the envelope of the radiofrequency, ν and (b) excitation profile.
Δν
GZ

B0

ν1

ν2

ν3

ν4

ν5

ν6

ν7

ν8

ν9

ν10

ν11

ν12

ν13

ν14

ν15 ν16

Figure 1.6 Slices that can be selected by applying slice selection gradient, Gz.

(sinc = sin(x)/x; half bandwidth of the principal lobe: t0 ) produces an excitation profile defined by the FT
of the pulse shape. A sinc pulse produces a quasi-rectangular profile with a width of about 1/t0 (Figure 1.5).
Slice gradient: For example, (Figure 1.6), using a selective pulse (bandwidth = ν) of frequency ν 8
simultaneously with Gz application, only protons inside slice 8 will contribute to the signal. Slice thickness
depends on the gradient intensity and the frequency bandwidth of the selective pulse.
Once a slice has been selected with an initial slice selection gradient, signals from each slice voxel need
to be differentiated. This is known as space encoding of the image. This can be achieved by applying two
additional gradients – frequency encoding and phase encoding. For example, if a slice has been selected
in the z direction, a frequency encoding gradient can be applied in the x direction, and a phase encoding
gradient can be applied in the y direction.

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The Chemistry of Contrast Agents in Medical Magnetic Resonance Imaging

1.3.1.3

Frequency encoding

Spins precess at different frequencies depending on their position in the x direction (Figure 1.7). They
show different frequencies due to the frequency-encoding gradient Gx applied during signal recording.

1.3.1.4

Phase encoding

The previously mentioned spins precess at the same frequency and the same phase for the same position
relative to the x axis. If we now introduce a second gradient (phase-encoding gradient) along the y direction,
they will precess at different frequencies and will be dephased. If this gradient is turned off, the spins will
precess at the same frequency but stay dephased. There will be a dependency of the signal according to
the position relative to the phase encoding gradient in the y direction (Figure 1.8).
The main difference between the frequency-encoding and the phase-encoding gradients is that the former
is only turned on during the acquisition of the signal and the latter operates before the acquisition of
the signal.
We can now match each slice voxel to a signal which is characterized by its own frequency and phase
depending on its position (x, y), according to the frequency- and phase-encoding gradients.

1.3.1.5

Image formation

The signal from a small element of the slice can be written as
dS = dM e −i ω(x ,y)t (with ω = 2π ν)

(1.2)

The whole signal received by the coil will be
S (t) =

dS

(1.3)

slice(x ,y)

v1

0

v2
x

Bo

Figure 1.7 Evolution of the (x,y) magnetization frequency according to the frequency-encoding gradient (Gx),
for spins situated at different positions on the x axis.


9

0

φ1

General Principles of MRI

φ2

Bo

Y

Figure 1.8 Evolution of the (x,y) magnetization phase according to the phase-encoding gradient (Gy), for spins
situated at different positions on the y axis.

as ω(x,y) = γ (Gx x + Gy y) in rotating frame (ω ∼ ω0 ). If relaxation is neglected, S(t) can be expressed as
M (x , y) e −i γ (Gx x +Gy y )t dxdy =

S (t) =
x ,y

M (x , y) e −2i π γ

(GX x +GY y )t
2π

dxdy

(1.4)

x ,y

If we change the variable kx =

γ
2π Gx t

and ky =

γ
2π GY t,

the signal expression becomes

M (x , y)e −2i π (kx x +ky y ) dxdy

S kx , ky =

(1.5)

x ,y

The image is the spin density distribution ρ(x,y) which is proportional to M(x,y). An inverse FT of S(k)
in temporal space (k) leads to the spin density distribution in 3D physical space (x,y).
S kx , ky e 2i π (kx x +ky y ) d kx d ky

ρ (x , y) = A M (x , y) =

(1.6)

kx ,ky

In MRI, a 2D Fourier space S(kx , ky ) can be defined, called “k-space.” It contains raw acquisition data
(spatial frequencies).
In NMR, FT transforms temporal space t to frequential space ν (spectrum) (see Scheme 1.2).
The k-space is filled by the Gx frequency-encoding gradient (discrimination along x) and the Gy phaseencoding gradient (discrimination along y) (Figure 1.9).


10

The Chemistry of Contrast Agents in Medical Magnetic Resonance Imaging
NMR

MRI
2D FT−1

FT
Frequential

Temporal
(t )
FID

Spatial

Frequential
(kx, ky )
K-SPACE

(v)

SPECTRUM
FT−1

(x, y)
IMAGE
2D FT

ky

kx

Scheme 1.2

Figure 1.9 Sampling of the Fourier space: the collected signal S(kx, ky ) is a discrete sampling represented
graphically by a grid with uniformly spaced points.

After filling the Fourier space, we have a frequency representation (kx , ky ) of the imaged slice. These
frequencies are spatial frequencies (analogous to the temporal frequencies in NMR). Raw data are stored
in k-space in rows and columns.
An inverse double FT of this representation gives the final image in a 2D space (x, y) (Figure 1.10).
Rules for filling k-space are:
• Each point of the k-space corresponds to a particular value of Gx and Gy and to one acquisition point
of the echo signal.
• Frequency-encoding gradient Gx is a bipolar negative and positive gradient filling the negative and
positive parts of kx .


General Principles of MRI
ky

11

y

kx
x

Figure 1.10 Inverse Fourier Transform provides an image (right) from k-space (left). The center of the k-space
plane contains the low frequencies (image contrast), and the periphery of the plane contains the high frequencies
(image resolution).

• The phase-encoding gradient increases from negative values (to explore the negative part of ky ) to
positive ones.
• A line in the k-space does not correspond to a line in the image space but to a fraction of the whole
image (this process can be compared with the structure of a hologram).

1.4
1.4.1

MRI pulse sequences
Definition

This section describes the bases of pulse sequences used to create the MRI sequences that are commonly
used in routine clinical and preclinical experiments, and for advanced applications including the use of
contrast agents.