The chemistry of contrast agents in medical magnetic resonance imaging

The Chemistry of Contrast Agents in Medical Magnetic Resonance Imaging... Library of Congress Cataloging-in-Publication Data The chemistry of contrast agents in medical magnetic resonanc

The Chemistry of Contrast Agents in Medical Magnetic Resonance Imaging

The Chemistry of Contrast Agents in Medical Magnetic Resonance Imaging

CNRS, Orl´eans, France

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 2013 John Wiley & Sons, Ltd.

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Library of Congress Cataloging-in-Publication Data

The chemistry of contrast agents in medical magnetic resonance imaging – Second edition / edited by Lothar Helm, Andr´e E Merbach, ´ Eva T´oth pages cm

Includes bibliographical references and index.

Bich-Thuy Doan, Sandra Meme, and Jean-Claude Beloeil

1.5 Basic image contrast: Tissue characterization without injection of contrast agents

(main contrast of an MRI sequence: Proton density (P), T1 and T2, T2∗) 16

1.7.2 Angiography using intravascular contrast agent (Blood pool CA) injection 21

2.2.3 Proton/water exchange 39

2.4.4 Contrast agents optimized for application at high magnetic field 73

3 Synthesis and Characterization of Ligands and their Gadolinium(III) Complexes 83

Jan Kotek, Vojtˇech Kub´ıˇcek, Petr Hermann, and Ivan Lukeˇs

Ern˜o Br¨ucher, Gyula Tircs´o, Zsolt Baranyai, Zolt´an Kov´acs, and A Dean Sherry

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 ) 1584.2.2 A brief overview of the programs used in equilibrium calculations (calculation

of protonation constants, stability constants, and equilibrium speciation diagrams) 159

4.3.1 Stability of complexes of open chain ligands (EDTA, DTPA, EGTA, and TTHA) 160

4.3.4 Ternary complexes formed between the Ln(L) complexes and various bio-ligands 176

4.5.1 Inertness of complexes of open chain ligands (EDTA, DTPA, and AAZTA) 187

4.6 Biodistribution and in vivo toxicity of Gd3+-based MRI contrast agents 1934.6.1 Osmolality and hydrophobicity of Gd3+-based MRI contrast agents 193

4.6.4 Predicting in vivo toxicity of Gd3+-based contrast agents using thermodynamic

4.6.6 Kinetic inertness combined with thermodynamic stability is the best predictor

5.5 Anisotropic hyperfine interactions on the first coordination sphere water molecules 221

5.11.2 TTHA 236

6.2.7 Monte-Carlo simulation of the Gd3+ electronic relaxation:

6.3.4 Experimental determination of the dipolar time correlation function 292

6.A Appendix: Similar evolutions of the macroscopic magnetization of the electronic spin and of

7 Targeted MRI Contrast Agents 311

Peter Caravan and Zhaoda Zhang

Enzo Terreno, Daniela Delli Castelli, and Silvio Aime

9.3 Diamagnetic versus paramagnetic CEST agents 400

Sophie Laurent, Luce Vander Elst, and Robert N Muller

Klaas Nicolay, Gustav Strijkers, and Holger Gr¨ull

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 Br ¨ucher, 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 Gr ¨ull, Biomedical NMR, Department of Biomedical Engineering, Eindhoven University of

Tech-nology, 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´ıˇcek, 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

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

Tech-nology, 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

Magnetic Resonance Imaging is one of the most important tools in clinical diagnostics and biomedicalresearch The estimated number of MRI scanners operating around the world is about 20 000 The devel-opment of contrast agents, currently used in about a third of the 50 million clinical MRI examinationsperformed 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 imagingprocedure requires a molecular imaging probe, thus chemistry plays a pivotal role in the development ofnew applications As a result, the chemistry of MRI agents has witnessed a spectacular evolution in thelast 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 andiron-oxide probes and includes chapters dedicated to the most significant advances in molecular imagingprobes We also discuss Chemical Exchange Saturation Transfer which is a novel means of generatingMRI contrast This treatise covers all aspects of production, use, operating mechanism, and theory of thesediagnostic agents used to produce high contrast images in MRI

This book assembles a distinguished team of experts who have been largely involved in successiveCOST (European Cooperation in the Field of Scientific and Technical Research) D1, D8, D18, D38 andTD1004 Actions These collaborations, as well as the annual COST meetings, largely contributed to thedevelopment 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 andsaturation 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 widevariety of chelates, as assessed by17O NMR Analysis of the NMRD profiles is also discussed Simulationsthat help optimize relaxivity as a function of water exchange rate, rotational correlation time, and magneticfield 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 andkinetic inertness of the chelate The methods used to assess these properties are discussed, and stabilitydata from the literature are reported

In Chapter 5, the authors review the structure, dynamics, and computational studies of linear and cyclic lanthanide chelates This includes interpretation of solution lanthanide-induced NMR shifts andrelaxation rate enhancements, evaluation of geometries by fitting NMR parameters, two-dimensional NMR,

macro-139La and89Y 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-basedcontrast agents

The first contrast agents approved for human use were untargeted, discrete gadolinium complexes such

as [Gd(DTPA)(H2O)]2− Chapter 7 is dedicated to ongoing efforts to make contrast agents more specificfor 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, couldallow 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-sizedCEST 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 ironoxide nanoparticles with control of their microstructures have been reported Below a critical size, theparticles 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 phos-pholipids 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 hybridimaging 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 withmultiple 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 resonanceimaging probes, this book intends to be a useful tool for both experts and newcomers in the field Wehope that it helps inspire further work in order to create more efficient and specific imaging probes thatwill allow materializing the dream of seeing even deeper and better inside the living organisms

General Principles of MRI

Bich-Thuy Doan,1 Sandra Meme,2 and Jean-Claude Beloeil2

1CNRS, Chimie-Paristech, Universit´e Paris Descartes, Paris, France

2Centre de Biophysique Mol´eculaire, CNRS, Orl´eans, France

1.1 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” wasdropped 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 briefoverview of the technique explaining the notion of relaxation time and saturation transfer used in MRI, wewill describe localization techniques, which are less well-known in chemistry The purpose of this shortchapter is not to provide a complete theory of MRI [5–8], but to understand the rest of the book concerningthe 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 thisaspect This is a “nuts and bolts” description of MRI Whenever possible, we refer to chemists’ knowledge

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

Edited by Andr´e Merbach, Lothar Helm and ´ Eva T´oth.

c

 2013 John Wiley & Sons, Ltd Published 2013 by John Wiley & Sons, Ltd.

sphere rotating with a magnetic moment and collinear angular momentum (in quantum mechanics, thesetwo entities are quantified as magnetic quantum number and spin quantum number (or spin)) Like aspinning top precessing in the Earth’s gravitational field, the nucleus 1H precesses in the static magnetic

field B0 of the spectrometer magnet This precession will occur at a frequency (ν0) dictated by the nature

of the nucleus and the strength of the magnetic field of the magnet (ν0= −(γ /2π)B0) (Larmor frequency)

There are two possible precessions (parallel and antiparallel to B0) corresponding to two energy states inthe presence of a strong magnetic field According to the Boltzmann equation, there are more1H 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

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 angleα 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 conversioninto 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 onlyinterested in H2O The signal intensity is proportional to the quantity of 1H protons and therefore theamount of H2O in the sample In NMR, it is observed that we have a temporal frequency (FID) and thatthe FID and spectrum are a Fourier pair (Scheme 1.1)

FT or reverse FT

Scheme 1.1

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

longitu-dinal 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 ment (1H 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

environ-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 themobility 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 andthe 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 medicalMRI

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 theparticles studied We will see later that it can be utilized in the action mechanism of very typical contrastagents (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, NH2function), the 1H protons of X–H are selectively saturated This involves using a magnetic

field B1 pulse to send so much energy that the 1H protons do not have time to return to equilibrium (therelaxation 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 B1to X–H, without affecting H2O 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 Throughselective saturation and chemical exchange, and provided the exchange is fast enough, the1H protons taketheir saturation on the H2O 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 differentfrequencies, except in specific cases We will now look at the concept of chemical shift, the resonancefrequency that is characteristic of a1H proton and which is determined by the electronic environment Themolecular 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 variesaccording to its position in space Resonance frequency is proportional to the strength of the magneticfield, it depends of the position in the “intramolecular” space We will see later that the same principleenables the position in space (imaging) to be coded

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 thistechnique allows virtual internal slices to be obtained Three-dimensional images can also be obtained Forclarity, we will focus on the 2D version Localization in 3D space is obtained by using linear magneticfield gradients

1.3.1 Spatial encoding

1.3.1.1 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: G x , G y , G z For a proton situated in positionu(x,y,z),

Larmor frequency (ν) will be:

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, phaseencoding, and frequency encoding) in three spatial directions

For simplicity, we will focus on the distribution of H2O in living tissue, knowing that the1H protonNMR signal is proportional to the local quantity of H2O We need to localize the signal Based on theexample cited here, we impose a spatial frequency encoding in one dimension, using a magnetic fieldgradient produced by suitable coil geometry It is of course possible to impose a linear gradient alongthe 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 itsintensity 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 bysimultaneously combining a selective excitation pulse with a gradient pulse The space frequency encodingcan be obtained from the gradient, and the selective excitation pulse selects the slice through a selectedbandwidth 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

cen-tral frequency (νi) (Figure 1.5) Long duration pulses (milliseconds) are used to excite narrow frequencybands corresponding to the thickness of the slice In addition, the pulse shape defines the selective exci-tation profile corresponding to the spatial frequency profile of the slice For example, pulse sinc shape

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.

B0

ν 1 ν 2 ν 3 ν 4 ν 5 ν 6 ν 7 ν 8 ν 9 ν 10 ν 11 ν 12 ν 13 ν 14 ν 15 ν 16

Δν

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 ν8simultaneously with G zapplication, only protons inside slice 8 will contribute to the signal Slice thicknessdepends 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 twoadditional 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 encodinggradient can be applied in the y direction

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 G x 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 positionrelative 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 willprecess at the same frequency but stay dephased There will be a dependency of the signal according tothe 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 ofthe signal

We can now match each slice voxel to a signal which is characterized by its own frequency and phasedepending on its position (x, y), according to the frequency- and phase-encoding gradients

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

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

asω(x,y) = γ (G xx+ G yy) in rotating frame (ω ∼ ω0) If relaxation is neglected, S(t) can be expressed as

M (x, y) e −2iπγ ( GX x+GY y2π ) t dxdy (1.4)

If we change the variable k x = 2γ π G x t and k y =2γ π G Y t , the signal expression becomes

M (x, y)e −2iπ ( k x x +k y y )dxdy (1.5)

The image is the spin density distributionρ(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).

In NMR, FT transforms temporal space t to frequential space ν (spectrum) (see Scheme 1.2).

The k-space is filled by the G x frequency-encoding gradient (discrimination along x) and the G y

phase-encoding gradient (discrimination along y) (Figure 1.9).

Spatial (x, y) IMAGE

Frequential

(k x , k y) K-SPACE

MRI

2D FT

2D FT −1 Frequential

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 G x and G yand to one acquisition point

of the echo signal

• Frequency-encoding gradient G x is a bipolar negative and positive gradient filling the negative and

positive parts of k x

k y

x y

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 k y) topositive ones

• A line in the k-space does not correspond to a line in the image space but to a fraction of the wholeimage (this process can be compared with the structure of a hologram)

1.4 MRI pulse sequences

1.4.1 Definition

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

Echo TE

The essential elements of an MRI sequence are: (i) a radiofrequency pulse for spin excitation based onNMR phenomenon; (ii) magnetic field gradients for the spatial encoding of the signal in the k-space; and(iii) an acquisition period to record the echoes signal with a defined contrast

The resulting signal S(k x , k y) is obtained and its equation is shown in Equation 1.5

At each repetition time (TR), one line of the k-space is recorded (Figure 1.12) The first RF pulse places

the acquisition at the center of the k-space With the G x gradient, we move along a line, parallel to the

x axis With the G y gradient, we move along a column, parallel to the y axis (Figure 1.12) With a 180◦

RF pulse, there will be symmetry with respect to the centerline of the k-space By applying the readoutgradient in the x direction, for example, one line of the k-space is filled Another line is filled at eachvalue of the incrementable phase-encoding gradient, in the y direction

The second dimension, obtained with this phase-encoding gradient (G p), can be understood by analogy

with 2D NMR: 2D NMR acquisition for the second dimension is obtained by an incrementable time t1

Here, in 2D MRI, t1 is replaced by an incrementable gradient G p Like the 2D NMR, a 2D MRI image isobtained by double FT

1.4.3 Basic pulse sequences

There are two main families of basic sequences: (i) spin echo and (ii) gradient echo (GE) sequences.Image contrast can be modified by changing sequence parameters In this way, it is possible to modify the

sensitivity of the experiment to T1, T2, T2*, or the proton density (ρ) It should be underlined that if in

NMR we obtained a F.I.D., in MRI we obtain an echo The echo is centered at time TE (Figure 1.11)

1.4.3.1 Spin echo sequence (SE)

A spin echo sequence (Figure 1.11) is an MRI sequence formed by an excitation pulse and one or morerefocusing RF pulses The flip angles are usually 90◦ and 180◦ for the excitation and refocusing pulsesrespectively, occurring at TE= 0 for the excitation pulse (90◦) and TE/2 for the refocusing pulse (180◦),

and the signal is recorded at the end This nominal module is repeated at TR intervals At each TR,one line of the k-space is filled due to an increment of the phase encoding The refocusing pulse (180◦allows permanent field inhomogeneities to be compensated for and produces an echo signal weighted by

T2 relaxation time This sequence has the advantage of being resistant to off-resonance artifacts created

by static magnetic field B inhomogeneities It is also resistant to magnetic susceptibility variations due

to heterogeneous tissues or to the presence of magnetic entities or impurities Spin Echo (SE) can alsorefocus chemical shift artifacts arising from lipids contained in the voxel signal SE may be in the form

of a single echo sequence or of a multi-echo sequence

Contrast and acquisition time With regard to echo train length, the images obtained are strongly T2weighted because the majority of lines in k-space are filled with echoes with long TE With this type ofsequence, a slice can be recorded in a few seconds

-• A short TR and a short TE provide a T1 weighted image

• A long TR and a long TE provide a T2 weighted image

• A long TR and a short TE provide a proton density or ρ weighted image.

It should be noted that the effect ofρ (proton density) can be reduced but never completely suppressed.

1.4.3.2 Gradient echo sequence (GE)

The GE sequence (Figure 1.13) differs from the SE sequence by its flip angle, which is generally inferior to

90◦, and by the absence of a 180◦refocusing RF pulse Instead, GE pulse sequences have a bipolar gradientenabling the signal to be refocused, as in high resolution NMR: a gradient reversal in the frequency-encoded

direction for MRI generates the echo signal and also allows the negative and positive k values to be filled.

The reduced flip angle enables a faster return to equilibrium significantly reducing TE and TR andreducing experimental time This is the main interest of this type of sequence

Contrast and acquisition time The transverse magnetization decrease which occurs in this GE sequence

is induced by several physical parameters: T2relaxation, magnetic field inhomogeneities, and susceptibility

effects All these phenomena are taken into account through the relaxation time T2*

The flip angle allows a T1 weighting of the contrast (the higher the angle, the higher the T 1 weighting);

The TE allows a T2* weighting of the contrast (the longer the TE, the higher the T2* weighting);

These sequences allow fast imaging (less than 1s) They are used for angiography imaging, fast anatomicimaging, for recording tissues with hemorrhage, and so on

1.4.3.3 Inversion recovery sequence (IR)

The Inversion-Recovery (IR) sequence is directly derived from a technique used in NMR to measure T1and will give an MRI sequence that is sensitive to T1 Using this technique, the magnetization is preparedduring an initial sequence module, called the IR sequence, and followed by a standard GE or SE sequence.First, a 180◦ inversion RF pulse flips the longitudinal magnetization (M z) into the negative axis (−Mz).During natural longitudinal relaxation, longitudinal magnetization will move toward equilibrium In order

to measure the actual M z magnetization, a 90◦RF pulse should be applied to obtain a transverse recordablemagnetization The time between the 180◦ inversion RF pulse and the “reading” 90◦ pulse is designated

Inversion Time (TI) and allows a T1 weighting

Contrast and acquisition time Weighting of the signal intensity in relation of its T1 value is performed,

leading to a T1 contrast The IR technique also makes it possible to choose a specific TI so that the

longitudinal magnetization signal is null for a given tissue with a specific T1 value For example, it ispossible to suppress undesired signals such as lipid molecules (Figure 1.14)

The IR module may be combined with either rapid SE or GE sequences to optimize the duration

of acquisition

Figure 1.14 IR in a gradient-echo MRI sequence, example of images of a human knee (a) without IR and (b)

with IR dedicated to suppressing lipid signals Courtesy of Centre Hospitalier R´egional Universitaire of Tours,France

1.5 Basic image contrast: Tissue characterization without injection of contrast agents

(main contrast of an MRI sequence: Proton density (P), T1 and T2, T2*)

MRI signal intensity is expressed in gray levels: a high intensity signal appears in white and a weak intensitysignal in black or dark gray An MR image is obtained by contrasts between different biological tissues.This contrast is created from the different signal intensities (SNR (signal-to-noise ratio)= Stissue/Standarddeviationnoise) between tissues obtained with MRI sequences The contrast-to-noise ratio is defined asCNR= (SNRtissue2− SNRtissue1) and is chosen by the MRI user who can modify the sequence parameters(TR, TE, flip angle, FOV: Field Of View, etc.) in order to obtain the desired contrast between tissues.The choice of the MRI parameters allows the image contrast to be varied according to the values of their

intrinsic physical parameters: T1, T2, T2*, and proton density (ρ) This action is called the T1, T2, T2*,and proton density (ρ) weighting of the image [5, 6].

Let us take two tissues A and B, with T1A< T1B and T2A< T2B,ρA> ρB After a 90◦ RF excitationpulse, the evolution of the MR signal [11] is a function of TR or TE values (see Figures 1.15–1.17) The

rate at which each tissue recovers its longitudinal magnetization depends on its T1 value The transversemagnetization is maximum at short TE The contrasts are defined by the choice of TR and TE, taking intoaccount the repetition of the basic sequence, in either an SE or a GE sequence

Proton density weighting

MRI Signal intensity

Figure 1.15 ρ weighting Evolution of the signal intensity as a function of TR, a long TR allows the differentiation

of the sample in function of their proton density

Short T1

sample or tissue

MRI Signal intensity

1.5.1 Proton density weighting

With a long TR, the remaining longitudinal magnetization is completely recovered before the next RF

excitation pulse, with an identical magnetization signal for the two T1 samples The contrast is called aproton density weighting (Figure 1.15)

1.5.3 T2 weighting

Considering a SE sequence, if a long TR is applied in order to remove the T1 effect, we can use a long

TE to obtain a contrast depending on differences in transverse relaxation time constant (T2) To obtain a

T weighted image, a long TR and a long TE are needed (Figure 1.17)

To sum up, Figure 1.18 displays experimental indicative TE and TR parameters required to supply the

different T1, T2, and proton density weightings

1.5.4 T2 * weighting

In a GE sequence, unlike an SE sequence, the signal dephased by magnetic inhomogeneities during the

TE delay is not refocused The duration of TE allows a T2* weighting; the longer the duration, the higher

the T2* weighting

1.6 Main contrast agents

This chapter gives a brief description of major classes of contrast agents; the detailed properties (selectivity,

“smart agents,” etc.) will be covered later Unlike other imaging techniques, MRI does not require the use

of contrast agents, and it is not the contrast agent itself that is “visible.” Indeed, the MRI contrast agentsinteract with H2O protons and either modify their relaxation times, or are directly involved in the level of

H2O proton magnetization

Figure 1.18 Scheme of TR and TE parameters values to supply the T1, T2and proton density weighting

1.6.1 Gadolinium (Gd) complex agents

The most widely used class of MRI contrast agents is based on the mechanism of longitudinal relaxation

(T1) [12] It is usually the motion of the neighboring 1H protons which creates an oscillating magneticfield that stimulates a return to equilibrium of the H2O protons If we now introduce molecules containingunpaired electrons (e−) into the H2O molecule environment, they will trigger the return to equilibrium

of the H2O protons much more effectively, because the magnetic moment of the electron is 658 timesstronger than that of the proton Through their position in the Mendeleev table, lanthanides contain unpairedelectrons, including gadolinium (as Gd3+) which contains seven unpaired electrons Although it is veryeffective, it is toxic, so it is always used as a very stable chelate The action of gadolinium complexes

will therefore be to reduce the value of neighboring water hydrogens T1 (and T2) In an acquisition, thismeans a reduction in signal intensity (line broadening) However, if one considers that the production of

an image requires the accumulation of many acquisitions to obtain a sufficient SNR, the “Gd3+” contrastagent will reduce the time of return to equilibrium of the magnetization (z axis) (see Figure 1.2) Thismeans that we can reduce the TR, achieve more accumulations per unit time (several TRs), and therefore

record more signal per unit time for spins with reduced T1 The presence of the contrast agent Gd3+ in aparticular location of a living tissue will result in a stronger signal (positive enhancement) in this region ofthe image For example, in normal tissue, the “large” molecule Gd3+ chelate cannot cross the blood–brainbarrier; by contrast, in certain tumors the vascularization is higher than the surrounding tissues and theblood brain barrier is locally porous, so Gd3+ chelate can penetrate the tumor that appears hyperintense

on the corresponding MR image (Figure 1.19)

1.6.2 Iron oxide (IO) agents

A second class of contrast agents is composed of nanoparticles of iron oxide (Fe3O4/γ -Fe203) [13] Theyare designated according to their size: SPIO (Super Paramagnetic Iron Oxides, average diameter>50 nm

to several microns) or USPIO (Ultra-Small Super Paramagnetic Iron Oxides, average diameter <50 nm).

Super-paramagnetic properties are obtained when using ferro- or ferri-magnetic materials in the form

of small particles These particles behave like small movable magnets, creating a strong magnetic field

inhomogeneity in the environment and considerably reducing the T2 relaxation time of H2O protons intheir vicinity They are signal “killers” (negative enhancement) For example, these nanoparticles can beembedded in cells, and they can be “followed” by MRI [14] (Figure 1.20, [15])

1.6.3 CEST agents

A third class of contrast agents, which has emerged more recently, are CEST agents [16] These compounds,unlike those mentioned above, are not based on direct action on the relaxation time of H2O They aremolecules that contain hydrogens that are chemically exchangeable with hydrogens of H2O (e.g., –NH2)

If the 1H protons of exchangeable hydrogens are selectively saturated during their exchange with H2Ohydrogens, the intensity of the H2O signal decreases, and this effect is locally visible with MRI (Figure 1.3)

(a) (b)

Figure 1.20 Images of a human liver without (a) and with (b) IO particles, displaying normal liver tissue with

dark spots Liver malign tumors don’t uptake IO Namkung et al Journal of Magnetic Resonance Imaging, 25:755–765 (2007)

These agents present the advantage of having a “trigger” effect; in other words, their contrast agentproperties can be triggered at will by using a selective pulse that can only act on protons of exchangeablehydrogens, without affecting those of H2O However, the signal of these exchangeable protons must besufficiently distant from that of H2O to allow their selective excitation One way to overcome this problem

is to use “PARACEST” agents which contain a lanthanide ion in their structure which strongly movesaway the signal of the exchangeable hydrogens on the same molecule This makes selective saturationeasy Chemists will note that this is a “return” of “chemical shift” reagents used to clarify NMR spectrabefore the appearance of 2D NMR!

This peculiar property enables novel applications such as the detection of more than one agent in the same

MR image, or the setting-up of ratiometric methods for the quantitative assessment of the physicochemicaland biological parameters that characterize the micro-environment in which they are distributed TheseCEST agents are of particular interest in the field of MR-molecular imaging [17]

To carry out these experiments with CEST and PARACEST agents, a “soft” saturation pulse just needs

to be added at the beginning of a pulse sequence

1.7 Examples of specialized MRI pulse sequences for angiography (MRA)

Flows, like all movements in MRI, are the source of disturbance and spatial coding artifacts [11] Thesensitivity of MRI to physiological flow has been used to develop vascular imaging, using the physicalchanges associated with flow (endogenous contrast), that is, “Time-of-Flight (TOF),” “Phase contrast,” and

“Fresh blood imaging (FBI).”

Magnetic resonance angiography (MRA) with contrast agents uses the relaxivity properties of contrastagents to visualize vascular structures

Whatever the principle employed, these sequences use a strategy to remove the background signal created

by stationary tissues These techniques can all be tailored in 3D, then post-processed (reconstruction bymaximum intensity projection: MIP) For all these angiographic techniques, the pulse sequences are derivedfrom T1-weighted GE sequences

A vascular contrast can be obtained using two main techniques which are described next

1.7.1 Time of flight angiography: No contrast agent

The TOF phenomenon uses the movement-related changes in blood, which will not be subject to all RFpulses, in contrast to stationary tissues This is a natural intrinsic magnetic labeling In TOF MRA [11],

GE sequences are optimized to favor the vascular signal over surrounding tissues Considering a slice ofinterest, the stationary tissue signal is saturated with very short TR, and the longitudinal magnetization ofthese tissues does not have time to recover The signal thus weakens Because the circulating blood thatenters the explored area within the slice is not saturated, it has maximum longitudinal magnetization Thesignal from the bloodstream is high compared to the signal from saturated tissue (Figures 1.21 and 1.22)

1.7.2 Angiography using intravascular contrast agent (Blood pool CA) injection

The principle of this technique is very simple: a contrast agent bolus is injected into the vascular systemand MRI displays the transit of this bolus [18] The key point is to record the information during the

passage of the contrast agent This can be achieved using a T1-weighted fast GE imaging sequence.MRA is a good example of a specialized MRI technique MRI has been adapted to visualize spe-cific information through the design of many pulse sequences (“Cine-MRI,” “Cardiac-MRI,” MRI of theskin, etc.)

r~90°

Static protons

in slice ≠ 0

After several repetition

of the elementary sequence

Figure 1.21 Principle of the Time-Of-Flight (TOF) MRI, fresh blood imaging sequence.

Figure 1.22 Human inferior members 1.5 T MRA Courtesy of Centre Hospitalier R´egional Universitaire of

Tours, France

1.7.3 DSC DCE MRI

In addition to anatomical image of the vascularization supplied by MRA, quantitative microvascular acteristics like perfusion can be obtained by dynamic MRI using an injection of an exogenous contrastagent These methods are based on imaging rapid changes in the signal and then modeling the signal curve

char-to obtain the parameters characterizing blood volume, blood flow, and other perfusion parameters TwoMRI methods are used:

DCE-MRI [19] (Dynamic Contrast-Enhanced Magnetic Resonance Imaging), which provides flow surement and is also sensitive to the presence of the contrast agent in the interstitial space, used to study

mea-capillary permeability by exploiting induced changes in T1 respectively during the initial passage and atthe consecutive “plateau.”

Dynamic Susceptibility Contrast-enhanced Magnetic Resonance Imaging (DSC-MRI [20]) that is tive to the effect of the first passage of the contrast agent and can be used to study capillary perfusion by

sensi-exploiting the effect of induced magnetic susceptibility T2*

References

1 Ernst, R.R., Bodenhausen, G., and Wokaun, A (1987) Principles of Nuclear Magnetic Resonance in One and Two Dimensions, Clarendon Press, Oxford.

2 Canet, D (1996) Nuclear Magnetic Resonance: Concepts and Methods, John Wiley & Sons, Ltd, Chichester.

3 Freeman, R (1987) A Handbook of Nuclear Magnetic Resonance, Harlow, Longman Scientific & Technical.

4 G¨unther, H (1995) NMR Spectroscopy: Basic Principles, Concepts, and Applications in Chemistry, 2nd edn,

John Wiley & Sons, Inc., New York

5 Haacke, E., Brown, R.W., Thompson, M.R., and Venkatesan, R (1999) Magnetic Resonance Imaging: Physical Principles and Sequence Design, John Wiley & Sons, Ltd, Chichester.

6 Callaghan, P.T (1991) Principles of Nuclear Magnetic Resonance Microscopy, Oxford University Press, New

York

7 Ernst, R.R (1987) Q Rev Biophys., 19, 183–220.

8 Young, S.W (1988) Magnetic Resonance Imaging: Basic Principles, Raven Press, New York.

9 Zhou, J and van Zijl, P.C.M (2006) Prog NMR Spectrosc., 48, 109–136.

10 Aime, S., Castelli, D.D., and Terreno, E (2002) Angew Chem Int Ed., 1, 4334–4336.

11 Bernstein, M.A., King, K.F., and Zhou, X.J (eds) (2004) Handbook of MRI Pulse Sequences, Elsevier, New

York

12 T´oth, ´E., Helm, L., and Merbach, A.E (2004) in Applications of Coordination Chemistry, Vol 9 (ed M Ward),

Elsevier, Oxford, pp 841–881

13 Krause, W (2002) Contrast Agents I., Magnetic Resonance Imaging, Vol 221, Springer, Heidelberg.

14 Bulte, J.W.M and Muja, N (2009) Prog NMR Spectrosc., 55, 61–77.

15 Namkung, S., Zech, C J., Helmberger, T., et al J Magn Reson Imaging 2007, 25, 755–765.

16 Aime, S., Botta, M., and Terreno, E (2005) in Advances in Inorganic Chemistry, Vol 57 (eds R Van Eldik and

I Bertini), Elsevier, San Diego, CA, pp 173–237

17 Chauvin, T., Durand, P., Bernier, M., et al Angew Chem Int Ed 2008, 47, 4370–4372.

18 Zhang, H., Maki, J.H., and Prince, M.R (2007) J Magn Reson Imaging, 25, 13–25.

19 Tofts, P.S and Kermode, A.G (1991) Magn Reson Imaging, 17, 357–367.

20 Ostergaard, L (2005) J Magn Reson Imaging, 22, 710–717.

Relaxivity of Gadolinium(III) Complexes:

Theory and Mechanism

´ Eva T´oth,1 Lothar Helm,2 and Andr´e Merbach2

1Centre de Biophysique Mol´eculaire, CNRS, Orl´eans, France

2Ecole Polytechnique F´ed´erale de Lausanne, Lausanne, Switzerland

As most of the current contrast agent applications in MRI concerns Gd(III) complexes, this chapterwill focus on the discussion of relaxation theory and the experimental results on Gd(III)-based agents.Several reviews have been published on this topic [3–7] In addition to Gd(III) compounds, a Mn(II)chelate, Mn(II)DPDP, is the only metal complex which has been approved as an MRI contrast agent(DPDP= N,N-dipyridoxylethylenediamine-N,N-diacetate 5,5-bis(phosphate)) [8] Mn(II)DPDP is a weak

chelate that dissociates in vivo to give free manganese which is taken up by hepatocytes [9] The presence

of the ligand is necessary because it facilitates a slower release of manganese than would have been thecase had manganese been administered as a simple salt, such as manganese chloride

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

Edited by Andr´e Merbach, Lothar Helm and ´ Eva T´oth.

c

 2013 John Wiley & Sons, Ltd Published 2013 by John Wiley & Sons, Ltd.

The relaxation mechanism of paramagnetic particles is reviewed in Chapter 10 The discussion of freeradicals [10, 11] or of the rapidly emerging field of hyperpolarized substances [12–14] as MRI contrastagents is beyond the scope of this survey.

The general theory of solvent nuclear relaxation in the presence of paramagnetic substances wasdeveloped by Bloembergen, Solomon and others [15–20] A Gd(III) complex induces an increase of

both the longitudinal and transverse relaxation rates, 1/T1and 1/T2, respectively, of the solvent nuclei The

observed solvent relaxation rate, 1/T i,obs , is the sum of the diamagnetic (1/T i,d ) and paramagnetic (1/T i,p)relaxation rates:

1

T i ,obs = 1

T i ,d + 1

Although Equation (2.1) is widely used as a general description, strictly speaking, it is only valid for

dilute paramagnetic solutions, for which this condition is fulfilled The diamagnetic term, 1/T i,d, corresponds

to the relaxation rate of the solvent (water) nuclei in the absence of a paramagnetic solute The paramagnetic

term, 1/T i,p, gives the relaxation rate enhancement caused by the paramagnetic substance which is linearlyproportional to the concentration of the paramagnetic species, [Gd]:

relaxivity, r i (in units of mM−1s−1) If we consider the relaxation of water protons, which is the basis

of imaging by magnetic resonance, and is consequently significant from the practical point of view, we

can introduce the corresponding term proton relaxivity Proton relaxivity directly refers to the efficiency

of a paramagnetic substance to enhance the relaxation rate of water protons, and thus to its efficiency toact as a contrast agent It has to be noted that the simple term “relaxivity” is often used in the context ofMRI contrast agents and refers to “longitudinal proton relaxivity” even if the adjectives are omitted Inthe following, we deal primarily with the theory of proton relaxation in the presence of Gd(III)-containingparamagnetic species

The paramagnetic relaxation of the water protons originates from the dipole–dipole (DD) interactionsbetween the nuclear spins and the fluctuating local magnetic field caused by the unpaired electron spins.This magnetic field around the paramagnetic centre vanishes rapidly with distance Therefore, specificchemical interactions that bring the water protons into the immediate proximity of the metal ion play animportant role in transmitting the paramagnetic effect towards the bulk solvent For Gd(III) complexes,this specific interaction corresponds to the binding of the water molecule(s) in the first coordination sphere

of the metal ion These inner-sphere water protons then exchange with bulk solvent protons and in thisway the paramagnetic influence is propagated to the bulk This mechanism is depicted as the inner-spherecontribution to the overall proton relaxivity (Figure 2.1) Solvent molecules of the bulk also experiencethe paramagnetic effect when they diffuse in the surroundings of the paramagnetic centre The effect ofthe random translational diffusion is defined as outer-sphere relaxation Thus we separate the inner- andouter-sphere contributions based on the intra- and intermolecular nature of the interaction, respectively.This separation is also useful in explaining the observed proton relaxivities in terms of existing theories.The total paramagnetic relaxation rate enhancement due to the paramagnetic agent is therefore given as in

Figure 2.1 Schematic representation of a Gd(III) chelate with one inner-sphere water molecule, surrounded by

bulk water.τRrefers to the rotational correlation time of the molecule, kexto the water/proton exchange rate and

T1,2eto the relaxation times of the Gd(III) electron spin

Equation (2.3), or expressed in relaxivities in Equation (2.4):

1

T i ,p



=

1

T i ,p

IS

+

1

where the superscripts ‘IS’ and ‘OS’ refer to inner and outer sphere, respectively.

For certain agents, solvent molecules that are not directly bound in the first coordination sphere may alsoremain in the proximity of the paramagnetic metal for a relatively long time, for example due to hydrogenbridges to the ligand (e.g., to its carboxylate or phosphonate groups) or to the solvent molecule(s) in thefirst coordination sphere The relaxivity contribution originating from these interactions is called second-sphere relaxivity (even if the symmetry is not spherical), and can be described by the same theory as theinner-sphere term [21] However, very often this contribution is neglected or its effect is taken into account

in the outer-sphere term The three different types of water molecule (inner-, second- and outer-sphere)are represented in Figure 2.2

For the currently used, monomeric Gd(III)-based contrast agents, the outer- and inner-sphere relaxationmechanisms contribute approximately to the same extent to the observed proton relaxivity at the imagingfields It is the inner-sphere term that can be considerably augmented, whereas the outer-sphere contribution

is hard to modify Consequently, for the new of generation agents with higher efficiency (higher relaxivity),the inner-sphere term becomes relatively more important and it represents the major contribution to theoverall proton relaxation rate

In this chapter, we discuss first the inner-sphere relaxivity by analyzing each factor that determines thisrelaxation mechanism This will be followed by a survey of the second- and outer-sphere contributions toproton relaxivity We will also discuss in detail proton Nuclear Magnetic Relaxation Dispersion (NMRD),

a technique that is widely used and rather specific for the characterization of MRI contrast agents, andwhich is little-known outside this field In the last section of this chapter, we will draw conclusions from