The Chemistry of Contrast Agents in Medical Magnetic Resonance Imaging

By Andre S. Merbach, Lothar Helm and Éva Tóth

Magnetic Resonance Imaging (MRI) is one of the most important tools in clinical diagnostics and biomedical research. The number of MRI scanners operating around the world is estimated to be approximately 20,000, and 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 significant achievement.

This completely revised and extended second edition: 

• Includes new chapters on targeted, responsive, PARACEST and nanoparticle MRI contrast agents.
• Covers the basic chemistries, MR physics and the most important techniques used by chemists in the characterization of MRI agents from every angle from synthesis to safety considerations.
• Is written for all of those involved in the development and application of contrast agents in MRI.
• Presented in colour, it provides readers with true representation and easy interpretation of the images. 

A word from the Authors:

Twelve years after the first edition published, 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.

Reviews of the First Edition:

"...attempts, for the first time, to review the whole spectrum of involved chemical disciplines in this technique..."—Journal of the American Chemical Society

"...well balanced in its scope and attention to detail...a valuable addition to the library of MR scientists..."—NMR in Biomedicine

• Language: English
• Publisher: Wiley
• Release date: Feb 19, 2013
• ISBN: 9781118503676

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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, André E. Merbach, Éva Tóth.

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, André E., editor of compilation. III. Tóth, Éva, editor of compilation.

RC78.7.C65C48 2013

616.07′548–dc23

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 Moléculaire, CNRS, Orléans, France

Elie Belorizky, Université Joseph Fourier, Grenoble, France

Célia S. Bonnet, Centre de Biophysique Moléculaire, CNRS, Orléans, France

Mauro Botta, Dipartmento di Scienze e Innovazione Tecnologica, Università del Piemonte Orientale Amedeo Avogadro, Alessandria, Italy

Ern 1 Brücher, 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, Université 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 Grüll, 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 Fédérale 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

Zoltán Kovács, Advanced Imaging Research Center, University of Texas Southwestern Medical Center, Dallas, TX, USA

Vojt 1 ch Kubí 1 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 Lukeš, Department of Inorganic Chemistry, Faculty of Science, Universita Karlova v Praze, Prague, Czech Republic

Sandra Meme, Centre de Biophysique Moléculaire, CNRS, Orléans, France

André Merbach, Ecole Polytechnique Fédérale 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 Technology, Eindhoven, The Netherlands

Joop A. Peters, Delft University of Technology, Delft, The Netherlands

Carlos Platas-Iglesias, University of A Coruña, A Coruña, 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, Università 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 Tircsó, Inorganic and Analytical Chemistry, University of Debrecen, Debrecen, Hungary

Éva Tóth, Centre de Biophysique Moléculaire, CNRS, Orléans, 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 ¹⁷O 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, ¹³⁹La and ⁸⁹Y 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.

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 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.

Chapter 1

General Principles of MRI

Bich-Thuy Doan,¹ Sandra Meme,² and Jean-Claude Beloeil³

¹CNRS, Chimie-Paristech, Université Paris Descartes, Paris, France

²Centre de Biophysique Moléculaire, CNRS, Orléans, 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 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 Theoretical basis of NMR

1.2.1 Short description of NMR

In most cases, MRI focuses on one type of atomic nucleus, that of hydrogen in H2O. We will therefore only use this nucleus, termed the ¹H proton.

The physical phenomenon of NMR lies at the boundary between conventional and quantum treatment due to the small transition energies involved. Traditionally, the ¹H proton can be considered as a charged 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 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 in the presence of a strong magnetic field. According to the Boltzmann equation, there are more ¹H 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.

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.

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In an NMR experiment, the sample is subjected to the action of an oscillating electromagnetic field (B1) (frequency: ν1) perpendicular to B0 (Figure 1.1); if we place ourselves within a rotating frame around the z axis at frequency ν1 (ν1 close to ν0), it is as if the magnetization M0 precesses around the magnetic field 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).

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).

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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 H2O. The signal intensity is proportional to the quantity of ¹H protons and therefore the amount of H2O 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).

Scheme 1.1

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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 (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 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 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 (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 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. Through selective saturation and chemical exchange, and provided the exchange is fast enough, the ¹H protons take their saturation on the H2O molecules with them, leading to a reduction in signal intensity (Figure 1.4).

Figure 1.4 Saturation transfer principle. (a) ¹H spectrum without selective saturation; (b) spectrum with selective saturation of X–H. k1, k2, rate constants of the chemical reaction.

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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 ¹H 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.

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 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: Gx, Gy, Gz. For a proton situated in position (x,y,z), Larmor frequency (ν) will be:

1.1

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 H2O in living tissue, knowing that the ¹H proton NMR signal is proportional to the local quantity of H2O. 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 1.5).

Figure 1.5 Magnetic field gradients used to localize spins in MRI (z axis is vertical in vertical magnets and horizontal in horizontal magnets).

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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 (Δν), the excitation profile, and the central frequency (νi) (Figure 1.6). 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 (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 1.6).

Figure 1.6 Selective RF pulse and corresponding magnetization excitation profile: (a) sinc pulse shape which is the envelope of the radiofrequency, ν and (b) excitation profile.

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Slice gradient: For example, (Figure 1.7), using a selective pulse (bandwidth = Δν) of frequency ν8 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.

Figure 1.7 Slices that can be selected by applying slice selection gradient, Gz.

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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.

1.3.1.3 Frequency encoding

Spins precess at different frequencies depending on their position in the x direction (Figure 1.8). They show different frequencies due to the frequency-encoding gradient Gx applied during signal recording.

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

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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 1.9).

Figure 1.9 Evolution of the (x,y) magnetization phase according to the phase-encoding gradient (Gy), for spins situated at different positions on the y axis.

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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

1.2

The whole signal received by the coil will be

1.3

as ω(x,y) = γ(Gxx + Gyy) in rotating frame (ω ∼ ω0). If relaxation is neglected, S(t) can be expressed as

1.4

If we change the variable and , the signal expression becomes

1.5

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).

1.6

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).

Scheme 1.2

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The k-space is filled by the Gx frequency-encoding gradient (discrimination along x) and the Gy phase-encoding gradient (discrimination along y) (Figure 1.11).

Figure 1.11 Sampling of the Fourier space: the collected signal S(kx,ky) is a discrete sampling represented graphically by a grid with uniformly spaced points.

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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 1.12).

Figure 1.12 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).

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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.

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 MRI pulse sequences

1.4.1 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.

An MRI sequence is composed of series of radiofrequency pulses, gradients, and time intervals, which can be assembled as modules to create the final MRI sequence giving the specific contrast desired. It is graphically displayed in a pulse sequence diagram (Figure 1.13). These RF pulses and time intervals allow the spins to be excited and the desired signal to be selected, as in high-resolution NMR. The additional magnetic field gradients enable the spatial localization of the signal.

Figure 1.13 MRI pulse sequence scheme. (Spin Echo (SE) pulse sequence.) TE = Echo Time, TR = Repetition Time. TR is the duration of the elementary pulse sequence which is repeated several times to allow the increment of the phase encoding gradients for the creation of the image and to allow the signal to be accumulated until the SNR becomes satisfactory.

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The essential elements of an MRI sequence are: (i) a radiofrequency pulse for spin excitation based on NMR 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(kx, ky) is obtained and its equation is shown in Equation (1.5).

1.4.2 k-Space trajectory

The manner and time of acquisition of the MRI signal in a sequence are determined by the way the pulses and gradients are applied. The MRI signal is recorded in the k-space. The k-space trajectory is the path traced out by k(t). This path illustrates the acquisition strategy and determines the image reconstruction algorithm to be employed. The k-space is filled in different ways. Its trajectory depends on the data sampling, which will or will not speed up the acquisition. Although k-space trajectories are a continuous path, the signal is only sampled at discrete intervals along this path.

At each repetition time (TR), one line of the k-space is recorded (Figure 1.14). The first RF pulse places the acquisition at the center of the k-space. With the Gx gradient, we move along a line, parallel to the x axis. With the Gy gradient, we move along a column, parallel to the y axis (Figure 1.14). With a 180° RF pulse, there will be symmetry with respect to the centerline of the k-space. By applying the readout gradient in the x direction, for example, one line of the k-space is filled. Another line is filled at each value of the incrementable phase-encoding gradient, in the y direction.

Figure 1.14 The k-space trajectory. Here, frequency encoding is applied in the x direction and phase encoding in the y direction.

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The second dimension, obtained with this phase-encoding gradient (Gp), 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 Gp. Like the 2D NMR, a 2D MRI image is obtained 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 1.13).

1.4.3.1 Spin echo sequence (SE)

A spin echo sequence (Figure 1.13) is an MRI sequence formed by an excitation pulse and one or more refocusing RF pulses. The flip angles are usually 90° and 180° for the excitation and refocusing pulses respectively, 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 B0 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 also refocus 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 T2-weighted because the majority of lines in k-space are filled with echoes with long TE. With this type of sequence, 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 of ρ (proton density) can be reduced but never completely suppressed.

1.4.3.2 Gradient echo sequence (GE)

The GE sequence (Figure 1.15) 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 gradient enabling 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.

Figure 1.15 Gradient-echo MRI sequence.

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The reduced flip angle enables a faster return to equilibrium significantly reducing TE and TR and reducing 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: T2 relaxation, 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 T1 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 anatomic imaging, 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 T1 and will give an MRI sequence that is sensitive to T1. Using this technique, the magnetization is prepared during 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 (Mz) into the negative axis (−Mz). During natural longitudinal relaxation, longitudinal magnetization will move toward equilibrium. In order to measure the actual Mz magnetization, a 90° RF pulse should be applied to obtain a transverse recordable magnetization. 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 is possible to suppress undesired signals such as lipid molecules (Figure 1.16).

Figure 1.16 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 Régional Universitaire of Tours, France.

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

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 intensity signal 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/Standard deviationnoise) between tissues obtained with MRI sequences. The contrast-to-noise ratio is defined as CNR = (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 excitation pulse, the evolution of the MR signal [11] is a function of TR or TE values (see Figures 1.17–1.19). The rate at which each tissue recovers its longitudinal magnetization depends on its T1 value. The transverse magnetization is maximum at short TE. The contrasts are defined by the choice of TR and TE, taking into account the repetition of the basic sequence, in either an SE or a GE sequence.

Figure 1.17 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.

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Figure 1.18 T1 weighting. Evolution of the signal intensity as a function of TR. A short TR allows the stronger discrimination of the samples in function of their T1 values as displayed in the phantom samples and human brain images (samples with short T1 are in hypersignal).

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Figure 1.19 T2 weighting: Evolution of signal intensity as a function of TE. A long TE with a long TR allows the stronger discrimination of the samples in function of their T2 values, samples with long T2 are in hypersignal.

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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 a proton density weighting (Figure 1.17).

1.5.2 T1 weighting

If TR is short, the RF excitation pulse is repeated rapidly in order to flip the new longitudinal magnetization vector. There is a greater intensity of the magnetization vector recorded for sample A, which has a shorter T1. The image is called "T1-weighted" because the signal difference is mainly due to the difference in longitudinal magnetization at a given TR (Figure 1.18), but the signal intensity also depends on proton density (ρ).

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 T2 weighted image, a long TR and a long TE are needed (Figure 1.19).

To sum up, Figure 1.20 displays experimental indicative TE and TR parameters required to supply the different T1, T2, and proton density weightings.

Figure 1.20 Scheme of TR and TE parameters values to supply the T1, T2 and proton density weighting.

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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 agents interact with H2O protons and either modify their relaxation times, or are directly involved in the level of H2O proton magnetization.

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 magnetic field that stimulates a return to equilibrium of the H2O protons. If we now introduce molecules containing unpaired 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 times stronger than that of the proton. Through their position in the Mendeleev table, lanthanides contain unpaired electrons, including gadolinium (as Gd³+) which contains seven unpaired electrons. Although it is very effective, 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, this means 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+ contrast agent will reduce the time of return to equilibrium of the magnetization (z axis) (see Figure 1.2). This means 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 a particular location of a living tissue will result in a stronger signal (positive enhancement) in this region of the image. For example, in normal tissue, the large molecule Gd³+ chelate cannot cross the blood–brain barrier; by contrast, in certain tumors the vascularization is higher than the surrounding tissues and the blood brain barrier is locally porous, so Gd³+ chelate can penetrate the tumor that appears hyperintense on the corresponding MR image (Figure 1.21).

Figure 1.21 Images of a human brain with tumor without and with the Gd³+ chelate displaying the tumor with CA uptake in hypersignal.

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1.6.2 Iron oxide (IO) agents

A second class of contrast agents is composed of nanoparticles of iron oxide (Fe3O4/γ-Fe203) [13]. They are 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 in their vicinity. They are signal killers (negative enhancement). For example, these nanoparticles can be embedded in cells, and they can be followed by MRI [14] (Figure 1.22 [15]).

Figure 1.22 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).

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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 are molecules 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 H2O hydrogens, the intensity of the H2O signal decreases, and this effect is locally visible with MRI (Figure 1.4). These agents present the advantage of having a trigger effect; in other words, their contrast agent properties can be triggered at will by using a selective pulse that can only act on protons of exchangeable hydrogens, without affecting those of H2O. However, the signal of these exchangeable protons must be sufficiently 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 moves away the signal of the exchangeable hydrogens on the same molecule. This makes selective saturation easy. Chemists will note that this is a return of chemical shift reagents used to clarify NMR spectra before 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 physicochemical and biological parameters that characterize the micro-environment in which they are distributed. These CEST 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]. The sensitivity of MRI to physiological flow has been used to develop vascular imaging, using the physical changes 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 contrast agents 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 by maximum intensity projection: MIP). For all these angiographic techniques, the pulse sequences are derived from 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 RF pulses, 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 of interest, the stationary tissue signal is saturated with very short TR, and the longitudinal magnetization of these tissues does not have time to recover. The signal thus weakens. Because the circulating blood that enters the explored area within the slice is not saturated, it has maximum longitudinal magnetization. The signal from the bloodstream is high compared to the signal from saturated tissue (Figures 1.23 and 1.24).

Figure 1.23 Principle of the Time-Of-Flight (TOF) MRI, fresh blood imaging sequence.

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Figure 1.24 Human inferior members 1.5 T MRA. Courtesy of Centre Hospitalier Régional Universitaire of Tours, France.

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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 system and 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 specific information through the design of many pulse sequences (Cine-MRI, Cardiac-MRI, MRI of the skin, etc.).

1.7.3 DSC DCE MRI

In addition to anatomical image of the vascularization supplied by MRA, quantitative microvascular characteristics like perfusion can be obtained by dynamic MRI using an injection of an exogenous contrast agent. These methods are based on imaging rapid changes in the signal and then modeling the signal curve to obtain the parameters characterizing blood volume, blood flow, and other perfusion parameters. Two MRI methods are used:

DCE-MRI [19] (Dynamic Contrast-Enhanced Magnetic Resonance Imaging), which provides flow measurement and is also sensitive to the presence of the contrast agent in the interstitial space, used to study capillary permeability by exploiting induced changes in T1 respectively during the initial passage and at the consecutive plateau.

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

Chapter 2

Relaxivity of Gadolinium(III) Complexes: Theory and Mechanism

Éva Tóth,¹ Lothar Helm,² and André Merbach²

¹Centre de Biophysique Moléculaire, CNRS, Orléans, France

²Ecole Polytechnique Fédérale de Lausanne, Lausanne, Switzerland

2.1 Introduction

The aim of using a contrast agent in Magnetic Resonance Imaging is to accelerate the relaxation of water protons in the surrounding tissue. This objective can be achieved by paramagnetic substances. In 1948, Bloch et al. reported the use of the paramagnetic ferric nitrate salt to enhance the relaxation rates of water protons [1]. Some 30 years later, Lauterbur et al. applied a Mn(II) salt to distinguish between different tissues based on the differential relaxation times and thus produced the first MR image [2]. Nowadays, Gd(III) complexes are far the most widely used MRI contrast agents in the clinical practice. The choice of Gd(III) is explained by its seven unpaired electrons which makes it the most paramagnetic stable metal ion. Beside this, Gd(III) has another significant feature: owing to the symmetric S-state, its electronic relaxation is relatively slow which is relevant to its efficiency as an MRI contrast agent.

As most of the current contrast agent applications in MRI concerns Gd(III) complexes, this chapter will 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 the case had manganese been administered as a simple salt, such as manganese chloride.

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

The general theory of solvent nuclear relaxation in the presence of paramagnetic substances was developed by Bloembergen, Solomon and others [15–20]. A Gd(III) complex induces an increase of both the longitudinal and transverse relaxation rates, 1/T1 and 1/T2, respectively, of the solvent nuclei. The observed solvent relaxation rate, 1/Ti,obs, is the sum of the diamagnetic (1/Ti,d) and paramagnetic (1/Ti,p) relaxation rates:

2.1

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/Ti,d, corresponds to the relaxation rate of the solvent (water) nuclei in the absence of a paramagnetic solute. The paramagnetic term, 1/Ti,p, gives the relaxation rate enhancement caused by the paramagnetic substance which is linearly proportional to the concentration of the paramagnetic species, [Gd]:

2.2

In Equation (2.2), the concentration is usually given in millimoles per litre (mmol l−1); for nondilute systems the linear relationship is valid only if the concentration is expressed in millimoles per kilogram solvent (mmol−1 kg−1; millimolality). According to Equation (2.2), a plot of the observed relaxation rates versus the concentration of the paramagnetic species gives a straight line and its slope defines the relaxivity, ri (in units of mM−1 s−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 to act as a contrast agent. It has to be noted that the simple term relaxivity is often used in the context of MRI contrast agents and refers to longitudinal proton relaxivity even if the adjectives are omitted. In the following, we deal primarily with the theory of proton relaxation in the presence of Gd(III)-containing paramagnetic species.

The paramagnetic relaxation of the water protons originates from the dipole–dipole (DD) interactions between 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, specific chemical interactions that bring the water protons into the immediate proximity of the metal ion play an important 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 this way the paramagnetic influence is propagated to the bulk. This mechanism is depicted as the inner-sphere contribution to the overall proton relaxivity (Figure 2.1). Solvent molecules of the bulk also experience the paramagnetic effect when they diffuse in the surroundings of the paramagnetic centre. The effect of the random translational diffusion is defined as outer-sphere relaxation. Thus we separate the inner- and outer-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 Equation (2.3), or expressed in relaxivities in Equation (2.4):

2.3

2.4

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

Figure 2.1 Schematic representation of a Gd(III) chelate with one inner-sphere water molecule, surrounded by bulk water. τR refers to the rotational correlation time of the molecule, kex to the water/proton exchange rate and T1,2e to the relaxation times of the Gd(III) electron spin.

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For certain agents, solvent molecules that are not directly bound in the first coordination sphere may also remain in the proximity of the paramagnetic metal for a relatively long time, for example due to hydrogen bridges to the ligand (e.g., to its carboxylate or phosphonate groups) or to the solvent molecule(s) in the first 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 the inner-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.

Figure 2.2 Three different types of water molecules around a Gd(III) complex as obtained by molecular dynamics simulation of [Gd(DOTA)(H2O)]− in aqueous solution. The inner-sphere water is directly coordinated to the metal (its oxygen is red). Second-sphere water molecules are on the hydrophilic side of the complex, close to the carboxylate groups. They are oriented with their