MRI of Tissues with Short T2s or T2*s

The content of this volume has been added to eMagRes (formerly Encyclopedia of Magnetic Resonance) - the ultimate online resource for NMR and MRI.

Up to now MRI could not be used clinically for imaging fine structures of bones or muscles. Since the late 1990s however, the scene has changed dramatically. In particular, Graeme Bydder and his many collaborators have demonstrated the possibility – and importance – of imaging structures in the body that were previously regarded as being “MR Invisible”. The images obtained with a variety of these newly developed methods exhibit complex contrast, resulting in a new quality of images for a wide range of new applications.

This Handbook is designed to enable the radiology community to begin their assessment of how best to exploit these new capabilities. It is organised in four major sections – the first of which, after an Introduction, deals with the basic science underlying the rest of the contents of the Handbook. The second, larger, section describes the techniques which are used in recovering the short T2 and T2* data from which the images are reconstructed. The third and fourth sections present a range of applications of the methods described earlier. The third section deals with pre-clinical uses and studies, while the final section describes a range of clinical applications. It is this last section that will surely have the biggest impact on the development in the next few years as the huge promise of Short T2 and T2* Imaging will be exploited to the benefit of patients.

In many instances, the authors of an article are the only research group who have published on the topic they describe. This demonstrates that this Handbook presents a range of methods and applications with a huge potential for future developments.

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• Language: English
• Publisher: Wiley
• Release date: Dec 19, 2012
• ISBN: 9781118590515

Book preview

PART A

Basic Science

Chapter 1

An Introduction to Short and Ultrashort T2/T2∗ Echo Time (UTE) Imaging

Ian R. Young

Department of Electrical and Electronic Engineering, Imperial College London, London SW7 2AZ, UK

1.1 INTRODUCTION

Imaging of short T2/T2∗ tissues and fluids is often made possible by the use of short or ultrashort echo time (UTE) pulse sequences. There is no convenient, generally accepted definition of what is meant by an UTE or short echo time imaging. The claim that a particular echo time (TE) is ultrashort (the origin of the abbreviation UTE) is not quantitative, and what may seem extremely short or ultrashort to one group of scientists may appear sluggish and pedestrian to another. Solid-state investigators may regard the shortest times yet used in imaging as being quite unworthy of the title ultrashort. In this handbook, we have chosen to concentrate on the study of tissues and structures in human and animal subjects which have such short T2 and/or T2∗ values that signals from them are not observed with conventional, clinical imaging techniques. This is an elastic definition, since the TE values used for some types of cardiac imaging are very short compared with those that are used for diagnosing tumors. The use of the definition we have employed means that, in addition to those tissues or fluid components that do genuinely have very short T2s, we can logically include the effects of susceptibility, which can radically attenuate the signals from tissues with relatively long T2s.

A useful rule of thumb to describe the magnitudes of T2 and T2∗ is to name values in the range 1–10 ms as being short, those in the range 0.1–1 ms as being ultrashort, and those of less than 0.1 ms as supershort.¹ It is also helpful to have the option to include longer (but still relatively short) T2s such as those found in myelin water in the overall picture. Solid-state and ESR investigators might regard these definitions as being frivolous since the T2s they deal with are often measured in microseconds, but the grouping does have significance in the field of in vivo biological MRI and MRS where it largely determines the application of different classes of pulse sequences. We shall base our definitions in this handbook on these values because they make sense in the context of the development of UTE imaging applications to clinical MR.

Though the focus of this handbook is on the proton imaging of tissue, it does describe studies with nuclei other than protons which are generally investigated using spectroscopic methods. In reality, the abundance of some nuclei often thought of as being present in very small quantities may be very much greater in some tissues when they are observed using UTE techniques.² Figure 1.1 is an example of this. It is a phosphorous image. The ³¹P concentration of muscle metabolites – the normal subject of musculoskeletal MRI and MRS – is in the millimolar range. The bound phosphorous in cortical bone is present in molar concentration and can readily be imaged by the UTE methods discussed in this handbook. Though the primary aim of the book is to provide a comprehensive picture of the current state, and future possibilities of the UTE imaging of tissue, the methods employed are clearly relevant to the imaging of any fluids and materials containing short T2 and T2∗ components. Consequently, there are brief mentions of topics such as ESR imaging and imaging techniques using potentially large RF power levels. These may be barely relevant to human or animal imaging at present, but such is the speed and extent of the evolution of MRI that they could become important within a short time.

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Figure 1.1. ³¹P image of the leg of a volunteer, to illustrate the way in which a new imaging technique (in this case a variant of UTE imaging) can change perceptions of a tissue. Phosphorous is normally regarded as a spectroscopic nucleus, and it is a major shift of focus to see it as a perfectly good imaging nucleus. (a) Proton image. (b) Phosphorus image. (Reproduced from Ref. 2. © John Wiley & Sons, Ltd., 2004.)

The purpose of this introductory chapter is to provide a brief overview of the subject, and offer guidance to readers as to where they may find much more rigorous treatments of the topics described in it. It also aims to provide insight into why the handbook has been structured the way it has been, and to show how the various disparate approaches to detecting very fast decaying components are part of a coherent picture. At the time of writing, early 2012, the topic as a whole is still developing rapidly and only a few specific applications are available from the major manufacturers for immediate incorporation into standard clinical protocols. This means that any attempt to record the range and extent of short T2/T2∗ imaging may be outdated within a relatively short period when these techniques become more available. However, in order to speed progress, it is helpful to describe the many different aspects of the field in a single volume, and make it available to the MR community as quickly as possible.

1.2 STRUCTURE OF THE HANDBOOK

The book covers four main topics. The first section addresses the mechanisms that lead to shortened values of the two time constants that are the subject of the book. These cannot cover the whole range of such mechanisms in a fundamental way, but highlight factors most relevant to the technical approaches that have been designed and used in clinical studies. The next section of this handbook describes the techniques used in various forms of short and ultra-short component imaging, and includes a description of the kinds of problem likely to be faced in the implementation of short T2/T2∗ imaging techniques on otherwise conventional MRI equipment. The third part describes applications of short T2/T2∗ imaging techniques to animal and other non-human studies, while the last section briefly reviews clinical applications of the methods described as of the time of writing, as well as some indication of what may emerge in the near future. Forecasting the way in which MRI will evolve has never been a particularly accurate or fruitful endeavor but it does seem justifiable in the context of a major new extension to current practice.

1.3 MECHANISMS AND EXTENT OF SHORT T2 AND T2∗ TISSUE AND FLUID COMPONENTS

Though it is frequently impracticable to separate the approaches to recovering signals from components with short T2s from those with short T2∗s, scientists working with them have, possibly unwittingly, established a distinction between the two. T2 variations are due to molecular and nuclear phenomena, but T2∗ effects include macroscopic susceptibility effects, as well as microscopic ones – where the smallest components involved include the superparamagnetic nanoparticles used in one form of contrast agent. In conventional MRI, the distinction between the two is that signal can be recovered in the case of susceptibility effects by inverting the magnetization which refocuses after the same time as it was originally allowed to dephase. Signals lost through T2 relaxation are irrecoverable by this means, as, in practice, are signals lost through T2∗ effects if they are such that the time constant is very short, and/or random, or other motion effects destroy signal coherence. The mechanisms resulting in very rapid decays of the signals from an excited spin array are discussed in two of the first chapters (see Chapters 2 and 3).

The vast majority of tissues have more than one transverse relaxation component from which signals can be recovered, and the relaxation behaviors of these components are frequently markedly different. Commonly, there are the signals from largely free (loosely bound or unbound) components which are the basis of conventional clinical MRI, but it has always been apparent that there was additional data to be obtained from more rigid structures such as cell walls and from the free water components in structures such as cortical bone. It has been estimated that at least 20% to 30% of the hydrogen signal is not detected even in tissues which are normally considered to provide data of good quality in clinical MRI.³

It is not appropriate here to go into the extensive theory of the relaxation behavior of nuclei excited in an NMR experiment (those interested in further understanding of the processes involved are recommended to consult a major text book such as Abragam⁴ or study Chapters 2 and 3 in this handbook), but it is relevant to cite a small fraction of the key relationships in a simplified form to emphasize aspects that are particularly important.

In a rigid lattice, the coupling W between a pair of dipoles is given by the long-established relationship

(1.1) 1.1

where r is the distance between the interacting dipoles, which are assumed to be dissimilar, I is the spin operator; h is Planck’s constant, and γ1 and γ2 are the relevant gyromagnetic ratios.

This relationship, which can be evaluated for similar spins to give the familiar coupling term (3cos²θ − 1), turns out to have more significance in biological MR than is found in most liquid-based systems. This is because collagen-rich tissues in particular contain a structured matrix that is reminiscent of a crystal, with angles between neighboring nuclei that are relatively consistent. As discussed much more fully in Chapter 4, this possibility can be exploited to study the apparent T2 of tissues such as tendons as their angles relative to the static magnetic field are varied, providing new observations about tissue and a technique for imaging the short T2 components in tissue. The problems involved with this approach are not those of data recovery speed, but the very restricted environment of the imaging volume of typical MRI scanners which can make the necessary orientations of the tissue being studied impracticable at worst, or clumsy and uncomfortable for the subject being scanned at best.

In tissues, many of the sources of signals with very short T2s are protons located in the large molecules of the cell walls and other structures. The magnitude of both the nuclear coupling and other thermal interactions can be assessed experimentally for typical structures in tissue, but a theoretical analysis involves the need to establish too many very hard-to-measure parameters. There is invariably a multiplicity of factors affecting the behaviour of a spin species, and while their specific contributions to the observed value may be of considerable interest, this information is of little help to the imager who is forced to deal with whatever is present in the incompletely characterized system that is tissue. Another way of looking at this is to observe that all tissues have multiexponential transverse relaxation times – as is clearly the case of any tissue containing free water and cells. One of the main impacts of UTE imaging is that it emphasizes this point – which is often ignored in the everyday practice of clinical MRI.

The relationship between T2 and T2∗ is conventionally expressed as

(1.2) 1.2

where tprime2 is the effective transverse relaxation time due to field deviations inside the volume of interest. More commonly, 1/ tprime2 = γδB0, where γ is the gyromagnetic ratio and δB0 is the field deviation across the volume of a voxel, though, more correctly, this term is an integral of field levels and the fraction of the voxel at each field level in the range. The key term in the relationship is that describing the field variation (δB0). The scale of the susceptibility variations ranges from macromolecular (which is the situation with superparamagnetic particle-based contrast agents known as MIOPS (discussed fully in Chapter 22)) to variations that can have dimensions of many tens of millimeters (due to machine imperfections, implants, or sizable structures such as the sinuses, or tissues such as liver). It is hard, and not very productive, to try to model the impact of complex structures of differing susceptibilities on local field levels and predict signal performance from that data. The impact of susceptibility variations are complex and depend on their extent and magnitude, as well as other changes in their neighborhood, and little of this information is accurately known in most imaging situations. A few guidelines are available, and helpful, but not many. For example, there are more ways of coping with large-scale effects than there are with small ones. At the simplest level, reducing the volume from which the signal is being recovered can result in improved image performance⁵ as long as the periodicity of the susceptibility change is at least of similar size to, or greater than, the signal source (noting that, in imaging terms, the signal source is a voxel). Because a consequence of variations in the magnetic field is a corresponding spread of resonance frequencies, it may be possible to observe phase differences between signals from differing locations, offering another approach to imaging in the presence of susceptibility variations.⁶ As the handbook suggests (see Chapters 12, 17, 22 and 34) there are a variety of approaches to the problem of obtaining useful clinical data in the presence of significant susceptibility variations. The underlying strategies tends to be similar – recover enough data to try and correct spatial distortions, then over-sample space to obtain enough data to process using this information.

Nuclei couple in a variety of ways with all parts of the lattice. In principle, it is practical to study the consequences of those interactions, and some of the strategies for imaging short T2 components discussed in this handbook (see Chapters 16 and 21) are based on this approach. The information obtained can be very useful, but the range of different values obtainable from any one study can be quite limited.

1.4 TECHNIQUES FOR IMAGING TISSUE COMPONENTS WITH SHORT T2 AND/OR T2∗

The first chapters of this book review the phenomena that result in very rapidly decaying signals, essentially covering the ground outlined in the previous section of this article. The next group of contributions describe methods that can be used to obtain useful data, noting that though their descriptions are couched in terms of human (and animal) biology they are in normal circumstances relevant to the imaging of anything with appropriate relaxation behavior.

Designing sequences to recover data from very short T2 components involves facing up to a number of problems that do not exist in other forms of clinical MRI. For example, signal relaxation times are often short compared with the duration of typical pulses. Most importantly, substantial relaxation can occur during the exciting RF pulse. As has been reported in the literature,⁷ the flip angles achieved in these circumstances can be quite different from those that might have been predicted in more normal situations. This is illustrated in Figure 1.2, which shows how the effective flip angles are affected by the magnitude of the T2 of the tissue being studied. The simplest approach to this problem might seem at first sight to increase the RF field amplitude while reducing the pulse duration. The problem with this strategy is that RF power deposition increases as the square of the pulse amplitude, while a reduction in duration affects the excitation angle linearly, so that increasing amplitude results in a linear increase in deposited power (since the integral of pulse amplitude with time must be constant for a given flip angle).

Data recovery, too, requires very different approaches to those employed in the vast majority of clinical studies. The duration of a phase encoding pulse (as used in one form or another in all acquisition methods in which k-space is filled by parallel lines of data points from the original spin warp sequence⁸ through to more sophisticated approaches such as echo planar imaging⁹) is such that, even at its shortest, too much signal decay occurs during phase encoding to allow the acquisition of really short T2 components. This suggests that data acquisition should begin as soon as the excitation finishes and detection circuitry can be enabled. The center of k-space can be acquired in the absence of any encoding gradients as soon as any slice-selective gradient decays to zero, and further data points can be recovered as those gradients needed for spatial discrimination are applied. Some form of radial data acquisition is usually used, since these can all be arranged to avoid the phase-encoding step which necessarily takes significant time in the context of transverse relaxation times of a millisecond or less. This is in spite of the fact that more angular projections are needed to cover an n × n image matrix than if the same image range is recovered using a conventional rectangular k-space coverage (by a factor of π/2, even employing the full benefits of conjugate symmetry). This emphasizes the need to exploit every means of accelerating data recovery that is available, as it must be assumed that only one line of k-space can be recovered from each spin excitation. The use of array coils to exploit the acceleration of image recovery offered by array coil-based techniques such as SENSE¹⁰ (in particular) or SMASH¹¹ is very desirable wherever practicable, and, in future, the use of sparse sampling methods¹² will surely receive – and justify – substantial investigation of time saved against image quality in UTE imaging. While the latter technique is readily applicable to radial scanning, it is not obvious how to exploit array coil technology in this form of imaging, though there are studies that do suggest how progress might be achieved.¹³

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Figure 1.2. Plot showing how the effective flip angle is affected by tissue T2 during the excitation process. The figure shows the actual level of Mxy that is achieved for various flip angles up to 90° for materials with different T2 values. This is a theoretical model and was developed by Dr. Matthew Robson, Cardiovascular Unit, University of Oxford, UK, who very kindly supplied the figure.

The approaches that have been, or might be, investigated for imaging very short T2/T2∗ components are quite numerous. They include data acquisition methods, ways of increasing T1/T2∗, and methods for developing contrast in short T2/T2∗ images. Examples include the following:

1. Direct recovery of data from the short components fast enough for the effects of their rapid decay to be minimized so that significant signals can be recovered and reconstructed.

2. Exploitation of the dipolar coupling found in molecules such as, most importantly, collagen. This can be used to increase T2/T2∗ to make signal detection easier and to create useful contrast.

3. Use of magnetization transfer methods to image short T2/T2∗ components by exploiting the coupling between protons that are subsequently visible and those that are invisible, but affect the detected signal.

4. Exploring the dispersion characteristics of T1ρ which can reveal information about coupling effects.

5. Use of multiple and zero quantum effects to reveal data about molecules that are otherwise very difficult, or impossible, to detect in imaging systems.

6. Methods that use multiple RF pulses usually interleaving them with signal recovery at rates which are very much greater than with other forms of imaging.

7. Absorption methods that are normally thought of as being most appropriate for ESR imaging but which could have a significant role in MRI also.

It should be remembered that this list encompasses only techniques for magnetization preparation, or actual data recovery. In principle, most of the methods result in amplitude and phase data describing the signals detected. Beginning with this data, signal processing can be used to obtain a wide variety of different image presentations. In addition, data can be corrected for the effects of susceptibility variations whether due to the small but still signifi-cant differences between tissues and relative to air, or to the much larger effects of superparamagnetic particle-based contrast agents and implanted metallic prosthetic devices. Presentation of the data can be very different (for example, the use of positive contrast – effectively inverting the conventional form of display), and it is likely that many more methods of this type will be investigated.

In many ways, though, acquisition is key to what is achieved, including the recovery of several sets of data after the same excitation. Thus, it can be very productive to acquire more than one echo in a UTE study, since this allows the identification of the various tissue components and the quantification of those with particular T2s.¹⁴ Figure 1.3 illustrates results from such a study. However, it is currently hard to envisage how several different components all with very short T2s can be recovered and resolved in the time available in clinical MRI.

As has been mentioned previously, tissues in which molecules such as those of collagen are highly geometrically organized exhibit marked variations in effective T2 depending on their orientation relative to the applied magnetic field. Fullerton and coworkers demonstrated the extent of the changes that can be expected very early in the development of MRI,¹⁵ though little interest was taken in exploiting the phenomenon for imaging purposes.¹⁶ When appropriately aligned, the T2 of tissues such as tendon may change from the 1–2 ms observed with fibers parallel to B0 to in excess of 20 ms at the magic angle where conventional sequences can be used to image them. As will be discussed later, the configuration of typical MR systems is the main impediment to much fuller application of this type of investigation.

Though, in theory, much data of great interest might be detected using different contrast mechanisms (e.g., magnetization transfer, T1ρ dispersion, zero and multiple quantum coherence effects, and the use of strong off-resonance RF fields), relatively little work has been done in these areas. This is at least in part due to the extended scanning times that are required if enough data is to be recovered for detailed analysis.

Beyond methods that are, in reality, just variations of conventional imaging (including some approaches that have not been applied since the very early days of MRI, as Chapter 5 describes) in which novel pulse structures are used to reduce TE to tens of microseconds, there are other approaches that lean much more on the extensive studies of ESR imaging or the RF-intense methods used in high-resolution studies. Some of the latter are being actively pursued in the imaging of short T2 components, and are described in this handbook (see Chapter 14). The limitation on the use of RF-based methods, as with many other potentially useful approaches, is safety requirements. Because power deposition increases as the square of the RF pulse amplitude, the use of very short but intense RF pulses can easily exceed the maximum permitted dose, particularly at higher field strengths. In principle, any degree of excess power deposition can be avoided by extending TR (as deposition limits are determined by a set of simple time averages), but this can make some studies intolerably long, and machine manufacturers try to limit peak RF power to minimize the risk of any breach of guidelines such as those implemented by the Food and Drug Administration (FDA) and the European Union (EU). Furthermore, as is noted in Chapter 13, one of the little recognized problems in imaging patients with implants in situ is that these can significantly distort the RF excitation field, so that when the effects due to susceptibility have been addressed, there are still problems with image contrast as the expected flip angles are not achieved.

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Figure 1.3. Selected 2D UTE imaging of a bovine cortical bone sample with TEs of 8 ms (A), 0.2 ms (B), 0.4 ms (C), 0.6 ms (D), 0.8 ms (E), 1.2 ms (F), 1.6 ms (G), 2.0 ms (H), 3.0 ms (I), 4.0 ms (J), 5 ms (K), and 6 ms (L), single-component fitting (M) and the corresponding fitting residuals (N), and bicomponent fitting (O) and the corresponding fitting residuals (P). Single-component fitting shows significant residual signal (up to 5%). The residual signal is reduced to 0.3% by bicomponent fitting, which shows a short T2* of 0.29 ms and a long T2* of 2.81 ms with respective fractions of 88.6% and 11.4% by volume. Data supplied by Drs. J. Du and G.M. Bydder. (Reproduced from Ref. 14. © John Wiley & Sons, 2011.)

The final category – the absorption approach – is closely related to ESR imaging. While it would be extremely interesting to be able to generate maps of free-radical distribution in vivo in humans (for example), it still seems likely that this is may not be achieved within the foreseeable future.

1.5 PRACTICAL IMPLEMENTATION

The tools that are available to physicists faced with the task of implementing sequences that will image short transverse relaxation components are essentially the same as those available to any other machine user. As yet (early 2012), only a limited number of machines with hardware capabilities specifically aimed at improved UTE imaging are available. It is only the evolution and improvement of MRI systems that has provided the basis for this form of imaging, and it would be idle to pretend that satisfactory UTE imaging can be achieved on machines with specifications substantially less good than the best of those available today. However, as Chapter 7 describes, there is still a major gulf to be crossed in developing short T2/T2∗ imaging on a platform with all the necessary and desirable properties. Writing down the bare bones of the sequences to be used presents few difficulties. Implementing them, and eliminating the inevitable clutch of artefacts that follows their operation, can be a very different thing.

Intuitively, it is obvious that all operations must be carried out as fast as possible, but this alone is not enough. As Pauly and colleagues have shown,¹⁷ and as is described in detail in Chapter 6, the typical imaging sequence has to be broken down to its component parts, each of which has then to be constructed to perform well enough to observe short T2 components.

The traditional approach to slice selection in which the RF excitation pulse is applied in the presence of a gradient means that at its end all the magnetization has dephased resulting in little or no resultant signal. This is then followed by a reversed gradient pulse to restore the situation, which works beautifully as long as the transverse relaxation times of the components being investigated are long compared with the pulse durations. In UTE imaging, such an approach – even with the most effective machine components available – could still result in little or no signal. Instead, the kind of approach described in Chapter 6, in which the slice is assembled from composite pulses, usually results in the recovery of data of value.

Similarly, the standard spin-warp kind of data recovery, in which one axis of a planar image is encoded via a range of gradient prepulses while the other axis is read out in the presence of a fixed gradient pulse (itself requiring some form of prepulse), results in time delays before data can actually be recovered, which means that most of the data that is most relevant to short T2/T2∗ imaging is lost (see Chapters 6 and 8). Ideally, the data point at the center of k-space is acquired immediately after the cessation of the RF pulse. At this time, the readout gradient should also be started, with some data points being recovered as it increases to its final amplitude. This results in the need to vary the rate of the data sampling points. This procedure has been used since the very early days of MRI¹⁸ and its problems are well understood and readily solvable. In practice, such an approach can only be accommodated by one or the other of the radial scanning methods, though the rapid decay of the signal may restrict the general applicability of methods such as spiral¹⁹ (though as Chapters 5 and 9 show, this strategy can be applied in various ways), propeller,²⁰ and other hybrid strategies. However, these can also provide valuable results in some applications, as is illustrated in the chapter on sodium imaging (see Chapter 30). Radial scanning has advantages – relatively robust performance in the presence of patient motion, oversampling with consequent improvement in signal-to-noise ratio near the center of the image, and relatively benign use of gradients – but it also has problems. Most basic of these is that it requires more excitations to cover the same array of data points as is covered with spin-warp imaging and its derivatives. As noted earlier, in order to cover an n × n matrix, the latter requires collection of n lines of k-space data, while a radial scan needs a minimum of πn/2 lines and the use of conjugate symmetry to perform the same task. UTE imaging generates one line of k-space from each pair of excitations, which is a substantial potential penalty and so is justifiable only if the data that is recovered is significant (something that is helped by way in which the excess acquisitions improve the central parts of images). The form of the data recovery also does not lend itself to the receiver coil array techniques such as SENSE¹¹ and SMASH¹⁰ and their derivatives, so that useful acceleration is very hard to achieve though not impossible.¹³

In principle, this approach to imaging short T2 components and the indirect methods using traditional MR approaches involve no specialist hardware. Other possible lines of attack can do so. Thus, magic angle imaging can be performed without the aid of supporting instrumentation, but it seems likely that it will be more useful with it. As yet, however, progress in this direction has been relatively slight, with only one group having published a description of prototype devices.²¹ However, as is apparent from Ref. 21, the cylindrical form of most MRI systems, with diameters of 70 cm or at best just a little more, places major restrictions on the range of studies that are possible. Most interest in this area of activity focuses on tendons and cartilage, and thus on the musculoskeletal system, though, currently, magic angle studies of many important structures are impracticable. However, as Fullerton and his group have demonstrated,¹⁵ much can be learnt from these experiments, and it is to be hoped that suitable systems will be developed to exploit the clinical potential that is there.²²–²⁴ Figure 1.4 illustrates the possibilities that exist in this area, though realization lags far behind promise.

The RF systems supplied with typical clinical scanners are very circumscribed in their performance, affecting the use of methods demanding high levels of RF energy, as described in Chapter 10. This situation arises from the requirements of the various regulators and is exacerbated as the level of B0 increases. In reality, since there seems no question of the emergence as yet of any credible model for the effects of RF radiation on the body other than the thermal one, very much larger RF fields could be made available to users as long as the repetition time of components of studies, and indeed of studies themselves, was made sufficiently great. The use of array transmitters may also be helpful since, unlike the more usual application of these systems (which is to make the RF field as homogeneous as possible in a situation where there is significant absorption), it may be possible to shape the RF field to minimize it outside the region of immediate interest.

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Figure 1.4. Composite figure to illustrate results from the use of robotic assistance in magic angle studies. (a) Photograph of the equipment used in the magic angle studies the results of which are shown here. (b) Image taken with the Achilles tendon lying roughly parallel to the main field. (c) Image of the same section acquired with the tendon at about 55° to the main field. (d) Plots of signal against angle for three different volunteers, where the data was obtained using a unit like that shown. (Partly reprinted from Tse ZTH, et al., IEEE/ASME Transactions on Mechatronics, 2008, 13, 316–324 with permission.)

Short T2/T2∗ imaging has reawakened interest in tissue time constants, as well as in the signal manipulation and image processing that are necessary to distinguish the multiple components that are routinely observed with this type of imaging (as is discussed in Chapter 18). Contrast management is, of course, another aspect of these processes as is described in Chapter 15. Increasingly, it is likely that sparse sampling methods will be used in UTE imaging, and it is quite likely that specialized approaches will be developed to cater to the combined problems of being only able to collect a limited amount of data from each excitation and the need to allow significant TR for magnetization recovery.

1.6 APPLICATIONS

It is surprising how extensively short T2/T2∗ imaging techniques (in the broadest definition of the title) have been used already, bearing in mind the very limited resources that are yet available. The number of workers who have well-functioning imaging capabilities of this type is still small, and most of the application papers have come from this minority. This handbook aims to give coverage of what has already been achieved and, on occasion, suggests what may be possible in the near future.

The editors of this handbook have used some licence in their approach to applications. Nuclei other than hydrogen are covered (phosphorus and sodium in Chapters 25 and 30, respectively, and sodium and oxygen in a different context in Chapter 29), though their transverse relaxation time constants are, in some instances, not so very short. However, it is arguable that some of the most promising imaging results have been obtained from the use of UTE techniques in their study.

Many of the most practical UTE imaging studies have been aimed at T2∗ effects. These were really initiated by observations of trabecular bone (see Chapter 24), then moved on to understanding and controlling the impact of contrast agents based on superparamagnetic particles as described in Chapter 22. Finally, workers have demonstrated how to image in the presence of metal prostheses which have susceptibilities very different to those of the surrounding tissue (see Chapter 12). All of these are very practical applications, and can be expected to deliver valuable diagnostic information from the very start of their clinical application. However, as is so often the case with MRI, quantification of the observed effects can be complicated by artefacts – and, to illustrate this, this handbook includes a chapter on the distortions of the RF field caused by otherwise MR-compatible prostheses which will result in incorrect contrast behavior (see Chapter 13). Nevertheless, it is already apparent how much more data can be obtained about bone using UTE methods, leading both to fruitful research as well as clinical benefit for patients with studies using both proton and phosphorous imaging.

Magic angle studies are described by Fullerton and coworkers, who first observed the phenomena in excised tissue and have developed their original work to reveal much new information.²⁵ Regrettably in many ways, this work has involved few other investigators²²–²⁴ in what is potentially a very productive field, though the reasons for this slow progress have been hinted at in the Section 1.5, which points out the limitations imposed on studies by the lack of space in which to perform them.

Much of the clinical evaluation of techniques described in this handbook exploits the techniques described, and largely introduced, by Pauly and his colleagues (see Chapter 6). Though many of the earliest studies were of the musculoskeletal system,²⁶,²⁷ as Chapters 21, 24, 26 and 27 show, UTE imaging has proved to be a powerful tool in many parts of the body.²⁸,²⁹ Excellent examples of this work are to be found in Chapters 23 and 28, while Chapters 31 and 32 are disease-oriented – respectively dealing with cancer and aspects of cardiovascular disease. However, this is still early in the evolution and application of short T2/T2∗ imaging, and many of the authors concerned are the only people who have published results of research on their chosen topic.

The same is true of applications of short T2/T2∗ imaging techniques to situations that have been handled by other methods in the past but where workers have seen that improved performance can be achieved if these methods are applied. The imaging of very fast flows is one such example, as is demonstrated in Chapter 20. Similarly, the application of UTE imaging to MRI/PET (positron emission tomography) is another case where there is no a priori reason why the UTE approach should be adopted, but its use results in much more satisfactory performance, as is pointed out in Chapter 19 while significant benefits have also been found from the use of UTE imaging methods to monitor cryotherapy (see Chapter 33). It is reasonable to expect that other similar applications will emerge during the next very few years.

A few of the chapters are avowedly forward looking – estimating the future impact of short T2/T2∗ imaging in applications in which significant results may be expected. If this type of imaging were to make a significant contribution to the diagnosis of cancer (see Chapter 32), or prove capable of routinely identifying calcification (see Chapter 31), it would accelerate its adoption into clinical practice to an extent that could surprise the whole MRI community.

1.7 CONCLUSION

This introductory chapter is intended to provide an overview of this handbook as a whole. It has avoided detail in places where a full chapter covers a topic much more extensively than is appropriate here. It is, the author believes, a demonstration of the extent to which we are only at the beginning of what may very well become both an extensive and clinically significant component of MRI. As Chapter 7 makes clear, the implementation of appropriate techniques on clinical scanners is not a trivial task, so that around 20 years from the original demonstration of the effectiveness of the approach it is still unusual to buy a standard machine with the capability for UTE imaging installed on it.

MRI, building on its NMR heritage, has proved to be extraordinarily productive (as its parent has been as well), and we can look forward with confidence to the development of UTE imaging into a major component of clinical investigations.

RELATED ARTICLES IN THE ENCYCLOPEDIA OF MAGNETIC RESONANCE

Imaging of Trabecular Bone

Imaging of Wide-Band Systems by Line-Narrowing Methods

Imaging Techniques for Solids and Quasi-solids

Projection–Reconstruction in MRI

Radiofrequency Fields: Interactions, Biological Effects, and Safety Issues

Spatial Encoding Using Multiple rf Coils: SMASH Imaging and Parallel MRI

Susceptibility Effects in Whole Body Experiments

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Chapter 2

The Physics of Relaxation

John C. Gore and Adam W. Anderson

Institute of Imaging Science, Vanderbilt University, Nashville, TN, 37232, USA

2.1 INTRODUCTION

There are many different varieties of magnetic resonance images, corresponding to an array of tissue nuclear magnetic resonance (NMR) properties, which may provide information on tissue microstructure, physiology, biophysics, or composition. In principle, the methods used to spatially encode and reconstruct NMR information for imaging are very similar for recording quite different NMR properties, but the manner in which such properties affect the NMR signal controls the image contrast and the nature of the information obtained. Ultrashort echo-time (UTE) imaging attempts to selectively detect and map protons whose transverse relaxation times span a specific range, typically much shorter than the majority of signals from tissue water which dominate conventional images. Their separability indicates that within a tissue volume there exist different subpopulations of protons—some in water (those water molecules themselves may be in multiple different environments) and others perhaps in lipids, proteins, other molecules—so that transverse relaxation involves multiple components and not a simple exponential decay. The identification and characteristics of those subpopulations is a continuing topic of intense research and interest, but before later chapters introduce specific discussions of UTE signals, here we consider the basic physics of relaxation of the nuclear magnetization of hydrogen protons in tissue water and other molecules in an attempt to set the basis for understanding how the peculiar properties of UTE signals may arise.

Relaxation processes are important in conventional magnetic resonance imaging (MRI) because much of the contrast that is apparent in clinical MR images of soft tissues used for radiological diagnoses usually arises from the heterogeneous distribution of tissue proton relaxation times. The sensitivity of MRI to pathological changes and variations in tissue composition, which underlies its clinical usefulness, most often relies on detecting small changes in tissue water relaxation rates. Therefore, it is of practical importance to understand the mechanisms responsible for proton relaxation in heterogeneous media such as tissues, and to be able to explain the changes that occur in tissue relaxation in the diseased state. In addition, relaxation times set limits on the speed of imaging and other aspects of image quality. We first will provide a theoretical description and background to the physical processes that account for proton relaxation in water, though the same principles may apply to protons in other molecules. It should be emphasized that many detailed aspects of relaxation in complex biological media are not well understood in a quantitative sense, by which we mean there do not exist adequate models that can be used to account precisely for the observed relaxation in many practical cases. Furthermore, since tissues are heterogeneous, have complex internal structures, and vary widely in their detailed composition, and because different pathological processes involve different types of change in tissue composition and character, it is often not possible to explain observations of changes in relaxation in terms of specific underlying causes. However, we do possess a reasonably complete understanding of the various processes and factors that contribute to relaxation in simple solutions and aqueous biological media, and these are described in the following in some detail. Changes in relaxation that occur, for example in disease, will then correspond to structural or chemical modifications, which in turn modulate one or more of these contributing processes. Furthermore, from these simple media, the origins of UTE signals may also be understood.

In this chapter, the concepts of relaxation are first reviewed, and the atomic view of relaxation of protons in simple homogeneous liquids is described. We use a simple extension of the Bloch equations to derive expressions for T1 and T2 in water. Human tissues are 70–90% comprised of water, so most signals in conventional MRI are derived from water, and understanding relaxation in pure water is a useful first step to understand relaxation in more complex situations. For more complete descriptions of relaxation, the interested reader may consult several excellent texts including those by Levitt,¹ Cowan,² Carrington and McLachlan,³ and Ferrar and Becker.⁴

2.2 CLASSICAL DESCRIPTION OF RELAXATION IN SOLUTIONS

Relaxation connotes the recovery back toward equilibrium of the magnetic state of a system of nuclear dipoles that have been disturbed by radio frequency (RF) excitations. First, we consider some underlying basic concepts of nuclear magnetization and magnetic resonance. From a simple quantum mechanical viewpoint, NMR experiments involve inducing transitions between energy states, which correspond to different nuclear spin orientations. For hydrogen nuclei with spin = 1/2, in equilibrium in a magnetic field, there are two such allowed energy levels, and the lower energy level is more populated so that there is a macroscopic magnetization. For a nucleus with magnetic dipole moment μ (= 1/2γ ħ for protons, where γ is the gyromagnetic ratio and ħ is the Planck constant) in a magnetic field B, transitions between the allowed energy levels may be induced by absorption or emission of quanta with energy ΔE, that is

(2.1) 2.1

where ω0 = γB is the resonant frequency. The spin system can absorb energy so that the population of the upper energy level increases while that of the lower level decreases. If the energy absorbed is sufficient to equalize the populations of the two levels, saturation is said to have occurred, and no further absorption will take place. A completely or partially saturated system will return to equilibrium because of two simultaneous processes. First, the absorbed energy will be redistributed within the spin system by processes in which every transition of a nucleus from a higher to a lower level is accompanied by a transition of a nucleus from the lower to the higher state, a process called spin–spin relaxation. Second, there will be a gradual loss of energy to the other nuclei and electrons in the material, collectively called the lattice, resulting from transitions of nuclei from the upper state to the lower state. This second process is spin–lattice relaxation. The time constants characterizing these two processes are T2 and T1, respectively, the spin–spin (or transverse) and spin–lattice (or longitudinal) relaxation times.

The time constants T1 and T2 yield valuable information about the local interactions experienced by nuclei. T1 describes the rate at which a nonequilibrium spin distribution exponentially approaches equilibrium following absorption of RF energy. However, because the energy change involved is very small, an excited nuclear spin does not spontaneously lose its energy (or rather, it would do so at an exceptionally slow rate) but relies almost entirely on interaction with the surrounding material. We will see that spin–lattice relaxation, where the lattice is the environment surrounding the nucleus (and includes the remainder of the host molecule as well as other solute and solvent molecules), occurs because of interactions of the excited nuclear spin dipole with random fluctuating magnetic fields that exist on an atomic scale inside tissues. These originate from neighboring nuclei and are modulated by the motion of other surrounding nuclear dipoles in the local environment (usually called the lattice) which may have components fluctuating with the same frequency as the resonance frequency ω0. Spin–lattice relaxation is a type of stimulated recovery, in which the spins that have been excited to the upper energy level by the transmitted RF pulse are encouraged to return to the lower level by the action of an alternating magnetic field of appropriate frequency.

c2f1

Figure 2.1. A water molecule contains two hydrogen nuclei or protons, each of which has a magnetic moment and thereby generates a local magnetic field (depicted as lines of force) throughout its immediate neighborhood. The other protons in the same molecule, as well as adjacent molecules, experience this field and may change their spin state accordingly.

This stimulated recovery is very efficient when there is a local fluctuating field that can provide a magnetic perturbation at the Larmor frequency, so that there is available a quantum of energy exactly equal to the difference in levels of the nuclear spin states. A suitable source of stimulating interaction can be discovered by close inspection of the atomic environment of the protons in the tissue. For example, in water, each proton in a water molecule has a neighboring proton which is also a magnetic dipole that generates a magnetic field at the proton of about 5 G (0.5 mT) (Figure 2.1). If the water molecules were frozen in a rigid state (e.g., at temperatures close to absolute zero), then in a sample of nuclei, the fields experienced would average around the mean applied field B but would vary by ±5 G. Consequently, their resonance frequencies would vary by ±21.3 kHz, which would be the measured line width in a high resolution spectrum. After excitation, this wide range of signals would superimpose and destructively cancel rapidly—by the bandwidth or uncertainty principle, the lifetime of the net signal (T2) would be of the order of 1/(2 × 21.3 × 1000 × π) ≈ 7.5 μs. Above absolute zero, however, this field is not constant but, instead, is continuously changing in amplitude and direction as the water molecules rotate and move about in the medium. It also changes as a result of intermolecular collision, molecular vibrations, translation, or chemical dissociation and exchange. The magnetic field experienced by any nucleus will therefore fluctuate in time with a frequency spectrum that is dependent on the molecular tumbling due to the random thermal motion of the host and surrounding molecules (Figure 2.2). The resonance line is then much narrowed—the process is termed motional narrowing—and the signal lifetime T2 is much longer. The mean strengths of the local fields are determined by the strength of the magnetic dipoles in the medium and how close they approach the hydrogen nuclei. Only the component of the frequency spectrum that is equal to the resonant frequency ω0 (or, for reasons beyond our discussion, 2 ω0) turns out to be effective in stimulating an energy exchange to induce transitions between nuclear spin states and lead to thermal equilibrium, i.e., T1 relaxation. In liquids, such as water, the characteristic frequencies of thermal motion are on the order of 10¹¹ Hz or higher, much greater than NMR frequencies of 10⁷–10⁸ Hz. Consequently, the component of the frequency spectrum from molecular motion that can induce T1 relaxation is small and the process is relatively slow. As the molecular motion becomes slower, perhaps because of a lower temperature, or increased molecular size, the intensity of the fluctuations of the magnetic field at the resonance frequency increases, reaches a maximum, and then decreases again as the energy of the motion becomes increasingly concentrated in frequencies lower than the NMR frequency range. Thus, T1 passes through a minimum value as the molecular motion becomes slower (see Figure 2.3). The effect of the molecular motion is usually expressed by a correlation time τc, which is characteristic of the time of rotation of a molecule or its translation into a neighboring position. Relaxation rates in simple liquids are affected, for example, by viscosity, temperature, and the presence of dissolved ions and molecules, which alter the correlation times of molecular motion, as discussed further below. In addition, relaxation will be faster if the amplitudes of the local dipolar fields increase, which is the case when water molecules pass close to paramagnetic ions such as gadolinium, an effect that is exploited in the design of MRI contrast agents.

c2f2

Figure 2.2. As molecules tumble, rotate, or otherwise move around in a medium, the local magnetic field Blocal (shown on the left) experienced by hydrogen protons will vary randomly with time and fluctuate with a characteristic timescale, the correlation time τc. The random local field may be decomposed, as shown on the right, by a Fourier transform into its component power spectrum J(ω), the intensity of field variations that occur at different frequencies. When the local field varies very rapidly (e .g., at higher temperatures), the power spectrum of the local field is spread over a broad range and the component at low frequencies is small. As the characteristic time scale of the field becomes longer (e.g., by immobilizing nuclei or by lowering the temperature), the intensity of the field increases.

c2f3

Figure 2.3. The variation of relaxation rates with the timescale τc of the variations of the local field. As the correlation time increases, the relaxation rates 1/T1 and 1/T2 deviate and T2 may become very short.

Whereas T1 is sensitive to the RF components of the local field, T2 is also sensitive to low-frequency components. T2 reflects the time it takes for the ensemble to become disorganized and for the transverse component to decay. Any growth of magnetization back toward equilibrium must correspond to a loss of transverse magnetization, so all contributions to the longitudinal relaxation rate 1/T1 affect 1/T2, at least as much. In addition, components of the local dipolar fields that oscillate slowly, that is, at low frequency, may be directed along the main field (z) direction and thus can modulate the precessional frequency of a neighboring nucleus, in similar fashion to the main field in the same direction. This situation also arises when water molecules are trapped in an environment in which they cannot tumble and rotate isotropically, such as when they are oriented preferentially on a surface. Such frequency perturbations within an ensemble of nuclei result in rapid dephasing of the transverse magnetization and accelerated spin–spin relaxation. The low-frequency content of the local dipolar field increases monotonically as molecular motion progressively slows (Figure 2.2), so although T1 passes through a minimum value, T2 continues to decrease and then levels off, so that T1 and T2 then take on quite different values (see Figure 2.3).

2.2.1 Motional Narrowing

An analogy from the world of signal analysis is useful for providing insight into how motional narrowing occurs and how the spectral density of the local magnetic field changes as spins move more rapidly. The behavior of a nuclear spin system is similar to that of the signals transmitted using frequency and phase modulation schemes—as used, for example, for FM radio transmissions. Consider, for example, a small magnet that rotates uniformly in a circle so that the magnetic field it generates at a point is well approximated by a simple harmonic variation

(2.2) 2.2

where Bo is the background steady field and our rotating magnet produces a field that oscillates with amplitude Be and frequency ωr. As the magnet rotates, the magnetic field at some point in space nearby is modulated in time, and any NMR process in the presence of this field will experience a time-dependent magnetic field such that the resonance frequency for spins in this space will also vary with time. If we write the NMR frequency as

(2.3) 2.3

then the instantaneous NMR frequency is ω(t), and the signal at time t is given by

(2.4) 2.4

so there is a sinusoidal frequency modulation. A is the amplitude, which depends on the proton density and instrumental factors. The term on the right, γBe ∫ cos(ωr(t))dt, represents a phase variation in the instantaneous signal. For a simple harmonic modulation of the field (i.e., uniform rotation speed), the spectrum is given by the Fourier transform of S(t):

(2.5) 2.5

This can be evaluated using standard relationships that involve expanding the cosine and sine functions of the sinusoidal argument in terms of a series of Bessel functions. We then obtain

(2.6) 2.6

This function is shown schematically in Figure 2.4 for different values of the ratio γBe/ωr. It consists of a series of delta functions at the frequency ω0 (equal to the NMR frequency in the absence of the rotating perturbation) and at discrete frequencies above and below this spaced at integral increments of the rotation frequency ωr. The amplitude of the component at ω0 is Jo (γBe/ωr), while the amplitude at the first sideband is J1 (γBe/ωr). The response is confined to a range of frequencies centered on ω0 and mostly within ±γBe. As the speed of rotation ωr increases, the amplitudes of the sidebands change. Of special note, as the speed of rotation increases such that γBe/ωr is of the order or less than 1, so the response becomes increasingly confined to the central absorption line at ω0. The amplitude of this component increases, while those of all the sidebands decrease monotonically (as well as becoming more spaced out). As the rotation speed decreases, the sidebands become much more significant. This is precisely the behavior of a frequency-modulated signal used in radio communication: indeed, the ratio γBe/ωr plays the part of what engineers would term the modulation index. Here we see how modulation of the magnetic field experienced by the precessing nuclei leads to a motional line-narrowing. As the speed of rotation of the field increases, there reaches a point at which the field changes are too rapid to be effective in altering the dominant resonance response. Of course, in a material the local fields are never pure sinusoidal variations, so the discrete nature of the sidebands is lost. In solids, the motions are slow and the resonance line is broad (here, spread into discrete sidebands), whereas in liquids the line is narrow because the molecular motions cause the field experienced by nuclei to rapidly change.

c2f4

Figure 2.4. The spectra produced by a sinusoidally modulated variation in the Larmor frequency. The left-hand example (when (γ Be/ωr) ≈ 1) depicts the component frequencies as a main contribution at ω0 with sidebands separated at integer