RF Coils for MRI

By John R. Griffiths

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

To date there is no single reference aimed at teaching the art of applications guided coil design for use in MRI. This RF Coils for MRI handbook is intended to become this reference. 

Heretofore, much of the know-how of RF coil design is bottled up in various industry and academic laboratories around the world. Some of this information on coil technologies and applications techniques has been disseminated through the literature, while more of this knowledge has been withheld for competitive or proprietary advantage. Of the published works, the record of technology development is often incomplete and misleading, accurate referencing and attribution assignment being tantamount to admission of patent infringement in the commercial arena.  Accordingly, the literature on RF coil design is fragmented and confusing.  There are no texts and few courses offered to teach this material. Mastery of the art and science of RF coil design is perhaps best achieved through the learning that comes with a long career in the field at multiple places of employment…until now.

RF Coils for MRI combines the lifetime understanding and expertise of many of the senior designers in the field into a single, practical training manual. It informs the engineer on part numbers and sources of component materials, equipment, engineering services and consulting to enable anyone with electronics bench experience to build, test and interface a coil. The handbook teaches the MR system user how to safely and successfully implement the coil for its intended application. The comprehensive articles also include information required by the scientist or physician to predict respective experiment or clinical performance of a coil for a variety of common applications.  It is expected that RF Coils for MRI becomes an important resource for engineers, technicians, scientists, and physicians wanting to safely and successfully buy or build and use MR coils in the clinic or laboratory.  Similarly, this guidebook provides teaching material for students, fellows and residents wanting to better understand the theory and operation of RF coils.

Many of the articles have been written by the pioneers and developers of coils, arrays and probes, so this is all first hand information! The handbook serves as an expository guide for hands-on radiologists, radiographers, physicians, engineers, medical physicists, technologists, and for anyone with interests in building or selecting and using RF coils to achieve best clinical or experimental results.

About EMR Handbooks / eMagRes Handbooks 

The Encyclopedia of Magnetic Resonance (up to 2012) and eMagRes (from 2013 onward) publish a wide range of online articles on all aspects of magnetic resonance in physics, chemistry, biology and medicine. The existence of this large number of articles, written by experts in various fields, is enabling the publication of a series of EMR Handbooks / eMagRes Handbooks on specific areas of NMR and MRI. The chapters of each of these handbooks will comprise a carefully chosen selection of articles from eMagRes. In consultation with the eMagRes Editorial Board, the EMR Handbooks / eMagRes Handbooks  are coherently planned in advance by specially-selected Editors, and new articles are written (together with updates of some already existing articles)

• Language: English
• Publisher: Wiley
• Release date: Dec 19, 2012
• ISBN: 9781118590454

Book preview

Abbreviations and Acronyms

Series Preface

The Encyclopedia of Nuclear Magnetic Resonance was published in eight volumes in 1996, in part to celebrate the fiftieth anniversary of the first publications in NMR in January 1946. Volume 1 contained an historical overview and ca. 200 short personal articles by prominent NMR practitioners, while the remaining seven volumes comprise ca. 500 articles on a wide variety of topics in NMR (including MRI). Two spin-off volumes incorporating the articles on MRI and MRS (together with some new ones) were published in 2000 and a ninth volume was brought out in 2002. In 2006, the decision was taken to publish all the articles electronically (i.e. on the World Wide Web) and this was carried out in 2007. Since then, new articles have been placed on the web every three months and a number of the original articles have been updated. This process is continuing. The overall title has been changed to the Encyclopedia of Magnetic Resonance to allow for future articles on EPR and to accommodate the sensitivities of medical applications.

The existence of this large number of articles, written by experts in various fields, is enabling a new concept to be implemented, namely the publication of a series of printed handbooks on specific areas of NMR and MRI. The chapters of each of these handbooks will comprise a carefully chosen selection of Encyclopedia articles relevant to the area in question. In consultation with the Editorial Board, the handbooks are coherently planned in advance by specially selected editors. New articles are written and existing articles are updated to give appropriate complete coverage of the total area. The handbooks are intended to be of value and interest to research students, postdoctoral fellows, and other researchers learning about the topic in question and undertaking relevant experiments, whether in academia or industry.

Robin K. Harris

University of Durham, Durham, UK

Roderick E. Wasylishen

University of Alberta, Edmonton, Alberta, Canada

November 2009

Volume Preface

The RF coil is the component of the MRI system by which the MRI signal is stimulated and received or lost. Therefore informed specification, design, construction, evaluation, and application of properly selected RF coils are critical to a safe and successful MRI scan. Toward this goal, this handbook serves as an expository guide for engineers, scientists, medical physicists, radiographers, technologists, hands-on radiologists and other physicians, and for anyone with interests in building or selecting and using coils to achieve the best clinical or experimental results.

Since Purcell, Torrey, and Pound’s re-entrant cavity resonator and Bloch, Hansen, and Packard’s crossed transmit and receive coil pair (Physical Review, 1946), RF coils have evolved from the simple test-tube loaded, wire-wound solenoids and copper- tape resonators of chemistry laboratories to the complex multichannel transmitters and receivers of modern clinical and preclinical MRI systems. With deference to the literature already covering basic coil structures, this guide primarily addresses the dearth of reporting on modern coils for state-of-the-art MRI systems used in clinical diagnostics, biomedical research, and engineering R&D. Current RF coil designs and methods are covered across 33 chapters, divided into seven sections: surface coils, loop arrays, volume coils, special purpose coils, coil interface circuits, coil modeling and evaluation, and RF safety.

The first topic addressed is surface coils, which are loosely defined as coils placed adjacent to a surface of a region of interest (ROI) in an NMR- active sample such as human anatomy. A surface coil is used for localizing a near-surface ROI, with high transmit efficiency and/or receive sensitivity. The first two chapters introduce surface coils by their history of development, design, and application. Chapters 3–6 include designs for quadrature surface coils, double-tuned surface coils, nested multinuclear surface coils, and surface coils built of transmission line (TEM) elements.

A loop array might be regarded as an array of surface coils. There are surface arrays to be applied to surfaces, and volume arrays to subtend sample volumes. Developed initially as a means of efficiently transmitting to and receiving from larger ROIs with the sensitivity and efficiency of a surface coil, receive, transmit, and transceiver arrays of loops or transmission line elements have found new and more powerful applications in parallel imaging and parallel transmit schemes to further improve imaging speed, quality, and safety. To address this important topic, four chapters are included covering receiver loop arrays, array design for parallel imaging, transceiver loop arrays, and bench top characterization of multichannel coil arrays.

Volume coils, as their name suggests, encompass a sample volume. Common clinical examples are head, limb, and body coils. While there are a number of volume coil technologies by various names, two popular designs are the birdcage and TEM coils and their many variants. The birdcage was originally developed and used as a transceiver head and body coil. It continues to be the most widely used body coil in clinical systems today for exciting a uniform field over a large ROI in the body. Chapters 11 and 12 cover birdcage, and double-tuned birdcage volume coil design. The TEM coil is essentially an array of transmission line elements surrounding a volume, or adjacent to a surface. This structure preserves the inherent field uniformity of a birdcage, but gains the benefits of an array with independent element operation. Accordingly, it is a popular option for parallel-transceiver and parallel-transmit applications. Chapters 13–16 give examples of TEM volume coil designs. Chapter 17 extends the topic further with antenna array elements.

A wide variety of coils offering significant solutions to problems in clinical diagnosis and preclinical science but not neatly fitting into the above categories have been classified as special purpose coils.

Examples of five such coils are given in Chapters 18–22. Catheter coils for MRI-guided catheterization and high resolution vascular wall imaging is one example for clinical utility. Micro coils of sub-micrometer scale for nanoliter samples are an example of nanotechnology in coil design. Three popular approaches to preclinical probes are included with cryogenic and superconducting coils, single and double resonance litz probes, and millipede coils.

RF coils are of course not stand-alone devices. They must be designed within the context of the MRI system to which they interface. Receive coils must interface the system receiver(s). Transmit coils must interface the system power amplifier(s). Interfaces to the transmitter and receiver require close attention to impedance matching and baluns. The design, interface, and implementation of the receiver, transmitter, and impedance matching are covered in Chapters 23–25.

Coil design requires rigorous modeling and evaluation. The engineer must be familiar with these methods to design and build a safe and successful coil. Models are heavily relied upon by MRI technicians and physicians for predicting image quality and specific absorption rate (SAR) characteristics of a coil for a given application. This section lists six chapters dedicated to methods and examples of analytical and numerically based design and evaluation. A standard approach to RF coil analysis is given in Chapter 26. Chapter 27 reviews the analytical, finite difference time domain, finite element and moments methods of coil field modeling. Chapters 28–31 contribute specific examples of how to model fields and losses (SAR) for the birdcage and TEM coil designs.

The final section is reserved for the foremost concern for all coil designs and applications: RF safety. Chapter 32 reviews the current SAR-based safety standards by which safety practices and procedures for coil design and use are regulated. SAR and how to calculate SAR in the body with different coils and implants are explained. Tissue heating is demonstrated adjacent to implants and lead wires due to RF-E-field coupling. Chapter 33 addresses the primary safety concern, RF heating, through design and validation of a more accurate bioheat equation. The electrodynamics (SAR) as well as thermodynamics (perfusion and convective heat transfer) and physiology (thermoregulatory reflex) must all be considered for an accurate prediction of temperature contours in the MRI subject. Phantom, animal, and human experimental models are described for measuring systemic and local RF-induced temperature rise.

Thirty nine outstanding authors contributed 33 chapters for this handbook on RF Coils for MRI. Authors were invited by the editors to contribute RF designs or design methods for which they are best known; in many cases they are the inventors and leading innovators of their respective technologies. In an effort analogous to collecting recipes for a community cookbook, authors were asked to contribute an expository account of their favorite RF recipes. Emphasis on the materials and methods sections was requested. This was an opportunity for the senior experts to teach the next generation of coil builders and users how to design, build, and use their most effective designs. Tricks of the trade and other proprietary information were called for, information that could not be found in the sparse and disparate literature on these topics. With little more than copyediting, the results are before the readers in the authors’ own words. The personalities of the chapters therefore vary in style and content, but are preserved giving the reader an opportunity to meet the authors as well as to learn from them. Finally, Professor Vaughan wishes to thank his friend and colleague, Professor Griffiths whose steadfast patience, gentle prodding, and compensatory toil were necessary ingredients in baking this cake.

Above all else, we hope that engineers, scientists, technicians, and physicians will find RF Coils for MRI to be a useful addition to their laboratory benches and library shelves.

J. Thomas Vaughan

University of Minnesota, Minneapolis, Minnesota, USA

John R. Griffiths

Cancer Research UK, Cambridge Research Institute, Cambridge, UK

April 2012

PART A

Surface Coils

Chapter 1

An Historical Introduction to Surface Coils: The Early Days

Joseph J. H. Ackerman

Department of Chemistry, Campus Box 1134, Washington University, Saint Louis, MO 63130, USA

1.1 INTRODUCTION

Before the advent of modern magnetic resonance (MR) imaging scanners possessing superb magnetic-field-gradient systems and RF pulse shaping capabilities, it was common for objects that were to be examined by MR to be placed inside what are today known as RF volume transmit/receive coils. MR magnets back in the day had relatively narrow bores (few centimeters/inches) and similarly small samples, the most common sample-containing glass tube having an outer diameter of 5 mm. Small-diameter RF volume transmit/receive coils are highly sensitive on a per-unit-volume basis and provide quite homogeneous RF fields. The 5-mm MR probes now in use, common to all high-field, high-resolution analytical (structural chemistry/biology) magnetic resonance spectroscopy (MRS) systems, are highly evolved, offering extraordinary sensitivity, linewidth resolution, and multinuclide detection capabilities.

The introduction of larger bore superconducting magnets motivated the use of MRS for study of larger samples, in particular, intact biological systems, including small laboratory-animal models such as mice and rats. Volume coils had two disadvantages for studies such as these: they became increasingly insensitive with increasing sample size (receptivity scaling roughly as the inverse of the coil radius) and they offered no spatial selectivity (i.e., were unable to focus on a single organ or tissue of interest). Driven by a need for greater signal-to-noise sensitivity and spatial localization, surface coils were introduced, enabling numerous MRS studies of living systems and motivating additional engineering developments in concert with advances in magnet, magnetic-field-gradient, and RF technology.

1.2 BACKGROUND

Before their introduction for in vivo MRS, surface coils had been employed—and remain so today—in oil well logging. Oil well logging refers to the practice of interrogating the terra firma at various depths of and immediately surrounding an oil well borehole, with the aim of inferring its oil carrying/producing characteristics. While well-logging tools employ a variety of technologies (e.g., electromagnetic, radioactive, and acoustic) to investigate geologic formations penetrated by a borehole, MR logging probes have played a prominent role.

In MR logging, a magnet designed to produce a relatively homogeneous field at a defined distance outside the borehole (sometimes referred to as an inside-out magnet) is inserted down into the borehole to the desired depth, polarizing the ¹H spin populations of fluid molecules (e.g., water and oil) in the surrounding rock. An RF receiver coil, which has been designed to detect ¹H spins precessing within the isocenter of the inside-out magnetic field, i.e., external to the coil and the borehole, monitors the ¹H MR response of fluid molecules external to the bore-hole. The well-logging MR procedure allows derivation of important geologic properties such as pore size and fluid permeability. While a far cry from the laboratory or clinical environment of in vivo surface coil measurements, the key underlying principle is the same—the MR signal is detected from a region remote from the interior of the coil, i.e., from outside the coil.¹, ²

Perhaps, the earliest in vivo MR implementation of the surface coil was reported by Morse and Singer in their now iconic Science report in which time-of-flight effects were employed to monitor blood flow in the arm of a volunteer human subject.³ This early MR angiography demonstration employed two small surface coils separated by a distance of 1–3cm and placed over a vein in the arm (Figure 1.1). The transmit RF from the upstream coil produced a perturbation (inversion via adiabatic fast passage) in the blood–water ¹H magnetization, a perturbation detected by the downstream receive RF coil at a timing dependent on the velocity of blood flow. This pioneering application did not exploit high-resolution MRS capabilities (i.e., narrow linewidth resonances). Indeed, the sample volume, a human volunteer’s forearm, was substantially greater than the homogeneous magnetic field volume produced by the iron magnet (pole faces separated by ∼10 cm). However, Morse and Singer did demonstrate the principle of localized excitation and detection of spin populations external to the surface coil with a living subject, one whose overall dimensions obviously far exceed that of the surface coil(s).

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Figure 1.1. A copy of Figure 1.1 from the 1970 Science magazine article by O. C. Morse and J. R. Singer titled Blood Velocity Measurements in Intact Subjects.³ This figure shows a volunteer with her arm in the space between the pole faces of a 0.36 T (15.4 MHz) iron magnet. Two surface coils separated by 2.5 cm are visible, lying over a vein on top of the subject’s forearm. The upstream coil served to perturb the flowing venous blood ¹H (water) magnetization via adiabatic fast passage. The downstream surface coil served to detect ¹H the magnetization as a function of time following upstream perturbation. This time-of-flight angiography demonstration is the earliest known (to this author) published use of surface coils in vivo. (Reproduced from Ref. 3. © American Association for the Advancement of Science, 1970.)

1.3 SURFACE COILS FOR MR SPECTROSCOPY IN VIVO

1.3.1 First Report

Superconducting, vertical bore, magnet diameters had become sufficiently large by the mid-1970s (e.g., 9–10cm) that organs of small animals such as rat liver, heart, and kidney could carefully be excised, continuously perfused with media supplying oxygen and nutrients, placed within an RF coil, and sited in an MR magnet such that the volume of homogeneous field was reasonably centered about the organ. This arrangement allowed high-resolution MRS studies of functioning, intact, mammalian organs to be performed. By the end of the decade, such procedures were being pursued to great advantage on both sides of the Atlantic.

It was recognized that organs supported on perfusion media, while valuable as model systems, were not entirely representative of the in situ blood-perfused in vivo state. Thus, in the latter part of the decade, an invasive strategy was introduced whereby, in a deeply anesthetized small animal, the organ of interest was surgically exposed while remaining fully connected to its vasculature, placed within an RF coil, and the living subject placed in the magnet such that the organ was in the homogeneous region of the field.⁴ Although successful, such procedures were not without technical challenges. Indeed, it was during such attempts to monitor the high-resolution ³¹P MRS signal from rat kidney in vivo that the presence of contaminating signal emanating from phosphocreatine in muscle tissue external to the kidney-containing RF coil suggested a new approach to MRS in vivo, the surface coil.⁵, ⁶

Surface coils presented immediate and substantial advantages for MRS studies of small animals. Planar or slightly shaped/bent coils of a few turns and a few centimeters diameter allowed localized MRS interrogation of rat brain and leg muscle (Figures 1.2 and 1.3). They were also compatible with the tight space limitations imposed by vertical magnets with 9–10cm bore diameters which, at the time, were common in laboratories pursuing MRS of intact biological systems. Soon, the introduction of significantly larger diameter, horizontal bore magnets allowed surface coil experiments with larger subjects such as humans.

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Figure 1.2. Photograph of early surface coil, circa 1980, designed to perform ³¹P MRS for study of rat leg skeletal muscle, and resulting spectrum acquired in vivo. Subjects were oriented in a vertical position and secured in a clear, plastic, half-cylinder housing. This enabled placement of the entire apparatus with subject up into the vertical bore (∼9 cm diameter) of the superconducting magnet. The reader’s attention is drawn to the simplicity of coil design and of the frequency tuning and impedance matching circuit. These were important, robust attributes that led to rapid adoption by MR laboratories focused on studies of metabolism and physiology. Spectrum (a): nonischemic muscle below the knee joint; spectrum (b): ischemic muscle from the same area as in (a) after application of tourniquet above the knee; and spectrum (c): muscle above the tourniquet. Chemical shift assignments are β-phosphate of ATP, −16.1 ppm; α-phosphate of ATP, −7.5 ppm; γ -phosphate of ATP, −2.5 ppm; phosphocreatine, 0.0 ppm; and inorganic phosphate, 4.9 ppm. (Spectra adapted from Ref. 6. © Nature Publishing Group, 1980.)

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Figure 1.3. Photograph of early surface coil, circa 1980, designed to perform ³¹P MRS for study of rat brain, and resulting spectrum acquired in vivo. Spectrum (a) original brain spectrum showing a broad baseline feature (hump) due to bone and membrane ³¹P resonances; spectrum (b) same spectral data as in (a) but following application of strong apodizing filter function; and spectrum (c) difference spectrum. Chemical shift assignments are the same as in Figure 1.2 with, in addition, phosphodiesters, 3.0 ppm and sugar phosphates, 6.7 ppm. (Spectra adapted from Ref. 6. © Nature Publishing Group, 1980.)

Surface coils also offered a variety of other advantages. It was quickly recognized that the strong, localized B1 field of the surface coil yielded highly localized signal detection capability, while conferring immunity to coil loading (noise) from regions of the (electrically conducting) subject remote to, and thus not interrogated by, the coil. Further, given that most surface coils were relatively low-inductance devices and that tissue water is an enormously concentrated source of protons (∼80 M), the strong ¹H MRS signal from tissue water provided a convenient means to shim the static magnetic field even with the coil tuning adjusted for other nuclides (e.g., ³¹P, ¹³C).⁷ Finally, MR scanners with magnetic-field-gradient systems were rather a rarity in the early 1980s, precluding the use of localization schemes based on the use of field gradients, making surface coil localization much more practical. Laboratories interested in probing metabolism and physiology by high-resolution MRS were much more likely to possess strong expertise in biological science than in MR-related en-it provided immediate entrée for biologically oriented laboratories to employ MRS in studies of small animal models.

1.3.2 Early Developments at Washington University in Saint Louis

Early development of surface coil techniques in our laboratory at Washington University in Saint Louis explored methods for making T1 measurements,⁸ determining absolute molar concentrations of detected species,⁹ optimizing signal-to-noise and localization,¹⁰ using a double-resonance tuning scheme to allow ¹H decoupling, while detecting ¹³C-labeled substrates and their metabolic products,¹¹ selectively suppressing the large-amplitude, broad, underlying ³¹P background resonance(s) from membrane and bone tissues when examining brain,¹² quantifying the consequences of using the surface coil as a receiver in the presence of homogeneous B1 transmission,¹³ electrically decoupling coaxial transmission and reception surface coils,¹⁴ and enhancing surface coil spatial localization with an inhomogeneous surface gradient.¹⁵–¹⁷ Reviews of gineering. Thus, because the surface coil was truly these developments and their further extensions have simple in design and exceptionally robust to operate, been published.¹⁸, ¹⁹

1.3.3 Advances in Pulse Sequences and Designs for Surface Coils

Other laboratories developed important pulsesequence-related methods for leveraging the surface coil’s inhomogeneous B1 field to improve spatial selectivity. Depth pulses, a family of phase-cycled pulse sequences that provided improved spatial selectivity with surface coils, were described by Bendall and colleagues.²⁰ Bottomley et al. employed magnetic-field-gradient enabled slice-selective excitation parallel to the plane of the surface coil to improve localization at depth, a technique referred to as depth-resolved surface coil spectroscopy(DRESS).²¹ Mike Garwood and coworkers introduced the Fourier series window (FSW) method,²² a perceptive variation of the rotating-frame zeugmatography experiment,²³ to produce a localized region of detected signal intensity at a predefined depth from the coil plane. The FSW and depth-pulse methods shared complementary attributes, and the Garwood and Bendall teams collaborated to combine the FSW approach with depth-pulse procedures to improve performance for a number of important MRS experiments.²⁴ In a seminal advance, Garwood et al. demonstrated in 1989 that adiabatic pulses using a single surface coil for both B1 transmission and signal reception (i.e., single-coil mode) could overcome many of the disadvantages of the surface coil’s inhomogeneous B1 profile, allowing uniform excitation, refocusing, and slice-selective inversion over a 10-fold or greater variation in B1 magnitude.²⁵

In concert with efforts to optimize surface coil pulse sequences, coil designs were modified to suit various applications. Presaging today’s use of the surface coil as an element for construction of multi-coil arrays for parallel imaging, Hyde et al. published a series of insightful papers describing the design of noninteracting coil sets.²⁶, ²⁷ These efforts led the Hyde team to introduce the quadrature detection surface coil,²⁸ providing a 40% (√2) improvement in signal sensitivity.²⁹ In 1992, these and other advances in surface-coil-related hardware designs, pulse sequences, and applications to metabolic and physiologic research questions were reviewed in the three-volume Springer-Verlag compilation on the state of in vivo MRS, edited by M. Rudin and J. Seelig, to which the interested reader is referred.³⁰

1.4 POSTSCRIPT

The early use of surface coils provided high signal sensitivity and localized detection in an era when MR laboratories did not have access to scanners with high-quality magnetic-field-gradient systems. With the introduction of modern, actively shielded magnetic-field-gradient assemblies, the role of the surface coil evolved to complement and take advantage of pulsed field-gradient methods. Today, surface coils continue to play an important role when spatially targeted, high-sensitivity MR detection is desired. They are especially well suited for high-field MRI and MRS applications with small laboratory animals (e.g., mice and rats), where they are often used in receive-only mode with a volume coil providing homogeneous transmit B1. When surface coils are employed as elements of a large-scale receiver array, prior information, in the form of sensitivity profile maps for each array-element, allows under-sampling of k-space with significant acceleration of image acquisition.

Morse and Singer would surely be pleased.

RELATED ARTICLES IN THE ENCYCLOPEDIA OF MAGNETIC RESONANCE

Ackerman, Joseph J. H.: Oxford Knights

Coils for Insertion into the Human Body

Gadian, David G.: From Brawn to Brain

Hoult, D. I.: Biomedical NMR Instrumentation—A Personal Viewpoint

Radda, George K.: The Development of In Vivo NMR in Oxford

Radiofrequency Systems and Coils for MRI and MRS

Shaw, Derek: From 5-mm Tubes to Man. The Objects Studied by NMR Continue to Grow

Surface and Other Local Coils for In Vivo Studies

Surface Coil NMR: Detection with Inhomogeneous Radiofrequency Field Antennas

Well Logging

Whole Body Machines: NMR Phased Array Coil Systems

REFERENCES

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2. R. L. Kleinberg, The Industrial Physicist, 1996, 2, 18.

3. O. C. Morse and J. R. Singer, Science, 1970, 170, 440.

4. T. H. Grove, J. J. H. Ackerman, G. K. Radda, and P. J. Bore, Proc. Natl. Acad. Sci. U.S.A., 1980, 77, 299.

5. J. J. H. Ackerman, Ackerman, Joseph J. H.: Oxford knights, in Encyclopedia of Nuclear Magnetic Reso- nance, Historical Perspectives, eds E. D. Becker, John Wiley and Sons, Ltd: Sussex, England, 1996, Vol. 1, p. 164.

6. J. J. H. Ackerman, T. H. Grove, G. G. Wong, D. G. Gadian, and G. K. Radda, Nature, 1980, 283, 167.

7. J. J. H. Ackerman, D. G. Gadian, G. K. Radda, and G. G. Wong, J. Magn. Reson., 1981, 42, 498.

8. J. L. Evelhoch and J. J. H. Ackerman, J. Magn. Reson., 1983, 53, 52.

9. K. R. Thulborn and J. J. H. Ackerman, J. Magn. Reson., 1983, 55, 357.

10. J. L. Evelhoch, M. G. Crowley, and J. J. H. Ackerman, J. Magn. Reson., 1984, 56, 110.

11. N. V. Reo, C. S. Ewy, B. A. Siegfried, and J. J. H. Ackerman, J. Magn. Reson., 1984, 58, 76.

12. J. J. H. Ackerman, J. L. Evelhoch, B. A. Berkowitz, G. M. Kichura, R. K. Deuel, and K. S. Lown, J. Magn. Reson., 1984, 56, 318.

13. M. G. Crowley, J. L. Evelhoch, and J. J. H. Ackerman, J. Magn. Reson., 1985, 64, 20.

14. W. Chen and J. J. H. Ackerman, J. Magn. Reson., 1992, 98, 238.

15. M. G. Crowley and J. J. H. Ackerman, J. Magn. Reson., 1985, 65, 522.

16. W. Chen and J. J. H. Ackerman, NMR Biomed., 1990, 3, 147.

17. W. Chen and J. J. H. Ackerman, NMR Biomed., 1990, 3, 158.

18. C. S. E. Bosch and J. J. H. Ackerman, in NMR Basic Principles and Progress, Vivo Magnetic Reso- nance Spectroscopy II: Localization and Spectral Edit- ing, eds P. Diehl, E. Fluck, H. Gunther, R. Kosfeld, J. Seelig, M. Rudin, and J. Seelig, Springer-Verlag: Berlin and Heidelberg, Germany, 1992, Vol. 27, p. 3, Chapter 1.

19. C. S. Bosch and J. J. H. Ackerman, Surface coil NMR: Detection with inhomogeneous radiofrequency field antennas, in Encyclopedia of Nuclear Magnetic Resonance, eds D. M. Grant and R. K. Harris, John Wiley & Sons, Ltd.: New York, Sussex, England, 1996, Vol. 7, p. 4649.

20. M. R. Bendall and R. E. Gordon, J. Magn. Reson., 1983, 53, 365.

21. P. A. Bottomley, T. H. Foster, and R. D. Darrow, J. Magn. Reson., 1984, 59, 338.

22. M. Garwood, T. Schleich, B. D. Ross, G. B. Matson, and W. D. Winter, J. Magn. Reson., 1985, 65, 239.

23. D. I. Hoult, J. Magn. Reson., 1979, 33, 183.

24. M. Garwood, T. Schleich, M. R. Bendall, and D. T. Pegg, J. Magn. Reson., 1985, 65, 510.

25. M. Garwood, K. Ugurbil, A. R. Rath, M. R. Bendall, B. D. Ross, S. L. Mitchell, and H. Merkle, Magn. Reson. Med., 1989, 9, 25.

26. J. S. Hyde, A. Jesmanowicz, W. Froncisz, J. B. Knee- land, T. M. Grist, and N. F. Campagna, J. Magn. Reson., 1986, 70, 512.

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30. M. Rudin and J. Seelig, eds., in NMR: Basic Principles and Progress: In vivo Magnetic Resonance Spectroscopy I, II, & III, eds P. Diehl, E. Fluck, H. Gunther, R. Kosfeld, and J. Seelig, Springer-Verlag: Berlin and Heidelberg, Germany, 1992, Vol. 26, 27, & 28.

Chapter 2

Radiofrequency Coils for NMR: A Peripatetic History of Their Twists and Turns

Eiichi Fukushima

ABQMR, Albuquerque, NM 87106, USA

2.1 INTRODUCTION

Nuclear magnetic resonance (NMR) is now a mature field but shows no sign of slowing down in terms of new protocols. The associated hardware has also experienced huge strides, although much of that is due to the spectacular development of computer technology over the past half a century. Throughout these changes, the NMR detection coil has remained surprisingly unchanged, except for the new developments at the very high frequencies where the signal wavelengths are getting comparable to the physical size of the coils. This short review explores the various coils used over the years and, in particular, examines the reasons for the longevity of the solenoid for use at relatively low frequencies as well as other coils that offer particular advantages for special situations.

Because NMR deals with nuclear spins that precess in a magnetic field, the vast majority of experiments use coils for both detection and transmission. This presupposes a loose definition of coils; the dictionary definition of a coil being a connected series of spirals ... into which a rope can be wound, which is consistent with a solenoid that we are all familiar with. Some modern coils, however, do not look anything like this definition. For the purpose of this short review, coils are taken to be the devices used to receive NMR signals, whatever their shapes may be. At the same time, some commonly used coils, especially those used at high frequencies, are not discussed for arbitrary reasons. This review is not so much history per se but a compilation of interesting ways to effect NMR detection. Most coils not specifically referenced here are described in the book by Lupu et al., listed under Further Reading.

2.2 HISTORY OF COILS

We start the list with a coil having the least likely geometry. It is known that a periodically varying electric field has a periodically oscillating magnetic field associated with it. Gersch and Lösch¹ demonstrated in 1957 that NMR signal can be detected from samples in an oscillating electric field of capacitors. The capacitor was placed between the pole pieces of an electromagnet in such a way that the RF electric field was parallel to the static magnetic field. To the author’s knowledge, this experiment did not elicit much interest and remains an academic curiosity.

The simplest geometry for an electric current that can generate a magnetic field is a straight line. The next simplest element may be that line bent into a loop. Both these geometries are used for NMR but do not represent the most straightforward applications due to the spatially inhomogeneous magnetic fields generated by them. In order for the generated magnetic field B1 (and the sensitivity per spin—to be discussed later) to be uniform for a sample that has significant physical extent, there must be many wires so that they look the same, or at least similar, to the spins located at different parts of the sample. It will also turn out that the sensitivity per spin is enhanced, in general, if the spin is close to more wires carrying a certain current rather than fewer wires carrying the same current. For these and other reasons, the most common coil used in NMR is the solenoid, at least for reasonably low frequencies where the inductive reactance remains manageable.

The fact that solenoids perform extremely well is often taken for granted but it is worth considering in some detail. It would make sense to incorporate the features responsible for their good performance into other coil designs. The reciprocity theorem for NMR, as described by Hoult and Richards,² states that the sensitivity to NMR signal from a sample element is proportional to the intensity of the magnetic field at the position of the sample element due to a unit current in the coil. Because the magnetic field strength drops off with distance from any source, including coil wires, the sample needs to be close to the current elements by some measure in order to achieve the best signal-to-noise ratio (SNR). The solenoid works well compared to many other geometries because it does a good job of putting the current elements relatively close to all parts of an arbitrary sample placed within the coil, provided the coil has a reasonable ratio of length to diameter and its pitch is acceptably fine, i.e., the wire thickness is approximately equal to the gap between the wires. Another way to look at it is to realize that the magnetic field inside the solenoid is caused by currents flowing in all the turns of the solenoid, so the process is extremely efficient. By the same token, a small solenoid is much more efficient per spin than a large solenoid because an average spin will be closer to the wires in the small coil.

A counter-example would be a disproportionately short solenoid, the extreme case being a single loop of wire, the so-called surface coil. The surface coil, somewhat misnamed because there are other coil geometries that are equally or perhaps even more exclusively suited for surface use, is simple to make and it is likely that it was used in NMR since close to beginning of (NMR) time. It was formally introduced in the 1970s and 1980s primarily for in vivo biological applications in longitudinal fields of axial superconducting magnets for samples that are too large for the usual solenoid coil or where there is a need to spatially localize the signal source by the placement of the coil.

Despite the surface coil’s simplicity and usefulness, the field is inhomogeneous compared to the solenoid; the relative magnetic field strength varies by a huge factor between a sample element at the center of the loop versus an element at the wire. This effect results in the most effective position of the surface coil not being at the surface against which the coil can be placed but at a distance that is comparable to the radius of the loop. At this separation, there is a balance between manageability of the inhomogeneity and making the distance from the coil not so great that it compromises the sensitivity. Thus, the usual rule of thumb is to make a coil with a radius approximately equal to the desired depth for the region of sensitivity.

This effect is used in an NMR application having an unusual scale: Earth’s field NMR detection of underground water or other liquids. This application, pioneered in Siberia more than 25 years ago, uses a large circular or rectangular loop coil on the ground, with a typical dimension of 100 m, to detect NMR signals from depths comparable to the coil radius and, in favorable cases, even the diameter. Earth’s field NMR is notoriously insensitive because of the weak static magnetic field of typically ∼5 ×10-5 T, which leads to a relative sensitivity compared to 4.7 T of (10-5) raised to, say, 3/2 power, or a factor of ∼30 million, although this estimate is likely to be inaccurate because of the immense range of extrapolation over five orders of magnitude in field strength. This deficit is recovered by having a sample that is larger than the usual sample in linear scale by the cube root of ∼30 million or ∼300. If the usual NMR sample is taken to be 1 cm across, an Earth’s field NMR sample with large spin density, for example water, will have to be at least 30 m across so a loop coil that is ∼ 100 m across might be sufficient. This turns out to be true in many cases, and there are now commercial instruments by companies such as Iris in France (www.iris-instruments.com) and Vista Clara in the United States (www.vista-clara.com) based on this principle for use in geophysical exploration without having to use expensive boreholes. Incidentally, this community calls its activity surface NMR which is a misnomer because it looks at samples quite far from the surface although it does make use of surface coils.

This brings us back to the surface coil nomenclature. The usual surface coil is called so because it lies on a surface, not because it is good at looking at a surface. If it is desired to see NMR signals near a surface, i.e., a flat region that is close to the coil access, a big loop is inefficient because B1 is acutely nonuniform across the loop coil and the tip angle varies wildly across the plane that the coil is placed against. The reciprocity theorem requires that the wires be close together, so that a good compromise will be to have wire spacings approximately equal to the distance from the coil to the region of interest. Depending on the relative orientation of the static field and the surface coil, one could think of using an array of small loops with currents alternating in adjacent loops, a meanderline coil (a zig-zag coil that is useful in nuclear quadrupole resonance (NQR) detection), or parallel wires with currents flowing in the same direction, all with characteristic dimensions approximately equal to the depth of the sample. However, arrays of loops with radii approximately equal to depth of interest have the problem that the components of the magnetic field vary on the scale of the separation of the loops so the filling factor is less than optimal. This is also true for the meanderline, which generates magnetic fields that alternate in direction from one wire to the next, so the field strength and orientation have a periodicity in the direction perpendicular to the wires.

The array of parallel wires, on the other hand, can generate quite a uniform magnetic field parallel to the plane of the coil and perpendicular to the wires at a distance equal to approximately the inter-rung spacing. Therefore, such a coil can be used in a static field that is perpendicular to the access direction, as you might find in old-fashioned electromagnets or permanent magnets with the static field perpendicular to the access direction. Another suitable situation would be Earth’s field NMR experiments in which the static magnetic field is mainly perpendicular to a coil that is laid on the ground, as it is in much of the world, and it is desired to detect or characterize a sample that has a large extent at a shallow depth. An added feature of such coils is their ability to be used for rotating B1 experiments by having two coplanar flat coils with one rotated 90° with respect to the other and driven in quadrature to attain an extra factor of √2 in SNR and more efficient transmitter operation (see Chapter 3).

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Figure 2.1. A single-sided NMR magnet and coil built by Southwest Research Institute showing the pancake coil in the center and the electromagnet driven by the blue coils. (Photo supplied by Armando De Los Santos, Southwest Research Institute.)

As we have discussed, loop coils naturally lend themselves to unilateral NMR geometries. One of the earliest applications of such coils was for a unilateral device built by Southwest Research Institute, San Antonio, TX, USA, for examination of soil and moisture in concrete as shown in Figure 2.1. It was mounted behind a tractor to be dragged around a field, or mounted on wheels to be moved around on the concrete surface as measurements were made. These instruments were the forerunners of the commercially available NMR MOUSE.³

A saddle coil can be thought of as two loops on opposite sides of a cylinder that provides (or is sensitive to) a magnetic field that is perpendicular to the axis of the cylinder.² The pair of loops are, first, deformed into rectangles and, second, wrapped around the cylinder. Shaping them as rectangles allows the placement of the two coils on a relatively narrow cylinder and obtains good coverage in the axial direction. Wrapping the coil elements around the cylinder that serves as the coil form, of course, makes the coils compact and, more importantly, places the coil wires closer to the sample, thereby making the coil more sensitive to NMR signals.

As an aside, two single loop coils can be placed at right angle to each other for circularly polarized B1 operation, i.e., the coils can be driven in quadrature to be sensitive to circularly polarized magnetization rather than linearly polarized fields, enhancing transmit efficiency as well as for received SNR.⁴ This is easy to do with flat coils such as loops but much harder (or impossible) with axial coils that surround the sample, e.g., solenoids, because they get in the way of each other. Besides the flat array mentioned above, Helmholtz coils, saddle coils, or birdcage-like coils can be driven in quadrature, as is commonly done these days for coils in standard superconducting magnets.

This is also true for a pair of coplanar but adjacent loop coils with currents opposed so the predominant field is in the plane of the loops. A typical application is that of figure 8 coils used, for example, as large-scale surface coils for detection of underground water. In an early application, the author participated in setting up such a coil in Siberia. A 100 m diameter loop was twisted to form a figure 8 with two opposed loops of diameter 50 m. Several of us placed ourselves around one loop and pulled on it to change its shape (and, therefore, its area) to change the far-field noise pickup as monitored by an operator at the console. This geometry, with the resulting useful field parallel to the plane of the coil, is ideal for making it into one-half of a quadrature transmit/receive coil by adding an identical pair of coils with their interloop axis rotated 90° from the first.

There are other situations in which a normal solenoid is not appropriate. An example is where the solenoidal geometry is inconsistent with geometrical constraints such as the shape of a magnet that restricts access. The best known examples are the use of transverse B1 field coils in superconducting magnets that have static fields parallel to the bore. This has given rise to coils such as the saddle,² Alderman-Grant, and birdcage. Another novel solution is a tilted solenoid⁵ in which each loop of wire is wound in a plane that is tilted approximately 45° from the axial direction. It works quite well—comparable to other nonsolenoidal coils—because the sacrifice in efficiency due to its tilt is compensated by the inherent superiority of the solenoid over other geometries such as birdcage and saddle, due to the high density of wires close to the sample, as mentioned repeatedly in this chapter.

A relatively new development is a family of extremely small coils that go by the label microcoils. Despite the range of sizes of coils called microcoils, we will arbitrarily define them as coils smaller than 1 mm in the largest dimension. The majority of such microcoils in use are for obtaining high-resolution spectra in strong magnetic fields of samples that are severely limited in volume.⁶ Microcoils work well because they take advantage of the reciprocity relation, already mentioned, i.e., that the sensitivity per spin is proportional to the strength of the magnetic field generated at the site of the spin by a unit current in the receiver coil if it were to be used for transmitting, simply by being small. Although, sometimes thought of as a corollary to the filling factor, this effect is independent of it. It is simply a statement that the spin should be as close as possible to the wire in order that the sensitivity is maximized regardless of the filling factor. The simple fact that all parts of the sample inside the microcoil are very close to the coil wires guarantees good sensitivity per spin, which compensates for the relatively small size of the sample and relatively large resistance of the thin coil wire (see Chapter 19).

Microcoils, by their nature, have extremely small inductances, and this fact goes hand in hand with their uses at high frequencies where both capacitance and inductance of resonant circuits need to be small. Therefore, the recent development of microcoils for use at relatively weak fields⁷ was not anticipated. In addition to the penalty of working in a weaker field, microcoils at low frequencies have a practical handicap of being difficult to tune/match because their inductances are so small. Resonating a small inductor in a resonant circuit at low frequencies requires a large capacitor that will, at best, make it inconvenient to tune because there are limits to the range of tuning variable capacitors. Furthermore, large capacitors tend to be more lossy compared to small capacitors because they usually use materials with higher dielectric constants in order to keep the volume compact and such materials happen to be lossy.

Low-inductance microcoils can be used at low frequencies if auxiliary inductors are used instead of the microcoil itself to define the resonant parameters.⁸ The microcoil, say in series with the auxiliary coil, will represent only a small resistor and, provided the auxiliary coil has negligible resistance so that it does not contribute noise to the tank circuit, the SNR is surprisingly good. This is because the microcoil has favorable reciprocity parameters with only its resistance contributing to the degradation of the performance, i.e., the sample is close to the wire, which leads to excellent sensitivity. The presence of the auxiliary capacitor in the circuit has no effect on the overall sensitivity provided it adds no noise to the received signal. The use of an auxiliary inductor has the added advantage of making the probe tuning insensitive to the sample coil’s interaction with the surroundings, including the sample.

The low-field microcoil is an example of an adaptation of a standard technique, i.e., of a solenoid, to a case in which standard parameters could not be used and some modification was required. Specifically, the inductance was too small to be tuned in the usual manner at the required frequency. The opposite case is more common with the push toward stronger fields and larger samples, which results in the normal coils having inductances that are too large for the frequency. The solution to this problem is well known, i.e., to distribute the capacitances and reactances so that resonance frequency is determined not by the overall values of C and/or L but in smaller subsections of the coil.

One early example of distributed coil of this type was the pigtail coil.⁹ It was a solenoidal coil in which the turns were periodically interrupted by capacitive connections between turns that were formed by twisting the free end of each turn with a free end of the next turn, resembling pigtails. The tightness of the twists of these insulated wires and the lengths of the pigtails determined the capacitance. Figure 2.2 shows a more recent adaptation of this idea for a coil under construction that was going to be too large to be resonated as a simple solenoid, i.e., a human wrist coil that works in a 1 T field in a permanent magnet where the field is transverse to the common access direction. In this case, it was sufficient to have each section of the resonant section be two turns of wire rather than one for the original Cook & Lowe coil. Such distributed reactance strategies, though not in the pigtail form, are now commonplace in clinical magnetic resonance imaging (MRI) where the coil needs to be large enough to accommodate humans in relatively strong magnetic fields.

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Figure 2.2. A partially finished pigtail coil for human wrist imaging. The solenoid was interrupted every two turns with a capacitor formed by the pigtails so the resonance condition was governed by two turns of wire resonating with the capacitance of a pigtail which could be adjusted by its length or tightness. The pigtails simplify the initial setup of the resonance condition and can be replaced by ordinary capacitors, if desired, after the capacitance values have been determined.

This scheme was also used in the late 1970s and early 1980s in what may have been the most powerful NMR experiment to that time or perhaps even now. Southwest Research Institute, San Antonio, TX, USA, had a contract with the Federal Aviation Administration to design and build a detector for dynamite in checked airline baggage. Their ingenious solution was to create a pulse proton NMR system, large enough for suitcases, to perform solid and Hahn echoes in order to pick out samples that had very long T1 and very short T2 characteristics nearly unique to dynamite. The apparatus had a solenoidal coil of rectangular cross section that was placed between the pole pieces of an electromagnet. In order to reduce the inductance to a manageable value, the coil was made in six sections, three sets each of a pair of coils wound in opposite senses, connected in parallel, and driven between the junction and the two ends in a way similar to the semi-toroid described later (see Figure 2.3). The entire coil, made of copper water tubing, was enclosed in a glass sleeve containing gaseous sulfur hexafluoride (SF6) in order to suppress arcing when the 1.4 MW pulses were applied. (Even with a Faraday shield in addition to the SF6 gas, putting one’s hand along the inside surface of the sample space elicited sparks from the high-voltage sections of the coil to the hand. This made it simple to find the locations of the three high-voltage feed points.) The amplifier vacuum tube (Eimac 4CX35000C) for the transmitter’s last stage dissipated 2kW just in its filaments. That is equivalent to a major kitchen appliance such as an electric oven!

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Figure 2.3. A semi-toroidal surface coil and the back side of the ground plane to which the two ends are electrically connected. A slot between the two holes eliminates the eddy currents that would otherwise attenuate the field past the ground plane. The useable field is on the front side of the ground plane and in an orientation that is parallel to the slot.

Other examples of a distributed component coil are the already mentioned Alderman-Grant coil and the birdcage coil. The latter can be thought of as a ladder of inductors and capacitors (which would be either a high- or low-pass filter depending on whether the rungs—of the ladder—were made of inductors or capacitors, respectively) that is closed onto itself in such a way that the time delay of the signal around the loop is one cycle of the RF field being applied to the coil. The uniform transverse magnetic field is generated by a longitudinal electric current density around the cylindrical surface that is a single cycle of a sinusoid. Thus the resonating elements are local rather than global, i.e., basically an inductor and a capacitor, so that the whole coil can be made much larger at the same resonance frequency than if the entire coil were made of one inductor to be resonated by a capacitor, as is done with a simple solenoid. An additional benefit of such distributed component coils is the reduction of capacitive (or dielectric) coupling to the sample. In short, this is due to the reduction of the largest potential difference generated within the coil by distributing the inductive and capacitive reactances.¹⁰

Over the years there have been a few coils designed and used wherein the transmit and/or receive coils were placed away from the actual sample space. The reasons for wanting to do such things include needing the space/clearance around the sample for optical or thermal access. The earliest such probe to the author’s knowledge is due to Arnold in what was called the race track probe. His work is referenced by Halliday et al.¹¹ who published a later adaptation of Arnold’s probe.

The downhole well-logging community uses some unusual coils, at least as far as the rest of the magnetic resonance community is concerned. These are some of the earliest examples of inside-out NMR for these geometries wherein the sample is not contained within the coil but outside the coil. One such coil used by Schlumberger as described by Kleinberg in a special issue of Concepts in Magnetic Resonance¹² is, perhaps, the simplest possible coil imaginable. It is topologically equivalent to a single wire plus suitable return paths that do not generate magnetic fields that counteract the primary field. Such a coil that runs longitudinally along the bore hole surface will generate an azimuthal field just outside the borehole. NMR signals can be generated from the surrounding strata containing oil or water in a radial static field that is generated by a suitably arranged permanent magnet blocks in the bore. Several such examples are described in Ref. 12.

We finish this review with another coil that has not found any practical applications but may be an instructive example.¹³ The simple loop coil has already been described as a coil that is used for looking at a sample that is outside the coil. The field coming out of a solenoid’s end has the same property except there is little or no gain over the simple loop because the increase in the number of turns is compensated by the volume of the solenoid in which there is no sample. (It would be more efficient to make a multiple turn loop with minimal volume inside the loop.) Some of that loss could be regained if both ends of the solenoid could be used and that led to the semi-toroid that is shown in Figure 2.3. (A toroid would be a terrific coil for a sample that fits in the coil because it can be considered to be a solenoid without end. However, its accessibility is a serious handicap for most applications.) This coil is topologically the same as the figure 8 coil we described earlier but with a third dimension instead of it being a flat coil. An embellishment is the two halves of the coil being wound in opposite senses with the two ends of the coil connected to a ground plane that is presented to the sample. The electrical feed point is the junction of the two halves, far from the sample region. So, this coil also has minimal electrical interactions, i.e., it is not detuned by a dielectrically lossy sample that can come in contact with it. In addition, having the two halves connected electrically in parallel raises the tuning frequency for its size. Finally, one could conceive of inserting some material inside the semi-toroid that will amplify the signal in an analogous fashion to what a ferrite would do at lower frequencies.

RELATED ARTICLES IN THE ENCYCLOPEDIA OF MAGNETIC RESONANCE

Birdcage Resonators: Highly Homogeneous Radiofrequency Coils for Magnetic Resonance

NMR Probes for Small Sample Volumes

Probe Design and Construction

Radiofrequency Systems and Coils for MRI and MRS

Sensitivity of the NMR Experiment

Solid State NMR Probe Design

Surface and Other Local Coils for In Vivo Studies

Surface Coil NMR: Detection with Inhomogeneous Radiofrequency Field Antennas

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9. A. F. McDowell, U.S. Pat. 7,405,567, (2008).

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13. R. J. S. Brown, R. Chandler, J. A. Jackson, R. L. Kleinberg, M. N. Miller, Z. Paltiel, and M. G. Prammer, Concepts Magn.