NMR Instrumentation

**3**

**Chapter 1**

**Abstract**

*Qiuliang Wang*

functions and developments.

**1. Introduction**

ological information.

frequency (RF) coil [8].

**2. Main magnet**

Hardware of MRI System

**Keywords:** MRI, superconducting magnet, gradient coil, RF coil

Magnetic resonance imaging (MRI) is comprehensively applied in modern medical diagnosis and scientific research for its superb soft-tissue imaging quality and non-radiating characteristics. Main magnet, gradient assembly, and radio-frequency (RF) assembly are main hardware in an MRI system. The hardware performance has direct relationship with the ultimate system overall performance. The development of MRI system toward high magnetic field strength will acquire high signal-to-noise ratio (SNR) and resolution, and meanwhile the manufacture difficulty of main magnet, gradient assembly, and RF assembly will also be significantly elevated. This will make challenges on the design, materials, primitive device, and also the whole machine assembly. This chapter introduces the main hardware of the MRI system and corresponding

In the 1950s, it was discovered in the biomedicine field that hydrogen atoms in water molecules can produce nuclear magnetic resonance phenomena [1]. Nuclear magnetic resonance was used to obtain information from the distribution of water molecules in the human body, by which the internal anatomy of the human body could be mapped accurately [2]. After decades of development, MRI has become indispensable medical imaging devices [3]. The influence of MRI on the clinical and life science comes from its unrivaled imaging capabilities, and it can obtain not only clear structural images of the anatomic structure and the organic lesion completely without trauma [4], but also the other physi-

In recent years, MRI techniques have developed rapidly, especially toward high-field imaging, such as 7 T, 9.4 T or even higher field strengths [5]. MRI technique development requires an associated performance improvement in the system hardware, which mainly includes the main magnet [6], gradient coil [7], and radio-

Early MRI magnet system mainly used ferromagnetic shield structure [9]. The use of large amounts of ferromagnetic shield [10] makes the weight and size of the system relatively large and installation costs of the system high. With the rapid development of magnet technologies, the active shield structure

## **Chapter 1** Hardware of MRI System

*Qiuliang Wang*

## **Abstract**

Magnetic resonance imaging (MRI) is comprehensively applied in modern medical diagnosis and scientific research for its superb soft-tissue imaging quality and non-radiating characteristics. Main magnet, gradient assembly, and radio-frequency (RF) assembly are main hardware in an MRI system. The hardware performance has direct relationship with the ultimate system overall performance. The development of MRI system toward high magnetic field strength will acquire high signal-to-noise ratio (SNR) and resolution, and meanwhile the manufacture difficulty of main magnet, gradient assembly, and RF assembly will also be significantly elevated. This will make challenges on the design, materials, primitive device, and also the whole machine assembly. This chapter introduces the main hardware of the MRI system and corresponding functions and developments.

**Keywords:** MRI, superconducting magnet, gradient coil, RF coil

## **1. Introduction**

In the 1950s, it was discovered in the biomedicine field that hydrogen atoms in water molecules can produce nuclear magnetic resonance phenomena [1]. Nuclear magnetic resonance was used to obtain information from the distribution of water molecules in the human body, by which the internal anatomy of the human body could be mapped accurately [2]. After decades of development, MRI has become indispensable medical imaging devices [3]. The influence of MRI on the clinical and life science comes from its unrivaled imaging capabilities, and it can obtain not only clear structural images of the anatomic structure and the organic lesion completely without trauma [4], but also the other physiological information.

In recent years, MRI techniques have developed rapidly, especially toward high-field imaging, such as 7 T, 9.4 T or even higher field strengths [5]. MRI technique development requires an associated performance improvement in the system hardware, which mainly includes the main magnet [6], gradient coil [7], and radiofrequency (RF) coil [8].

## **2. Main magnet**

Early MRI magnet system mainly used ferromagnetic shield structure [9]. The use of large amounts of ferromagnetic shield [10] makes the weight and size of the system relatively large and installation costs of the system high. With the rapid development of magnet technologies, the active shield structure has been successfully developed for the high-field magnet system [11], which greatly reduces the scope of 5 Gauss line. Generally, the superconducting magnet consists of multiple solenoidal coils and shielded coils [12]. The inner solenoid coil is called the primary coil, generally through forward current. The outer solenoid coil is called shield coils, through the reverse current. Open MRI system helps improve patient comfort and expands the scope for the patient [13]. It is easy to achieve a high magnetic field by using combination of iron core and superconducting coil. The cryogenic system is used to keep superconducting wire in a cryogenic environment and ensure safe operation of the superconducting magnet.

In the Institute of Electrical Engineering, Chinese Academy of Sciences, (IEE, CAS), several sets of MRI magnets have been designed or fabricated, including 0.7 T planar whole-body MRI system, 1.5 T cylindrical whole-body MRI system, 7.0 T animal MRI system, and 9.4 T cylindrical whole-body MRI system [14].

Due to structural advantages of the open MRI system, it can be applied to interventional therapy. The shape of magnetic field depends mainly on yoke and pole, and coils provide magnetic source. The magnet system has less superconducting wire, and only 120 L of liquid helium with zero boiling off liquid helium by one GM cryocooler. Magnetic field strength of superconducting open MRI is generally higher than 0.7 T due to a higher uniform magnetic field produced by superconducting coils [15]. **Figure 1** shows a 0.7 T open MRI system designed by IEE, CAS.

A 9.4 T whole body imaging system is developed in IEE, CAS, shown in **Figure 2**. The magnet has a horizontal length of 3.5 m and large warm bore with a diameter of 0.8 m. The magnet system is designed with the minimum cost of wire consumption. By means of the optimal algorithm, the coil sizes and positions are optimized to reduce the coil volume and constrain the magnetic field inhomogeneity. In the optimization, the coil stress and current margins are also constrained to satisfy the coil safety requirements. Fully stable NbTi superconducting wire type WIC (Wire-In-Channel) is employed to wind the coils. Both active and passive quench protection system are employed to protect the magnet from damage during a quench event. The magnet system will reach the final field homogeneity as low as 0.1 ppm (peak to peak) in the central 30 cm DSV and the stability of 0.05 ppm/h.

**5**

strong Lorentz force.

*Hardware of MRI System*

*DOI: http://dx.doi.org/10.5772/intechopen.89132*

densed by two re-condensing cryocoolers.

*A 9.4 T superconducting magnet for whole-body MRI system.*

parameters must be highly optimized.

**3. Gradient coil**

**Figure 2.**

The magnet is cooled by liquid helium bath, and the evaporated helium is con-

produces linear gradient magnetic fields that are superimposed over a strong uniform magnetic field. The uniform magnetic field is produced by a main magnet, which aligns with the proton precession direction. The superimposed gradient magnetic field slightly changes the proton precession frequency or phase, thus encoding the spatial information of an imaged object in the frequency associated with a position in space [16]. In general, the magnetic field gradient produced by the gradient coils is required to be as linear as possible, and a well-designed gradient coil should also have low inductance, low resistance, high efficiency, etc. [17]. This is especially pertinent in high-field imaging and fast imaging when all the coils'

A gradient coil set is an important component in a standard MRI scanner which

In a gradient assembly, there are three gradient coils, called the x, y, and z coils

[18]. **Figure 3** shows a set of actively shielded gradient coils (here the actively shielding gradient coil is a coil pattern containing both the primary coil and shielding coil [19]). The red and blue colors of the gradient coils indicate where the current flows in clockwise and anticlockwise [20]. The three-axis gradient coils are fixed by epoxy resin in an encapsulated gradient assembly [21], as is shown in **Figure 4**. In an integrated gradient assembly, there are also cooling devices and a shim tray installed [22]. The hard epoxy resin largely impedes the vibration of the gradient coils [23], which avoids torsion and deformation of the gradient coils under

**Figure 1.** *A 0.7 T whole-body open MRI system.*

*Nuclear Magnetic Resonance*

magnet.

IEE, CAS.

has been successfully developed for the high-field magnet system [11], which greatly reduces the scope of 5 Gauss line. Generally, the superconducting magnet consists of multiple solenoidal coils and shielded coils [12]. The inner solenoid coil is called the primary coil, generally through forward current. The outer solenoid coil is called shield coils, through the reverse current. Open MRI system helps improve patient comfort and expands the scope for the patient [13]. It is easy to achieve a high magnetic field by using combination of iron core and superconducting coil. The cryogenic system is used to keep superconducting wire in a cryogenic environment and ensure safe operation of the superconducting

In the Institute of Electrical Engineering, Chinese Academy of Sciences, (IEE, CAS), several sets of MRI magnets have been designed or fabricated, including 0.7 T planar whole-body MRI system, 1.5 T cylindrical whole-body MRI system, 7.0 T animal MRI system, and 9.4 T cylindrical whole-body MRI system [14]. Due to structural advantages of the open MRI system, it can be applied to interventional therapy. The shape of magnetic field depends mainly on yoke and pole, and coils provide magnetic source. The magnet system has less superconducting wire, and only 120 L of liquid helium with zero boiling off liquid helium by one GM cryocooler. Magnetic field strength of superconducting open MRI is generally higher than 0.7 T due to a higher uniform magnetic field produced by superconducting coils [15]. **Figure 1** shows a 0.7 T open MRI system designed by

A 9.4 T whole body imaging system is developed in IEE, CAS, shown in **Figure 2**. The magnet has a horizontal length of 3.5 m and large warm bore with a diameter of 0.8 m. The magnet system is designed with the minimum cost of wire consumption. By means of the optimal algorithm, the coil sizes and positions are optimized to reduce the coil volume and constrain the magnetic field inhomogeneity. In the optimization, the coil stress and current margins are also constrained to satisfy the coil safety requirements. Fully stable NbTi superconducting wire type WIC (Wire-In-Channel) is employed to wind the coils. Both active and passive quench protection system are employed to protect the magnet from damage during a quench event. The magnet system will reach the final field homogeneity as low as 0.1 ppm (peak to peak) in the central 30 cm DSV and the stability of 0.05 ppm/h.

**4**

**Figure 1.**

*A 0.7 T whole-body open MRI system.*

**Figure 2.** *A 9.4 T superconducting magnet for whole-body MRI system.*

The magnet is cooled by liquid helium bath, and the evaporated helium is condensed by two re-condensing cryocoolers.

## **3. Gradient coil**

A gradient coil set is an important component in a standard MRI scanner which produces linear gradient magnetic fields that are superimposed over a strong uniform magnetic field. The uniform magnetic field is produced by a main magnet, which aligns with the proton precession direction. The superimposed gradient magnetic field slightly changes the proton precession frequency or phase, thus encoding the spatial information of an imaged object in the frequency associated with a position in space [16]. In general, the magnetic field gradient produced by the gradient coils is required to be as linear as possible, and a well-designed gradient coil should also have low inductance, low resistance, high efficiency, etc. [17]. This is especially pertinent in high-field imaging and fast imaging when all the coils' parameters must be highly optimized.

In a gradient assembly, there are three gradient coils, called the x, y, and z coils [18]. **Figure 3** shows a set of actively shielded gradient coils (here the actively shielding gradient coil is a coil pattern containing both the primary coil and shielding coil [19]). The red and blue colors of the gradient coils indicate where the current flows in clockwise and anticlockwise [20]. The three-axis gradient coils are fixed by epoxy resin in an encapsulated gradient assembly [21], as is shown in **Figure 4**. In an integrated gradient assembly, there are also cooling devices and a shim tray installed [22]. The hard epoxy resin largely impedes the vibration of the gradient coils [23], which avoids torsion and deformation of the gradient coils under strong Lorentz force.

**Figure 3.**

*Actively shielded gradient coils used in an MRI scanner: (a) x gradient coil, (b) y gradient coil, and (c) z gradient coil. The red and blue colors indicate the direction in which the current flows.*

**Figure 4.** *Illustration of the three-axis gradient coils fixed in the epoxy resin.*

## **4. RF coil**

RF coil is the key component of the MRI system, which serves as the transmitter as well as receiver in the formation of the final images [8]. There are various kinds of RF coils. The difference between coils lies in different parts of human body and different field strengths.

According to imaging part of the human body, it can be classified into head coils, body coils, knee coils or foot coils, etc. No matter how many kinds of coils there may be, all the coils can be basically treated as two kinds of coils, namely surface coil and volume coil. For the surface coils [24], the shape of which is usually a circle, which will facilitate the fabrication of coil. Surface coils are often used as receivers, the reason is that the field it produces is inhomogeneous, which is detrimental to the imaging process. But the signal-to-noise ratio (SNR) of the surface coils is higher than volume coils, partly because it can be located closely to the imaging area. Nowadays, surface coils are not used alone to achieve the receiving purpose. A bunch of surface coils [25], which we call loop array, are used for its good performance in receiving as well as transmitting. An illustration of surface coil is shown in **Figure 5**.

**7**

can result in a highly uniform B1 field.

*Sketch map of volume coils: (a) birdcage coil and (b) TEM coil.*

*Hardware of MRI System*

**Figure 5.**

**Figure 6.**

**Figure 7.**

*DOI: http://dx.doi.org/10.5772/intechopen.89132*

*Diagram of surface coils: (a) single coil and (b) array coil.*

Another kind of RF coil is the volume coil, and the most popular volume coil is the birdcage coil [26–29], which is shown in **Figure 6**. A prominent character of birdcage coil is its quadrature excitation strategies both spatially and temporally. The distinctive excitation technology generates a circularly polarized field, which

*Diagram of volume coils: (a) high-pass birdcage volume coil and (b) low-pass birdcage volume coil.*

An alternative volume coil named TEM coil [30] maybe used in ultra-high field MRI as illustrated in **Figure 7**. TEM is the most general term for "transmission line," and it can be realized through many kinds of circuit, such as coaxial lines, strip lines, microstrips or waveguides. In birdcage coils, the end rings form the "return path" of the current on the rungs. But in high frequencies, the end rings can be problematic. The inductance and resonant frequency of birdcage coils are limited by the size of the end rings. And the end rings are related to the diameter of the coil. The magnetic

*Hardware of MRI System DOI: http://dx.doi.org/10.5772/intechopen.89132*

**Figure 5.** *Diagram of surface coils: (a) single coil and (b) array coil.*

#### **Figure 6.**

*Nuclear Magnetic Resonance*

**6**

**4. RF coil**

**Figure 4.**

**Figure 3.**

different field strengths.

*Illustration of the three-axis gradient coils fixed in the epoxy resin.*

RF coil is the key component of the MRI system, which serves as the transmitter as well as receiver in the formation of the final images [8]. There are various kinds of RF coils. The difference between coils lies in different parts of human body and

*Actively shielded gradient coils used in an MRI scanner: (a) x gradient coil, (b) y gradient coil, and (c) z* 

*gradient coil. The red and blue colors indicate the direction in which the current flows.*

According to imaging part of the human body, it can be classified into head coils, body coils, knee coils or foot coils, etc. No matter how many kinds of coils there may be, all the coils can be basically treated as two kinds of coils, namely surface coil and volume coil. For the surface coils [24], the shape of which is usually a circle, which will facilitate the fabrication of coil. Surface coils are often used as receivers, the reason is that the field it produces is inhomogeneous, which is detrimental to the imaging process. But the signal-to-noise ratio (SNR) of the surface coils is higher than volume coils, partly because it can be located closely to the imaging area. Nowadays, surface coils are not used alone to achieve the receiving purpose. A bunch of surface coils [25], which we call loop array, are used for its good performance in receiving as

well as transmitting. An illustration of surface coil is shown in **Figure 5**.

*Diagram of volume coils: (a) high-pass birdcage volume coil and (b) low-pass birdcage volume coil.*

**Figure 7.** *Sketch map of volume coils: (a) birdcage coil and (b) TEM coil.*

Another kind of RF coil is the volume coil, and the most popular volume coil is the birdcage coil [26–29], which is shown in **Figure 6**. A prominent character of birdcage coil is its quadrature excitation strategies both spatially and temporally. The distinctive excitation technology generates a circularly polarized field, which can result in a highly uniform B1 field.

An alternative volume coil named TEM coil [30] maybe used in ultra-high field MRI as illustrated in **Figure 7**. TEM is the most general term for "transmission line," and it can be realized through many kinds of circuit, such as coaxial lines, strip lines, microstrips or waveguides. In birdcage coils, the end rings form the "return path" of the current on the rungs. But in high frequencies, the end rings can be problematic. The inductance and resonant frequency of birdcage coils are limited by the size of the end rings. And the end rings are related to the diameter of the coil. The magnetic

#### *Nuclear Magnetic Resonance*

field generated by end rings is along with the B0 field, which is nonproductive for the excitation of nucleus. So, in TEM coils, the end rings are replaced by shield to serve as the return path. The inductance and resonant frequency of TEM coil are independent of the diameters of the coil. A length determined TEM coil can be built to arbitrary diameter, without influence on the frequency. So, its use in the ultrahigh field imaging is flexible. The TEM coil can be regarded as a toroidal array of many transmission line elements. The impedance of each element can be modified individually. The reactance between each element can be controlled to achieve parallel imaging applications.

## **Author details**

Qiuliang Wang Institute of Electrical Engineering, Chinese Academy of Sciences, Beijing, China

\*Address all correspondence to: wongsm17@mail.iee.ac.cn

© 2019 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

**9**

2011;**33**:372-376

*Hardware of MRI System*

**References**

*DOI: http://dx.doi.org/10.5772/intechopen.89132*

[11] Gabrielse G, Tan J. Self-shielding superconducting solenoid systems.

[12] Wang Q, Dai Y, Zhao B, et al. A superconducting magnetic system for whole-body metabolism imaging. IEEE Transactions on Applied Superconductivity. 2012;**22**:4400905-4400905

[13] Wang QL, Xu G, Dai Y, et al. Design of open high magnetic field MRI superconducting magnet with continuous current and genetic algorithm method. IEEE Transactions on Applied Superconductivity.

[14] Dai Y, Wang Q, Wang C, et al. Structural design of a 9.4 T wholebody MRI superconducting magnet.

[15] Ni Z, Hu G, Li L, Yu G, Wang Q, Yan L. Globally optimal algorithm for design of 0.7 T actively shielded whole-body open MRI superconducting magnet system. IEEE Transactions on Applied Superconductivity. 2012;**23**:4401104-4401104

[16] Pykett IL, Newhouse JH,

Imaging. 1993;**11**:903-920

1982;**143**:157-168

Buonanno FS, Brady TJ, Goldman MR, Kistler JP, et al. Principles of nuclear magnetic resonance imaging. Radiology.

[17] Tuner R. Gradient coil design: A review of methods. Magnetic Resonance

[18] Jin JM. Electromagnetic Analysis and Design in Magnetic Resonance Imaging. Boca Raton: CRC Press; 1999

[19] Sanchez H, Liu F, Trakic A, et al. A simple relationship for high

Journal of Applied Physics.

1988;**63**:5143-5148

2009;**19**:2289-2292

IEEE Transactions on Applied Superconductivity. 2012;**22**:4900404-4900404

[1] Gutowsky H. Nuclear magnetic resonance. Annual Review of Physical

[2] Brown RW, Cheng YN, Haacke EM, et al. Magnetic Resonance Imaging Physical Principles and Sequence Design. Hoboken, New Jersey: John

[3] Lakrimi M, Thomas AM, Hutton G, et al. The principles and evolution of magnetic resonance imaging. Journal of Physics: Conference Series. IOP Publishing. 2011;**286**:012-016

[4] Wang Q, Dai Y, Zhao B, et al. Development of high magnetic field superconducting magnet technology and applications in China. Cryogenics.

[6] Wang Q. Practical Design of Magnetostatic Structure Using Numerical Methods. Singapore: John

[7] Siebold H. Gradient field coils for MR imaging with high spectral purity. IEEE Transactions on Magnetics.

[8] Vaughan JT, Griffiths JR. RF Coils for MRI. Chichester, West Sussex: John

[9] Wang Q, Wang H, Zheng J, et al. Open MRI magnet with iron rings correcting the Lorentz force and field quality. IEEE Transactions on Applied

[10] Yandong Y, Dai Y, Wang H, et al. Geometrical optimization of iron shield for high field superconducting magnetics in MRI system. Chinese Journal of Low Temperature Physics.

Superconductivity. 2014;**24**:1-5

[5] Robitaille PM, Berliner L. Ultra-High Field Magnetic Resonance Imaging. New York, NY, USA: Springer, LLC; 2006

2007;**31**:364-379

Wiley & Sons; 2013

1990;**26**:897-900

Wiley and Sons, Ltd; 2012

Chemistry. 1954;**5**:333-356

Wiley and Sons, Ltd; 2014

## **References**

*Nuclear Magnetic Resonance*

lel imaging applications.

field generated by end rings is along with the B0 field, which is nonproductive for the excitation of nucleus. So, in TEM coils, the end rings are replaced by shield to serve as the return path. The inductance and resonant frequency of TEM coil are independent of the diameters of the coil. A length determined TEM coil can be built to arbitrary diameter, without influence on the frequency. So, its use in the ultrahigh field imaging is flexible. The TEM coil can be regarded as a toroidal array of many transmission line elements. The impedance of each element can be modified individually. The reactance between each element can be controlled to achieve paral-

Institute of Electrical Engineering, Chinese Academy of Sciences, Beijing, China

© 2019 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium,

\*Address all correspondence to: wongsm17@mail.iee.ac.cn

provided the original work is properly cited.

**8**

**Author details**

Qiuliang Wang

[1] Gutowsky H. Nuclear magnetic resonance. Annual Review of Physical Chemistry. 1954;**5**:333-356

[2] Brown RW, Cheng YN, Haacke EM, et al. Magnetic Resonance Imaging Physical Principles and Sequence Design. Hoboken, New Jersey: John Wiley and Sons, Ltd; 2014

[3] Lakrimi M, Thomas AM, Hutton G, et al. The principles and evolution of magnetic resonance imaging. Journal of Physics: Conference Series. IOP Publishing. 2011;**286**:012-016

[4] Wang Q, Dai Y, Zhao B, et al. Development of high magnetic field superconducting magnet technology and applications in China. Cryogenics. 2007;**31**:364-379

[5] Robitaille PM, Berliner L. Ultra-High Field Magnetic Resonance Imaging. New York, NY, USA: Springer, LLC; 2006

[6] Wang Q. Practical Design of Magnetostatic Structure Using Numerical Methods. Singapore: John Wiley & Sons; 2013

[7] Siebold H. Gradient field coils for MR imaging with high spectral purity. IEEE Transactions on Magnetics. 1990;**26**:897-900

[8] Vaughan JT, Griffiths JR. RF Coils for MRI. Chichester, West Sussex: John Wiley and Sons, Ltd; 2012

[9] Wang Q, Wang H, Zheng J, et al. Open MRI magnet with iron rings correcting the Lorentz force and field quality. IEEE Transactions on Applied Superconductivity. 2014;**24**:1-5

[10] Yandong Y, Dai Y, Wang H, et al. Geometrical optimization of iron shield for high field superconducting magnetics in MRI system. Chinese Journal of Low Temperature Physics. 2011;**33**:372-376

[11] Gabrielse G, Tan J. Self-shielding superconducting solenoid systems. Journal of Applied Physics. 1988;**63**:5143-5148

[12] Wang Q, Dai Y, Zhao B, et al. A superconducting magnetic system for whole-body metabolism imaging. IEEE Transactions on Applied Superconductivity. 2012;**22**:4400905-4400905

[13] Wang QL, Xu G, Dai Y, et al. Design of open high magnetic field MRI superconducting magnet with continuous current and genetic algorithm method. IEEE Transactions on Applied Superconductivity. 2009;**19**:2289-2292

[14] Dai Y, Wang Q, Wang C, et al. Structural design of a 9.4 T wholebody MRI superconducting magnet. IEEE Transactions on Applied Superconductivity. 2012;**22**:4900404-4900404

[15] Ni Z, Hu G, Li L, Yu G, Wang Q, Yan L. Globally optimal algorithm for design of 0.7 T actively shielded whole-body open MRI superconducting magnet system. IEEE Transactions on Applied Superconductivity. 2012;**23**:4401104-4401104

[16] Pykett IL, Newhouse JH, Buonanno FS, Brady TJ, Goldman MR, Kistler JP, et al. Principles of nuclear magnetic resonance imaging. Radiology. 1982;**143**:157-168

[17] Tuner R. Gradient coil design: A review of methods. Magnetic Resonance Imaging. 1993;**11**:903-920

[18] Jin JM. Electromagnetic Analysis and Design in Magnetic Resonance Imaging. Boca Raton: CRC Press; 1999

[19] Sanchez H, Liu F, Trakic A, et al. A simple relationship for high efficiency-gradient uniformity tradeoff in multilayer asymmetric gradient coils for magnetic resonance imaging. IEEE Transactions on Magnetics. 2007;**43**:523-532

[20] Lopez HS, Liu F, Poole M, et al. Equivalent magnetization current method applied to the design of gradient coils for magnetic resonance imaging. IEEE Transactions on Magnetics. 2009;**45**:767-775

[21] Hidalgo-Tobon SS. Theory of gradient coil design methods for magnetic resonance imaging. Concepts in Magnetic Resonance Part A. 2010;**36**:223-242

[22] You XF, Yang WH, Song T, et al. Asymmetric gradient coil design by numerical approach for MRI brain imaging. IEEE Transactions on Applied Superconductivity. 2012;**22**:4401904-4401904

[23] Suits BH, Wilken DH. Improving magnetic field gradient coils for NMR imaging. Journal of Physics. 1989;**22**:565-573

[24] Ackerman JJ, Grove TH, Wong GG, et al. Mapping of metabolites in whole animals by 31P NMR using surface coils. Nature. 1980;**283**:167-170

[25] Roemer PB, Edelstein WA, Hayes CE, et al. The NMR phased array. Magnetic Resonance in Medicine. 1990;**16**:192-225

[26] Hayes CE, Edelstein WA, Schenck JF, et al. An efficient, highly homogeneous radiofrequency coil for whole-body NMR imaging at 1.5 T. Journal of Magnetic Resonance. 1985;**63**:622-628

[27] Leifer MC. Theory of the quadrature elliptic birdcage coil. Magnetic Resonance in Medicine. 1997;**38**:726-732

[28] Vaughan JT, Hetherington HP, Otu JO, et al. High frequency volume coils for NMR imaging and spectroscopy. Magnetic Resonance in Medicine. 1994;**32**:206-218

**Chapter 2**

**Abstract**

**1. Introduction**

**11**

*Gabriele Barbaraci*

Control Flow Strategy in

of resonance move to a desired value of frequency.

a Receiver Coil for Nuclear

Magnetic Resonance for Imaging

A mathematical discussion is introduced to describe the receiver coil characterizing the NMRI system starting from a general shape of the conductor. A set of different inductance calculations have been introduced varying the shape of the conductor. The inductance calculation led to a general expression of the magnetic field of a single coil characterized by a rectangular shape. A dynamic model of the receiver coil has been developed to represent the natural frequencies that characterize the operational bandwidth. A nonstationary control strategy is implemented to make a real-time changing of the operational bandwidth. The frequency response of the coil generates the necessary conditional expression in order to let the peak

**Keywords:** magnetic resonance, inductance, magnetic field, transfer function

For a NMRI system to work, a set of operations must be completed in a time order. The first operation is characterized by choosing the point of the human body that must be analyzed; determining the resonance magnetic field which must be associated to that point; the RF magnetic field pulsing sequence; phase encoding process; and data extraction processed by a digital microprocessor proving a high computational burden. In this chapter, one step characterizing the NMRI system that represents the most important physical effect involving a dynamic aspect which is the transmitter coil will be discussed. In the NMRI systems, it is strictly necessary to have a transmitter coil and a receiver coil, respectively, to excite the magnetization vector inside the human body and transform in electrical current signal the magnetic field variation coming from the magnetization vector. The modern NMRI exhibit a more compact design characterized by associating to one coil the task to generate the RF pulse and receive the signal. This is the reason why in the literature and in the real operating NMRI, the use of a term that refers to a coil performing both tasks called trans-receiver is very common. In this chapter, a model of receiver coil will be studied by focusing the attention in the receiving task because of the importance that is related to the image's quality. The receiver coils can be considered as a filter that allows to capture signal's frequency of interest. As a filter, the receiver coil can be a low-pass, high-pass, or band-pass filter. The challenge of all NMRI manufacturers and of most of the scientific researchers is to

[29] Tropp J. The theory of the birdcage resonator. Journal of Magnetic Resonance. 1989;**82**:51-62

[30] Pascone RJ, Garcia BJ, Fitzgerald TM, et al. Generalized electrical analysis of low pass and high pass birdcage resonators. Magnetic Resonance Imaging. 1991;**9**:395-408

## **Chapter 2**

*Nuclear Magnetic Resonance*

2007;**43**:523-532

2009;**45**:767-775

2010;**36**:223-242

1989;**22**:565-573

1990;**16**:192-225

1985;**63**:622-628

Nature. 1980;**283**:167-170

[25] Roemer PB, Edelstein WA, Hayes CE, et al. The NMR phased array. Magnetic Resonance in Medicine.

[26] Hayes CE, Edelstein WA,

elliptic birdcage coil. Magnetic

Schenck JF, et al. An efficient, highly homogeneous radiofrequency coil for whole-body NMR imaging at 1.5 T. Journal of Magnetic Resonance.

[27] Leifer MC. Theory of the quadrature

Resonance in Medicine. 1997;**38**:726-732

efficiency-gradient uniformity tradeoff in multilayer asymmetric gradient coils for magnetic resonance imaging. IEEE Transactions on Magnetics.

[28] Vaughan JT, Hetherington HP, Otu JO, et al. High frequency volume coils for NMR imaging and spectroscopy. Magnetic Resonance in

[29] Tropp J. The theory of the birdcage

[30] Pascone RJ, Garcia BJ, Fitzgerald TM, et al. Generalized electrical analysis of low pass and high pass birdcage resonators. Magnetic Resonance

Medicine. 1994;**32**:206-218

Imaging. 1991;**9**:395-408

resonator. Journal of Magnetic Resonance. 1989;**82**:51-62

[20] Lopez HS, Liu F, Poole M, et al. Equivalent magnetization current method applied to the design of gradient coils for magnetic resonance imaging. IEEE Transactions on Magnetics.

[21] Hidalgo-Tobon SS. Theory of gradient coil design methods for magnetic resonance imaging. Concepts

in Magnetic Resonance Part A.

[22] You XF, Yang WH, Song T, et al. Asymmetric gradient coil design by numerical approach for MRI brain imaging. IEEE Transactions on Applied Superconductivity. 2012;**22**:4401904-4401904

[23] Suits BH, Wilken DH. Improving magnetic field gradient coils for NMR imaging. Journal of Physics.

[24] Ackerman JJ, Grove TH, Wong GG, et al. Mapping of metabolites in whole animals by 31P NMR using surface coils.

**10**
