RF Coils Design for Small Animal MRI 
Lung Imaging at 3T Using Hyperpolarized 
129Xe and Inert Fluorinated Gases 
 
 
by 
 
 
Tao Li 
 
 
A thesis submitted to the faculty of graduate studies 
in partial fulfillment of the requirements for the degree of 
Masters of Science in Electrical and Computer Engineering 
 
 
 
 
 
Department of Engineering 
Lakehead University 
 
 
Thunder Bay, Ontario, Canada 
July 16th, 2013 
 2 
 
ABSTRACT 
This thesis described the investigation, construction and testing of two sets of RF coils for 
their applications in novel lung MRI imaging techniques.  
In the first part of the thesis, a quadrature-driven birdcage coil for rat lung MRI using inert 
fluorinated gases was developed. Methods for coil tuning and impedance matching were 
presented and discussed. The sensitivity improvement resulted from a quadrature-driven 
mode was quantitatively measured, and compared to the linear reference. A dual-angle 
method (DAM) was studied and implemented to quantitatively measure the B1 field 
homogeneity, and a B1 field map was generated at the center of the coil. In vivo rat lung 
imaging experiments were conducted using the constructed coil, and the multi-slice images 
acquired from the rat lung were presented. 
In the second part of the thesis, a 1H-129Xe double-birdcage coil for rat lung MRI using 
hyperpolarized 129Xe gas was developed. The Q factors of each coil was measured and 
compared before and after the double-birdcage structure was formed. The coupling between 
the two coils was tested, and a geometrical decoupling method was implemented and 
optimized. Imaging scans using thermal xenon phantom and saline syringe phantom were 
conducted with image registration post-processing performed, and the dual-frequency scan 
ability of the developed coil was verified and evaluated. 
 3 
 
ACKNOWLEDGEMENT 
Firstly, I would like to thank my co-supervisor Dr. Mitchell Albert, whose support, advice, 
accessibility and encouragement has been invaluable to me throughout my graduate study 
and thesis research. And I also would like to thank my supervisor Dr. Laura Curiel, for her 
continuous support and help. 
I would like to express my sincerest gratitude to Mr. Ralph Hashoian (Clinical MR Solution, 
LLC), a great engineer and mentor, not only for his expert tutoring in RF knowledge, and 
generous sharing of many invaluable experiences in coil engineering, but also for his kind 
encouragement that inspires me to become a professional engineer. 
Many thanks must go to Dr. Matthew Fox for his help in NMR theory and supports in animal 
experiments preparations. And I also would like to thank Mr. Marcus Couch for his help 
through my courses study.  
I reserve my special thanks for Dr. Iain Ball, for our countless hours of Starbucks MRI talks, 
and his professional support that have greatly helped me in my study and research.   
Finally, I am eternally grateful to my families for their never-end love and support.  
 
 4 
TABLE OF CONTENTS 
 
ABSTRACT ............................................................................................................................. 2 
ACKNOWLEDGEMENT ...................................................................................................... 3 
LIST OF FIGURES ................................................................................................................ 6 
LIST OF TABLES .................................................................................................................. 8 
LIST OF SYMBOLS .............................................................................................................. 9 
LIST OF ABBREVIATIONS .............................................................................................. 10 
CHAPTER 1 INTRODUCTION ......................................................................................... 11 
1.1 Background ................................................................................................................... 11 
1.2 Motivation of the study ................................................................................................. 12 
1.3 Scope of the thesis ........................................................................................................ 12 
CHAPTER 2 NUCLEAR MAGNETIC RESONANCE .................................................... 14 
2.1 Spin Angular Momentum ............................................................................................. 14 
2.2 Bulk Magnetization and Polarization ............................................................................ 15 
2.3 Interaction with external magnetic field - Precession ................................................... 16 
2.4 Spin Excitation and Relaxation ..................................................................................... 17 
2.5 Bloch Equations and FID Signal ................................................................................... 19 
2.6 Magnetic Resonance Imaging (MRI) ............................................................................ 20 
2.6.1 Slice selection ........................................................................................................ 20 
2.6.2 Spatial encoding ..................................................................................................... 21 
2.6.3 K-space and image reconstruction ......................................................................... 22 
2.7 Hyperpolarized Noble Gases MRI ................................................................................ 22 
CHAPTER 3 RF COILS THEORY .................................................................................... 24 
3.1 Transmission and Reception ......................................................................................... 24 
3.2 Resonance Circuits and Coil Tuning ............................................................................ 25 
3.3 Q Factor ........................................................................................................................ 26 
3.4 Impedance Matching ..................................................................................................... 27 
3.5 Signal to Noise Ratio (SNR) and Signal losses ............................................................ 28 
3.5.1 SNR ........................................................................................................................ 28 
3.5.2 Coil loss and sample loss ....................................................................................... 29 
 5 
3.6 Filling Factor ................................................................................................................. 30 
3.7 Surface coil & Volume coil .......................................................................................... 30 
3.7.1 Surface coil ............................................................................................................ 30 
3.7.2 Volume coil ............................................................................................................ 31 
3.8 Birdcage Coil ................................................................................................................ 32 
CHAPTER 4 19F QUADRATURE BIRDCAGE COIL ..................................................... 37 
4.1 Introduction ................................................................................................................... 37 
4.2 Coil Geometry and Tuning ........................................................................................... 37 
4.3 Impedance Matching ..................................................................................................... 38 
4.4 Quadrature Driving ....................................................................................................... 41 
4.4.1 Quadrature mode .................................................................................................... 41 
4.4.2 Quadrature coil construction .................................................................................. 42 
4.4.3 ? / 8 Hybrid coupler ............................................................................................... 44 
4.5 Results ........................................................................................................................... 47 
4.5.1 Phantom spectroscopic scan results ....................................................................... 48 
4.5.2 Phantom imaging scan results ................................................................................ 49 
4.5.3 B1 field mapping and field inhomogeneity calculation .......................................... 50 
4.5.4 Animal in vivo scan results .................................................................................... 53 
4.6 Discussion ..................................................................................................................... 54 
CHAPTER 5 1H - 129Xe DOUBLE-BIRDCAGE COIL ..................................................... 55 
5.1 Introduction ................................................................................................................... 55 
5.1.1 1H and 129Xe birdcage coils construction ............................................................... 55 
5.1.2 Double-birdcage structure and coils re-tuning ....................................................... 58 
5.2 Field Decoupling and Coil Isolation ............................................................................. 59 
5.3 Results ........................................................................................................................... 63 
5.3.1 Q factor value ......................................................................................................... 63 
5.3.2 Imaging scan results and image registration .......................................................... 63 
5.4 Discussion ..................................................................................................................... 66 
CHAPTER 6 CONCLUSION .............................................................................................. 68 
 6 
 
LIST OF FIGURES 
Figure 2.1 Spin precession. A Spin M, precesses around Bo at Larmor frequency. .............. 17 
Figure 2.2 T1 relaxation of the magnetization. ....................................................................... 18 
Figure 2.3 T2 relaxation of the magnetization. ....................................................................... 19 
Figure 2.4 Slice selection. Z is the direction of main magnetic field. A slice of thickness ?z is 
selectively excited by the RF pulse of the corresponding frequency. ..................................... 20 
Figure 2.5  (a) Phase encoding in y direction, and (b) frequency encoding in x direction. .... 21 
Figure 3.1 Equivalent RLC resonant circuit of a coil. ............................................................ 25 
Figure 3.2 A loop surface coil (a) and its equivalent circuit (b). ............................................ 31 
Figure 3.3 An illustrative saddle coil structure [14]. ................................................................ 32 
Figure 3.4 Illustrative structure of a birdcage coil in its high-pass mode. .............................. 33 
Figure 3.5 Equivalent circuit of a high?pass birdcage coil element. ...................................... 33 
Figure 3.6 Illustrative schematic of a high-pass birdcage coil element (a), and matrix diagram 
of a high-pass birdcage coil (b). .............................................................................................. 34 
Figure 3.7 Illustrative cosine currents distribution in a 8-rungs birdcage .............................. 36 
Figure 3.8 Illustrative field distribution in the transverse plane inside the birdcage coil [14]. 36 
Figure 4.1 Top view of the 19F birdcage coil .......................................................................... 38 
Figure 4.2 Schematics of a L-C Balun. ................................................................................... 39 
Figure 4.3 S11 responses of the two channels on Smith chart. ............................................... 40 
Figure 4.4 Developed B1 magnetic field pointing toward one direction in linear mode (a), and 
rotating in the same direction with the magnetization in quadrature mode (b). ..................... 42 
Figure 4.5 Schematics of the quadrature-driven birdcage coil with impedance matching 
Balun circuits for both I and Q channels. ............................................................................... 43 
Figure 4.6 Signal phase shifting (a) in a ? / 8 hybrid coupler (b). .......................................... 44 
Figure 4.7 Equivalent circuit of a ? / 8 hybrid coupler. .......................................................... 45 
Figure 4.8 Completed lumped elements ? / 8 hybrid coupler. ................................................ 46 
Figure 4.9 A 90-degree phase shift observed at the two output ports of the ? / 8 hybrid. ...... 47 
 7 
Figure 4.10 S21 response between the port1 and port 4 of the hybrid. An isolation of -36dB 
was achieved at the frequency of 120.15MHz. ....................................................................... 47 
Figure 4.11 FID signal (a) and spectrum response (b) for the coil in linear mode, and FID 
signal (c) and spectrum response (d) for the coil in quadrature mode. ................................... 49 
Figure 4.12 Transverse (a) and coronal (b) images of the PFP gas phantom. ........................ 50 
Figure 4.13 Normalized B1 map of a transverse slice at the center of the coil. ...................... 51 
Figure 4.14 (a) Normalized B1 field distribution in one slice of the map (4 cm),  and (b) 
histogram of the normalized B1 field throughout the center region of the coil (4 cm * 4 cm).
 ................................................................................................................................................. 52 
Figure 4.15 Multi-slice images acquired in a healthy rat lung using 3D FFE sequence. FOV = 
90*90 mm, Slice thickness = 10mm, TR / TE = 20 / 1.94 ms, NSA = 150. ........................... 53 
Figure 5.1 S11 responses of the xenon coil (a) (b) and the proton coil (c) (d). ...................... 57 
Figure 5.2 Illustrative structure of a double-birdcage coil. ..................................................... 59 
Figure 5.3 Front view (a) and side view (b) of the constructed 1H - 129Xe double-birdcage coil.
 ................................................................................................................................................. 59 
Figure 5.4 Isolation V.S. the relative positions of the two birdcage coils. ............................. 61 
Figure 5.5 S11 response of the xenon coil (a) and S21 response between the xenon and 
proton coils (b). ....................................................................................................................... 62 
Figure 5.6 S11 response of the proton coil (a), and S21 response between the proton and 
xenon coils (b). ........................................................................................................................ 62 
Figure 5.7 Xenon thermal phantom and saline syringe phantom (a) are set up inside the coil 
(b). ........................................................................................................................................... 63 
Figure 5.8 Transverse (a) and coronal (b) images of the saline syringe phantom; transverse (c) 
and coronal (d) images of the xenon thermal phantom; and transverse (e) and coronal (f) 
registered images of xenon and proton. .................................................................................. 65 
Figure 5.9 In vivo chemical-shift spectrum obtained from a health rat using the quadrature-
driven xenon birdcage coil. ..................................................................................................... 67 
 
 8 
 
LIST OF TABLES 
Table 4.1 19F birdcage coil dimensions and materials ............................................................ 37 
Table 4.2 Comparison of the SNR and power consumption .................................................. 48 
Table 5.1 129Xe Inner Birdcage Coil Dimensions ................................................................... 56 
Table 5.2 1H Outer Birdcage Coil Dimensions ....................................................................... 56 
Table 5.3 Scan parameters and results .................................................................................... 64 
 
 9 
LIST OF SYMBOLS 
Symbol Meaning 
T Tesla 
129Xe Xenon ? 129 
19F Fluorine - 19 
3He Helium - 3 
1H Proton 
I Quantum number 
M Magnetization 
h Planck constant 
?  Gyromagnetic ratio 
g Lande g-factor 
e Charge of an electron 
m Mass 
B0 Main magnetic field 
kB Boltzmann constant 
B1 Excitation magnetic field 
?  Flip angle 
T1 Longitudinal relaxation time 
T2 Transverse relaxation time 
J Current density 
E Electric field 
Q Quality factor 
f?  3-db bandwidth 
?  Reflection coefficient 
? Susceptibility 
f?  Filling factor 
0?  Permeability 
 10 
 
LIST OF ABBREVIATIONS 
Abbreviation Meaning 
NMR Nuclear magnetic resonance 
MRI Magnetic resonance imaging 
RF Radio frequency 
FID Free induction decay 
SNR Signal to noise ratio 
FOV Field of view 
ROI Region of interest 
PFP Perfluoropropane 
SV Single voxel 
TR Repetition time 
TE Echo time 
FFE Fast field echo (pulse sequence) 
DAM Double angle method 
 
 11 
 
CHAPTER 1 INTRODUCTION 
1.1 Background 
The phenomenon of Nuclear Magnetic Resonance (NMR) was firstly discovered by Purcell 
[1] and Bloch [2] in 1946. In 1973, Lauterbur [3] and Mansfield [4] developed the techniques to 
generate images of a subject from NMR signals using Fourier Transform. Ever since then, 
magnetic resonance imaging (MRI) technique has been rapidly developed and has become  
one of the most valuable and widely-used diagnostic imaging modalities. This non-invasive 
diagnostic imaging technique has the ability to provide tomography images with structural 
information of an interested region of the human body. In addition, the development of 
functional MRI (fMRI) has made it an essential research tool in psychology and physiology, 
providing not only the structural, but also functional information of the human brain. 
Nevertheless, there are important tissues and organs in the human body that resist the 
conventional MRI techniques, such as the lungs, to name one. This is because the 
conventional MRI technique adopts proton (1H) as the imaging contrast for its abundance in 
human body.  However, the proton density in the lungs is very low due to the vast cavity 
inside, which drastically limits the NMR signal strength from generating images of 
diagnostic values. Besides, the micro structures of the bronchus and alveolar create countless 
interfaces between the lung tissues and the air, and result in a very inhomogeneous 
susceptibility and thus a distorted field distribution. This further handicapped the 
conventional MRI from generating useful lung images. 
In 1994, Albert et al. [5] developed a novel technique using hyperpolarized novel gases as 
imaging contrasts to image the lungs with MRI techniques. In this technique, 
hyperpolarization of the noble gas nuclei (3He, 129Xe) is achieved by either spin exchange 
with optically pumped rubidium atoms (SEOP), or metastability exchange optical pumping 
(MEOP), and the signal intensity from the hyperpolarized nuclei can be increased up to a 
hundred thousand times. Hyperpolarized noble gas MRI has shown dramatic results for 
imaging of the lungs, and proven to be an effective method for evaluating, and staging the 
progress of treatment of, pulmonary diseases.  
 12 
On the other hand, Kuethe et al. has demonstrated the first use of inert fluorinated MRI 15 
years ago[6]. And recently Soher et al. [7] has shown another approach to MRI lung imaging 
using inert fluorinated gases, such as sulphur hexafluoride (SF6), hexafluoroethane (C2F6), 
and perfluoropropane (C3F8 or PFP). These gases are nontoxic, abundant and inexpensive, 
and do not require specialized hardware for hyperpolarization prior to their use in MRI, while 
their very short longitudinal magnetization recovery times (T1), enables efficient signal 
averaging, and the high gyromagnetic ratio of 19F, promises improved SNR in the lung 
images. 
1.2 Motivation of the study 
To better understand and develop these novel lung imaging techniques, a vast number of pre-
clinical small animal experiments using rats and mice have been conducted [8-11]. Due to the 
different experimental protocols for small animal imaging experiments, as well as their small 
sizes, it is always preferable and desirable to build dedicated RF coils that are optimized for 
each different experiment, and more importantly, to quantitatively evaluate and improve their 
performances that directly affect the signal and image quality, such as the generated field 
homogeneity and coil sensitivity. In addition, it is commonly required in many lung imaging 
experiments to acquire both the proton images for anatomical structure information, and non-
proton images for the structural and functional information of the lungs. In order to perform 
an accurate image registration, the experimental subject shouldn?t be moved during the two 
different scan protocols. This will require a coil tuned to work at both the proton frequency 
and the non-proton frequency, or two coils tuned to two different frequencies working in 
close proximity. 
1.3 Scope of the thesis 
In this work, two sets of RF coils were developed and optimized for rat lung imaging 
experiments using inert fluorinated gases and hyperpolarized xenon gas. For 19F rat lung 
imaging experiments, a quadrature-driven birdcage coil dedicated for rat lung imaging 
experiments was developed. Improvement in sensitivity and power consumption obtained 
from the quadrature structure were measured and studied. The generated B1 field 
homogeneity was quantitatively investigated, and a B1 field map in the middle of the coil was 
 13 
generated. Phantom spectroscopy and imaging scans and in vivo rat lung imaging scans were 
performed. 
For hyperpolarized xenon lung imaging experiments, a double-birdcage coil working at 
proton and xenon frequencies was developed; the decoupling between the two coils was 
quantitatively measured and optimized. The Q factors of the two coils were measured and 
compared before and after the double-birdcage coil was constructed. 1H - 129Xe dual-nuclei 
imaging scans and image registrations were performed on phantoms.  
Chapter 2 introduces the fundamental principles and physics of nuclear magnetic resonance. 
Chapter 3 discusses the theories of RF coil design for NMR and MRI. The essential 
parameters of a RF coil are generally explained. The principal and resonance modes 
calculation of a birdcage coil are discussed. 
Chapter 4 discusses the design and construction of the 19F quadrature birdcage for rat. The 
tuning of the resonance frequency and impedance matching using Balun circuits are 
described. The sensitivity and power consumption improvement from the quadrature 
structure are measured and verified. A method to quantitatively measure the homogeneity is 
discussed and the B1 map in the center of the coil is generated. Phantom scan results and in 
vivo rat lung imaging scan results are presented and discussed. 
Chapter 5 discusses the design and construction of the 1H - 129Xe double-birdcage coil. The 
coupling issue between the two birdcage coils are discussed and the optimization of the 
decoupling are presented. The Q factors measurements and comparison for both two coils are 
discussed. Phantom scan results and the image registration result are presented and discussed. 
Chapter 6 presents the conclusion that can be drawn from the thesis, as well as the areas of 
future work.   
 14 
 
CHAPTER 2 NUCLEAR MAGNETIC RESONANCE  
2.1 Spin Angular Momentum 
Spin angular momentum, like mass and charge, is an intrinsic property of the nuclei. In 
quantum mechanics, this property is characterized by spin quantum number I, which is either 
an integer or half integer. Spin of a nucleus can be considered as a sphere of distributed 
charge rotating about its own axis, and the small current resulted from this rotation gives rise 
to a ?magnetic moment?. The orientation of the magnetic moment is random without the 
presence of an external magnetic field, and its magnitude is: 
)1( ?? II??? , (2-1) 
where ? = h / 2?,  where h is Planck's constant, and ? is gyromagnetic ratio, defined as, 
m
ge
2??
, (2-2) 
where g is the Lande g-factor, e is the charge of an electron, and m is the mass of the nucleus.  
When the spins are placed in a magnetic field B0, the energy of the nuclei is splitted into 2I+1 
states, known as Zeemann effect. Taking proton for example, which has the I = 1/2, the two 
energy states are: 
02/1 2 BE ?
????
. (2-3) 
These two energy states correspond to the magnetic moments being aligned in parallel with 
B0 and anti-parallel with B0, respectively. A transition between these two energy states can 
happen by absorbing or emitting the energy equal to the energy difference between them. 
0BE ?? ?? ??? . (2-4) 
Combining equation (2-3) and (2-4) equation, one obtains, 
0B?? ? , (2-5) 
 15 
where ? is called Larmor frequency. The above equations show that a transition between the 
two energy states occurs only when absorbing or emitting electromagnetic energy at this 
frequency.  
2.2 Bulk Magnetization and Polarization 
When a group of spins is placed in an external magnetic field B0, each spin aligns in either 
parallel or anti-parallel with the field, as described above. In real NMR process, one usually 
deals with a large number of spins, rather than just one. To describe their general behaviour, 
the concept of the net magnetization was introduced, which is the summation of all the spin 
magnetic momentum vectors.  
At room temperature, the number of spins in the parallel state N+ is slightly higher than that 
of anti-parallel state N-. The difference in the numbers between the spins in these two states 
is given by Boltzman statistics: 
)/()/( 0 kTBkTE eeN
N ????
?
?
?? , 
(2-6) 
where k is Boltzmann constant and T is the absolute temperature. If the total number of spins 
N is N+ + N-, then the population difference is given as: 
)2/tanh(1
1
0)/(
)/(
0
0
kTBne
enNN kTB
kTB
??
?
??
?
??
??? ?
?
?? . 
(2-7) 
The polarization P of the spins is defined as: 
kTBkTBn
NNP 2/)2/tanh( 00 ?? ?? ????
?? . (2-8) 
Therefore the magnitude of the net magnetisation vector is; 
Tk
IIBNMM
B3
)1(022
0
??? ?? . 
(2-9) 
 16 
2.3 Interaction with external magnetic field - Precession 
This magnetization, when put into an external static magnetic field B0, will experience a 
magnetic torque. The motion of the magnetization M can be described by the equation: 
BMdt
Md ??? ?? ? . 
(2-10) 
In laboratory frame of reference, assuming a uniform external magnetic field B in the 
direction of z axis, B = B0, the above equation can be rewritten with three coupled linear 
equations representing the three components, 
0BMdt
dM
y
x ?? , 
 
0BMdt
dM
x
y ??? , 
(2-11) 
0?dt
dM z . 
 
Further derive the first and second equation above, giving: 
x
x MBdt
Md
0
2
2
2
??? , 
 
y
y MBdt
Md
0
2
2
2
??? , 
(2-12) 
Set the initial conditions as Mx(0), My(0), and Mz(0), the solutions to above equations are: 
)sin()0()cos()0()( 00 tBMtBMtM yxx ?? ?? , 
 
)cos()0()sin()0()( 00 tBMtBMtM xyy ?? ??? , 
(2-12) 
)0()( zz MtM ? . 
 
 17 
Equations (2-12) describe the motion of the magnetization in an external field.  They indicate 
that the magnetization precesses about the magnetic field B0 at Larmor frequency, as shown 
in Fig 2.1 below. 
 
 
Figure 2.1 Spin precession. A Spin M, precesses around Bo at Larmor frequency. 
 
2.4 Spin Excitation and Relaxation  
When a second magnetic field B1, generated by a RF pulse of Larmor frequency, is applied to 
the magnetization, by absorbing the energy from the B1 field, the magnetization will then be 
?pushed? and tilted away from the z axis. This is called ?excitation? of the magnetization, 
which is often described by the flip angle, 
?? ? ?? 0 1 )( dttB , 
(2-13) 
where t is the duration of the RF pulse. 
Following the RF pulse, the magnetization starts to relax in two directions at the same time. 
In the ?longitudinal? direction which is in parallel with the external magnetic field, the 
magnetization recovers back to its equilibrium state. This process is called "spin-lattice" 
relaxation, or T1 relaxation. The rate of this relaxation is governed by the equation: 
 18 
1
0
T
MM
dt
dM zz ?? , 
(2-14) 
where M0 is the magnetization in equilibrium state, and Mz is the magnetization in 
longitudinal direction. The solution to this equation is, 
)1( )/1(0 1Tz eMM ??? . 
(2-15) 
After a time period of T1, the longitudinal magnetization is recovered to 63% of M0, and after 
five times T1, it is recovered back to equilibrium M0.  
 
 
Figure 2.2 T1 relaxation of the magnetization. 
 
At the same time, the magnetization in the "transverse" plane, which is orthogonal to the 
external magnetic field, starts to lose its phase coherence because the protons are 
experiencing different fields due to the interactions with adjacent protons. Transverse 
magnetization eventually relaxes back to zero. This process is called ?spin-spin? relaxation, 
or T2 relaxation. The rate of this relaxation is governed by the equations: 
2T
M
dt
dM xx ?? , 
(2-16) 
2T
M
dt
dM zy ?? , 
(2-17) 
 19 
where Mx and My are the magnetization components in x and y directions in the transverse 
plane. The solutions of there equations are, 
)/( 2)0()( Ttxx eMtM ?? , 
(2-18) 
)/( 2)0()( Ttyy eMtM ?? . 
(2-19) 
After the time period of T2, the transverse magnetization is recovered to 37% of Mxy(0). 
 
 
 
Figure 2.3 T2 relaxation of the magnetization. 
 
2.5 Bloch Equations and FID Signal 
When the previous equations of motion with the equations of relaxation are combined, the 
complete equations of motion for the magnetisation, known as Bloch equations, are obtained: 
2
0 )( T
MBMdt
dM x
y
x ??? ?
?? , 
 
2
01 )( T
MBMBMdt
dM y
xz
y ????
?
??? , 
(2-20) 
1
0
1
)(
T
MMBMdt
dM z
y
z ??? ? . 
 
 20 
During the process of spin relaxation, an oscillating magnetic field will be generated that can 
be detected by a coil tuned to resonate at the same frequency. According to Faraday?s Law of 
Induction, the magnetic flux through the coil loop will then induce an electromagnetic force 
across the coil, kwon as the Free Induction Decay (FID) signal. The FID signal decays 
exponentially immediately after the magnetization starts to relax. By applying gradient 
magnetic fields and spacially encoding the FID, various MR images can be obtained.  
2.6 Magnetic Resonance Imaging (MRI) 
2.6.1 Slice selection 
MRI is a tomography technique, which means it generates a cross-sectional image of the 
human body in a certain direction. Hence the first step of generating a MRI image is to 
determine the slice to be imaged and distinct it from the rest of the body (or a sample). This 
is achieved by adding a gradient magnetic field to the existing main magnetic field B0 to 
make it increasing (or decreasing) gradually within a certain range that enclose the slice of 
interest. From previous sections, we know that Larmor frequency is proportional to the 
magnetic field strength, thus by applying a RF pulse at a frequency of the Larmor frequency 
of a particular slice, the spins within this slice can be excited only, whilst the rest will remain 
unaffected. 
 
 
Figure 2.4 Slice selection. Z is the direction of main magnetic field. A slice of thickness ?z is 
selectively excited by the RF pulse of the corresponding frequency. 
 21 
2.6.2 Spatial encoding 
Once the slice has been selectively excited, one has to identify the spatial position of an MR 
signal. This is achieved by spatial encoding, which consists of phase encoding and frequency 
encoding of the MR signals in two orthogonal directions (here defined as x and y directions). 
For phase encoding, after the spins have been excited, a magnetic field gradient in the y-
direction is switched on for a short amount of time. This phase-encoding gradient changes 
the Larmor frequencies of the spins according to their location along the gradient. As a result, 
after the gradient is switched off, all spins return to their initial Larmor frequency, but a 
phase shift has been developed among the spins, meaning that phase varies linearly along the 
y-axis and each line within the slice can thus be identified by its unique phase, as shown in 
Fig.2.5 (a). 
The second spatial encoding of the MR signal is realized by changing the frequencies along 
the x direction. Similar to the phase encoding, a frequency-encoding gradient is applied in the 
x direction. This gradient changes the Larmor frequencies of the spins along the x direction. 
When one is sampling the MR signal while the frequency-encoding gradient is switched on, 
not single frequency but a whole frequency spectrum is obtained. Now each column of the 
slice is identified by a specific frequency, as shown in Fig.2.5 (b).  
Phase and frequency together enable spatial identification of each element, defined as 
?voxel?. 
  
(a) (b) 
  
Figure 2.5  (a) Phase encoding in y direction, and (b) frequency encoding in x direction. 
 22 
2.6.3 K-space and image reconstruction 
When a MR signal is sampled after being spatially encoded as described above, it contains 
two information contents, frequency and phase. The frequency locates the signal along the x-
axis and it can be extracted directly by applying a Fourier transform to decompose the signal 
into its frequency components along the frequency encoding direction (x direction in this 
case). On the other hand, the phase distribution within each frequency provides information 
of the position of the corresponding signal component along the y direction. However, the 
phases of the individual spins cannot be derived from a single signal but can only be 
extracted from a set of signals, thus in an imaging scans, the excitations are usually repeated 
with a different phase encoding gradient strength each time, to provide a sets of MR signal in 
order to derive the phase encoded spatial information via a second Fourier transform. To do 
so, each spatially encoded MR signal will then be recorded in a mathematical space, called k-
space. It is a matrix of sampled MR signals, and by applying a 2D Fourier transform on the 
k-space data, and NMR image can be reconstructed. 
2.7 Hyperpolarized Noble Gases MRI 
Hyperpolarisation is a technique that increases the polarisation of a nucleus to be five orders 
of magnitude (about 100,000 times) higher than its equilibrium polarisation. This drastic 
increment in polarisation will increase the signal from the nucleus by a proportionate amount. 
This overcomes the signal loss from the lower gas density, which is about 3 orders of 
magnitude lower than that of protons. Noble gases, specifically 3He and 129Xe, are most 
widely used contrasts for hyperpolarisation MRI. This is mainly because of their nuclei 
possessing long spin-lattice relaxation times (T1), and also 3He and 129Xe are the only non-
radioactive noble gases with a spin number of 1/2.  
Spin exchange optical pumping (SEOP), is a well-established method for noble gases 
hyperpolarisation. In this method, angular momentum is transferred indirectly from a 
polarised laser beam to 129Xe or 3He nuclei via alkali metal atoms (usually rubidium). For 
3He, metastable exchange optical pumping (MEOP) is an alternative method to SEOP. In 
this method, hyperpolarization is created directly in the nuclei via polarized laser, when 3He 
atoms are excited to the metastable state by a radiofrequency discharge. 
 23 
In conventional MRI, after a RF pulse has excited the longitudinal magnetisation (Mz), it 
recovers to thermal equilibrium by T1 relaxation. For hyperpolarized gases, the longitudinal 
magnetisation will not recover, and each RF pulse destroys a portion of the longitudinal 
magnetisation. For such a reason, one normally uses a small flip angle in each excitation to 
achieve a full k-space sampling. Since there is no longitudinal recovery, the repetition time, 
TR, can be made as short as possible to reduce the scan time, and the signal detected from the 
nth excitation is given by [13]: 
?? sincos)0()( )1()])(1([ 1 ???? nT
Tn
Z
R
eMnS . 
(2-21) 
And the longitudinal polarization remained available for the nth excitation is: 
?)1(cos)0()( ?? nZZ MnM . 
(2-22) 
 
 
 24 
 
CHAPTER 3 RF COILS THEORY 
3.1 Transmission and Reception 
In NMR processes, RF coils are used for two purposes: during transmission, they generate a 
magnetic field (B1 field) to excite the magnetization, and during reception, they work as 
receivers to detect the FID signal from the spin relaxation process. The principle of a transmit 
coil is governed by one of the most primary laws in electromagnetism, Ampere's law:  
? ? ??? S dSJdlB0
1
?
. (3-1) 
After the excitation, a rotating magnetic field resulted from the precession of the 
magnetization will generate an induced EMF in the receive coil according to the Faraday?s 
law of induction, 
? ? ????? S dSBdt
ddlE? . 
(3-2) 
As a transmit coil, it is usually expected to be able to generate a most uniform rotating 
magnetic field B1 over a region of interest in a subject. On the other hand, as a receive coil it 
is essential to have a high signal sensitivity to ensure a maximized SNR. Though it has been 
experimentally verified that there is reciprocity nature between the RF signals in transmitting 
and receiving process [12], due to the different preferences of coil performances in 
transmitting and receiving modes, it is very common to use separate coils for transmitting 
and receiving, as each coil can be designed and optimized for different performances. For 
example, volume coils are usually used as a transmitting coil due to their symmetrical 
structure and thus the intrinsic advantage in field homogeneity, while a surface is more 
preferred for signal receiving because of its high sensitivity. Nevertheless, a single coil with 
optimized design can be used for both.  
 25 
3.2 Resonance Circuits and Coil Tuning 
RF coils are generally designed to be resonant at the Larmor frequency of at least one certain 
nucleus of interest under a given external magnetic field strength. A coil can always be 
described using a lumped element RLC equivalent circuit [14]. The probe of a coil is made of 
an inductor of inductance L with resistance of r, and by adding capacitive component C it can 
be tuned to a desired frequency.   
 
 
Figure 3.1 Equivalent RLC resonant circuit of a coil. 
 
The total impedance of this equivalent circuit can be expressed as a complex number: 
?jXRZ ?? , 
(3-3) 
where X? is the total reactance of the probe inductor and capacitors, and equals to XL + XC, 
where, 
LX L ?? , 
(3-4) 
CXC ?
1? . 
(3-5) 
The resonant circuit comes to resonance at frequency ? when X? is minimized to zero, giving 
the resonance condition, 
LC
1?? . 
(3-6) 
 26 
When this resonant condition for a coil is met, the electric and magnetic energy transfer 
equally between reactive components at the resonant frequency during each cycle, and only 
dissipates energy through the real resistance R, governed by Ohm?s law, 
RIW 22
1? , 
(3-7) 
where I is the current in the coil. 
The impedance of a coil at its input / output port then can be expressed as: 
Cj
Ljr
Cj
Ljr
Z
?
?
?
?
1
1
)(
??
?
?
 . 
(3-8) 
 
3.3 Q Factor 
In a resonant coil, energy is oscillating electrically and magnetically between the reactive 
components. The efficiency of the coil can be measured by quality factor Q, which is defined 
as the ratio of the energy stored in the coil to the energy dissipated during one cycle, 
Dissipated
Stored
Energy
EnergyQ ?? ?2  
(3-9) 
The Q factor of a coil of inductance L and resistance r is given as 
r
LQ ??  
(3-10) 
 
 
 
 
 27 
Another way of defining the Q factor is given in term of the frequency bandwidth as, 
f
fQ
?
? 0  
(3-11) 
where f0 is the resonant frequency and ?f is the bandwidth, defined as the frequency range 
between two frequencies of the half peak power value. A typical value of Q for a NMR coil 
is between 50 and 500 [14], depending on the loading conditions. 
3.4 Impedance Matching 
Transmitting the signal from the coil to the pre-amplifier efficiently is as important as 
detecting a strong FID signal from the coil. Matching the probe impedance to that of the 
transmission line, which is usually 50 ?, is crucial to avoid any re-flections which leads to 
higher power consumption and image signal loss. The reflection coefficient can be expressed 
as the ratio of voltage of the reflected signal V- and that of the input signal V+: 
?
?
?? V
V . 
(3-12) 
Also, it can be written as: 
TLCoil
TLCoil
ZZ
ZZ
?
??? , 
(3-13) 
where Zcoil and ZTL are the coil and transmission line impedance, respectively. In order to 
assure maximum power dissipation in the load and minimize the reflection, the impedance of 
the load should be maintained the same as that of the transmission line (normally 50 ?). This 
can be achieved by transforming the impedance of the load using conjugate matching 
method, in which the imaginary part of the load impedance is cancelled via an impedance 
matching circuit, whose impedance ZM is a conjugate value of that of the load: 
*CoilM ZZ ? . 
(3-14) 
The real part of the impedance is then equal to, or can be transformed to that of the 
transmission line, via an impedance transforming circuit (such as a Balun), and thus 
minimize the reflection coefficient to be zero. 
 28 
 
3.5 Signal to Noise Ratio (SNR) and Signal losses 
3.5.1 SNR 
As described in Chapter 2, NMR signal is generated by the precession of nuclear 
magnetization in the B0 field. The magnetization can be given by: 
SBTk
BIINBM 3
)1( 022
0
0
0
??? ??
?
? , 
(3-15) 
where ? is the susceptibility of the sample, N is the number of spins, ? is the gyromagnetic 
ratio, I is the spin quantum number, kB is Boltzmann's constant, TS is the sample temperature.  
The magnetization, when excited by a circularly polarized magnetic field B1 generated by a 
coil, will precess at an angle of ? in B0 at frequency ?, and induces a voltage in the receive 
coil according to Faraday?s law of induction. The voltage signal can be expressed as: 
VrBMS
S
d)(sin 10 ????
. (3-16) 
From equation (3-15) and (3-16), the signal received can be expressed as: 
VTk
BBIInS
SB
s ?? sin)3
)1(( 10
22 ?? ? . 
(3-17) 
 
Johnson-Nyquist noise (or thermal noise) is the dominant noise in NMR, which arises from 
random electrical fluctuations created by Brownian motion of electrons. The mean square 
voltage induced by the thermal noise in a conductor of resistance R, temperature T and 
bandwidth ?f is: 
fTRkN B ?? 4 . 
(3-18) 
Coil and sample are both the main sources of thermal noise in NMR. In reality, a coil is made 
of an inductor with a resistance (Rc), and the sample, when coupled to the coil, will be seen 
as a equivalent resistor (Rs). Other noises such as background radiation and interferences 
 29 
usually are or can be made negligibly small. Considering R = Rc + Rs, the total noise signal 
generated in a loaded coil can be expressed as: 
fTkRRN BSC ??? )(4 . 
(3-19) 
 
From equation (3-17) and (3-19), the SNR can be calculated as: 
fRRTk
VBBIIn
V
VSNR
SCB
s
Noise
Signal
??
???
)(8
sin)1(
2/32/3
10
22 ?? ?. (3-20) 
 
3.5.2  Coil loss and sample loss 
In equation 3-20, RC and RS represent coil loss and sample loss, respectively. In order to get 
an improved SNR, both the two losses should be minimized. 
Coil loss is caused by both the power dissipated to the Ohmic resistances of the copper wire 
and the electrical components, and radiation loss. Power dissipated in the equivalent resistor 
that is introduced by non-ideal components, such as inductors and capacitors, will transfers 
into heat and causes loss in signal. On the other hand, an ideal RF coil would be expected to 
act more as an energy conserving coil and less as a radiating antenna. However, in reality 
coils inevitably lose energy to the surrounding free space due to radiation. To minimize the 
radiation loss, one should generally limit the size of the coil under 0.1 ? , where ?  is the 
wavelength of signal. Besides, using distributed capacitors to break the coil inductor into 
multiple shorter sections will also reduce the radiation loss. 
Sample loss is another major cause that degrades the SNR. During transmission of the B1 
field, eddy currents will be induced in the sample, which is within the field. Some of this 
transmitted power is dissipated within the sample and causes local sample heating. Based on 
the principle of reciprocity of the RF coil, these eddy currents will then induce voltages in the 
receiver coil causing noise. On the other hand, because of the dielectric effect of the sample, 
displacement currents will also be introduced to the sample, which causes dissipation within 
the sample, and through the capacitive coupling between the sample and the coil, generates 
noise in the receiver coil.  
 30 
3.6 Filling Factor 
A magnetic filling factor ? f is defined as 
[15]:  
U
dVB
f
0
2
1
?
? ?? , 
(3-21) 
where U is the total energy in the magnetic field, and the integration of a constant field B1 is 
over the sample volume. This is the ratio of the energy in the positive rotating circularly polarized 
field, to the total magnetic energy. The above equation can lead to a useful relationship:  
c
s
f V
V
20
2?? ? , 
(3-22) 
where ? is a dimensionless function of coil geometry. Vs is the sample volume, and Vc is the volume 
of the coil.  
Usually a high filling factor is desired. To maximize the filling factor, a volume coil should be 
designed to have an inner volume close to the volume of the sample. 
3.7 Surface coil & Volume coil 
3.7.1 Surface coil 
A surface coil is a single coil placed directly next to the region being imaged, without 
wrapping the entire subject. In the reception mode of NMR or MRI, surfaces coils are more 
preferable for their higher sensitivity and thus better SNR performance. A surface coil in its 
simplest shape is a circular or square loop which can be represented as a simple LC circuit, 
and the lumped element circuit is one of the ways that can be used for modeling the coil, as 
shown in Figure 3.2. 
 31 
 
 
(a) (b) 
  
Figure 3.2 A loop surface coil (a) and its equivalent circuit (b). 
In practical design, capacitors in a surface coil are usually distributed around the 
circumference of the coil to improve the current distribution and reduce radiation and electric 
losses. Despite a high SNR, surface coils are usually limited in providing a large field of 
view (FOV), especially in clinical imaging scans. This is because the sensitivity of a surface 
coil decreases along with the increment of its size. In order to overcome this problem, one 
can use multiple small-size surface coil elements to form a large coil array, and provide a 
large FOV without any cost of SNR [16], such as sensitivity-encoding (SENSE) [17]. 
3.7.2 Volume coil 
While transmitting RF pulses, a coil is expected be able to generate a uniform magnetic field 
over a region of interest (ROI). A uniform rotational magnetic field can be ideally generated 
by a uniform current distribution on a spherical surface. Helmholtz coil is an example of this 
configuration. In a Helmholtz coil, two parallel loops are driven by in phase currents, and this 
gives a uniform field distribution. Besides, an ideally cosine current I distribution on a 
cylindrical surface can also generates an ideal homogeneous field within the coil, as shown in 
Fig 3.3. The current distribution on the surface can be expressed as: 
)cos(0 nn II ??  
(3-23) 
where ?n is the azimuthal angle and ?n = 2? / n, where n is a positive integer. The currents 
directed are along the magnet field Z direction.  
 32 
The saddle coil is an approximation of this configuration with n of 4. It consists of two pairs 
of axial wires laid over two halves shells and connected with arc shape wires as return 
current loops. Saddle coils are widely used as gradient coils. 
 
 
Figure 3.3 An illustrative saddle coil structure [14]. 
 
When using a receive-only surface coil in combination with a transmit-only volume coil, the 
two coils will couple to each other. While transmitting, a current will be induced in the 
surface coil and this might causes skin burns to the subject or patient. And during the 
reception, a portion of the FID signal will dissipate in the volume coil and deteriorate the 
SNR. Therefore, a decoupling circuit or PIN diodes are usually used to decouple the coils 
during transmission and reception. 
3.8 Birdcage Coil 
The concept and first design of ?birdcage? coil was initially introduced by Hayes et al. in 
1985 [18]. Birdcage coils have been widely chosen for MRI for its ability of providing 
circularly polarized field of high homogeneity. A birdcage coil is made of multiple parallel 
conductive segments (rungs) that are parallel to the external magnetic field B0. These rungs 
connect a pair of conductive loop end-rings. Capacitors can be put either on the rungs, end-
ring segments or both, to tune the coil to a desired frequency. A birdcage coil can be 
considered as a circular network of identical filter elements, each of which is connected to 
another and the last one is connected to the first one to form a circle. By different types of the 
 33 
filter element, it can be classified as high-pass mode, low-pass mode, or band-pass mode. A 
typical high-pass birdcage coil and its filter element are shown in Figure 3.4 and Figure 3.5. 
L1 represents the equivalent inductance in an end-ring segment, C1 is the tuning capacitor 
placed in one end-ring segment, and L2 is the equivalent inductance in a rung. 
 
 
Figure 3.4 Illustrative structure of a birdcage coil in its high-pass mode. 
 
 
 
 
Figure 3.5 Equivalent circuit of a high?pass birdcage coil element. 
 
There are many numerical ways to analyze the behavior of a birdcage coil. A method using 
ABCD matrix is very useful and effective in calculating the resonance mode of a birdcage 
coil [14]. Consider the filter cell as a two-port network, the total impedance of the end-ring 
segment consisting of the segment inductance (and the capacitance of the end-ring capacitor 
if a high-pass mode) is Z1, and the total impedance of the rung consisting of its inductance 
(and the capacitance of the rung capacitor if in a low-pass mode) is Z2, respectively, as 
 34 
shown in Figure 3.6 (a). A birdcage coil of 2N rungs can be then described as a circular 
ladder network made of 2N elementary networks, shown in Figure 3.6 (b). 
 
 
 
(a) (b) 
  
Figure 3.6 Illustrative schematic of a high-pass birdcage coil element (a), and matrix diagram of 
a high-pass birdcage coil (b). 
 
Let A be the ABCD matrix of a filter element, described as, 
?
?
?
?
?
?
?
?
?
?
?
?
?
?
1
1
1
2
1
2
1
Z
Z
Z
Z
A
. 
(3-24) 
The input and output of this filter element are defined as, 
??
?
?
??
?
?
???
?
?
??
?
?
?
?
1
1
n
n
n
n
i
v
A
i
v . 
(3-25) 
For a birdcage of 2N identical elements, we have, 
??
?
?
??
?
?
???
?
?
??
?
?
?
?
12
122
0
0
N
NN
i
v
A
i
v . 
(3-26) 
Given the fact that the last filter element is connected to the first one, the input (v0, i0) equals 
to the output (v2N-1, i2N-1), therefore, 
IA N ?2 . (3-27) 
 35 
By solving equations (3-24) and (3-27), we obtained the relationship of birdcage coil 
resonance modes and the impedances of the end-ring segment and the rung,  
?
?
??
?
??? N
k
Z
Z
2sin4
2
2
1 ?, (3-28) 
where k is an integer between 0 and N. Equation (3-28) implies that there are k resonant 
modes in a birdcage coil for the given end-ring segment and rung impedances [19], which are 
determined by the coil geometry and tuning capacitors. The currents that generate the 
magnetic field are distributed in the legs as: 
? ??? ?? NknIIn /cos0 , (3-29) 
where ?  is the spatial phase factor dependant on the way the coil is excited and usually 
considered 0. From the NMR point of view, the k = 1 mode is usually preferred since in this 
mode the currents phase changes at the lowest speed in the rungs and formed a ?fine? cosine 
distribution, thus generates a homogeneous magnetic field in the middle of the coil for 
excitation, as shown in the Figure 3.7 and Figure3.8. 
 36 
 
 
 
Figure 3.7 Illustrative cosine currents distribution in a 8-rungs birdcage 
 
 
 
Figure 3.8 Illustrative field distribution in the transverse plane inside the birdcage coil [14]. 
 37 
 
CHAPTER 4 19F QUADRATURE BIRDCAGE COIL  
4.1 Introduction 
Recently, 19F MRI using inert fluorinated gases such as sulphur hexafluoride (SF6), 
hexafluoroethane (C2F6), and perfluoropropane (C3F8 or PFP) has shown great potential to 
become a useful and efficient lung imaging technique [6, 21 - 23].  Due to the high gyromagnetic 
ratio of 19F nuclei, one can obtain sufficiently high signal intensity without the need of 
hyperpolarization, and the short longitudinal relaxation time (T1) of fluorinated gases allows 
rapid signal averaging.  Thus, these non-toxic and abundant gases have become a promising 
alternative to hyperpolarized noble gases as novel lung imaging contrast, and numerous 19F 
MRI experiments using small animals have been conducted [8 - 11].  
In this chapter, a quadrature-driven birdcage T / R coil dedicated for rat lung imaging 
experiments using inert fluorinated gases was presented. Coil construction, parameter 
calculations and performance tests are discussed in details.   
4.2 Coil Geometry and Tuning 
An 8-rungs birdcage coil was built using copper tapes sticking to the surface of a machined 
acrylic tube. Dimensions of the coil were carefully designed for an optimized filling factor 
and suitability for small animal lung imaging experiments, especially for the rats. The 
diameter of the tube is 90mm and the overall length is 100mm. The end-ring width and the 
rungs width are both 6.5mm, and the rungs length is 68.5mm. The extra space on the surface 
of the acrylic tube was reserved for matching circuit deployment. 8 gaps were made on each 
end-ring to accommodate all 16 capacitors, forming a high-pass structure.  
Table 4.1 19F birdcage coil dimensions and materials 
 Material 
Length  Width Thickness Diameter 
(mm) (mm) (mm) (mm) 
Coil frame Acrylic tube 100 - 3.25 83.5 
End-rings Copper tape - 6.5 0.06 90 
Rungs Copper tape 68.5 6.5 0.06 - 
 
 38 
 
 
Figure 4.1 Top view of the 19F birdcage coil 
 
In order to tune the birdcage coil to 120.15MHz (the Lamour frequency of 19F under 3 Tesla 
field), calculations for the end-ring tuning capacitor values were performed using the 
BirdcageBuilder software [19, 20]. With the dimensions specified above, the value of each end-
ring capacitor is calculated to be 43pf. After 16 tuning capacitors were placed on the end-
rings, the resonant frequency of the birdcage coil was measured using two RF pick-up probes 
previously tuned to 120MHz on a HP 8751A network analyzer.  Specifically, the two pick-up 
probes were connected to the two ports of the network analyzer, and the two probe heads 
were placed across the birdcage coil, the resonance frequency was measured by viewing the 
S21 responses. The network analyzer was set at a center frequency of 120.15MHz with 
10MHz span, in order to include only the dominant resonance mode of the birdcage coil. 
4.3 Impedance Matching  
As discussed in section 3.4, to minimize the power reflection, the impedance of a coil at its 
input / output port should be matched to that of the device it electrically connected, such as 
the network analyzer, the scanner, a transmission line, or a hybrid coupler. There?re many 
different ways to transform the input impedance of a coil to a desired value. In this work, two 
L-C Balun circuits were used to match both the two ports of the coil to 50ohm impedance.  
 39 
Balun (balance-to-unbalance) is a type of coupler that connects a symmetrical (balanced) 
circuit to an asymmetrical (unbalanced) circuit, and it provides a 180 degree phase shift 
between the input and output signals. L-C Balun is a type of Balun that has four components 
and a very symmetrical structure, as shown in Fig 4.2.  
 
 
Figure 4.2 Schematics of a L-C Balun. 
L-C Balun can be used as impedance transformers. In Fig 4.2, RTL is the impedance of a 
transmission line (pure resistive), and Rload is the impedance of a balanced load (pure 
resistive). At a certain working frequency? , define loadTLRRZ ?0 , then the components L 
and C can be calculated as : 
?
0ZL ? , 
(4-1) 
?0
1
ZC ?
. (4-2) 
The impedance of a load (such as a coil) is usually a complex with a reactance component, 
thus when using L-C Balun as impedance transformer, one must first cancel out this 
reactance and leave it pure resistive. This can be done easily by adding an inductor (or 
capacitor ) in series with the load.  
As shown in Figure 4.3, L1 and C1 were calculated according to equations 4-1 and 4-2, with 
the given 19F Larmor frequency. At 120.15MHz, L1 is calculated to be 198nH and C is 
 40 
calculated to be 8.9pf. Inductors L2 were used to cancel out the imaginary part of the 
impedance, thus achieve a pure resistive impedance. The value of L2 is calculated to be 35nH. 
The Balun matching circuits were built on the outside of the coil cylinder right next to each 
port.  
 
 
Figure 4.3 Schematics of the linear 19F coil with balun impedance matching circuits. 
 
The measurement for the impedance was performed on each port to verify and investigate the 
performance of the impedance matching circuits. The S11 parameters for the two ports are 
shown in Figure 4.3. Each port has obtained approximate 50ohm impedance.  
  
(a) (b) 
  
Figure 4.3 S11 responses of the two channels on Smith chart. 
 
When coupling the birdcage coil to other equipment such as the scanner or a network 
analyser, one should minimize the dissymmetry introduced to the structure of the coil, to 
maintain an accurate tuning and a uniform B1 field.  Inductively coupling method by putting 
 41 
a second loop close to the birdcage coil is one that is commonly used to keep the symmetrical 
structure. However, it may create some distortion of the B1 field distribution, hence 
capacitive coupling methods using lumped capacitors are also commonly used. When 
external connections are added to the birdcage, it breaks the symmetrical structure of the 
birdcage coil, and thus the ideal cosine current distribution among the legs, but it can be 
approached very closely [14].The B1 field homogeneity of the birdcage coil presented in this 
work will be further studied and quantitatively mapped in Section 4.5. 
4.4 Quadrature Driving 
4.4.1 Quadrature mode  
A RF coil can work on linear or quadrature mode, depending on the geometry and driving 
method. When the RF pulse is fed via a single port, the RF coil is then working at a linear 
mode and the generated B1 field is linearly polarized, meaning it will be directed toward a 
single direction. By decomposing this linear polarized field to two components, B1
+ that 
rotates clockwise, and B1- that rotates counter clockwise, we can clearly see that only one of 
the two components will interact with the spins during the excitation, since it rotates in the 
same direction with the spins, while the other component, which rotates reversely, doesn?t 
contribute at all. On the other hand, a coil can also be fed with two signals that have a 90-
degree phase shift. In this case, a circularly polarized magnetic field will be developed, 
meaning it will rotate in a certain direction. Hence during the excitation, when the field 
rotates in the same direction with the spin precession, it becomes totally efficient in exciting 
the spins. Therefore, compared to a linearly polarized field generated by a linearly driven coil, 
a quadrature-driven coil will halve the power requirement for the excitation. The linear and 
quadrature fields are shown in Figure 4.4. 
 42 
  
  
(a) (b) 
  
Figure 4.4 Developed B1 magnetic field pointing toward one direction in linear mode (a), and 
rotating in the same direction with the magnetization in quadrature mode (b). 
 
On the other hand, during the signal receiving, the two outputs of a quadrature coil will be 
combined and thus increase the signal intensity by a factor of two, while the combined noise 
components from the two orthogonal channels will only increase by a factor of square root 
two, since they are not correlated. Hence, an improvement in SNR by a factor of square root 
two can be gained from the quadrature-driven mode [25].  
4.4.2 Quadrature coil construction  
As described above, in order to implement the quadrature driving method, two signals of the 
same amplitude are required to be fed into two coils that are geometrically orthogonal.  When 
these two signals have a 90 degree phase difference (electrically orthogonal), a circularly 
polarized field will be developed inside the coil. The quadrature mode is relatively difficult 
to be developed in two surface coils, since the orthogonal geometry could raise coupling 
issue between the two coils. In contrast, one of the advantages of the birdcage coil is that it is 
intrinsically suitable for working in a quadrature mode for its cylindrically symmetric 
structure. The original coil was re-constructed for quad-operation. Another signal feed port 
was added on the end-ring two segments away from the previous port. This makes the two 
ports geometrically perpendicular to each other in the axial plane. The impedance was 
matched to 50 ohm at the new port, using an identical Balun circuit.    
 
 43 
 
 
 
 
 
 
 
Figure 4.5 Schematics of the quadrature-driven birdcage coil with impedance matching Balun 
circuits for both I and Q channels. 
 44 
 
4.4.3 ? / 8 Hybrid coupler  
Hybrid coupler is a particular kind of directional couplers that divides the input power 
equally for two outputs. There are many ways to implement a hybrid coupler for microwave 
frequencies [26]. As described before, in order to implement a quadrature driving method, one 
needs to create two Tx signals of the same amplitude having a 90-degree phase shift. A ? / 8 
hybrid coupler was used in its lumped elements equivalent circuit for such an implementation, 
to maintain a desirable device dimensions. Figure 4.6 shows the structure of a ? / 8 hybrid 
built with two transmission lines of the standard characteristic impedance, where C = 1 / Z0 ?. 
 
 
 
Figure 4.6 Signal phase shifting (a) in a ? / 8 hybrid coupler (b). 
 
As previously mentioned, the Larmor frequency of 19F at 3T magnetic field is 120.15MHz, 
which corresponds to a ? / 8 of 31.21cm. To make the hybrid circuit in a minimum size, the 
two original transmission lines were replaced using lumped elements equivalent circuits.  
 45 
 
 
Figure 4.7 Equivalent circuit of a ? / 8 hybrid coupler. 
 
As shown in the Figure 4.7, the ? / 8 transmissions lines are replaced by the Pi-network 
equivalent circuit, illustrated in the dash-line box. Obviously C1 equals to C in Figure 4.6, 
and is 1 / Z0 ?. To calculate the values of C2 and L, which are components in a Pi-network, 
the equations below are used, given that all the ports are matched to 50ohm,  
K
ZX c 0?
, (4-1) 
1
2
20 ?? K
KZX L
. (4-2) 
The value of K can be determined by a condition derived from the character of the 
transmission line, that is, a ? / 8 transmission line of characteristic impedance of Z0 will 
exhibit an impedance of jZ0 when shorted. Hence, 
2
0
11 CjLjjZ ?? ??
. (4-3) 
From equations (4-1) and (4-2), the values of L and C2 are obtained, 
 46 
?2
2
0
ZL ? . 
(4-4) 
?0
2
12
ZC
?? . 
(4-5) 
By substituting the frequency ? into equations (4-4) and (4-5), the values of C1, C2 and L can 
be easily calculated. In this work, C1 was calculated to be 27 pf, C2 was calculated to be 11 pf, 
and L was calculated to be 47 nH. The hybrid coupler was built on a PCB from Clinical MR 
Solutions. Inductors were winded on bench and tested using the network analyzer to verify 
its value. Figure 4.8 showed a picture of the hybrid. 
 
 
Figure 4.8 Completed lumped elements ? / 8 hybrid coupler. 
The hybrid coupler was tested on the bench using an Agilent 5000 oscilloscope and the HP 
8751A network analyzer. Port 1 (Tx port) of the hybrid was connected to port 1 of the 
network analyzer,  the two output ports, Port 2 and Port 3, were connected to two input 
channels of the oscilloscope, respectively. The input impedances of the oscilloscope had been 
previously set to 50 ?. And Port 4 (Rx port) of the hybrid was connected to port 2 of the 
network analyzer. By doing a S21 measurement and setting the central frequency to 
120.15MHz with a 0Hz span, we obtained two signals on the oscilloscope, having the same 
amplitude and a 90-degree phase shift, as showed in the Figure 4.9.   
It is desired to achieve a good isolation between port 1 (Tx) and port4 (Rx) to provide 
protection to the pre-amplifier during the excitation.  The isolation between these two ports 
was measured with the same configuration, and the span of the network analyzer was set to 
 47 
20MHz. From the test result we obtained an isolation of -36dB between the Tx port and Rx 
port at the resonance frequency of 120.15MHz.  
 
 
Figure 4.9 A 90-degree phase shift observed at the two output ports of the ? / 8 hybrid. 
 
 
 
Figure 4.10 S21 response between the port1 and port 4 of the hybrid. An isolation of -36dB was 
achieved at the frequency of 120.15MHz. 
4.5 Results 
The performance of the coil was firstly evaluated on the bench by the measuring the matched 
impedance and Q factor for both the two channels. With a saline bag set inside the coil to 
mimic the load of a real rat, the impedances of the two channels were matched to 50+j6 ohm 
and 47+j2 ohm, and the S11 responses obtained are -24dB and -27dB, respectively. The 
 48 
loaded Q factors of each channel were measured through S11 response, and the Q of the two 
channels were calculated to be 130 and 136.  
To further evaluate the performance of the 19F quadrature birdcage coil in actual NMR 
experiments, a series of MR spectroscopic and imaging scans were performed on a Philips 
Achieva 3T scanner in a well-RF-shielded scanner room. A 500ml saline bag was set in the 
loading position to mimic the load of a rat during the phantom scans, and the S11 response of 
both the two input ports were measured and finely tuned on the network analyzer after the 
coil was put into the magnet bore. The coil was calibrated prior to all the scans by doing a 
several multi-flip-angle spectroscopic scans and adjusting the scanner power output, to 
perform a true 90-degree excitation pulse. 
4.5.1 Phantom spectroscopic scan results 
A 19F phantom was made by sealing 5ml Perfluoropropane (PFP) gas into a 5ml syringe. 
When performing the scans, the syringe was held by a hollow cylindrical foam which was 
placed in the middle of the coil, to keep it in a region where the homogeneous B1 field was 
generated. 
Single voxel (SV) spectroscopic scans were performed with the coil on both linear and 
quadrature modes in order to measure the SNR improvement. To configure the coil for the 
linear mode, one of the input ports was connected to a 50ohm terminal, while the other one 
was directly connected to a linear transmit / receive switch. A non-selective sequence was 
performed with TR of 131ms and TE of 0.14ms. The power required to generate a 90-degree 
pulse of the same pulse length and the calculated SNR of the received FID signals for each 
mode are shown the in table 4.2. 
Table 4.2 Comparison of the SNR and power consumption  
Coil mode 
RF Pulse length 
Amplifier Power 
Output 
Calculated SNR 
(us) (watt) - 
Linear 89 338 110 
Quadrature 89 162 156 
 
In the result, the power required to generate 90-degree pulse of 89us length is 48% less than 
that of the linear reference.  Meanwhile, the SNR of the signal obtained in quadrature mode 
 49 
is approximately 1.4 times higher than the linear signal reference, which agreed with the 
calculation and presents an improvement of a factor of square root two. The FID and 
spectrum results from linear mode and quadrature mode are shown in Figure 4.11. 
  
(a) (b) 
  
  
(c) (d) 
  
Figure 4.11 FID signal (a) and spectrum response (b) for the coil in linear mode, and FID signal 
(c) and spectrum response (d) for the coil in quadrature mode. 
 
4.5.2 Phantom imaging scan results 
Imaging scans of the phantom were also performed using the constructed quadrature birdcage 
coil. A 2D FFE sequence was used to acquire transverse and coronal images. For the 
transverse image, the FOV is 50mm by 50mm, resolution is 128 by 128, TR = 150ms, TE = 
3.1ms, 4 signal averages, bandwidth is 200Hz / pixel, and the measured SNR of the image is 
16.6. For the coronal image, the FOV is 100mm by 100mm, resolution is 128 by 128, TR = 
150ms, TE = 1.7ms, 16 signal averages, bandwidth is 200Hz / pixel, and the measured SNR 
of the image is 12. The transverse and coronal images are shown in Figure 4.12. In the 
 50 
coronal image, a ghost can be observed, this is resulted from the chemical shift of the PFP 
gas due to its two intrinsic responses in the NMR spectrum that are approximate 48ppm away 
from each other.  
 
 
Figure 4.12 Transverse (a) and coronal (b) images of the PFP gas phantom. 
 
4.5.3 B1 field mapping and field inhomogeneity calculation 
As described above, one of the most essential performance measures of a transmit coil is the 
B1 field homogeneity. There are several NMR techniques that can be used to quantitatively 
measure and mapping the B1 field 
[27-29]. In this work, a technique called double angle 
method (DAM) [30, 31] was used. With this method, two RF pulses are applied to excite the 
magnetization to a flip angle of ? and 2?, respectively. When set a long repetition time 
(TR >> T1) between the two scans, the two acquired FID signals S1 and S2 can be considered 
independent of relaxation times, and only proportional to sin ?: 
?sin011 MMS xy ?? , 
(4-6) 
?2sin022 MMS xy ?? . 
(4-7) 
By combining the equation (4-6) and (4-7), one obtains the value of ?; 
)2arccos( 1
2
S
S?? . 
(4-8) 
It should be noticed that the above calculation is based on the assumptions that the durations 
of RF pulses are significantly smaller than T1 and T2, so the relaxation terms in the Bloch 
 51 
equations can be ignored, and that M0 is constant during the RF pulse. These are known true 
for small flip angles, and work well for a flip angle up to 90 degree [32]. At a small flip angle,   
B1 ? ?, thus by calculating and generating flip angle maps, one can evaluate the field 
homogeneity of the coil. The limit of this method is that it is inherently slow, since the TR 
must be long enough to ensure a full relaxation of magnetization between the two flip angles. 
This may result in a very long scan time, especially in the case of long T1 nucleus.   
A balloon filled up with pure SF6 gas was put into the coil to create a homogeneous spin 
system inside the coil. The B1 mapping scan was performed on a 20mm-thick slice at the 
center of the coil in the axial direction for the test, with ? of 45 degree and 2? of 90 degree. 
The repetition time TR was set to be 166ms, comparing to that the T1 of pure SF6 under 1 
atm is about 2ms [33]. This assures a full recovery of the longitudinal magnetization, and thus 
an accurate calculation results. The full normalized B1 map of the 
19F birdcage coil is shown 
in Figure 4.13. A plot of the normalized B1 field of a selected center slice was shown in 
Figure 4.14. 
 
 
Figure 4.13 Normalized B1 map of a transverse slice at the center of the coil. 
 52 
 
 
 
 
  
(a) 
 
  
(b) 
 
Figure 4.14 (a) Normalized B1 field distribution in one slice of the map (4 cm),  and (b) 
histogram of the normalized B1 field throughout the center region of the coil (4 cm 
* 4 cm). 
 
A 4 cm * 4 cm * 3 cm region at the center of the coil, where the lungs of the rat will be 
maintained during the experiments, was chosen for quantitative inhomogeneity study.  The 
average normalized B1 throughout the entire region was calculated to be 0.8731, with a 
 53 
standard deviation of 0.0426. Therefore the variation of the B1 field strength at the center 
region of the coil is about 4.9%. 
4.5.4 Animal in vivo scan results 
Rat in vivo lung imaging experiments were performed on a healthy rat using the Philips 3T 
Achieva scanner. During the experiment, perfluoropropane (PFP) gas mixed with O2 was 
delivered to the rat through a custom-built small animal ventilator. All the images were 
acquired during 17 minutes of continuous breathing of the PFP / O2 mixture.  
 
 
 
Figure 4.15 Multi-slice images acquired in a healthy rat lung using 3D FFE sequence. FOV = 
90*90 mm, Slice thickness = 10mm, TR / TE = 20 / 1.94 ms, NSA = 150. 
 54 
 
4.6 Discussion 
As transmit / receive coil, the two essential performances, the transmitting field homogeneity 
and coil sensitivity were quantitatively evaluated. The spectroscopy scan results proved a 
sensitivity and SNR improvement of a factor of square root two obtained from a quadrature-
driven structure, and meanwhile, the power required to excite the spin magnetization has 
been halved. These improvements agreed very well with the quadrature-driving theory. 
In order to evaluate the field homogeneity of the coil, two conventional techniques for B1 
field mapping were studied and investigated. Based on the intrinsic NMR characteristics of 
the 19F nuclei, that it has a very short T1 relaxation time, the dual flip angle method (DAM) 
was chosen to provide a more accurate map and an easier experiment implementation. Pulse 
sequences parameters were adjusted based on the flip angle calibration results. From the 
acquired B1 map, a homogeneous B1 field distribution was obtained at the center region of 
the coil.  
During the in vivo rat lung imaging experiment, the coil has shown very good suitability 
regarding the dimensions and filling factor. A rat was kept inside the coil where its lung 
stayed in the center region within the most homogeneous field.  Though a volume coil 
normally has a lower SNR compared to that from a proper sized and positioned surface coil, 
the diameter of the 19F birdcage coil was set to maximize the filling factor and thus resulted 
in an optimized SNR. 
 55 
 
CHAPTER 5 1H - 129Xe DOUBLE-BIRDCAGE COIL  
5.1 Introduction 
Hyperpolarized noble gases MRI using 3He and 129Xe have emerged as promising lung 
imaging modalities that can provide pulmonary structural and functional. Although 3He can 
achieve a higher polarization and thus higher signal intensity, its usage and transfer to 
clinical application are drastically limited for its natural scarcity and high cost. On the other 
hand, despite the lower polarization, 129Xe has been widely studied and used as an alternative 
imaging contrast for its abundance [34, 35]. Moreover, xenon is soluble in blood [36] and can be 
taken into other organs, such as the brain, and gives possibilities to carry out imaging and 
localized spectroscopy scans in these regions, and obtains functional information. In addition, 
129Xe has a chemical shift of 202 ppm in NMR spectrum, which makes it a useful tool to 
detect the local chemical environment [37-39].  
In many 129Xe MRI experiments, coils are expected to provide the abilities of exciting / 
receiving for both proton and xenon nuclei. For example, in localized spectroscopy scans, 
proton images are usually required for localization. And more generally, a proton channel is 
preferred for shimming purpose. This can be best done by either a dual-tune coil [40, 41] which 
can work at both proton and xenon frequencies, or a switch-tuned coil, whose resonant 
frequencies can be switched between proton and other nuclei. In this way one ensures 
identical field profile and filling factor for both frequencies. Nevertheless, one can also adopt 
two separate coils that are tuned to different frequencies to work in close proximity and 
obtain a dual-frequency structure [42, 43], especially when the two frequencies are relatively far 
from each other.  
In this chapter, a double-birdcage coil developed and constructed to work at both proton and 
xenon frequencies is discussed. Double-Birdcage Structure 
5.1.1 1H and 129Xe birdcage coils construction 
Two linear high-pass birdcage coils were made separately using the same acrylic tube and 
copper tape as described in the previous chapter. One coil was tuned to 35.33MHz for xenon 
 56 
frequency, and the other one was tuned to 127.74 MHz for proton frequency. The two coils 
were made in different sizes in order to implement the double-birdcage structure. The 
dimensions of these two coils are shown in table 5.1 and 5.2, respectively. The xenon coil 
was made the same size with the 19F coil, in order to optimize the filling factor when an 
experimental subject (such as a rat) is put in. For the proton coil, because of the larger 
diameter required for the double-birdcage structure, it inevitably has a poorer filling factor, 
compared to that of the inner xenon coil. Though this can be easily compensated by the high 
intensity of proton signal, it is made as small as possible, not only to maximize the filling 
factor, but also to minimize the coupling issue with the proton quadrature body coil (QBC) 
that is integrated in the scanner. 
On the other hand, the mutual inductance between the rungs of the two coils become larger 
as the diameter of the proton coil decreases and the distance between the two rungs gets 
smaller. As described in Chapter 2, the resonant modes of a birdcage coil are determined by 
the ratio of the impedance of the eng-ring segment and that of the rung. Thus when the 
effective inductance of the rung is changed due to the mutual inductance, the resonant modes 
of both xenon and proton coil will shift in the spectrum. The same also applies to the end-
ring, however, it is rather feasible to make the proton coil long enough to keep a sufficient 
distance between the two end-rings to minimize the mutual inductance, without jeopardizing 
a suitable coil dimension for rats. The two coils need to be re-tuned to retain the desired 
resonant frequencies once they are put together. Decoupling between the two coils will be 
further discussed in section 5.2.  
Table 5.1 129Xe Inner Birdcage Coil Dimensions 
 
Material Length  Width Thickness Diameters 
 (mm) (mm) (mm) (mm) 
Coil frame Acrylic tube 128 - 3.25 83.5 
End-rings Copper tape - 6.5 0.06 90 
Rungs Copper tape 81.5 6.5 0.06 - 
Table 5.2 1H Outer Birdcage Coil Dimensions 
 
Material Length  Width Thickness Diameters 
 (mm) (mm) (mm) (mm) 
Coil frame Acrylic tube 130 - 3.25 95.5 
End-rings Copper tape - 6.5 0.06 102 
Rungs Copper tape 110 6.5 0.06 - 
 
 57 
The tuning capacitor values were calculated for both coils using the BirdcageBuilder 
software. For the xenon coil, the tuning capacitor on the end-ring segment is 500 pf, for the 
proton coil, the tuning capacitor on the end-ring segment is 31.5 pf. Impedance matching was 
performed using the lumped elements Balun circuit on each coil, the same as described in 
Chapter 4. Both the two coils were tested on the bench individually before implementing the 
double-birdcage structure.  The S11 responses for the two coils are shown in Figure 5.1. 
 
  
(a) (b) 
  
  
(c) (d) 
  
Figure 5.1 S11 responses of the xenon coil (a) (b) and the proton coil (c) (d). 
 
 58 
5.1.2 Double-birdcage structure and coils re-tuning 
The double-birdcage structure was constructed by setting the xenon coil in the middle of the 
proton birdcage coil in such a way that the two coil frames are kept concentric, as shown in 
Figure 5.2. As discussed above, the proton coil was made as small as possible to achieve the 
best possible filling factor. This resulted in a limited space inside for the xenon coil. Thus, 
the Balun matching circuit of the xenon coil was set on the inner surface of the frame, while 
that of the proton coil was maintained outside its frame.  
The resonance mode for each coil was re-tested after the double-birdcage structure had been 
implemented. A resonance frequency shift was observed in both the xenon and the proton 
coil. In the xenon coil, the resonance frequency moved from 35.33MHz to 37.5MHz, whilst 
in the proton frequency it moved farther from 127.7MHz to 116MHz. These resonance 
frequency shifts result from the mutual inductance between the rungs of the two coils, 
introduced by their close proximity, which changes the rung effective inductance and hence 
the impedance. Though the same will also happen between the end-rings of the two coils, it 
has been reduced to negligibly small by separating the end-rings farther away from each 
other. Both coils must be re-tuned back to their proper working frequencies. In order to re-
tune the proton birdcage coil to the correct frequency, instead of changing the tuning 
capacitors, the length of the rungs was extended from 8.5cm to 11cm. This extension 
changed the rung inductance and hence the resonance modes of the proton coil. In addition, it 
also increases the distance between the end-rings of the two coils, which further decrease the 
mutual inductance and coupling between them. 
At this point, the xenon coil was not fixed to a position but keeping the possibility to rotate 
inside the proton coil, this helps find out a position for the best geometrically decoupling 
between the two coils, which will be further discussed in the next section. 
 59 
 
 
Figure 5.2 Illustrative structure of a double-birdcage coil. 
 
  
(a) (b) 
  
Figure 5.3 Front view (a) and side view (b) of the constructed 1H - 129Xe double-birdcage coil. 
 
5.2  Field Decoupling and Coil Isolation 
The field coupling between two adjacent coils should always be handled with care, for its 
many deleterious effects on both the B1 field homogeneity and the SNR of the acquired 
signals. When the coupling exists, during the transmitting, current will be induced in the 
other coil, which then will create a second magnetic field and conversely distort the main B1 
field. On the other hand, during the receiving, a portion of the electromagnetic energy of the 
signal will be dissipated in the coupled coil, and thus decrease the SNR by simply reducing 
the signal intensity. This is especially critical when the two coils are working at close 
frequencies.  
 60 
In such cases, active decoupling methods are usually required to achieve the best decoupling 
performances more effectively. In these methods, one coil is decoupled from another by 
either shifting its resonance frequency far away from the other, or adding one or multiple RF 
chocking circuits to the coil to cancel the induced currents. PIN diodes are commonly used to 
selectively add de-tuning capacitors or chocking inductors to the coil during appropriate 
periods. In other cases, when the two coils are working at different frequencies that are far 
away from each other, the coupling between the two becomes less severe. At a cost of 
decoupling performance, the active decoupling circuits may be omitted for an easier 
implementation, and the two coils are decoupled geometrically to gain an acceptable 
isolation in between. 
In the double-birdcage structure, the two coils are working at two frequencies of 35.33MHz 
and 127.74MHz. The distance between their resonance frequencies implies the possibility of 
geometrically decoupling method. As previously discussed in Chapter 4, a linearly driven 
birdcage coil creates a linear polarized magnet field in a plane perpendicular to the coil?s 
end-ring plane. Hence, the coupling between two birdcage coils can be possibly minimized 
when they are placed in such a position where their magnet fields are orthogonal to each 
other. With the advantage of a concentric structure, it is possible to do quantitative 
adjustment and measurement to find the positions for a minimized decoupling and optimized 
isolation.  
The xenon birdcage coil was rotated counter clockwise regarding the proton birdcage coil, 
starting at a position where both the feeding ports of the two coils are at 6 o?clock position, 
and proceed with a step of ? / 8 degree. To measure the isolation between the two coils, the 
xenon coil and proton coil were connected to port 1 and port 2 of the network analyzer, 
respectively. At a transmitting frequency of xenon (35.33MHz), the S21 parameter was 
measured for each step. Then, the measurements were repeated again with the two coils 
switched the ports of the network analyzer, and the transmitting frequency adjusted to that of 
proton (127.74MHz). The measurements results are shown in the Figure 5.4. 
 61 
 
 
Figure 5.4 Isolation V.S. the relative positions of the two birdcage coils. 
 
From Figure 5.4, the solid line showed the isolation between the two coils when the xenon 
coil was used as a transmitting coil, and the broken line showed the isolation when the proton 
coil was used as a transmitting coil. In both situations the isolation between the two coils 
achieved the optimum when there was a 90 degree between the two feeding ports, indicating 
that the generated magnetic fields from the two coils are orthogonal to each other, obviously. 
At xenon frequency of 35.33MHz, the maximum isolation between the two coils had reached 
28dB, and at proton frequency of 127.74MHz, it had reached 45dB. These isolations have 
proved that the two coils are sufficiently electrically decoupled using geometrically 
decoupling method. Figure 5.5 and Figure 5.6 showed the simultaneous test results of S11 
parameter, as impedance matching measurement, and S21 parameter, as coil decoupling 
measurement, for both xenon coil, and proton coil, respectively. 
 62 
 
 
Figure 5.5 S11 response of the xenon coil (a) and S21 response between the xenon and proton 
coils (b). 
 
 
 
Figure 5.6 S11 response of the proton coil (a), and S21 response between the proton and xenon 
coils (b). 
 
 63 
5.3  Results 
5.3.1 Q factor value 
The Q factors of both proton and xenon birdcage coils were measured on the bench before 
and after the double-birdcage structure was formed, respectively, through the S11 responses. 
A 500ml saline bag, simulating a real rat, was used to load the coils. When measured 
separately, the xenon birdcage coil obtained a loaded Q of 104, while the proton birdcage 
coil had a loaded Q of 91. Subsequently, the xenon coil was set into the proton coil and the 
loaded Q values of the two coils were measured again. In the double-birdcage structure, the 
xenon and proton coils obtained a loaded Q of 106 and 95, respectively. From the values we 
can see clearly that the Q factors of both the two coils maintained about the same value after 
they were put together and form the double-birdcage structure. In other words, the 
sensitivities of the two coils are not affected by forming the double-birdcage structure. 
5.3.2 Imaging scan results and image registration 
In order to test and verify the xenon / proton dual-frequency imaging ability of the double-
birdcage coil, phantoms imaging experiments were performed using a glass ball of thermal-
polarized xenon phantom and a 5ml saline syringe proton phantom, as shown in Figure5.8a. 
The xenon and proton phantoms are placed inside the double-birdcage coil, as shown in 
Figure 5.8b, to simulate a real rat lung imaging scan, when xenon images will be acquired 
from the lung and proton images are acquired to obtain the anatomical structure of the body.  
  
(a) (b) 
Figure 5.7 Xenon thermal phantom and saline syringe phantom (a) are set up inside the coil (b). 
 64 
 
Scans were performed on the Philips Achieva 3T scanner. The two birdcage coils are 
interfaced to the scanner via a commercially purchased Dual Frequency Gateway (DFG) 
interface device from Clinical MR Solution. Firstly, the proton images were acquired using a 
FFE sequence for both transverse and coronal views. Subsequently, without moving the coil 
and the phantoms, the xenon images were acquired as well. Scan parameters are listed in the 
table 5.4.  
Table 5.3 Scan parameters and results 
Nuclei Sequence View 
FOV 
Resolution 
TR / TE 
Slice 
Thickness 
Average 
SNR 
(mm) (ms) (mm)  
1H FFE Transverse 150*150 128*128 150/1.24 5 1 21.5 
1H FFE Coronal 150*150 128*128 150/1.12 5 1 39 
129Xe FFE Transverse 150*150 64*64 250/5 300 16 6.5 
129Xe FFE Coronal 150*150 64*64 250/5 300 16 7.2 
 
From the proton and xenon image results, image registration post processing was performed 
in Matlab. Two images (transverse view and coronal view) were generated with the proton 
image registered on the xenon image. Since during the two different nucleus scans, the 
subject had not been moved, and the sequences were deliberately set to have the same FOV 
and matrix size, these registration images reveals the true spatial structural information with 
great accuracy between the two phantoms, which will be of great use in the case of in vivo 
animal studies.  
 65 
 
  
(a) (b) 
  
(c) (d) 
  
(e) (f) 
Figure 5.8 Transverse (a) and coronal (b) images of the saline syringe phantom; transverse (c) 
and coronal (d) images of the xenon thermal phantom; and transverse (e) and 
coronal (f) registered images of xenon and proton. 
 66 
 
5.4 Discussion 
The key part of the double-birdcage coil design is the decoupling between the two individual 
coils. Unlike that between a transmit-only coil and a receive-only coil, which always adopts 
an active decoupling method using PIN diodes, the decoupling between these coils is solely 
achieved by geometry. This is possible because of the resonance frequencies of the two coils 
are distant from each other. From the measurement results, a maximum isolation of 40dB 
was obtained at the proton frequencies, while at xenon frequency, the maximum isolation 
achieved was 28dB. This difference possibly results from the fact that both birdcage coils 
have a high-pass structure, meaning they both have three other resonance modes of which the 
frequencies are lower than that they?re currently working at. During the proton transmitting, 
the proton frequency of 127.74MHz is far away from the xenon frequency of 35.33MHz, 
which is the highest resonance frequency of the xenon coil, thus very small coupling 
occurred. However, when the xenon coil is transmitting a pulse of 35.33MHz, one of the 
resonance modes of proton birdcage coil has a resonant frequency close to it, thus part of the 
signal was picked up by the proton birdcage coil, and it degrades the isolation between the 
two coils. Nevertheless, the isolations between the two coils at both proton and xenon 
frequencies are sufficiently high to eliminate the coupling effects from the image quality, and 
to assure the ability of double-frequency scan without relocating the subject for this coil 
structure.  
It hasn?t been possible to do an experiment with hyperpolarized xenon gas, due to the 
unfinished polarizer installation in the facility. Scans with the thermal xenon phantom were 
performed and results were compared with that from a previously made, single linear xenon 
birdcage coil. The SNR of the signal from the double birdcage coil is 7, lower than that of 9 
from the single linear birdcage coil. This difference mainly resulted from the increased noise 
that was introduced by the presence of the proton birdcage coil, as well as possible distortion 
of the xenon B1 field, due to the imperfect isolation between the two coils. Besides, the 
thermal xenon phantom couldn?t provide signal good enough to perform an accurate B1 
mapping scan, this will be done after the xenon polarizer is ready and hyperpolarized xenon 
gas is available. 
 67 
In the future work, in order to overcome the issue of decreased SNR in the double birdcage 
coil, further investigation on the possibility of a quadrature-driven structure implementation 
on the xenon birdcage coil will be conducted. As described in Chapter 4, a quadrature-driven 
mode will increase the SNR by a factor of square root of two. This will compensate the SNR 
loss in a double-birdcage coil. However, a quadrature-driven coil will develop a circularly 
polarized B1 field, which makes it impossible to keep the two B1 field orthogonal all the time, 
thus will greatly degrade the isolation between the two coils. In this case, an active 
decoupling method might be required. 
After the work in this thesis had been finished, the xenon coil was taken outside the proton 
birdcage coil and was modified temporarily to a quadrature-driven mode, to evaluate the 
performance in a normal in vivo rat scan. Chemical-shift spectroscopic scans were performed 
using hyperpolarized xenon gas in a healthy rat, and results are shown in Fig5.9. 
 
 
Figure 5.9 In vivo chemical-shift spectrum obtained from a health rat using the quadrature-
driven xenon birdcage coil. 
 
 68 
 
CHAPTER 6 CONCLUSION 
Firstly, a quadrature birdcage coil was developed to work at 19F frequency under 3T 
magnetic field. It was optimized to suit in vivo rat lung imaging experiments using inert 
fluorinated gases. Compared to the linear reference, coil sensitivity was improved by a factor 
of 1.4, and power consumption was halved with the quadrature structure. The transmit B1 
field distribution was quantitatively investigated using Dual Angle Method (DAM), and a 
homogeneous B1 map was obtained at the center of the coil. In vivo rat lung imaging 
experiments were performed using inert fluorinated gas, and multi-slices lung images of the 
rat were obtained.  
Secondly, a 1H - 129Xe double-birdcage coil was developed to provide the deal-frequency 
imaging ability without having to re-configure the coil or relocating the experimental subject. 
The decoupling between the two birdcage coils was quantitatively investigated. With 
geometrically decoupling, an isolation of 28dB was obtained at xenon frequency, and an 
isolation of 45dB was obtained at proton frequency.  Images were acquired from both xenon 
and proton phantoms, and images registration processing was able to be performed 
accurately. 
In order to further improve the SNR for the two sets of coils, RF shielding will be 
constructed and applied to both sets of coils in future work. Also, the B1 mapping tests will 
be performed on the double-birdcage coils using hyperpolarized xenon gas, to quantitatively 
evaluate the B1 field homogeneity, and distortion resulted from the coupling between the two 
coils.  
 69 
REFERENCES 
[1] E. M. Purcell, H. C. Torrey, and R. V. Pound. Resonance absorption by nuclear magnetic 
moments in a solid. Physical Review, 69:37?38, 1946. 
[2] F. Bloch. Nuclear induction. Physical Review, 70:460?474, 1946. 
[3] P. C. Lauterbur. Image formation by induced local interactions: Examples employing nuclear 
magnetic resonance. Nature, 242:190?191, 1973. 
[4] P. Mansfield and P. K. Grannell. NMR ?diffraction? in solids? Journal of Physics C: Solid State 
Physics, 6:L422?426, 1973. 
[5] Albert, M.S. et al. (1994) Biological magnetic resonance imaging using laser polarized 129Xe. 
Nature, 370, 199-201. 
[6] Kuethe DO, Caprihan A, Fukushima E, Waggoner RA. Imaging lungs using inert fluorinated 
gases. Magn Reson Med 1998; 39: 85-88. 
[7] Soher BJ, Ainslie M, MacFall J, Hashoian R, Charles HC, editors. Lung Imaging in Humans at 
3T using Perfluorinated Gases as MR Contrast Agents. Proceedings of the 18th Annual Meeting 
ISMRM; 2010; Stockholm, Sweden. 
[8] Kuethe DO, Caprihan A, Fukushima E, Waggoner RA. Imaging lungs using inert fluorinated 
gases. Magn Reson Med. 1998; 39(1):85-8. 
[9] Schreiber WG, Eberle B, Laukemper-Ostendorf S, Markstaller K, Weiler N, Scholz A, et al. 
Dynamic 19F-MRI of pulmonary ventilation using sulfur hexafluoride (SF6) gas. Magn Reson 
Med. 2001;45(4):605-13. 
[10] Kuethe DO, Behr VC, Begay S. Volume of rat lungs measured throughout the respiratory cycle 
using 19F NMR of the inert gas SF6. Magn Reson Med. 2002; 48(3):547-9. 
[11] Adolphi NL, Kuethe DO. Quantitative mapping of ventilation-perfusion ratios in lungs by 19F 
MR imaging of T1 of inert fluorinated gases. Magn Reson Med. 2008; 59(4):739-46. 
 70 
[12] D. I. Hoult. The principle of reciprocity in signal strength calculations: a mathematical guide. 
Conc. Magn. Reson., 12(4):173-187, 2000. 
[13] H.E. Moller, X.J. Chen, M.S. Chawla, B. Driehuys, L.W. Hedlund, and G.A. Johnson. Signal 
Dynamics in Magnetic Resonance Imaging of the Lung with Hyperpolarized Noble Gases. J. 
Magn. Reson., 135:133-143, 1998. 
[14] J. Mispelter, M. Lupu and A. Briguet, NMR Probeheads for Biophysical and Biomedical 
Experiments: theoretical principles and practical guidelines. Imperial College Press, 2006. 
[15] F. D. Doty, Y. A. Yang, and G. E. Entzminger, "Magnetism in NMR Probe Design Part I: 
General Methods," Concepts in Magn. Resn., Vol 10(3) , 133-156 (1998). 
[16] P. B. Roemer, W. A. Edelstein, C. E. Hayes, S. P. Souza, and O. M. Muller. The nmr phase array. 
Mag. Reson. Med., 16:192-225, 1990. 
[17] K. P. Pruessmann, M. Weiger, M. B. Scheidegger, and Peter Boesiger. Sense: Sensitivity 
encoding for fast mri. Mag. Reson. Med., 42, 1999. 
[18] C. E. Hayes et al., ?An efficient, highly homogenous radiofrequency coil for whole-body NMR 
imaging at 1.5 T?, Journal of Magnetic Resonance, (63): 622-628; 1985. 
[19] C.L. Chin and M.B. Smith, ?Circular and elliptical birdcage coil design for magnetic resonance 
imaging?, New York: IEEE, 1998. 
[20] C. L. Chin et al., ?BirdcageBuilder: Design of specified-geometry birdcage coils with desired 
current pattern and resonance frequency?, Concepts in Magnetic Resonance, 15(2): 156-163, 
2002. 
[21] Couch MJ, Ball IK, Li T, Fox MS, Littlefield SL, Biman B, Albert MS. 19F Ultra-Short Echo 
Time MRI of Human Lungs Using Inert Fluorinated Gases. American Thoracic Society  
[22] Jacob RE, Chang YV, Choong CK, Bierhals A, Hu DZ, Yablonskiy DA, Woods JC, Gierada DS, 
Conradi MS. 19F MR imaging of ventilation and diffusion in excised lungs. Magn Reson Med 
2005; 54:577?585. 
 71 
[23] Ruiz-Cabello J, Perez-Sanchez JM, Perez de Alejo R, Rodriguez I, Gonzalez-Mangado N, Peces-
Barba G, Cortijo M. Diffusion-weighted 19F-MRI of lung periphery: Influence of pressure and 
air-SF6 composition on apparent diffusion coefficients. Resp Physiol Neurobiol 2005; 148:43?
56. 
[24] M.C. Leifer, ?Resonant modes of the birdcage coil?, Journal of Magnetic Resonance, vol. 
124,(no.1), pp. 51-60, 1997. 
[25]  N. Chen, D. I. Hoult, and V. I. Sank. Quadrature detection coils ? a further improvement in 
sensitivity. J. Magn. Reson., 54:324-327, 1983. 
[26] R. K. Mongia, I.J. Bahl, P. Bhartia, J. Hong. RF and Microwave Coupled-Line Circuits. Artech 
House, Incorporated, 2007. 
[27] Oh C, Hilal S, Cho Z, and Mun I. Radio frequency field intensity mapping using a composite 
spin-echo sequence. Magn Reson Imaging 1990; 8:21-25. 
[28] Morrell GR. A phase-sensitive method of flip angle mapping. Magn Reson Med 2008; 60:889-
894. 
[29] Sacolick LI, Wiesinger F, Hancu I, and Vogel MW. B1 mapping by Bloch-Siegert shift. Magn 
Reson Med 2010; 63:1315-1322. 
[30] Insko E and Bolinger L. Mapping of the radiofrequency field. J Magn Reson A 1993; 103:82-85. 
[31] Hornak JP, Szumowski J, and Bryant RG. Magnetic field mapping. Magn Reson Med 1988; 
6:158-163. 
[32] Pauly J, Nishimura D, and Macovski A. A k-space analysis of small-tip-angle excitation. J Magn 
Reson 1989; 81:43-56. 
[33] Pablo J. Prado; Bruce J. Balcom; Igor V. Mastikhin; Albert R. Cross; Robin L. Armstrong; Alan 
Logan. Magnetic Resonance Imaging of Gases: A Single-Point Ramped Imaging with T1 
Enhancement (SPRITE) Study. J. Magn. Reson., (137): 324-332, 1999 
 72 
[34] Mata JF, Altes TA, Cai J, Ruppert K, Mitzner W, et al. (2007) Evaluation of emphysema 
severity and progression in a rabbit model: Comparison of hyperpolarized 3He and 129Xe 
diffusion MRI with lung morphometry. J Appl Physiol 102: 1273?1280. 
[35] Driehuys B, Cofer GP, Pollaro J, Mackel JB, Hedlund LW, et al. (2006) Imaging alveolar-
capillary gas transfer using hyperpolarized 129Xe MRI. Proc Natl Acad Sci U S A 103: 18278?
18283. 
[36] Chen RYZ, Fan FC, Kim S, Jan KM, Usami S, et al. (1980) Tissue-blood partition-coefficient 
for xenon: Temperature and hematocrit dependence. J Appl Physiol 49: 178?183. 
[37] Lowery TJ, Doucleff M, Ruiz EJ, Rubin SM, Pines A, et al. (2005) Distinguishing multiple 
chemotaxis Y protein conformations with laser-polarized 129Xe NMR. Protein Sci 14: 848?855. 
[38] Dubois L, Da Silva P, Landon C, Huber JG, Ponchet M, et al. (2004) Probing the hydrophobic 
cavity of lipid transfer protein from Nicotiana tabacum through xenon-based NMR spectroscopy. 
J Am Chem Soc 126: 15738?15746. 
[39] 9. Wolber J, Cherubini A, Leach MO, Bifone A (2000) Hyperpolarized 129Xe NMR as a probe 
for blood oxygenation. Magn Reson Med 43: 491?496. 
[40] A. R. Rath, ?Design and performance of a double-tuned birdcage coil?, Journal of Magnetic 
Resonance, (86): 488-495; 1990. 
[41] G. X. Shen et al., ?Dual-frequency, dual-quadrature, birdcage RF coil design with identical B1 
pattern for sodium and proton imaging of the human brain at 1.5 T?, Magnetic Resonance in 
Medicine, (38): 717- 725, 1997. 
[42] J.R. Fitzsimmons et al. ?Double Resonant quadrature birdcage?, Magnetic Resonance in 
Medicine (MRM), (30): 107-114, 1993. 
[43] T. Lanz et al., ?Double tuned 23Na 1H nuclear magnetic resonance birdcage for application on 
mice in vivo?, Review of Scientific Instruments, 72(5): 2508-2510; 2001.