Hyperpolarized 129Xe Nuclear Magnetic Resonance at 1.89 T and 85 G: A Signal-to-Noise

Ratio Cornparison

Mark McDonald, B.Sc.

.A thesis submitted to

the Faculty of Graduate Studies and Research

in partial fulfillment of

the requirements for the degee of

Master of Science

Depart ment of Physics

Carleton University

Ottawa. Ontario, Canada

January 2001

@copyright

2001, Mark NcDonald

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Abstract Suclear polarization of 12'Se can be enhanced by up to five orders of magnitude

by optical pumping and spin eschange. The resulting rnagnetization can be used

as a powerful probe for magnetic resonance imaging. Because the magnetization is

largely independent of the magnetic field strength. field strengths up to three orders

of magnitude lower than conventional field strengths (1.5 T) can be used to image

hyperpolarized lZ9Se. This. among other things, may drastically reduce the cost of

t lie magnet used.

Suclear magnetic resonance of hyperpolarized I2'Se gas is investigated at 85

G and the signal-to-noise ratio compared to that of signals acquired at 1.89 T. A

dcdicated 85 G resistive magnet aas constructed and used to acquire the signals. Tl

relasation time measurements were made and radiation damping effects checked for.

The SSR at 85 G was measured to be 4 0 0 while the SSR at 1.89 T !vas measured

to be 4 0 0 0 0 . This nork suggests that Magnetic Resonance (UR) imaging at 85 G

should be feasible using hyperpolarized l2'Xe gas.

Acknowledgement s

1 rvould like to thank my supervisor. Giles Santgr. for his support and encour-

agement throughout this project. 1 rould also like to thank the students and staff

of the Carleton Nagnet ic Resonance Facility (CSIRF)! part icularly Albert Cross for

his patience and help with al1 matters electronic and Julia Wallace for her insight

and for verifying some of my results. -4s well. thanks go out to Philippe Gravelle

and to George Curley for technical heip regarding the construction and cooling of

the magnet.

Thanks to al1 the people in collaboration with this project at the Steacie Institute

for .\Iolecular Sciences (SIMS) of the National Research Council (SRC). particularly

J i Dong S u for constructing the spectrometer and Igor Moudrakovski for providing

a senon sample to work with.

Thanks to Greg, Bob. Dan, Ken, Juan, Gosia. Dave, Mike. Chris, Cath. Seamus,

Rhian, and Justin for getting me out of the lab once in a while and for listening.

Finally, 1 aant to thank Blom, Dad, Brad and Lisa for their unwavering support,

and Lisa Desai for her confidence in me and her love. 1 would not be here without

any of them.

Contents

... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Abstract "1

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Acknowledgenients iv

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Table of Contents ..* . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . List of Tables vm

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . List of Figures. is

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . List of Abbreviarions s i

1 Introduction 1

9 . . . . . . . . . . . . . . . . . . . . . . 1.1 Magnetic Resonance Iniaging - . . . . . . . . . . . . . . . . . . . . . . . 1.2 Hyperpolarized Soble Cases 3

. . . . . . . . . . . . . . . . . . . . . . . . . . 1.3 Lon-Field SIR Imaging 9

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.4 Overview 13

2 Theory 14

. . . . . . . . . . . . . . . . . . . . . . . 2.1 Suclear AIagnetic Resonance 14

. . . . . . . . . 2.1.1 Suclear Properties in a Static Magnetic Field lS

. . . . . . . . . . . . . . . . . . . . . . . . 2.1.2 Bulk hlagnetization 17

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.3 RF Pulses 19

. . . . . . . . . . . . . . . . . . . . . . . . . 2.1.4 Signal Acquisition 21

. . . . . . . . . . . . . . 2 1 . Other Factors Affecting ?;UR Signal 26

. . . . . . . . . . . . . . . . . . . . 2.2 Laser Polarization of Xoble Gases 36

. . . . . . . . . . . . . . . . . . . . . . . . . 2.2.1 Optical Pumping 36

. . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.2 Spin Exchange 38

. . . . . . . . . . . . . . . . . . . . . . . . 2.2.3 Polarization Factor 38

. . . . . . . . . . . . . . . . . . . . . . 2.2.4 Relayation Mechanisms CIO

2.3 Magnetic Resonance Imaging of Hyperpolarized lZ9Se . . . . . . . . . 16

. . . . . . . . . . . . . . . . . . . . . . . . . . . 2 .3.1 Slice Selection 46

. . . . . . . . . . . . . . . . . . . . . . . 2.3.2 Frequency Encoding 47

. . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.3 Phase Encoding 47

3 hlethods 50

. . . . . . . . . . . . . . . . . . . . . . . . . 3.1 Resistive Electromagnet 50 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 SSIR Spectrorneter a s . . 3.3 Laser Polarization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1

3.4 SSR Neasurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

. . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.1 Predictions 61

. . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.2 lleasurements 63

4 Results 69

. . . . . . . . . . . . . . . . . . . . . . . . . 4.1 Resistiw Electromagnet 69

. . . . . . . . . . . . . . . . . . . . . . . . . 4.1.1 Field Cniformity 69 - . . . . . . . . . . . . . . . . . . . . . . . . . . . -1.1.2 Field Stability ( 2

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 BI Calibration 71

. . . . . . . . . . . . . . . . . . . . . . . . 1.3 Polarization LIeasurements 74

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4 Electronic Factors 76

4.5 Esperimental Confirmation of the SSR Dependence on Field Strength 78

. . . . . . . . . . . . . . . . . . . . . 4.6 Relaxation Time Neasurements 79

4.7 Radiation Damping . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

5 Discussion 83

A Low-Field Polarimeter Modifications 97

B Axial Symmetry in Magnetic Fields 100

Bibliography 104

List of Tables

1.1 Properties of 3He and '"Se. . . . . . . . . . . . . . . . . . . . . . . . 6

3.1 Pti!*sical and electrical specifications of the resistire electromagnet . . 56

-- 4.1 Polarization values for t hermally and hyperpolarized '"Sr. . . . . . . r CI

4.2 Soise figure nieasurements. . . . . . . . . . . . . . . . . . . . . . . . . 79

4.3 SSR valiles fur 1.89 T and 83 G thermally and hypcrpolarizcd '"Se. 79

4.4 A Comparison of the measured SSR ratios to the calculated values. . 79

4 . Parameters used to estimate the ratio of SSR. . . . . . . . . . . . . . 80

4.6 A comparison of flip angle calibrations at different acquisition times

along the FID.. . . . . . . . . . . . . . . . . . . . . . . . . . . - . . . 81

. . . . . . . . . . . . . 3.5 The polarization setup used for Our experiments 58

3.6 The bore of the 85 G magnetic coi1 (photograph) . . . . . . . . . . . . 59

. . . . . . . . . . . . . . . . . The 85 G resistive magnet (photograph) 60

The axial magnetic field strength dong the 2 axis of s y m r n e t ~ . . . . 70

The axial magnetic field strength in the xy plane of symmetry . . . . . 71

Repeatability data for the low-field resistive electromagnet (3D) . . . . 72

Repeatability data for the low-field resistive electromagnet (7D) . . . . 73

. . . . . . . . . . . . . . . . . . . . . . . . . Tip angle calibration data 74 m. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . BI calibration plot I a

. . . . . . . . . . . . . .A 'H free induction decay from a nater sample 76

-4 comparison of thermally and hyperpolarized signals at 1.89 T and .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.5 G r i

. . . . . . . . . . RF coi1 baridwidth measurements at 1.89 T and 85 G 78

. . . . . . . . . . . . . . . . . . . . . . . . . . Tl relasatioii tirne data 81

. . . . . . . . . . . . . . . . . . . . . . . Signal intensity vs . flip angle 82

Modelling the FID: a cornparison between T; and Trd . . . . . . . . . . 87

. . . . . . . . . . . . . . . . . llodifications to the transmitter circuit 98

. . . . . . . . . . . . . . . . . . . . . . . . Quadrature phase detection 99

List of Abbreviations

EPI

FLASH

FID

FOY

FWHM

PFOB

SSR

Constant Bip angle

Carr-P urcell

Carr-Purcell-Meiboom-Gill

Echo-planar imaging

Fast low-angle shot

Free iriduct ion decay

Field of view

Full width half m ~ ~ i m u m

Gradient echo

Higli-field (1.89 T)

H yperpolarized

Low-field (83 G )

Slagnet ic resonance

Suclear magnetic resonance

Perfluorooctyl bromide

Radiofrequency

Signal-to-noise ratio

Longitudinal relaxation time

Transverse relaxation t ime

T E Echo time

TH Thermally polarized

TR Rcpet it ion time

F A Yariable Bip angle

sii

Chapter 1

Introduction

Traditiorially. physiological and anatomical understanding of the human body has

been acquired throiigh either direct observation or more invasive techniques such as

postniortem esaniination. Modern imaging techniques allow non-invasive observa-

tions that not only help the understanding of the human form but &O aid in the

detectiori and planned treatment of diseases early in their developnient. Among the

i-ariety of aiailable modalities. Magnetic Resonance (.\IR) imaging is a non-invasive.

non-ionizing technique well known for its minimal patient risk. excellent soft tissue

contrast . and miil ti-planar cross-sectional view.

\l'hile clinical I R imagers use hydrogen nuclei. or protons ( l H) as the nucleus of

interest for the anatomical imaging of proton-rich regions, noble gases such as helium

( 3 ~ e ) and senon ( '"Se) can be used to image proton-deficient gas spaces, such as the

lungs. and for dynamic or functional imaging, such as measuring blood flow to the

brain. This proïides an escellent complement to proton XIR imaging. Furthermore,

noble gas UR imaging can be performed at much lower magnetic field strength.

therefore providing a more economical alternative to &IR imaging by replacing high

field (> 1 T= 10000 G) superconducting magnet technologv nith lon-field (< 100

G ) resistive or permanent magnets, while still maintaining the signal-to-noise ratio

and image resolution of a high-field system. The implications of low magnetic field

st rengt h LIR imaging are the development of low-cost , accessible imagers designed

with specific geometries and dedicated to specific imaging tasks. This chapter will

introduce the relevant concepts required to understand low-field MR irnaging with

' T e gas.

1.1 Magnet ic Resonance Imaging

SIR iniaging is an estension of nuclear magnetic resonance (SMR) spect roscopy.

a trchnique first realized by Bloch[l] and Purcell[2] in 1946. In the prescnce of a

st ür i r magnet ic field. a nucleus will have a preceçsional frequency dependent upon

the nuclcar species and the strength of the field. This is the basic tenet of nuclear

rnagnctic resoriance. NR imaging exploits this field dependence of the frequericy

by altering the magnetic field strength spatially. through the use of magnetic field

gradients. tlius creating a spatial frequency map which can be used to generate an

irnagc.

Developments in SIR irnaging. based largely on the detection of hydrogen atoms

in Luter. began in the 1970's. Damadian (1971)[3] reported that certain malignant

tumours of rats differed from normal tissues in their proton ?AIR properties. and

suggested that proton S3IR might therefore have diagnostic value. The first linear-

gradient images were formed by Lauterbur[?] and by Mansfield and Grannell[fi]. both

in 1973. An image of a finger !vas reported in 1976 by àlansfield and Maudsley[ô].

studies of the hand by .\ndrew[7] and wrist by Hinshaw[S] both followed in 1957,

and before long rvhole-body images were being obtained. Image quality continually

impro~ed. partly through engineering and technological developments, and partly

through increasing skills and esperience in the manipulation of field gradients and

radiofrequency (RF) pulse sequences. By 1980. the clinical evaluation of magnetic

resonance imaging had begun, and since that time there have been continuing deyel-

opments in instrumentation and application which have led to the present situation

in which wer 6000 whole-body imagers are installed world-wide.

The most aide-spread medical use of magnetic resonance is in diagnostic radiol-

00; it is the imaging method of choice for esamination of disorders of the central

nervous system. and is increasingly used for the investigation of diseases in ottier

organ sptems[9][10] and for tumour detection. The technique provides excellent

spatial resolution and a rich soft tissue contrast particularly for the linibs and head.

which are least susceptible to motion artifacts.

Together with the diagnostic applications of SIRI. there is increasing awareness

of the role of '\IR1 in the investigation of tissue physiology and function. To a large

estent these more research-oriented studies esploit the dependencc of SlRI signais on

hemodynamic effects. including blood Row and the osygenation state of hemoglobin.

In addition. there are further 'IIRJ approaches such as diffusion-aeighted imaging.

which are proving particularly sensitive to pathophysiolog', and rhich promise to

add significantly to our understanding of a number of disease states. as well as

estending the scope of diagnostic SIRI. A more estensive review of these topics and

ttieir references can be found in the aork by Gadian[ll].

1.2 Hyperpolarized Noble Gases

Although. in principle, any nucleus with an odd number of nucleons (protons or

neutrons) has a net magnetic moment and thus can contribute an MR sigr al, hydro-

gen nuclei are the primary nuclei under investigation in XIR imaging. The magnetic

moment of a nucleus is determined by its gyromagnetic ratio, y. Therefore, because

hydrogen nuclei have the highest promagnetic ratio: resulting in a high magnetic

moment. and because 60-80% of biological tissue is composed of water, proton imag-

ing yields a large signal. MR imaging with nuclei other than protons is not as

successful due to the small magnetic moment and Ion. density of these nuclei in

tTivo. 31P and 23?Ea are the best candidates for MR imaging other than protons.

While the natural abundance of both isotopes is 100%, their respective densities in

the human body are approximately 10 mM/cm3 and 80 mlI/cm3 compared to a

typical proton density of 100 11. -4s well, their magnetic moments are about 6.63%

and 9.23% that of protons, respectively. The lori- magnetic moment and low density

of these nuclei can only be compensated for by increasing the acquisition time from

seconds to hours thereby making them impractical to work r i t h .

\\'hile proton imaging is successful in the areas of anatomical .\IR imaging of the

brain and interna! organs, it cannot be used to riew proton-deficient regions. such as

the gas space of the lungs. Therefore, since no other organic nuclear species provides

the necessary signal intensity. a suitable. biologically compatible. external species is

desirable.

In the presence of a static magnetic field a nucleus with a spin of 1/2 d l be in

one of two possible states. the ratio of the population density of which is close to one.

This ratio is the polarization factor and is proportional to the signal obtained. \\'hile

proton imagirig does provide the most MR signal of any of the nuclei available in

the human b o d s the polarization of protons is only on the order of Therefore.

considerable effort has been put into higher field systems (1-9 T). improved RF

coi1 design. and low-noise receiver systems to raise the signal-to-noise ratio (SSR)

permitting increased spatial, temporal, or spectral resolution. In t e m s of the SSR.

an' substantial increase of the polarization will result in a significant improvement in

image quality. Such a prospect has been realized aith the advent of laser polarization

techniques using spin 112 noble gases, specifically 3He and '*'Xe. Noble gases are

used because they are biologically inert and while an? non-zero spin nuclei can be

useci to perform an S l i R experiment, spin 112 nuclei are preferred as they yield the

highest det ectable NMR signal. Laser polarization, or hyperpolarization, of these

gases forces the nuclei into one of the two possible energy States, therefore increasing

the polarization and hence the signal by a factor of up to 10'. This will be discussed

in greater detail in Chapter 2.

The techniques inrolved in laser polarization were first developed in 1950. when

increasing nuclear polarization was of interest to nuclear physics. Kastler[lG] first

described how nnuclear spins could selectively populate their ground state via opti-

cal punipirig. ahere a circularly polarized light in the presence of a magnetic field

wi l l selecti~ely escite one of the two ground state energy lerels of an alkali metal

electron createcl by the magnetic field. These escited nuclei will relax back to both

ground statc energy levels thus increasing the population of the energy level not

bcing escited. In the 1960's. Colegro~e et a l [ l T ] reported on the polarization of

3He by metastability eschange (a technique whereby the nuclear polarization results

froni the strong hyperfine coupling between the electronic and nuclear spins of the

metastable atom). while Bouchiat[lS] was measuring the nuclear polarization of 3He

obtaincd by spin eschange from optically pumped rubidium atoms (where nuclear

polarization results from the transfer of the alkali metal electronic polarization to

the noble gas nucleus). This nork focuses on the spin eschange method using 12'Se.

Netastable eschange using '29Se is not an option as l2'Xe does not have a metastable

state.

3He and 1 2 9 ~ e are the on l - nonradioactive spin 112 noble gases that can be laser

polarizod. An excellent cornparison of these t a o gases can be found in a reriew article

by IIugler[l2]. Table 1.1 lists the physical characteristics of these two isotopes.

3 ~ e is produced cheaply from tritium (3H) decay at 4100 US pet litre-atm. while

natural abundance IZgSe is collected as a byproduct of the liquid air industry and

priced at 4 1 0 CS per litreatm. 80% enriched 129Se is more expensi~e at 4 1 0 0 0

1 Nucleus 1 3He 1 129 ~e

1 Gyromagnetic Ratio (rad/T/s) / 20.378 x 10' 1 7.4003 x 10'

1 Xatural Abundance (%) / IO-' ( 26

Table 1.1 : Properties of 3He and 12'xe. Self-diffusion coefficients are measured at 1 atm aiid 20° C[12].

Self-DiffusionCoeff. (cm2/s)

Ostaald Solubility Coeff.

- Water

- Blood

- Oil

US pcr litre-atm. \\-hile xenon and its isotopes are readily available, tritium is a

stratcgic material used in the manufacturing of nuclear arms and is therefore not

eiisil). accessilile to the public. This may lirnit the use of 3He for imaging purposes.

Both nuclei are good for gas space imaging (cracks. voids. lungs. sinus cavities)

[G2][2Z]. As the SSR is directly proportional to y ? 3He will have a SSR 2.8 times

better tlian that of '29Se[12]. The low diffusion constant of lZ9Se reduces signal

attenuation while the smaller results in a lower signal decay rate. To counter this.

the higli diffusion constant of 3He is ideal for characterizing the microstructure of

cornples gas spaces such as the h g . -4s well, helium son't dissolve into the blood-

Stream as readily as xenon would. as xenon has a greater affinity for fatty molecules.

such as are found in red blood ce11 membranes, than helium. .Uso. signal decay

rates of 3He are larger than those of 129Se in uico therefore allowing measurements

of smaller voids.

Initially. hyperpolarired noble gases found application in the 'IIR imaging of

animal lungs. Albert et al[22] imaged the excised lungs of a mouse with '*'Se where

the nuclear polarization \vas increased by a factor of 4 0 5 via optical pumping

1.8

0.0098

0.0099

0.018

and spin exchange (1994). Wagshul et a1[23] obtained 2D lung images from live

mice using the same setup as Albert. The dynamics and lineshapes of gas-phase

spectra from mice thorax were also investigated (1996). These results suggested

that a temporal variance in the amounts of gas in various structural compartments

could be determined from the gas spectra based on the associated bulk magnetic

susceptibility enrironments. Sakai(241 also obtained lung images from live rats.

The first human lung studies using L29Se were performed by a team of researchers

from the Cniversity of \'irginia, Princeton University and the State Cniwrsity of Sew

York at Stony Brook[Z5] in 1997, where lung images were obtained from two healthy

voluntcers during suspended respiration. Human oral and nasal cavities and the

paranasal sinuses have also been imaged[26][27].

.As indicatrd in Table 1.1. L29Se is soluble in a variety of substances while 3He is

higlily insoliiblr. 12'Se is lipophilic. dissolring readily in oils and lipid-rich materials.

'''Se is estremcly sensitive to its environment. with a huge range in its relative

resonarit frequency. or chernical shift: upon adsorption and solution. Chernical shift

is due to a nucleus' sensitivity to its electronic environment. Therefore. it is possible

that senon is more sensitive than helium due to the greater polarizability of its

niore complicated electronic structure. The result is that 1 2 9 ~ e is both an escellent

materials science and biological probe.

In its dissolved phase '*'Se can be used for perfusion imaging of the brain.

lung and other organs. Khen inhaled. it rapidly dissolves in the bloodstrearn and is

subsequently transported throughout the body with preferential distribution to lipid-

rich regions. However. in humans. lz9Se is an anesthetic at concentrations >TOR

and so must be inhaled at concentrations of 30% a t most[l3], or the patient ail1

fa11 asleep (possibly reducing cerebral blood flow making functional imaging more

dificult). -1s an alternative to inhalation delivep. site specific injections of '*'Se

dissolved in a biologically-compatible carrier[l4] (e.g.: perfluorocarbon emulsions.

CH.4 PTER 1. IXTRO D CrCTIO!V 8

lipid suspensions) may have several advantages: an increase in local concentration

providing increased SSR, decreased transit time and therefore less signal degradation

due to relaxation. targetability to specific organs or discrete sites, and a decreased

syst emic concentrat ion compared to inhalation, potentially avoiding the anesthetic

effects of the gas. In contrast, 3He, with its lon solubility, provides the opportunity

to encapsulate the gas in the form of microbubbles. thereby using the gas along

n i t h its intrinsically greater y for visualizing the structure and dynamics of fluidic

systenis[l5].

The high solubility of 12'Se in lipids and its enormous range of chemical shifts

upon solution or adsorption are fundamental to the wide range of potential applica-

tions for '"Se. Both \\àgshul et al [23) and Sakai et a1[2-l] focussed on the temporal

dynaniics of dissolved-phase lZ9Se in the chests of animals. Both groups found three

dissolved-phase resonanccs in mouse and rat thorax. with a range in chemical shift

of 190-200 ppni. Wagshul assigned these to the blood (199 ppm). lung parencfiyma

(195 ppm) and other well-vascularized tissues in the thoras such as the heart (190

ppm). Both groups also measured apparent Tl relaxation times (a time constant

characterizing the esponential decay of the '*'Se polarization lifetirne) between 10

and 50 seconds. The long apparent Tl times found in these two studies indicated

that the lifetime of hyperpolarized IZ9Se in the bloodstream should be sufficient to

allow for transport to organs distant from the lungs. such as the brain. Considering

the range of chemical shifts. these results also suggested the possibility for dissolved-

phase imaging of individual tissue components. Wilson et a1[80] measured Ti in

homogenates of rat brain, kidney. and lung at varying oxygenation levels to be as

loa as 4.4 s in deosygenated lung homogenate and as high as 22 s in deosygenated

brain homogenate. indicating that 129Se n-il1 make a unique and effective physiologie

tracer for SIR imaging with high tissue contrast.

In the first human studies using hyperpolarized 12'Se. conducted b . Slugler

CHAPTER 1. INTRODUCTION 9

et al[25]. dissolved-phase signals were detected from both the chest and the head.

The overall lineshapes of the dissolved-phase spectra in the human chest were v e q

similar to those found by Sakai in the rat[24], rhi le other resonances found in the

head matched with signals found in rat brain[28]. Subsequent studies performed

by SIaier[PO] using higher polarization levels, revealed four separate dissolved-phase

resonances in the human brain. The specific compartments corresponding to these

multiple resonances have not been determined.

The first dissolved-phase L2gSe images re re made by researchers at the Univer-

sity of .\lichigan[28]. Here. Swanson et al acquired dissolved-phase images of the rat

brain and. more recently. have estended their work to investigate the dynamics and

tissue distribution of '''Se in the lung. heart, brain and kidneys of the rat. Duhamel

ct al 18 11 also acquired dissolved-p hase images of rat brain tissue and intravascular

r issue via lipid-emulsified '?'Se injected into the carotid artery. These results show

t hc potent ial of lrJSe for measuring cerebral blood flow, cardiac perfusion. kidney

perfusion and lung function[30]. L'tilization of these techniques in humans will prob-

ably require relatively large volumes of hyperpolarized lZ9Se and polarization levels

higlicr than those currently achiewd (> 5%).

Another novel possibility with hyperpolarized noble gases is the potential to

t ransfer the polarization from the gas to other nuclei such as protons[-lO]. Here. the

spin polarization-induced nuclear Overhauser enhancement (SPISOE) can be used

to transfer polarization from 129Se to protons and be detected in both proton spectra

and images.

1.3 Low-Field MR Imaging

Khereas the nuclear polarization of conventional. thermally polarized nuclei is a

linear function of magnetic field strength. the polarization of hyperpolarized nuclei

CH-4 PTER 1. INTROD UCTlOX 10

is no t strongly dependent upon field strength, instead relying on ot her indepen-

dent properties such as laser power and gas mixture. As a result, hyperpolarized

AIR esperiments can be performed at considerably lower (- 10 mT) magnetic field

strengths than the average clinical MR imagers, rh i ch typically operate at 1.5 T.

Hyperpolarized noble gases provide exciting possibilities for performing SIR imag-

ing at low (< 100 G) fields. The benefits of low-field MR imaging are potentially

numerous[60]. -4 low-field rnagnet would not require superconducting technology

to maintain its field strength and could instead rely upon more conventional. in-

espensive and feasible resistive or permanent magnet technology. Superconducting

magnets are espensive. require regular maintenance, and cryogenic cooling for their

operation. -4 low-field resistire magnet could be inespensire. portable and not re-

qiiire the special accommodations of a high-field magnet. As well. the low-field

s t rmgth roSults in a reduced operating. or Larmor. frequency (kHz) which would

sirn pli fy the RF electronics and reduce power consumption. These lower frequencies

also have large skin depths. allowing gas space imaging inside conductive materiais.

Firirilly. at low magnetic fields there is a reduced effect of magnetic susceptibility

hrterogeneity. resulting in reduced image distortion, line broadening, and longer Ti

thereby inipro~ing noble gas image resolution.

Low-field 1IR imaging began a i th Packard and \arian[l3] in 1954 with prepo-

larized MR imaging in the Earth's magnetic field (-0.5 G). a technique that starts

witb a sample of nuclei with a high polarization in a high-field strength which is

then transferred to a receiver coi1 aligned with the Earth's field and sarnpled before

the relaxation effects can take place. They applied a polarization pulse in a SMR

esperiment using a pulsed field of 100 G and. after turning off the polarizing field

nonadiabatically, were able to record the received signal in the Earth's magnetic

field. obtaining an SSR of 20. This allowed them to estimate the signal's frequency

accurately enough to compute the local magnetic field to 1 part in 13000.

.&O in 1931. Bloom and Mansir devised an experiment for measuring Tl relax-

ation times a t very Iow-fields[44]. After prepolarizing at 100 G, they depolarized the

sample for a variable tirne r at a field of about 2 G , and detected the received signal

rarying as e-'lT1. The freedom to customize polarization raveforms introduced the

possibility to create images weighted with a rich spectrum of Tl dispersion contrast.

Since Packard and Varian. considerable basic research has been done using the

Earth's magnetic field. Béné[45] has been working in this area since 1919 and in

1977 published in situ Tl dispersion results that discriminated between nornial and

pattiological aniniotic fluid. In 1980 he published an exhaustive overriew paper[46].

Borcard has continued the Tl dispersion investigation using an esperiment siniilar

to the one proposed by Bloom and Mansir. Koenig et al have used a similar esper-

imentaf sctiip to rneasure protein and tissue Tl dispersion curves[47][48]. In 1985.

the biophysics group at Lyon made the first phantom SUR images[49][ZO] using the

Earth's field. A similar approach aas used to obtain images of pears and apples by

Stepisnik et ai at Ljubljana[X][52].

Other techniques move away from the use of the Eanh's field as the static imag-

ing field. Sepponen of Instrumentarium Corporation has patented an NRI system

in whicli spins are left parallel to the 2 field after a polarizing field ramps ciown.

The irnaging process for this configuration proceeds as usual with RF pulses and

gradients. Le Rous has also proposed a pulse-polarized >IR system. .\Iacovski pro-

posed a perpendicular configuration that eliminates the need for an RF amplifier

for volumetric imaging. Recently, Carlson et al[53] built a prepolarized MR imaging

(PSIRI) system by adding a 1200 G polarizing field to a Toshiba ACCESS 640 G

imager. Carlson has also used this system to investigate Tl dispersion behaviour in

an imaging format using several shots with a stepped prepolarizing pulse[S][55].

Since Albert's[P'~] introduction of hlperpolarized noble gases to >IR imaging.

impro~ements at low-field have been made using these gases to circumvent the pre-

polarizing step described above. For example, Darasse et al recently demonstrated

laser-polarized 3He human lung imaging at 1000 G[56]. while Saam and coworkers

obtained one-dimensional profiles of cells filled with laser-polarized 3He at 31 G [Ji].

In addition, using superconductive quantum interference devices (SQC'IDS), Augus-

tine et al imaged laser-polarized 3He and solid 12'Se at liquid helium temperatures

(4K) and 5.4 G[J8]. Most recently. Wong et al demonstrated fast, single-scan 1D

imaging at 20.6 G of laser-polarized 3He in sealed glass phantoms[59] and escised rat

Iungs[60]. Radiation damping measurements and the low-field imaging systern used

for thesc esperiments were also described[60]. Finally, a low-field hyperpolarized

""e image of a live rat lung was obtained by Yang et a1[87] by lowering t he field

strcngth of a superconducting magnet to 0.015 T (150 G).

The development of a lon-field f l R imaging system based on hyperpolarized

noble gases opens the door to a wide variety of new applications. Esamples in the

bior~icdical field include portable systems for diagnostic lung imaging for humans. and

tablet op )IR instruments for research in aninials. Dissolred phase imaging studies.

like those performed at high-field strengths. could also be investigated assuming a

sufficient SSR is obtained. Furthermore. a low-field M R imager would be compatible

with operation in restricted environments. such as on board a space station. and may

permit lung imaging of patients with art ificial transplants such as pacemakers[61].

In the physical sciences, low-field hyperpolarized noble gas -\IR imaging will

be effective in imaging voids in two classes of materials that are problematic for

high-field SIR: ( i ) heterogeneous systems? such as porous and granular media. which

distort high-field images because of large, solid-gas magnetic susceptibility gradients:

and (ii) electrical conductors. rhich prevent high-field '\IR imaging by RF shielding.

Also. low-field N I R measurements of the restricted diffusion of noble gas imbibed

in porous media may provide an effective and practical study of fluid permeability

in such media[62].

The result should be a smaller. more portable, and more cost-efficient imager

which could become cornmonplace in hospitals and clinics where the more expensive

superconducting systems could not be sited.

1.4 Overview

The purpose of the research described in this thesis was to compare SSR at 1.89 T

a i t h 85 G as a step towards the imaging of hyperpolarized lZ9Se at low-field. The

thesis describes the design and construction details of a prototype S l I R system for

hyperpolarized " ' ~ e as well as the esperimental methodolog' for acquiring hyper-

polarized "'Se gas signals. -4 sample 1'9Se ce11 was analyzed and its parameters

(Tl relasa t ion t ime, polarizat ion lerel. flip angle calibration) determined. -4 t tieo-

retical and esperinientally validared SSR cornparison of the low-field system nith a

high-field superconducting system was performed.

Chapter 2

Theory

The theoretical background necessary for the understanding of the topics discussed

in this thesis is presented in this chapter. The core topics include the fundamental

t licory of S 1lR. SIR imaging. the laser polarization theory behind hyperpolarized

notdr gascs. and specific modifications in the case of low-field hyperpolarized nobk

gas irriaging.

2.1 Nuclear Magnetic Resonance

Fuiidamerital nuclear magnetic resonance theory begins with a single nucleus and

its behaviour in a static magnetic field. From here. large populations of nuclei are

considered and the effects of RF pulses applied to those populations. Combined with

the relaxation mechanisms of the nuclei? equations governing the behaviour of the

net nuclear magnetic moment are formed and the signals received by a spectrorneter

are esplained. S'r IR spectroscopy is also discussed in t his section.

\\'hile SSIR is a quantum mechanical phenomena, the classical description is

sufficient for the purposes of the research involved in this thesis. Quantum mechan-

ical concepts will be introduced only when necessary or when deemed helpful in the

uriderstanding of the material. For a rigorous quantum mechanical explanation of

CH.4 PTER 2. THEORY

S )IR, see Slichter[63].

2.1.1 Nuclear Properties in a Static Magnetic Field

Suclei possess the quantum mechanical property of nuclear spin, 1' the ~ a l u e of nhich

is dcpendent upon the intrinsic spin of the protons and neutrons that the nucleus

is coniposed of. Suclei with unpaired protons or neutrons have a net spin which is

non-zero and can give rise to SUR. This property determines the different possible

values of the total angular rnornenturn, 1, by quantizing the 2 axial cornponent and

fixing the magnitude of the vector. The relationships are:

~ = 1 ~ 1 = h J 1 ( 1 + 1 ) ~

J= = hm.

wiiere J is the magnitude of the vector. JI is the 2 componen

I l is Planck's constant. The possible values of rn are:

(2.2)

it and A = h/Zr where

d i e r e : ,In1 = 1.

Suclei ni th I # O also possess a magnetic moment. p. which is the result of the

nioting nuclear charge about the nucleus as well as the intrinsic magnetic moments

of the nucleons. ji can be espressed in terrns of the angular momentum. by:

n+iere: y is the gvromagnetic ratio, defined as the ratio of the magnetic moment to

the angular momentum and given as e/2m. the ratio of the electronic charge. e? to

nuclear m a s . m. and therefore is a constant specific to the nuclear species under

in\-est igat ion. Tlierefore, because of this proportionality and the discrete nature of

f. ji is quantized. For lH, 7 = 26.7510~10~ radT-'s-' a d for '29Se, y = 7.1003~10~

radT-'s-l.

In the presence of a static magnetic field, Bo, the magnetic moment experiences

a torque. ?:

Substituting from Eq. 2.4 this becomes:

which is the equatioii of motion of jï about Bo with solution:

Eqiiat ion 2.8 is the well knor~n Larmor equation and describes the precession of j7

about as s h o w i in Figure 2.1. When defined in units of cycles per second (Hz).

io is rcfcrred to as the Larmor frequency. vo:

e.g. for 12%e vo=??.16 MHz at 1.89 T.

The interaction of with @ can be described by a Harniltonian, R:

The dot product can also be represented as a scalar product of two components. one

representing the total magnitude and the other representing a projected value. The

allowd energies of the systern with l? = Bof are therefore:

Figure 2.1: A single nucleus in the + presence of a static magnetic field. go. ha, a magnetic iiioment. 17. that precess about Ba with frequency w.

For I = 1/2 (the only case to be esamined in this thesis). m can have only two

possible 1-alues. referred to as spin-up ( m = +l /2) and spin-down ( m = -112).

resultiiig in: i h B o

E = *-. (2.12) 2

corririionly referred to as a Zeeman splitting. illustrated in Figure 2.2. Electromag-

rictic radiation of frequency:

is sufficient to induce a transition from the lower energ- state to the higher one. On

esaniination. Eq. 2.13 is the Larmor equation (Eq. 2.8). indicating that a resonance

condition esists: nuclear magnetic resonance.

2.1.2 Bulk Magnetization

In the preseiice of go. thermal energv provided to the nuclei by the lattice at a

temperature. T (i.e. Tl or spin lattice relasation mechanisms), causes an escess of

nuclei in the spin-up state (n;). m = +1/2, cornpared t o the spin-down state (no'

m = -1/Z This sets up a population ratio of the spin-up to the spin-down nuclear

I

Figure 2.2: A Zeeman splitting of the nuclear energy levels.

States descriLed by the Boltzman distribution and given by:

whcrc k is Boltzman's constant. This escess fraction of

which cari contribute to an S l l R signal. is given by the

(5.14)

nuclei in the spin-up state.

polarization factor. P:

nt - nc 1 - e-'WO/kT - - (2.15) R; f R 4

1 + e - h u ~ l k T

is defined as the net dipole moment per unit volume Tlic bulk rnagnetization. 10. and is proportional to the polarization factor and is illustrated in Figure 2.3. Clas-

sically. this can be described as the sum of the dipole moment vectors? both parallel

and anti-parallel to go. Each dipole moment. p' will rotate about Bo at an angle 0.

As the dipoles are out of phase with each other, only the net magnetic moment d l

g iw rise to .o. parallel to go. The relationship between the two is:

wliere is the magnetic susceptibility of the sample. - Classicallc the rnagnetization. iG, will esperience a torque and precess about BO

in the same fashion as the individual dipoles (Eqs. 2.5-2.7). Its equation of motion

Figurc 2.3: The net dipole moment. or bulk rnagneti~ation~ .hl. is parallel to the r axis bccaiise the individual dipoles are out of phase, reducing hlzY to zero.

is espressed siniilar to Eq. 2.6:

At equilibrium. the magnitude of the rnagnetization, &. for a sample containing

S = r2: + ni nuclei is espressed as[66]:

and is parallel to the static field. $.

2.1.3 RF Pulses

As seen in Eq. 2.13, the resonant condition is met when the nuclei absorb energv

at the Larmor frequency. For typical IIR imaging, these frequencies are in the

radiofrequency (RF) band (e.g.: 80.15 MHz at 1.89 T). In NMR, an RF pulse at the

Larmor frequency is applied to a population of spins such that an electromagnetic

field. BI. nith frequency, w, is applied perpendicular to the static field, $, and f i . The net magnetic field then becomes:

:\I will now precess about Ëtot rather than Bo. This can be seen in the equation of

motion:

Choosing a frame of reference rotating with the applied RF frequency. d. sim-

plifies the analysis of the behaviour of the magnetization. In this so-called rotating

franic of reference. indicated by the prirned axes in Fig. 3.4. the effective field

strcrigt h brcornes[66]:

B.,, = (Elo - y ) l. + &i. (2.21)

-. -. -. For the case of on-resonance radiation (d = Be// = BI and .\l will tip a m y

Ironi t l i ~ i asis at a precessional frequency i i i = 7Bi in the rotating frame and ail1

do so as long as the RF pulse is applied in a process called nutation. The tip angle

rliat .\7 nutates through. o. is a function of the amplitude. Bi' and pulse duration.

t,. a is defined in radians by:

o = Ltpu1dt = . - , ~ , t ,

for a rectangular pulse.

.II, and .\I,, can be espressed in terms of û simply by[66]:

31: = Alz- cos a (2.23)

+ dl, = .21& sin a'

where - and + indicate before and after the RF pulse, respectirely. Because the

S U R receker is situated in the zy plane, the received signal ri11 be proportional

to JI,,. the m~xirnum value of which is obtained when a = 90°, as shonn is Figure

U ( a ) . For a = 180~. the magnetization is inverted. as s h o m in Figure Z.-I(b).

Figure 2.1: A rotating frarne representation of (a) a 90" pulse completely tipping the niagnetization into the zy plane and (b) a 180' pulse inverting the magnetization.

2.1.4 Signal Acquisition

Detecting the occurrence of a magnetic resonance condition relies upon the principle

of induction. i.c. that a changing magnetic field induces an electromotive force

(EMF) in a loop of electrical conductor through which the field passes. Following

the perturbation of the rnagnetization frorn its equilibriurn state. &, will precess

about go with angular frequency producing an alternating magnetic field in a

luop of \vire. S. as in Figure Z.5(a). Intuitively. if .Q is close to S. the induced

EILF will be large. whereas if the a is far a w v frorn So the EMF will be srnall.

Conversely. if a current is passed through S? as in Figure 2.5(b), it will generate

a magnetic field. BI. that d l be large close to the loop and smaller further away

from the loop. There is a direct relationship between the E4IF induced in loop S

by a rotating moment. ~ X S , where C W ~ is the sample volume, a t point P and the

field ËI created by current flowing through loop S. Beginning a i t h Faraday's Law

where G is the induced ElIF and defining the flus as: = BI * i \I , shere XI is the

magnet ization per unit current, we cm espress quantitatively the above relationship

Figure 2 .3: (a) The rotating rnagnetization M induces an EMF in loop S. (b) The signal from point P is proportional to the field BI at that point. This is the Principle of Rccipraci ty.

using the Principle of Reciprocity:

alierc d& is the signal from a single dipole moment. Defining JÏ as a vector with

asial and planar components. a e have from Eq. 2.7:

where a is the phase of the magnetization. It therefore f o l l o ~ s that:

where d is the phase of Ël with respect to 10. Khen evaluated and integated over

the sample. it can be sho1vn[77] that:

It should be noted that in the more general case: Bi,! hl,,, a and d d l al1 be

functions of position. Taking = A& sin cy and recalling Eq. 2.18 and the Larmor

relation (Eq. 2.8) we have:

The last term in Eq. 2.30 describes the esponential decay of the signal due to

transverse decay rnechanisms (T;), to be discussed in the following section. The

signal equation has the form of an esponentially decaying sinusoid and is commonly

referrecl to as a free induction decay. or FID. An esample is pro~ided in Figure 2.6.

O 0.002 0.004 0.006 o.ma 0.01 0.012 0.014 0.016 0.018 0.02 Tme (5 )

Figure 2.6: A free induction decay. or FID. characterized by a sinusoidal offset frequency, v = 500 Hz. and an exponential decay constant- T;.

The loop S is a simplified version of the RF coils used to induce ÊI and detect

-0. In practice. these coils may have varying geornetx-y (solenoids. saddle-shape.

Helniholtz sets) and essentially act as tuned circuits that resonate a t a specific fre-

quency. Two variable capacitors, one in parallel and one in series with the circuit.

control the resonant frequency of the tuned circuit. As the NàIR signal voltage is

on the order of a microvolt, any increase in signal amplitude is welcome. This can

be done by using a high-power transmitter, thereby increasing BI, a high-gain and

low-noise preamplifier, and a large sample volume.

Because the detector may not be exactly aligned a i th the magnetization in the ry

plane. two orthogonal detectors (real and irnaginary channels) are used to detect the

J I , and JI, components of the magnetization. The magnitude of this cornples

sigrial is then used as the signal amplitude. Detection in this. manner is referred to

as detection in quadrature.

The Signal-to-Noise Ratio

The signai-twnoise ratio (SSR) is a more meaningful figure of measurement than

siniply the signal strength. The SSR considers both the magnitude of the noise

as ne11 as the S!dR signal. In order to quantify the SSR. noise must first be

considered. \\*hile random noise resulting from spins undergoing Browniaii motion

is always present and important for large samples at high fields (Bo > 1 T)! the

dominant noise source for sufficiently sinall samples at high fields and for nearly an-

sized sample at low fields is Johnson, or thermal noise from the receiver coils[I7]. At

teniperature T[ïC]:

where Fs is the noise amplitude, R is the coi1 resistance and A j is the noise band-

width of the system. defined as the inverse of the sampling time ( l /TS)? the time

delay between data acquisitions. Taking the ratio of the signal (Eq. 2.30) and noise

equations (Eq. 2.31) and looking at the maximum amplitude (a = 90') we have for

CHAPTER 2. THEORY

the SSR at t = 0:

Here. the nucleus dependent parameters are 7 and p. The RF coi1 ni11 determine

both Bi and R, shile the data acquisition time (DAQ) will determine A f . If nTe

assume a specific number of spins, N, at a set volume, 1$, at a temperature T. the

only remaining variable is the static field strength. Bo, determined by the magnet

coil windings and curent.

By analyzing the relationship betaeen the energ' stored in the BI field. which

is a nieilsure of the coil inductance. and introducing the noise figure. F. to account

for the noise introduced by the receiver, it can be shown[Ti] that. for a solenoid. the

ahow espression is equivalent to:

whcrc I ï is a numerical factor depending on the receiving coil geometry: q is the

fillirig factor. Le.. the fraction of the coil volume occupied by the sample: po is the

pernieability of free space; and 1; is the volume of the coil. SSR improvements can

therefore be made by using low noise. high gain preamplifien to reduce the noise

figure. and by improving the RF coil Q factor to increase signal amplitude. The use

of RF shielding also improves SKR. as discussed in the nest section.

The ratio of SSR between two esperiments a t two different field strengths can

be calculated using the expression:

where h' - 1 in both cases and the ratio of dlo's is reduced to a ratio of P factors.

RF Shielding

SSR can also be increased by reducing the extraneous noise from surrounding radia-

tion sources (e-g.: computer monitors, powers supplies, etc.) through the use of RF

shielding. The effect of encasing the RF coi1 in an electrically conductive material of

thickness t . such as Al, Sn, or Cu, is the exponential attenuation of the RF signals

passing through the shield by a factor e-t 'd. The coefficient d is the skin depth of the

shielding matcrial, that is the distance required to attenuate the signal by a factor

e - ' . The skin depth will depend upon the frequency, u. of the signals as well as the

pernieability, p. and conductivity, o, of the shielding material. For a good conductor

(o » +). the relation is[65]:

For aluniinuni at 22 MHz. a = 2.8 s 10-8 R-lm-' and p = 1.3 s 1 0 - ~ S/A2 resulting

in a skin dcpth of 1.8 s 10-' m.

From Eq. 2.33 we see that at lower frequencies noise will be harder to attenuate

arid will have larger skin depths (e.g. d = 2.7 s IO-" m at 100 kHz). Conrersely.

penetration of RF will be much better at lower frequencies perhaps allowing imaging

of conductive objects (e.g.: metals) not possible at high frequencies.

2.1.5 Other Factors Affecting NMR Signal

Xfter the nuclear system has been disturbed from its equilibrium by an RF pulse.

the system will begin to relax to its equilibrium state (i.e. AI, = hlo and A l , =

0) via certain relaxation mechanisms specific to the nucleus under investigation.

Two variables characterizing these relaxation mechanisms are the spin-lattice, or

longitudinal relaxation tirne: Tl' and the spin-spin, or transverse relasation time'

T2. Tl gorerns the asial component of the magnetization. dl,, retuming to thermal

equilibrium. ivhile T2 deals with the dephasing of the spins in the transverse plane

CHAPTER 2. THEORY 27

and the esponential decay of hl, as it precesses about Bo. For a rigorous treatise

on relaxation effects see Abragam[86] or Slichter[63].

Spin-Lattice Relaxation Time, TI

Generally speaking. a spin relaxes by a component of local magnetic field within the

relaxing frame. .A nucleus experiences a fluctuating local magnetic field created by

its onn motion and that of neighboring magnetic moments' usually dipole moments

frorn elertrons and nuclei. This local field. Bi,, has cornponents parallel to and

perpendicular to $. The perpendicular component. when oscillating at the Larmor

frcquency. induces transitions between ene rg States? relasing .\& at a rate:

1 - i. B ~ J ( ~ ~ ) , (2.36) Tl

\ v l i ~ r c . J ( i . ) is the spectral density function. a frequericy distribution of the possible

frcquencies that Bloc ma- have.

The probability of inducing transitions is dependent upon the amplitude of J ( & )

at the resonant frequency of the nucleus in question. The spectral density function

is the Fourier t ransform of the autocorrelation function. G(t)? approsimated by:

ahere T, is the correlation time constant for reorientation of the neighboring dipole

moments. typically determined by inertial and viscosity effects. G( t ) expresses the

probability that a magnetic dipole source will have the same magnitude that it had

at t = O at some later time t : at the position of the relaving nucleus. J(J) can

t herefore be espressed as a Lorentzian function:

The shape of J (>) depends on nuclear and molecular tumbling rates. A n esample

is provided in Figure 2.7.

Figure 2.7: Hypothetical spectral density function for different 7,. Different correlation tirries. T,. correspondirig to the nature of the sample (solid. liquid. gas) influence the shape of the curvc.

Frorn Eqs. 2.36 and 2-38 it can be seen that Ti is dependent on d . This results in

a tkpendencc on Bo. due to the Larmor relation. and on temperature. T. as molecular

and atomic frequencies are dependent on the thermal contribution to t heir kinetic

energy. t kT .

The dominant Tl relaxation mechanisms include: dipole-dipole interactions. gen-

erally the most important mechanism for spin 112 nuclei, n-here the nucleus espe-

riences a fluctuating field due to the motion of neighboring magnetic dipoles. from

other nuclei or unpaired electrons; chemical shift anisotropy. where the chemical

shielding of the nucleus depends on the orientation of the moIecuIe with respect to

the direction of 4: and spin-rotation interaction. where local fields are induced as

CH-4PTER 2. THEORY 29

a result of the moring charges of electrons and nuclei which anse from a rotating

molecule.

-4 large Bi,, combined with wo = 7;' are conditions for efficient Tl relaxation.

Its time dependence can be expressed as[66]:

u-hcre it cari be shown that with increasing time. JI : approaches the thermal equi-

Ii brium value .\Io.

Spin-Spin Relaxation Time, TI>

Follo~ving an RF pulse. the magnetization is either partially or wholly tipped into

the transwrse plane depending on the tip angle. ct (Eq. 3.24). creating a transverse

magnetization component. JI,,. This component precesses about the z mis at the

Larmor frequency. However. because of the slightly differing local magnetic field

strengtfis about each of the spins. each spin will precess at a slightly different fre-

quency t han the rest. These local variations in the field are the result of the same

Ructuating rnagnetic field that gives rise to TI relaxation. The cornponent of 4, parallel to go alters the field strength that a nucleus experiences and therefore al-

ters its precessional frequency. This results in a gradua1 dephasing of the individual

nuclei and a decay of M,, characterized by the relaxation constant 12:

1 1 - = - + B:, ~ ( 0 ) + other, (2.41) T 2T1

where it can be seen that T2 also depends on the spectral density function at zero

frequency since the cornponents of Bi, parallel to 8 0 . and not rotating in the labora-

tory frame of reference, can affect dl,. -4s it includes Tl? T2 will also be susceptible

to Tl mechanisms and the temperature and field strength dependence that charac-

terize Tl 'i: as described previously. The Tl term indicates that half of the local field

available for relâuation can affect the transverse component, cornpared to the lon-

gitudinal component. In addition, the second term in Eq. 2.41 is quite large (Fig.

2.7) for solids (T2 << Tl) and typically dominates, but is srna11 for viscous liquids

and quite small for non-viscousliquids as Bi., decreases resulting in T2 = Tl. The

third term in Lq. 2.41 includes time dependent effects such as diffusion and chemical

eschange.

The equation of motion of JI, is given by[66]:

in the rotating frame of reference wi t h solution:

Further transverse relwation mechanisms include dephasing due to inhomo-

genei t ies in the staric magnetic field. ABo. magnetic susceptibility. y. and chemical

shift. 6. This results in a faster decay rate a i t h an effective decay constant, Ti < T2.

where:

As these additional dephasing contributions to T? are not time dependent, they can

be refocused a i th a spin echo. An esample of T; vs. T2 decay is shown in Figure

'2.6.

Spin Echoes

Spin echoes are created when the dephasing of the transverse magnetization is par-

tially refocused. as s h o m in Figure 2.8. -4s preriously discussed. Al, decays ac-

cording to an effective relaxation constant? Ti. rather than T2 (Fig. 2.6). A spin

echo utilizes a 180" pulse applied after the spins have been tipped into the transverse

plane via a 90" pulse. The 180" pulse is typically applied along the transverse avis

orthogonal to the 90" pulse so that the dephased spins will rephase. The echo time

occurs at time TE, where TE12 is the time between the initial 180" and the 90'

pulse. In this case, the e-tIT; term in Eq. 2.30 can be replaced bu:

tihere 1 /T$ is the sum of the refocused terms in Eq. 2.44. At t = T El'?. the spins

are flippcd within the xy plane and begin to rephase:

and at t = T E we find that:

Cs(t = T E ) x JI,, sin ae-TE/T2.

Sote that in Eq. 2.47 the signal decay is governed only by T?.

Radiation Damping

As previously discussed. the trans~erse component of magnetization, ;II,,, will pre-

cess about the ,- asis inducing a current into the receiver coi! which is detected as

the free induction decay. However, if this current is sufficiently large (i.e. dl, is

large) it will create its own magnetic field which ni11 interact with the surrounding

spin systern. producing a torque on the rnagnetization which will cause to rotate

back towards the : &.sis and hence reduce signal (a consequence of the Principle of

Reciprocit-). This rotation is referred to as radiation darnping. It is a dynamic

process resulting frorn the interaction between ig and the FID current. For a more

descriptive discussion. see Mao and 1é[61].

(a) t=O

(d) t=TE/2+

(b) O<t<TE/2

(e) TWZ<t<TE

Figure 2.8: Effect of a spin echo on the magnetization in the transverse plane: (a) the dipoles are tipped into the zy plane a11 pointing in the same direction: (b) the dipoles begin to dephase with TJ: (c) further dephasing of the spins; (d) a transverse 180' pulse is applicd at t = T E / 2 flipping the spins 180° out of phase: (e) the spins continue to precess rcsulting in a rephasing: ( f ) complete T; rephasing at t = TE. hl,, has decayed by e-TE/T: at t = T E .

Radiation damping resembles nutation. Both are rotations of the rnagnetization

induced by the coil-magnetization interaction. However. there are differences. Su-

tatiori is induced by an external RF pulse and is described as a uniform rotation

b'.:

?Bi = ai: (2.48)

whereas radiation damping is a nonuniform rotation espressed as:

CHAPTER 2. THEORY

nhere Trd is the radiation damping constant giwn b~[61]:

ahere rl is the filling factor and Q is the quality factor of the RF coil. Because

radiation darnping is inversely proportional to the magnetization, it is generally not

important in most NXIR applications except a t high fields rhere liquid-phase ther-

mal magnetization is large. Honever, it may also be observed when hyperpolarized

magnetizations are used[6O]. as will be discussed further in this thesis. Radiation

daniping is cliaracterized by a time dependence which is a hyperbolic secant function

~vhere .\Io is t he initial value of the magnetization and Ad is the offset frequency

from resonance. For n > 90' this mode1 of the signal will show an initially increasing

FID aniplitude before it decays. For large Trd. this relation reduces to:

A I,, = -\IO sin ae-""t. (2.52)

Therefore. radiation damping si11 be present depending on the relative values of Trd

and T . . and can be detected by the presence of an initially increasing FID. Figure

2.9 models Eq. 2.51 (without the exponential offset term) and illustrates how. for

increasing Trd: this function simplifies to a sinusoidal function.

For Trd » T;. it can be shown[64] that the intensity of the signal, here defined

as the tirne integral of the FID for O < t < x, will be a sinusoidal function of the

flip angle: OC

I = 1 sin aëtiT; dt = MaTi sin o. (2.53)

But for T . >> Trd. this relation breaks d o m and is replaced by a linear one. derived

in the same rnanner as Eq. 2.32 but integrating instead Eq. 2.51. The calculation

CHAPTER 2. THEORY

(a) El s (b) -1 30"

Figure 2.9: Eq. 2.52 for increasing Trd as a functiori of (a) flip angle. a. usiug a fixed tiriie. t= 1 s . and (b) time. t. using a fixed flip angle. ri = 130'. As Trd increases. and radiatioii da~iiping decreases. the sech function simplifies to a sinusoidal one. as indicated by the sirie wave (solid line). s ina . in (a) and the constant value. sin(130°) = 0.766. in (b).

is straightfonvard by ietting z = t/Trd - h[tan(a/2)] :

cy:

Masech [r - ln (tan 5) ] df = I J O T ~ ~ / sechxdx = TTd û . Tt d -In[ran(a/2)]

(2.54)

Sinre Eq. 2.51 is fundamentally different from Eq. 2.53. radiation damping is

important to consider when calibrating a and measuring SSR. The final expression

for the signal in a S U R experiment involring radiation damping is:

NMR Spectroscopy

SMR spectroscopy exploits the change in local magnetic field seen by a nucleus due

to its environment[84]. In the presence of a static magnetic field, B, a substance

with no unpaired electrons (e.g. water, 12gXe, etc.) eshibits diarnagnetism. where

currents in the electron clouds induced by the application of the magnetic field

oppose that field. The electronic shielding characteristic of diamagnetism results in

a nucleus seeing an effective magnetic field strength B(l -a) where a is the shielding

constant. dependent on the electron cloud. Therefore. two identical nuclei placed in

different electron clouds (e-g. molecules) will have two different resonant frequencies.

S U R provides a precise mesure of these resonant frequencies. or chemical shifts. 6.

of a sample. giving informat ion about the molecular enrironment.

Ir1 an M I R spectroscopy esperiment. a pulse is applied with a carrier frequency

; for a duration t,. This is referred to as a "hard" or square pulse. The bandwidth of

ttir frequencies irradiated is l l t , and the frequency resolution of the received signal

is defiiied as the sampling rate of the analog-digital converter (ADC) acquiring the

data. SR. Typical values for t , and SR are 50 ps and 10000 Hz. respectively. The

r~ceivcd signals are then Fourier transformed to separate the comples superimposed

fr~quencies that the FID is comprised of. For each 6 the Fourier transform shows a

scries of typically Lorentzian-shaped peaks as a function of frequency. espressed as:

nhere the relationship between the full spectral aidth at half the mavimum signal

intensity (FKHSI) and TT; is:

1 Fl!-HA\l = -. (2.57)

7iT;

Typically. spectral intensity is plotted against chemical shift. not frequency. The

chernical shift. 6. is defined as the relative deviation in frequency from a reference

frequency, dre,, pro~ided by a known standard (e.g. a gas phase xenon signal).

W - Wref 6 = x 106 = - a 106. (2.58) Ur e 1 1 - G e f

The units of chernical shift are parts per million (ppm). The advantage of using 6 over

frequency for the abscissa is that b is independent of field strength, allowing corn-

parisons of esperiments from different spectrometers and magnets. Chernical shift

can also be defined according to the shielding factor, o, using a reference shielding

2.2 Laser Polarization of Noble Gases

-4s discusseci. the nuclear spin may be polarized by spin lattice relasation at room

terriperature giving P 5 1 0 - ~ (Eq. 1.15). Laser polarization techniques can be

u s d to increase P bu up to five orders of magnitude. rvith respect to the thermal

polarization. \\.hile a number of laser polarization techniques esist, the one used

throughout this project \vas spin-eschange with optically pumped a lh l i vapour. in

this case rubidium (Rb). A more rigorous. quantum mechanical treatment of spin

eschange with optical pumping can be found in papers by HapperIZO] and \\alker[67].

2.2.1 Optical Pumping

The first step in the polarization process is the optical pumping of the sample cell.

Sample cells typically contain an alkali rnetal vapour (Rb, 88*C), a noble gas (12'Se),

and a quenching gas (typically X2). Optical pumping is a technique used to re-

populate a distribution of electronic spins, favouring one of the two possible spin

states for the ?S orbital electron of Rb as shown in Figure 2.10. The two spin states

are a result of the Zeeman splitting induced by a static magnetic field, Bo. Laser

light is applied at the transitional frequency, 791.8 nm, to excite electrons from the

'S to the ' P state. As photons carry one quantum of angular momentum, h, the

CHAPTER 2. THEORY

Ba

!P II? 4-

Optical Pumping Transition

- m = +1/2

- 1 Collisionai Mixing - 112

+I l2

Figure 2.10: Energy level diagram for Rb illustrating the opticai pumping of electron transit ions in accordance wit h the seiection rule Am = 1.

change i n the energy states \vil1 be from the 2S1,2 (m = - l/?) state to the

(rn = -112) state. obeying the Am = 1 selection rule. Collisions with the noble

gas in the sample will redistribute the spin states between the 2PlIz ( m = +1/2)

state and the PIi2 ( m = -112) state. Further collisions with the S2 gas will relax

the alkali electrons to their ground state. This results in a net increase in the

?SI;? (m = +1/2) population relative to the ( m = -112) population. Some of the

niechanisms inrolved in the destruction of the optically pumped spin distribution

include Rb-Rb collisions, radiation trapping, and wall relasation.

Radiation trapping occurs as a result of the de-excitation of the Rb spins. When

light is emitted from a 2P112 spin. it ni11 interact with several other spins in the

sample before esiting the cell. This results in the fluorescence of 2Si,2 (m = +1/2)

spins thereby reducing the population of the optically pumped spins. This effect is

eliminated by the presence of a quenching gas. such as Kz. Collisions with S2 result

in the de-escitation of Rb without the emission of light thus maintaining the highly

CHAPTER 2. THEORY

polarized state of the Rb vapour.

Wall relaxation occurs when Rb spins diffuse towards the sample ce11 walls before

in teract ing wi t h 12'Se. Upon contact, the spins completely depolarize. Diffusion

towards the laser beam windor of the cell, and subsequent depolarization of the

spins. effectively reduces the penetration depth of the beam. Therefore the bearn

requires a penetration depth greater than the mean diffusion length of the gas. This

can be accomplished by reducing the Rb vapour pressure. slightly detuning the laser.

or usirig a beam with a broader bandwidth.

Tlic Rb polarization rate. defined as r/2. depends on beam poaer. Rb vapour

pressure and temperatiire. Typical polarization times for Rb are on the order of mil-

liscwmls. S2 has a third role: pressure broadening. This increases the Rb linewidth

so tliat it niore closely matches that of the laser. This can also be accomplished

using tielium. as in this thesis.

2.2.2 Spin Exchange

Tlir nest strp involves eschange of spin (or angular momentum) between the Rb

electrons and the 1?9Se nuclei. as illustrated in Figure 2.11. Spin eschange occurs

as a result of the collisions between escited Rb atoms and 129Se gas atoms. The

interactioii is an interatomic hpperfine scalar coupling that results in the temporary

formation of a \ an der Waals molecule. During the lifetime of the molecule. the

elect ronic Rb spin is transferred to the nuclear 1 2 9 ~ e gas spin. The creation of t hese

molecules is partially dependent on the presence of which acts as a third body

to proride a greater probability of formation.

2.2.3 Polarization Factor

Once polarized. the 129>;e gas will reach an optimum polarization value. P, dependent

on the optical pumping rate. 1/Tp7 and the relaxation rate' 1/Ti. The pumping rate

Figure 2.1 1 : Vari der Waals molecule formation t hrougli 1 2 g l e ~ b collisions. Spin cx- change occurs when the molecule separates back into Rb and 1 2 9 ~ e . N? is used to increase t lie exchange efficiency.

is espressed as a function of the number of polarized Rb atoms. and the spin eschange

probahility:

d i e r e [Rb] is the Rb concentration. t: is the mean relative velocity between the senon

and the Rb and os, is the xenon gas spin eschange cross-section(68). The o~erall

time dependence of the polarization is given by:

wit h solution:

wtiere t H P is the polarization time of the laser. Taking the limit with t H p + 3~ the

maximum achievable polarization is[69] :

Typical values are in the range of a few percent (as opposed to -10-'% for thermally

polarized nuclei) and are as high as 70%[83].

2.2.4 Relaxation Mechanisms

Relasation mechanisrns have already been described in Section 2.1.5. The' are

described as originating with couplings between magnetic dipoles. Because 12%e is

a moriatomic inert gas. couplings of this nature are v e p weak escept during collisions

\vit h other atoms and the sample ce11 aall. As a result. care niust be taken in the

clcanirig of sample cells so as not to contaminaie the '?'Se n i t h impurities. such

as osygm. and the inside of the cells are coated nith Surfrasil. an organosilicon

cornpotincl used to negate the effects of the '''Se colliding with the ce11 walls. Also

of particular importance is relaxation due to collisions with paramagnetic nuclei.

surli as niolecular osygen. The coupling nith the unpaired electronic dipole moment

of paramagnetic osygen. ahich is three orders of magnitude greater than the nuclear

monicnt. will greatly enhance the relaxation of the nuclei. Therefore, cells need to be

free of O?. which ni11 also react with the rubidium vapour to form a rubidium oside.

Typical Tl values are in the range of 30-60 minutes for gaseous I2'Se in glass sample

cells and in the range of 2-3 minutes in the dissolved phase[ï9]. This is due to the

presence of addi t ional dipole moments in the dissolved state (i .e. =ter! dissolved

O?. etc.).

CHAPTER 2. THEORY

Tl Estimation

Following laser polarization, 12gXe nuclei wi ~llectively form a magnet izat iono A l i ,

due to the increased polarization, P! up to five orders of magnitude greater than the

thermal value, Mo:

AI; » -&[o. (2.63)

As a result of the polarization level not being in an equilibrium state. two im-

portant differences between thermally and hyperpolarized MR arise. First. the axial

cornponent of .\[A ni11 immediately begin to decay esponentially to Alo with relw-

ation time. Tl . Therefore there is a time constraint regarding the use of the gas

and espcriments must be carried out within a time short relative to Tl (TR <: 3 1 , ) .

Second. as the magnetization ivill be decaying. it will also be non-replenishable af-

ter an RF pulse. .A pulse with tip angle n will reduce .\Io by a factor (1 - coscr).

Ttierefore. srnall tip angles (a -- Y) must be used in order to conserve the magne-

t ization. Figure 2.12 illustrates the differerices between thermal and hyperpolarized

Tl relasatio~i behaviours.

Look and Locker proposed a one shot method of estiniating Tl using a train of

RF pulses at a constant. small tip angle. Q , separated by a constant repetition time.

TE[70]. ideal for hyperpolarized 12'Se. Following their notation. JI: and JI; are

t h e longitudinal magnetization just before and after the nth RF pulse of tip angle

a,. respectii-ely. Taking into account the magnetization decay of lZgSe:

= dl; cos û. (2.64)

tvhich. ivhen cornbined. yield:

JI;+, = ,II; cos O, e .

(a) M=O to M=MD @) M=Mi to M=M,

Figure 2.12: (a) Conventional Ti recovery for thermally polarized nuclei. The nuclei will recovcr to the .JI0 value. (b) Ti relawatioii for hyperpolarized nuclei. The nuclei will decay esponentially to ifIo - O fiom the initial value 11.4.

The recursive relation 14 thus be:

ahere. again. JI; is the initial value of the hyperpolarized magnetization. If al1 of

the tip angles are the same then this simplifies to:

This relation can be further compacted for purposes of modeling by realizing that

the (n + 1)th pulse takes place at a time t = (n + l)TR. Therefore. the relation can

CHAPTER 2. THEORY

be written as:

or:

where: 1 1 ln(cos a) = - - (2.71)

Tkff Tl TR In the liniit TR « Ti. û rnay be estimated, whereas in the limit SR » Tl . Ti ma!

be estimated.

Patyal[731 proposed a technique for measuring hyperpolarized lZ9Se Tl based on

the Look-Locker method. The ratio of successive signal intensities. S' from a train

of RF pulses separated by a constant repetition time. TR. can be given by:

.As TR is constant. the signal ratios ail1 be equal. Taking the mean of these ratios

and by setting the repetition time TR « Ti: thereby approsimating the esponential

in Eq. 2.72 to unit'. the flip angle can be calculated according to:

Variable Flip Angle Sequences

Based upon Eqs. 2.67 and 2.68, the signal equations for constant (CFA) and variable

(\'FA) flip angles can be r r i t t en as:

(Snii)CP;\ = sin a(cos a)nile-("+l)T~/T~.

Due to the non-replenishable nature of hyperpolarized lZ9Xe, a series of constant flip

angles leads to a diminishing signal over time. -4 sequence of variable flip angles can

be designed such that the measured signal remains a constant over the time, which

will allow for signal averaging. By forcing the measured signals to be constant for a

total of X RF pulses. and using a 90' pulse at the end of the sequence to employ al1

of the remaining magnetizatiori, the VF.4 sequence ri11 be[79):

T2 Estimation

Tl relaxation is measured using a Carr-Purcell (CP) pulse sequence for both ther-

rrially and hyperpolarized nuclei. Spin echos. introduced in Section 2.1.5. described

t h e refocusing of dependent rariables to obtain an echo shich has decayed only

\vit h TL. CP employs the same principles as the spin echo sequence (Fig. 2.8) where

a train of 180" pulses are applied following the initial 90" pulse. The sequence can

be repr~sented by:

90 - r - 150 - r- echo -T - 180 - T- echo ....

tvhere: TE = 27 + t,(180°). t,(180°) being the pulse duration. This is illustrated in

Figure 2.13.

The diffusion contribution to measured T2 via CP is aven -1661:

where D is the diffusion coefficient. G is the average static field gradient, r is one

half the echo time for CP and y is the gyromagnetic ratio. The diffusion contribution

introduces a dependence on magnetic field strength which arises from the G2 term:

Figure 2-13: A spin echo sequence. The signal decays and grows again n i th relaxation tinie T; due to the refocusing 180' pulse. The refocussed echo has decayed according to TL.

where 11 is the rnagnetic susceptibility in hornogeneity. Defining the calculated value

as an effective value, T2eM we have:

Therefore. by measuring T2cll twice, using the same settings and varying only the

echo time. TE (r=TE/2)? the actual T2 can be calculated by solring for T2 from

the two equations.

CHAPTER 2. THEORP' 46

2.3 Magnet ic Resonance Imaging of Hyperpolar- ized 1 2 g ~ e

Magnetic resonance imaging is a spatiall-localised version of XhIR used to obtain

2D images of objects through the use of magnetic gradient coils. By varying the

magnetic field strength in al1 three spatial dimensions? the density of spins (and Tl

and &) of an object can be mapped as a function of position. This section piil

describe the most popular )IR method. the 2D spin-echo imaging sequence. as an

esamplc. and is shown in Figure 2.14. A more in-depth discussion of SIR iinaging

principles can be found in Haacke[66].

The first step in the spatial localization of a three dimensional sample of spins is

the slice selection of the sarnple. Through the use of a gradient magnetic field mil.

wliicli alrers the field strength as a function of position tvithin the magnet. the field

srreiigth along the 2 axis varies linearly with z. This can be seen with the relation:

d i e r e Gf is the axial gradient magnetic field strength in G/cm espressed as:

In order to induce a resonance condition in the spins in a slice of thickness ilz

the transmitted RF pulse must have a bandwidth Asi, shere:

Such a bandwidth can be excited by applying a "soft" RF pulse with frequency ;; and

duration 1 / L . In SIR terminolog., a soft pulse usuaily means a sinc-modulated

RF pulse n i t h a Fourier transform clearly showing a frequency range w f b / 2 .

By applying a soft pulse with this bandwidth. the spins in a slice of the sample

of thickness Az are tipped and the resultant signals analyzed. By changing the

frequency of interest, w , different slices can be selected to form a 3D map of the

sample. This is called multislice LIR imaging.

2.3.2 F'requency Encoding

The second step in the spatial localization of the sample is the frequency encoding

of spiris alotig the r a ~ i s in the xy plane containing the selected slice. This encoding

is accomplished by using a gradient field, G,, aligned along the i axis but varying in

magnitude as a function of z. that alters the magnitude of B but not its direction:

B(x)i = Bo: + G,xf. ('2.83)

This gradient is applied during the read-out of the signal, coincident with the for-

niation of a spin echo ( t = TE), as shown in Figure 2.14. The gradient alters the

resoiiant freqiiencies of the spins as a function of t so that the signal is a super-

position of al1 the frequencies. When Fourier transformed. this provides a spatial

distribution of the spins along the x axis. The field of vie\\-, FOI '. provided along

the r a i s is:

where At is the sarnpling or daell time. The read-out time. T,. is given by:

where 3, is the nurnber of sample points.

2.3.3 Phase Encoding

The third and final step in the spatial localization of the sample is the phase encoding

of the spins. This gradient. G,! is applied along the y a i s for a duration r: between

the end of the excitation RF pulse and the beginning of the read-out, as shown in

Figure 2.11. While this gradient is active, nuclei located a t different y locations ri11

have different precessional frequencies and will acquire a phase that is dependent

upon their y position. When the gradient is deactivated, the spins niIl al1 precess

with the same frequency but will retain their y-dependent phase. This takes the

encoding one step further, making the detected signal a superposition of frequencies

with different phases along the y direction. For a given Gy this signal corresponds

to a single line in the Fourier space of the sample.

Obtaining a two-dimensional image of the sample requires that the process of

slice selection. phase-encoding. and reading-out with a frequency-encoding gradient

repeatcd .\Y times with an incremental AG, and a repetition time. TR. to yield an

.\; s .\y data set ivhich is subsequently Fourier transformed in 2D to giw an image.

Ttir resultaiit field of view along the y asis is:

Gradient Echoes

W i e n a rnagnetic field gradient is applied during an imaging sequence. the transverse

rnagnetization is dephased by an amour8 dependent on the strength. G. and the

duration. r: of the gradient. For phase-encoding purposes this is desirable. but in

the case of slice-selection and frequency-encode gradients this dephasing must be

compensated for. The application of the negative gadient at the same amplitude

and for one hall of the duration, 712 , will rephase the spins dephased by the slice-

selecti~e and frequency-encoding gradients. This is a gradient echo and is necessav

in order to acquire a proper SIR image. In fact, an entire image can be obtained

this way: without the need for a 180° refocusing pulse. This is called gradient echo

(GE) imaging. GE irnaging allows very rapid scan times (-1 s) usually by using a

CHAPTER 2. THEORY

RF Pulses

Slice-Selective Gradient

Phase-Encode Grridien t

Fmqurncy -Encode n I L . . . . t Gradient

Signai

Figure '2.11: Spin-echo irnaging pulse sequence timing diagram.

very short TR ( 4 - 1 0 rns) and a small flip angle (a <30°). This is also a preferable

method for imaging hyperpolarized 12'Se since the magnetization is non-renewable.

That is. once laser polarized. the magnetization can only be used once since it relaxes

to a ver! small value of .\L

Chapter 3

Met hods

The esperirnental procedures and apparatus used in this study are described in this

cliapter. The prima- topics include the design and construction of the low-field

rrsist iw ~ l r c t romagnet . laser polarization techniques and materials. the S'rlR spec-

troirieter spccifications. and pulse sequences used for relaxation time measurernents.

h block diagram of the complete apparatus is s h o w in Figure 3.1. This diagram

sliows the three main sections of the apparatus: the resistive electromagnet (dark

grcy ). the laser polarization (light grey). and the NUR spectrometer (white).

3.1 Resist ive Elect romagnet

The low-field elect romagnet constructed tvas a split-solenoid coil designed by Magnes

Scient ific Ltd. ( Abington, Oxfordshire, CK) . The split-solenoid design !\.as chosen in

order to optimize power and field hornogeneity, as this design provides a reasonable

region of hornogeneity (5 10 cm) ai th -20% less rindings and power than a single

solenoid. The coil \vas designed using Garrett's theory of asially synmetric magnetic

fields[Z] which describes the spatial variation of a magnetic field produced by a coi1

configuration as an espansion of spherical harmonics. A more detailed analysis can

be found in Hanson[;']. Franzen[TJ]. and Garrett [ i l ] .

CHA P TER 3. ME THODS

m MAGNET

COS1 PCTER ACQCISITIOS SY S T E M r z AMPLIFIER * MIXER

PHASE DETECTOR

Figure 3.1: A block diagram of the experimental setup used. The greyscale is used to iridicate t h three main sections of the apparatus: the resistive electromagriet (dark grey). t h e laser polarizatiori (light grey). and the NMR spectrometer (white). A sample ce11 (black) is laser polarized inside the magnet and kept a t a constant temperature (88 O C ) using an o w ~ i and temperature controller. The magnet is cooled using an antifreeze bath and chillcr. The transmitter sends an RF pulse to the sample and the received MR signals are detected and processed through a preamplifier. mixer, phase detector and amplifier. Data is axialyzed at a computer terminal.

The coordinate system used to describe the system involves the use of both cylin-

drical (p. o. 2) coordinates and spherical (r. 19.4) coordinates. Figure 3.2 illustrates

both the axis and plane of symmetry that characterize the coordinate system.

It has been sho\m[72] that the axial cornponent of the magnetic field strength of

a solenoid can be written as:

nhere Pn(cosO) is a Legendre polynomial. Since T = z when 19 = O and Pn(l) = 1.

it follo~vs that the field strength along the symmetry axis is given by:

Figure 3.2: The two coordinate systems used to describe the magnetic field in an axially syrnmetric system. Because of the cylindrical symmetry of the coil, the 4 coordinate in each coordinate systern can be ignored.

art1 the coefficients. This can be simplified to[7l]:

10 'Zr, ( 3 4

Here. .\; is the total number of turns of wire on the coil. I is the current through

tlic coil in aniperes. rS is the distance from the origin to the coil edge in centimeters.

8, is the angle between r, and the asis of syrnmetry: u, = cos& (see Fig. 3.3). and:

Eq. 3.4 was used to mode1 the field strength along the âxis of symmetry of the

magnet. the most sensitive region of the coil in terms of the field homogeneity(i21.

A more detailed esplanation of Garrett's theory is provided in Appendix B.

In considering the construction of the coil. the following design criteria were used:

a 10 cm diameter sphere imaging volume was to be the region of homogeneity with

a field honiogeneity ABo 5 1%; the inner diameter of the coil nas fised at 30.48 cm

(1 f t ) due to the outer diameter of the gradient coils to be placed inside the magnet

for future imaging purposes; and the field strength \vas to be 81.9 G in accordance

with the 100 kHz RF coil already constructed.

CHA P TER 3. METHODS 53

A split-solenoid resistive electromagnet was constructed as shown in Figure 3.3.

Based on Eq. 3.4, a split-solenoid can be treated as a solenoid with end turns at Osl

minus a solenoid with end turns at OS2, as shown in Fig. 3.3. Figure 3.1 shows the

theoretical field strength as a function of z for the split-solenoid based on Eq. 3.4.

Also. shown. for cornparison, is the field plot for a conventional single layer solenoid.

The magnet was designed for a 10 cm region of homogeneity at 81.9 Gauss. the field

strength corresponding to the 12%e resonant frequency (100 kHz). This choice of

field/frequency was dictated by the frequency of the spectrometer. as discussed in

the nes t section. This region of homogeneity \vas chosen as a space large enough to

eiiclosc a large gas saniple or small animal. such as a rat. At k5 cm from the center

of the coil the homogeneity of the coi1 tvas estimated to be 0.75% (0.6 G or 750

Hz) . This design predicts 428 turns of wire and approsimately 430 \\' of potver for

84.9 G. The mode1 shows that a single solenoid coil nould require 518 turns. which

corresporids to 100 \Y more than the split-solenoid design due to the increase in the

resistancc of the coil.

The coil was wound on a 1 ft diameter piece of cardboard concrete former re-

inforced with fibreglass cloth. It was nound on a lathe with number 18 . W G wire

arid simultaneously treated wit h marine strengt h eposy resin to prevent thermal

espansion of the wire.

Physical and electrical operating characteristics are provided in Table 3.1. TWO

power supplies. a Sorenson SRL 40-50 and a Harrison Laboratories Nodel 814.4 were

used to provide the necessary power (430 IV). This resulted in some heating of the

magnet. The magnet was cooled using chilled antifreeze circulated through 3/16"

copper tubing wound around the layered nindings.

The magnetic field of the coil \vas mapped using a FW Bell 610 Gaussmeter

with an axial magnitude probe. The temperature correction coefficient for the probe

was calibrated at 0.0013 K-l by measuring the variation in field strength at a set

Coil w i n g lEanrrcrt fanrrr)

h i S of S y l l u n a q Z

F igiirr 3.3: (a) A longitudinal cross-sectional view of the low-field resist ive electromagnet . The split-solenoid design is characterized by two bands of windings. each 6 cm wide and 4 Iqc r s of wirc deep. The bands are spaced 10 cm apart. Specifications are provided in Table 3.1. The inset shows the winding configuration of the coil. (b) A 3D schematic of the cyliiidrical coil.

distance frorn a magnetic field while varying only the temperature of the probe. The

field was also mapped along both the r avis and in the ry plane of symmetry at

2 = 0. A früme was constructed to hold the gaussmeter probe at a variable position.

both asially and radially. within the bore of the coil. The axial position of the

probe aas calibrated using one end of the coil (touching the tabletop when the coil

is mounted vertically) as a reference, while the radial position nas predetermined

by holes drilled into the frame at set 1 cm intervals. The azimutha! position within

tlie bore !-as measured using a protractor mounted on the frame set to a marked

reference position on the coil. Axial magnetic field accuracy \vas within - 5 mm.

radial accuracy within - 1 mm. and azimuthal accuracy nithin - 2". Sote that the

axial position of the probe aas offset by 0.5 cm due to the location of the Hall sensor

wit hin the probe. This aas compensated for in the magnetic field maps.

0.992 i SplitSolenoid (Solid) Salenoid (D88h.d)

Figure 3.4: A modelled homogeneity cornparison between a single layer solenoid electro- niagnet (dashed line) and a split-solenoid electromagnet (solid line). Both designs have an irihornogerieity of 5 0.75% at 5 cm. The split-solenoid uses 428 turns of wire while the single layer solenoid uses 518 turns. The difference in turns is equivalent to -12 V and -100 W. These results were calculated using Eq. 3.4

Current fluctuations were on the order of 1.0 m..\. or equi~alently 0.01 G or 15

Hz in the S U R signal frequency Typically. the magnet was allowed to warmup for

1 hour before an- measurements sere taken so that the coolant and the windings

could reach a steady state.

3.2 NMR Spectrometer

The S U R spectrometer is based on a 85 G polarimeter design proposed by Saarn[T4]

and built by a previous post-doctoral fellow in our labora to . Modifications to this

1 llechanical Characterist ics

/ Tot. turns

1 Electrical Characterist ics

Measured Value

Tdl~lc 3.1 : P hysical and electrical specificat ions of the resist ive electromagnet.

design ttiat were implementcd for this study inciuded isolating the preamplifier.

increasing sliielding for the RF coil. quadrature phase detecting. and interfacing the

system to an SIRRS (formerly S W S . Surrey Aledical Imaging Systems. Surrey. CI.;)

SIR3000 console by changing the output impedance to 5OR. Circuit diagrarns for

the modifications are provided in Appendis A.

The preamplifier sas isolated by removing it from the casing in which the SMR

elertronics aere contained and placing it in a separate casing to decrease the level

of elect ronic noise being amplified.

The RF coil used was a Helmholtz design tuned to 100 kHz ai th a bore diameter

of 1 cm and a length of 2.7 cm. The coil nas encased in an alurninum bos 3 mm thick

t O shield the coil from an!* estraneous electrornagnet ic interference (e-g. cornputer

monitors, power supplies, etc.). The RF coi1 ras tuned to 100 kHz by placing it in

parallel with two capacitors for a total of -570 pF.

The quadrature phase detector constructed was optimized by adjusting the vari-

able resistor which balances the amplitude of the received signals in each of the two

orthogonal channels. A Lissajous plot was first used to balance the signals (i.e. ad-

justing the variable resistor until the elliptical shape of the Lissajous plot changed

to that of a circle), followed by a superposition of the two signals while adjusting

the resistance to remove an? differences in their amplitudes.

3.3 Laser Polarization

Figure 3.5 shows a simplified schematic of the setup used. Figures 3.6 and 3.7 are

photographs of the setup. The L29Se gas was polarized inside the low-field magnet to

ensure that esperimental conditions are reproducible and to optirnize SSR (ae have

slionn that considerable loss of magnetization can occur while moving the sample

from a fringe polarizing field to the low-field ShIR system). -4 30 W .Al-Ga-As diode

array laser was used emitting at 794.8 nm and operating at 25.6 O C and 23 \Y (Opto-

Power. Tucson, -12). The beam was directed parallel to $ and circularly polarized

iising a X I 1 filter to ensure an angular momentum transfer of one unit ( h ) to the

Rb vapour. The laser was focussed on a g l a s polarization sample ce11 internally

coat ed a i t h SurfraSil (Pierce Chemical Laboratories), containing 730 mbar natural

abundance S e gas (26% ' * 'Se) , 102 mbar S2 and a few mg of Rb metal. SurfraSil

is an organosilicon compound used to reduce the relaxation of the L29Se gas due

to wall collisions. The ce11 was kept at 88OC in order to vapourize the Rb and to

maintain an optimum vapour pressure. Polarization time remained constant at 20

minutes. Optimization of both temperature and polarization time are described in

more detail else~here[79]. To ensure a maximum number of Se-Rb interactions, the

L e *

Figure 3.5: Polarization setup used component of the field and polarizes

for our experiments. The laser is aligned with the 2 the sample located in an oven inside the magnet.

saniple ce11 \vas made nith a diameter no larger than the nidth of the laser beam

( - 1").

The sample ce11 polarization level will decrease over long periods of t h e (-

nioiiths) if the ce11 is polarized regularly. This is due to a degradation of the Rb in

the ce11 which osidizes readily in the presence of trace amounts of osygen. This cari

bc partially compensated for by shaking the ce11 vigorously after the Rb has melted

to coat the inside of the ce11 in fresh. not-yet osidized Rb. Changes in the Rb quality

were checked for by looking for differences in the received signal intensities. S o such

changes were detected.

3.4 SNR Measurements

A comparison of the SSR at 1.89 T and 83 G was also made using Eq. 2.34, repeated

here: I

Figure 3.6: The bore of the 85 G magnetic coil. The sample ce11 and RF coil are placed inside of the RF shielding box at the center of the coil. Heating tape is wound about the box and acts as an oven for polarization purposes.

Figure 3.7: The 85 G resistive magnet. Copper tubing is wound about the windings to cool the coi1 with antifreeze. The power supplies are situated in the background.

ahere the HF and L F subscripts represent the high and low-field strengths of 1.89

T and 85 G , respectirely. Gsing this expression, the ratio of SSR's was calculated

and compared to the measured quantities for both the hyperpolarized and thermally

polarized scenarios.

3.4.1 Predictions

Polarization Factors

The thermal polarization. PTH of a sample of spins was calculated using Eq. 2.15.

repeated herc:

Hyperpolarized P ineasurements required the measurernent of both a hyperpolarized

and a thernially polarized signal. For the same nucleus/sample at the same field

strcngth. the ratio of polarizatioas is equivalent to the ratio of the measured signal

amplitudes. S. according to Eq. 2.30. The hyperpolarized polarization. PH p . can

t herefore be calculated by:

Acquisition of STH and SHp \riIl be discussed below.

Electronic Factors

As the Q values of the RF coils were not known, they were determined by measuring

the bandwidth of the coil. A fc: and calculating the Q values from the equation:

n-liere fo is the resonance frequency of the coil. The coil bandwidth i-as measured

by injecting a signal from a frequency generator centered on fo into the coil and

measuring the signal receiwd as the frequency sas ~ar ied by adjusting the output of

the Irequency generator. The bandwidth was calculated for the frequency range at

the FWHM mark and estimated as twice the standard deviation in a fit to a Gaussian

distribution. The error was taken from the error in the fit, using a Levenberg-

Slarquardt fitting routine.

The noise figures, F? of the tivo receivers were also measured. The noise figure

of a receiver is given as:

The noise figure of the receiver \vas measured by placing a 50 R shielded resistor

at the inpiit of the receiver and recording the receiver output using an oscilloscope.

Sest. the shielded resistor, attached to a small cable, ivas placed in a liquid nitrogen

bath and. after being allowed to cool to the bath temperature (77 K): the receker

output \vas again measured. If the receiver is perfect the noise would almost h a l w

as 77 1; is aliiiost one quarter of room temperature. and would require an atteriuatiori

factor of cr = 2 (6 dB) to match the room temperature measurement. In practice.

a < 2 and the noise figure is given as[82]:

F =lOlog ( 1 - - ;) - IO log (1 - $) . ivhere T is the room temperature in Kelvin (K). T h e noise was taken as the standard

deviation of the signals recorded. The error in the noise figure was estimated from

the standard deviation of 10 consecutive measurements of the noise.

Other Factors

The filling factor? Q. is given as the ratio of sample volume to coil ~olurne? 1;/1;,

which reduces to the squared ratio of sample and coil radii. ( r , / ~ , ) ~ . Assurning the

sample is the sarne, a ratio of filling factors therefore reduces to ( r f .F / r fF)2 . The coi1

radius of each coil was taken as the mean radius from the outer to inner windings.

The volume of a coi1 is given by nr:l,, where 1, is the coil length. Coi1 radius and

volume nere measured using Vernier calipers.

The coil temperatures were taken to be room temperature (298 K) in al1 cases es-

cept the low-field hyperpolarized signals, shere T = 361 K (88 OC) ' the temperature

that the sample ce11 nas polarized at. The polarization temperature was measured

using a thermocouple wire attached to the heating oven used to keep the Rb at a

constant vapour pressure. The receiver bandwidth, A f, \vas taken as the smaller of

the sanipling rate or the coil bandwidth.

ShIR signals were first obtained by recording a free induction decay at the predicted

field strcngth of 85 G. From there. finding the exact resonant condition (i.e. reducing

tlic offset frequency to -- 0) involved optimizing the magnetic field strength by

adjusting the poaer supply output. The reproducibility of the acquired signals \vas

nicasured by repeating a given esperiment five times and checking for fluctuations

in the spectral intensity and frequency. Consideration iw given to the frequency

resolution as a larger resolution tvould make checking for stability difficult. AI1

sigrials were acquired via quadrature detection. To avoid any DC offset artifacts in

t h spectrometer. signals nere acquired off-resonance by up to 700 Hz.

Signal amplitudes were measured as the integrated area under the Fourier trans-

formed FID over the receiver bandwidth of the signal, subtracting the integration

of the Fourier transformed empty coil signal. Soise rvas measured as the standard

deviation of the empty coil signal over the receiver bandwidth. The area was calcu-

lated using a trapezoidal integration algorithm. The error in the SSR was taken as

the statistical error in the integrated areas for multiple (3-3) signal acquisitions.

CH.4 PTER 3. AIETHODS

B1 Calibrat ion

The pulse flip angle. a, wras determined so that a maximum signal intensity cor-

responding to a = 90' could be obtained. The method for flip angle calibration

suggested by Patyal[i5] and discussed in Section 2.2.1 ivas used in this study. How-

el-er. because signals were acquired off-resonance, and BI ras small? the flip angle

calibration must be modified to account for the nutation of the magnetization about

an effective niagnetic field. 6icif, as described in Eq. 2.21. The effective flip angle.

n , f p is g i ~ e n by:

0.1 j = 7 Bel f t p (3.12)

siniiliir to Eq. 2.22. Bell is given as the magnitude of Eq. 2.21:

wtiich is a function of the resonant offset frequency. L. and B1. Therefore. to

calculare a,!,. Bi must bt determined.

Thc off-rcsonance cornponents of the rnagnetization JÏ can be g iwn b$]:

.II, = -\Io sin a,,! sin 0 (3.14)

JIy = .14(1 - cosoeff) sinecos0 (3.15)

BI, = dlo [cos2 0 + cos a,,f sin2 01 (3.16)

whrre 0 is the angle between BeIi and the : avis and is given as:

Ipplying these off-resonant conditions to the Look-Locker method of flip angle and

Ti estimation as described by Patyal[75]. ae have:

3, - = [cos2 0 + cos aefl sin2 81 ë T ~ / = l - Sn-1

Patyal's method was used to calibrate BI by repeating the experiment six times,

for pulse widths ranging from 50-100 ps in 10 ps intervais, and plotting pulse width,

t,, Y s . the dope of the signal decay, Sn/S,-i. The number of signais acquired for

each t, nas N = 16. Once BI was calibrated, a , l ~ could be calculated for any offset

frequency.

A result of Eq. 3.16 r a s that the mavimum off-resonance signal will not be

obtained using a tip angle of 90". The maximum signal is obtained when the magne-

tization is entirely in the xy plane. i.e. when = O. Solving Eq. 3.16 for i\I: = 0.

the effccti\-e 90" flip angle. aC1/(9O0), is:

For esarnple. an offset frequency of 300 Hz combined with a BI of 1 G results tvas an

optinial flip angle of 33.7" (rather than 90") for 12'xe. As a result of off-resonance

rffects. Eqs. 3.6 and 3.5: both of which assume a constant flip angle. must non

iriclude an additional term:

-4 = sin @&in2 a,jf + (1 - cos a,i1)2 cos2 B. (3.22)

The repetition time (SR) for these erperiments must be short enough to appros-

imate the esponential decay of the signal between pulses to unity ( e - = R j T i - 1).

Therefore. some knowledge of the value of Tl must be knosn beforehand. Tl nas

predicted to be on the order of 100 s, based on obsen-ations made in the fringe field

at 85 G. Therefore. SR was chosen to be 100 ms with a sampling time of 20 ps.

Signal Acquisition, 1.89 T

SSR measurements at 1.89 T were acquired on the aforementioned MRRS MR5000

console using an Osford 30 superconducting magnet (30 cm bore)? r i t h a sampling

time of 120 ps and a pulse a id th of 54 p. For thermally polarized 129Se signal

acquisition a separate sample was used: 5140 mbar of Xe and 1519 mbar 02. The

high pressure of the cell increases the low thermal 129Se signal amplitude, while the

presence of oxygen relaxes the 12'Se quickly enough so that short repetition times

can be used to shorten acquisition time betaeen consecutive acquisitions. This high

pressure sample ce11 had the same filling factor as the l o w r pressure ce11 and. while

the senon density \vas relati~ely higher. the loading characteristics of the the coi1 did

not change the Q since the sample was still in a gaseous state and had an overall low

dmsity (as opposed to a liquid or a solid). 138 signal averages were used to acquire

t hc sigrials.

Hyperpolarized sigrials at 1.89 T were measured in the sarne manner as the

t liermal signals but tvith a sampling time of 20 p s . without the use of signal averaging

and using the sample ce11 described in Section 3.3.

Signal Acquisition, 85 G

Even wit h the aid of a high pressure sample cell. detection of a thermally polarized

'?'Se signal at 83 G is extremelp difficult and b e o n d the capacity of the low-field

imager constructed. However: estimation of a signal strength was made based on the

signal strength of a different nucleus with a higher magnetic moment (i.e. protons)

detected from the same spectrometer. Beginning with a ratio of signal equations

(Eq. 2.30) and eliminating the exponentials we have for '29Se and hydrogen nuclei

(protons):

where w is the resonant frequency, B is the applied (RF) magnetic field strength, p

is the magnetic moment, N is the nurnber of nuclei per unit volume, P is the thermal

polarization, V is the sample volume, and A is the off-resonance correction factor.

1 s the spectrometer has a fixed resonant frequency and transrnitter power, reflected

in the B term, both and B will be independant of the nucleus and therefore cancel.

The polarization. as a function of both w and T will also cancel as T is constant.

Finally. recalling that p x 7 (Eq. 2.4) and assuming the sample volumes to be equal

where .Yy, = 4.6172 x 10" a t~ rns / rn -~ and = 6.6875 x 102' atorn~/rn-~. .bc vas calculated from the known pressure (730 mbar) according to the ideal gas law and

.YH wa calculated based on the molecular weight (18 gjmol) and density (1 g/cm3)

of water. The off-resonance terms, .L. sill. for a giren off-resonance frequencj: differ

only in the gyromagnetic ratios of the nuclei. In this manner a thermally polarized

'-'Se signal was measured from a proton signal a t the same resonant frequency (100

kHz). where the field strength is changed for the proton signal acquisition. from 85 G

to 13 G. in accordance to the Larmor relation. Thermal proton signals were acquired

nith a sampling time of ?O ps and a pulse width of 114 ps. 1000 signal averages

were used for a total acquisition time of 15 minutes.

Hyperpolarized signals at 85 G were obtained using the sample ce11 discussed

in Section 3.3. but with only a single acquisition. Signals were acquired using a

sampling time of 20 ps and a pulse width of 111 p.

Tl Measurement

The Tl relaxation time of the sample at 83 G n.as measured using the same sample

as described in Section 3.3 and the same technique as the flip angle calibration

discussed above escept using SR = 20 s .- Tl. Since D e l l was calculated (above).

Tl was estimated according to Eq. 3.18. The data were fitted using a Levenberg-

Xlarquardt nonlinear least squares fitting technique to extract Tl.

Radiation Damping

Radiation damping was investigated using two different techniques. First, the signal

intensity aas plotted against flip angle (Oo < cr < 120") and fit to both linear and

sinusoidal functions, as described in Section 2.1.5. A linear fit indicates that damping

is present. while a sinusoidal fit indicates that no damping is present.

Secoridly. tip angle calibrations for a series of 16 FIDs were compared at different

acquisition times along the FIDs. Different calibrated values of a would indicate that

the relasation rate of the signals was changing as a function of tirne along the FID.

This is the case for radiation damped signals as Trd IX AIo. where dlo is decreasing

with rime along a FID and also with eacii successive FID. If damping is not present.

no change in tiie flip angle calibrations will be observed. as T; is independent of JIo.

Chapter 4

Result s

Esperirnental results are provided in this chapter for the SSR at 83 G in comparison

n-itli the SSR at 1.89 T. Test results of the resistive elcctromagnet's field uniforniity

aiid stahility are pro~ided: measurements of SSR dependent parameters (P. Q. F.

r,. r,. I ;. and 1 f ) are given: flip angle calibration reçu1 ts and Ti measurements of

the saniple ce11 are provided: and radiation damping test results are presented.

4.1 Resistive Electromagnet

4.1.1 Field Uniformity

Llagn~tir field plots for the 85 G resistive electromagnet are prorided in Figures 4.1

and 4.2. Fig. 4.1 shows a plot of B: for 0 = O along the 2 avis of symmetry. Fig.

-1.hho1i-s B, at 2 = O in the xy plane of symmetry. -1s discussed in Section 3.1.

the resistive electromagnet sas designed to have a 10 cm region of homogeneity at

the coi1 centre. This is also shown in the modelled curve of Fig. 4.1. predicting a

field inhomogeneity of 1.25% at f 5 cm. The esperimental measurements meet that

prediction. within the esperimental error.

CH.4PTER 4. RESULTS

Figure 4.1: The axial magnetic field strength along the r axis of symmetry. Error bars are duc to gaussmeter fluctuations (5 0.2 G ) . AS predicted. the field is homogeneous within a 10 cni region at the center. with an inhomogeneity of 1.23%. The field map was corrected for the positional displacernent of the Hall probe by 0.5 cm.

CHAPTER 4. RESULTS

Figure 1.2: The axial magnetic field strength in the xy plane of symmetry. The greyscale indicates field strength. Inhornogeneities near the rim of the surface (near the windings of the coil) are likely due to interference £rom the power supplies located adjacent to the low-field coil. As predicted? the field is homogeneous within a 10 cm radius at the center. as designed.

Figure 4.3: Repeatabili ty data for the low-field resist ive electromagnet . The received signals have a frequency error or fluctuation of 1.5% and an intensity error of 2.2%. Here. t , = 4 1 1 p. with an offset frequency of 700 Hz and a sampling tirne of 20 p. A small DC offset artifact can be seen near the zero frequency mark.

4.1.2 Field Stability

Figures 4.3 and 1.4 show the fluctuations in magnetic field stability as a function

of spectral intensity and frequency at 83 G using the sample described in Section

3.3. Signal fluctuations were tested for over a time period of 3 hours, with spectra

fiuctuating within a frequency range of 50 Hz (1.5%) and a spectral intensity of

2.2%.

Figure 4.1: Repeatability data for the low-field resistive electromagnet. The received signals have a frequency error or fluctuation of 1.5% and an intensity error of 2.2%. Here. t , = 411 ps? with an offset frequency of 700 Hz and a sampling time of 20 p. A small DC offset artifact can be seen near the zero frequency mark.

Figure 4.5: Tip angle calibration data. The dope of the data sets changes according to t h pulse width. t,.

4.2 BI Calibration

Bi calibration data is provided in Figure 4.5 and shows the change in the signal

dcc- rate for different pulse widths. t,. Sn/Sn-I rs. t, is plotted in Figure 1.6 and

is fit to Eq. 3.18. giving an estimate of BI = 0.77 k 0.72 G. These signals were

recorded with an offset frequency of 4-10 Hz.

4.3 Polarization Measurements

Polarization factors, PHPy for both high and low-field strengths are presented in

Table 4.1 along n-ith the calculated thermal polarizations, PTH. A water FID. used

to calculate P at 83 G is shonn in Figure 4.7. Signals for al1 four cases are presented

Figure 1.6: Bi calibration plot. Bi = 0.77 1 0 . 7 2 G and the X2 = 0.7928 per degree of freedorii.

iri Figure 4.8.

Table 1.1: Polarization values. P, for the hyperpolarized and thermally polarized gas experinients. The thermal (or Boltzman) polarizat ions are provided for comparison. The errors in the laser polarizations were determined fiom the statistical repeatability of the hyperpolarized experiment SNR. as described in Section 3.1.2.

I 1 1 I O 0.002 0 . W 0.006 0.008 0.01 0.012 0.014 0.016 0.018 0.02

Ttme (s)

Figure 4.7: H free induction decay from a water sample at 23 G. Sampling tirne = 20 CIJ. t , = 114 ps (90°), 1000 signal averages.

4.4 Electronic Factors

Figure 4.9 shows the bandwidth estirnates used to calculate the Q7s with Eq. 3.9.

The high-field bandaidth aas estimated to be 1 Il.€$* 6.4 kHz a i th a Q of N8.2k 11.2

ahile the low-field bandwidth was measured to be 3.100 f 0.355 kHz with a Q of

29.41 f 3.07. The Q IV- also measured for the water-filled lor-field coil to check for

differences in the loading of the coil r hen acquiring the proton signal for the 85 G

polarization measurement.

The noise figure? F. was calculated for both sytems for the preamplifiers and

the receivers as discussed in Section 3.4.1, using Eq. 3.1 1. The results are tabulated

in Table 1.2. Soise figures of the receiver are used in funher calculations.

, 05 (a) HP-Xe at 85 G

1 (b) H ai 23 G

6OOOr 1

Figure 4.8: A cornparison of thermally (TH) and hyperpolarized (HP-Xe) signds at 1.89 T and 85 G . (a) Hyperpolarized 12'xe at 85 G. t, = 411 ps. 631 Hz frequency offset: (b) thermally polarized lH (water) at 23 G, 1, = 114 ps, 488 Hz fkequency offset, 1000 signal averages. SR = 1.5 S. total acquisition time was 25 minutes: (c) hyperpolarized 12'xe at 1.89 T. t , = 5.1 p. 49 Hz frequency offset. The dip in the spectrum near the middle is an artifact of the quadrature phase detector; (d) thermally polarized 12'xe at 1.89 T, t, = 54 ,us. 378 Hz frequency offset. 128 signal averages. TR = 2 S. total acquisition time was 256 S. Al1 intensities are in arbitrary units corrected for the number of acquisitions.

CHAPTER 4. RESULTS

(a) (ri&!2.16 MHz

I 0.2 0.2' '

221 22.15 22.2 2225 100 102 104 fil6 108 110 f (MHz) f (kHz)

Figure 1.9: (a) High-field (1.89 T) RF coil bandwidth is estimated to be 11 1.8 + 6.4 kHz. The Q is therefore calculated to be 198.2 k 11.2. (b) Low-field (85 G) RF coil bandwidth is estirnated to be 3.400 I0.355 kHz. The Q is therefore caiculated to be 29.41 * 3.01. Error bars are not displayed on either plot as they are not visible.

4.5 Experimental Confirmation of the SNR De- pendence on Field Strength

The rneasured SSR's are presented below in Table 1.3. Al1 four values are norrnalized

to the 730 mbar xenon sample used for the laser polarizat ion experiments.

The ratio of SSRs (high-field divided by low-field) for the hyperpolarized and

thermally polarized measurements is provided in Table 1.4. These values are then

compared to the theoretical calculation according to Eq. 3.6. Table 4.5 includes a

listing of the variables and their values used in this calculation. A ratio of measured

Table 1.2: Noise figure measurements for both 1.89 T and 85 G receivers and preamplifiers. Most of the noise from both receivers appears to originate with the preamplifiers.

Receivet

Table 4.3: hleasured SNR's for high and low-field hyperpolarized and thermally polarized 1 2 9 ~ e . While not al! of the signals were acquired using the sarne sample cell. the num- bers here are al1 scaled relative to the 730 mbar xenon sample used for laser polarization

4.26 * 0.11

Thermal

Laser

experiments.

to calculated values is also providcd in Table 4.4.

16.73 5.28

1 1 Thermally Polarized 1 Laser Polarized

1.89 T

(-1.40 k 0.68) x 102

(2.708 f 0.069) x 106

85 G

(1.830 f 0.016) s IO-*

(8.26 f 0.15) s 10''

Table 4.4: Cornparison of the measured SNR ratios to the calculated values.

Measured

Calculat ed

Ratio (Calc./Sleas.) i

4.6 Relaxation Time Measurements

Tl relaxation time data are provided in Figure 1.10. Tl was estimated to be 189.9 I

41.1 S.

(2.42 f 0.49) s 10"

(2.21 f 0.38) s 10"

1.09 It 0.25

32.8 i 1.5

28.8 z t 5.2

1.14 iz 0.21

Table -! ..5: Piirarrieters used to est iniate the ratio of SNR using two different spectrorrieters a t two ciiflerent static field strengths.

4.7 Radiation Damping

A plot of the signal intensity versus flip angle is pro~ided in Figure 4.11. The

siriusoidal fit (\' = 0.6604) is better than the linear fit (,y2 = 1.0388). S o radiation

ciamping \vas therefore indicated.

As a further check. signal decay \vas analyzed at different acquisition times along

a series of FIDs. Because the data al1 decayed at the same rate. radiation damping

does not appear to be present, as shown in Table -1.6.

Based upon this esperimental evidence, radiation damping does not appear to be

ari issue with our esperiments. Therefore? the hyperbolic secant radiation damping

term in the signal equation can be ignored and signal decay according to esponential

T,' cari be assumed.

Figure 4.10: Ti relaxation tirne decay: t,, = 42 p. 20 pulses. Ti was estiinated at 189.9 + 41.1 S. with a X' = 1.0012.

1 .-\cquisition Time (ms) 1 Flip Angle a ( O )

Table 4.6: Cornparison of flip angle calibrations at diflerent acquisition times along the FID. The results show that there is no statistically significant change in a along the FID. T herefore, no radiation damping is present.

Figure 4.1 1: Signal intensity vs. flip angle. a. The linear fit (solid line) bas a X 2 of 1.0388 per degree of freedom. while the sinusoidal mode1 (dashed Lne) has a X' of 0.6601 per degree of freedom.

Chapter 5

Discussion

The results of our esperiments indicate that the resistive magnet constructed is

operating within the predicted parameters (i.e. 10 cm region of homogeneity at 85

G ) and that the received signals are stable (i.e. fluctuate nithin 2.2%) for both

frequcncy and amplitude and do not appear to be affected by radiation damping.

The hyperpolarized 129Se ?;>IR signals obtained using this magnet and the low-field

spectrometer match the predicted signal strengths to within 20%. The BI applied

RF field was calibrated at 0.58 & 0.05 Gy the Tl relaxation time was measured to be

189.9 k 0.3 S. and the T; relasation time was measured to be 13.5 i 0.4 ms. These

results. thcir sources of error. and a comparison with Kong et a1[60] are discussed

below. This is followed by a discussion of the SSR requirements of irIR imaging.

how Our results compare to those requirements, what can be done to impro~e tthern.

and some future considerations of this researct project .

The xy plane of symmetry map of the magnetic field strength of the resistire coi1

provided in Fig. 4.2 indicates that the field outside the region of homogeneity, near

the windings. is higher on one side of the magnet than the other. This asymrnetry

is also present to a lesser degree in the axial z map of the field in Fig. 1.1. Garrett's

theor- does not predict this asyrnmetry and states that the field strength should

decrease radially from the axis of symmetry in a symmetric fashion (see Appendis

C'HA PTER 5. DISCUSSION 84

B). This is most likely due to the influence of the power supplies located near one

side of the magnetic coil, the electrical activity and ferromagnetic components of the

power supplies produciag a distortion in the field. The power supplies have since

been moved further away from the coil to reduce this asymmetry.

The homogeneity at 5 cm from the centre of the 85 G coil is 1.25RI as opposed to

a feiv parts per million (1 ppm = 0.0001%) for the 1.89 T superconducting magnet.

Hoivever. t hese values are relative to their static field strengths. Le.: a A B = 1G ni11

have a relatively higher homogeneity at 85 G than at 1.89 T. As it is the behariour

in the rotating frame that is important to '\IR (i.e. after the resonant frequency has

been removed). the A B will cause the same dephasing of the spins at loir7 field as

at high. Increased field homogeneity is still desirable. howeever. as it lengthens the

T; relaxation cime. alloning for longer read out cimes and better spatial resolution.

Field hornogeneity can be improved by shimming the magnetic field. Shimming is

the process of removing the spherical harrnonics (see Appendis 1) that comprise

the field inhomogeniety through the strategic placement of ferromagnetic materials

around the magnet and the use of harrnonic-cancelling magnetic field coils. or shim

coils.

The fringe field of the 1.89 T superconducting magnet changed the T; relaxation

tirne of the received signals from 6.9 ms to 13.3 ms? allowing for longer signal dura-

tions in the presence of the high-field and essentially acting as a shirnming source.

This indicates that a more thorough shimming of the magnet ri11 improve signal

duration. Shimming can be more properly provided by adjusting the field homo-

geneity over the volume of a shimrning phantom, typically a sphere of water with a

diameter matching the desired region of homogeneity. A simple shimming technique

in~olves placing plates of ferromagnetic materials (e.g. iron) near both ends of the

cylindrical coi1 and adjusting their relative positions to the coil until the contrat of

the phantom image (or the signal amplitude) is uniform.

CH.4 P TER 5 . DISCUSSION 85

the imaging field strength is usually a relatisely much stronger field. For 101.-field

imagers. this is not always the case. Here, the presence of the 1.89 T superconducting

magnet is beneficial to our results, but this may not always be the case. 1Iagnetically

shielding the coil from external static fields might therefore be considered. Such

shielding techniques involve encasing the resistive coil in p-metal to attenuate the

static fields.

Fitting for the TI relaxation time \vas very sensitive to the B

an!- error iii the flip angle ni11 present a large relative error ( 4 0 % )

the confounding effects of varying TR and a can be difficult for the

calibration. as

in the Tl . Also.

measurernent of

T l . Tlic larger the flip angle. the more it dominates the decay but the better the

rcceived signals are. therefore the better the fit. However. a longer TR increases the

TR/Tl weight in the fit but also reduces the number of pulses (i.e. the number of

points) uscd for the fit due to the increase in the decay between pulses. decreasing

the accuracy of the fit. Differerit combinations were tried but the combination used

(TR = 20 S. Q = l l . T o . and X = 20) presented the best combination of weighting

distribution and number of data points.

Tl of 3He nas measured by \\ongjôO] to be on the order of 100 hrs in a glass

sample cell. This differs from Our result by three orders of magnitude and is primarily

due to the differences in the nature of the atoms being observed. Senon has a much

larger elect ronic structure, and t herefore more electronic shells, t han helium. -4s

a result. the binding energies of the outer shell electrons of xenon will be weaker

t han t hose of the outer shell electrons of helium, a result of the inverse-square law

governing those binding energies. This indicates that. while both are noble gases. and

do not chemically react with their environments. a trait that makes them excellent

candidates when norking nit h biological substances. the senon atoms are. in fact.

more susceptible to esternal electronic environments. This elasticity or stickiness of

the senon atoms is one esplanation for their interaction with the sample ce11 ivalls.

Helium does not suffer from this limitation and will therefore have a considerably

longer longitudinal relaxation time, as indicated by the above results.

The data provided in Fig. 1.11 and Table 4.6 indicate that if radiation damping

is present it is playing a very small role. The signals acquired from the spectrometer

do not completely conform to either a damped or non-damped signal mode1 probably

due to non-ideal shimming of the magnetic field. However, while the free induction

decay. shown in Figure 5.1: did increase in amplitude before decaying. it was not

nearly as severe an increase as that of a damped signal. given the FID's flip angle

(130"). E~wen though Trd was not estimated. as the fit to the data faiied. we can still

infer tliat radiation damping \vas not present because the amount by which the FID

iiicreases is indicative of the flip angle (Fig. 2.9). Therefore. no matter what the

ralur of Trd is. the FID will increase bu a fised amount: Trd is a rneasure of the dway

of thc signal. miich the same way is. Figure 5.1 qualitatively illustrates this idea.

\\'hile radiation damping was present in work done by Wong[60]. that group used

"He rather than "'Se as the nucleus of interest. which has a g'romagnetic ratio -3

tinies greater than that of lZ9Se, and tvith which Kong had higher polarization l e~e l s

(10% rather than Our own 3.4%). These differences increased their magnetization

Irwls by a factor of -20, compared to ours' which in turn shonens the damping

tinie. Trd x 1/(-t2P), by a similar amount, making radiation damping a problem.

The! recorded Tvd - Ti 4 0 0 ms. which implies that oiir Trd 4 0 0 0 ms, 200 times

greater than Our Ti of 4 0 ms. Radiation damping was checked for at 1.89 T. as

well. and not found to be a factor. As the magnetization is much higher a t this field

strength (-10 times greater), and damping aas not indicated, then at 83 G damping

11-ould not be espected.

Radiation damping will become a problern with increasing magnetization. i-e.

increased polarization or spin density (Eq. 2.50). It will also be a problem for longer

T As Ti increases and the ratio of T;/Trd approaches unit'. damping effects

Figure 5.1: Models of the conventional exponential decay envelope and the radiation dariipirig Trd hyperboiic function envelope compared to the FID (a = 130"). Qualitatively. tlic T - fit is the better of the two.

will begin to manifest. As both increased 34 and T ' is desirable in every other

aspect of LIR imaging. radiation damping rnay be an ine~itable problem. It may

he corrected for by estimating the damping time. Trd. and correcting the acquired

images accordingly.

The aim of this research project \\.as to demonstrate that the constructed low-

field imager has an SSR that is sufficient for imaging in accordance a i t h the theory

proposed in Section 2.1.4. The SSR measurements recorded in Table 4.3 indicate

that the measured results and the calculated predictions are within each others

esperimental uncertaint?; thus validating this theoxy Discrepancies in the results

can. however. be accounted for in a number of ways.

CH.4 PTER 5. DISCUSSION 88

In modeling the noise, traditionally a difficult task, a nurnber of different sources

need to be taken into account. Here, as is standard practice[77], only the thermal

noise is accounted for in the Hoult SNR model. Other sources of noise are typically

ruled out as they have a negligible effect on signal strength at high-field strengths.

At lon field strengths. however, these same effects, such as 11 f noise and sarnple

noise. ma? be stronger (or conversely, the thermal noise rnay have less of an effect),

thereby influencing the SSR results to a more noticeable estent.

Another assumption made when modelling the SSR in these esperiments has

brcri tliat the I< factor in the SSR equation. a factor related to the geometry of

thr RF coil. is typically taken to be -1 and therefore ignored. However. because

t h e ratio of' SSR between the two field strengths uses two different RF coils with

diffcrerit geometries (solenoid rs. Helmholtz) the K factors ma' be different for

tlir two coils. tliiis influencing the SSR results. The K factor can be niore closely

studicd by looking at ratios of SXR at the same resonance frequency using the same

spectrorncter and sample but with two different RF coil geometries. Eq. 3.6 then

.\kasuring both Q and F in the same fashion as described in Section 3.4.1! the K

factors can be measured.

A third source of error in our results is the hyperpolarization factor. PI at 1.89

T. \\'hile al1 Ion field polarizations and esperiments were performed inside the 83 G

resistive magnet. high-field polarizations were performed in the fringe of the 1.89 T

magnet and the samples then transferred to the bore of the superconducting magnet.

Polarizations aere not made inside the bore of the superconducting magnet as the

geometry of the sample ce11 oven and the 1.89 T RF coil were not compatible. The

timc delay in transferring the sample and beginning signal acquisition allows for Tl

relaxation to occur, reducing the amplitude of the received signal by a factor e-'IT1.

where t is the tirne delay. The time delay is small (no longer than 20 s) and the

decay therefore on the order of e-20/t89 - 0.9, i.e. a 10% reduction in signal. This is

indicated by the different values of P in Table 1.1. While this potential correction

to the STR should. in theory, improve our results, it appears to worsen them. This

could be accounted for in the previous arguments with regard to noise and the K

factor. or simply the esperimental uncertainty of Our results.

-4s can be seen in the above discussion. the number of correction factors involved

iri coniparing S S R between different samples, RF coils. field strengths. etc. does

not allow for an- immediate recognition of the matching of the theory to the SSR

mcasiirerricnts. .A quick check of an- preliminary results can be made using the

following argument.

Eq. 2.33 (lescribes the signal-to-noise ratio for an SUR signal. It is ghen as:

Consider the ratio of SSR betwen the hyperpolarized and thermally polarized sig-

n a l ~ at a given field strength using a given sample. .issuming that the imaging

systeni used for both the thermal and hyperpolarized experiments is the same. this

ratio would reduce to a ratio of P factors:

where f i H is given by Eq. 2.15 and is linearly dependent on Bo. ahile PHp is

independent of the field strength and is dependent on parameters related to the

optical pumping and spin exchange of the nuclei in the polarization process (Eq.

2.6 1 ) . From Eq. 2.33 we see that the field dependencies corne from the Mollo: Q and

terms. as .\& x P and Q x f0 cx Bo. Since PTH is proportional to Bo we have:

CHAPTER 5. DISCUSSION 90

Therefore the SXR of the thermal signal mil1 be proportionai to Bi rhile the hyper-

polarized system ni11 have an SXR proportional to Bo. This relationship can now

be further simplified to:

So for two different field strengths, BA') and 3i2):

\\(. can therefore check the feasibility of Our results by using the four SSR measure-

nitmts frorn Table 1.3 in Eq. 5.6 and comparing to the ratio of field strengths. Csing

Our results. t he left-hand side of the equation is equal to 0.0014 5 0.0003. while the

ratio of field strengths is equal to 0.0015. N'hile these numbers are not the same.

th ry are withiri an order of magnitude. providing further validation that the acquired

sigiials are follotving the established theory.

The m~asured SSR for the low-field hyperpolarized I2'Se esperiments can be

conipared to siniilar esperirnents carried out by Wong et n1[60] using 'He. Kong

reports an SSR of 4 7 0 0 . It is important to note that the definition of SSR for

iniagirig purposes is typically taken as the spectral peak amplitude. not the inte-

grated area as we have used. di~ ided by the standard deriation of the noise. Area

calculations are used to compensate for different T; relaxation times for different

sigrials which alter the shape and therefore the height of a spectral peak. Csing this

definition. Our esperiments yield a SSR of -10000 at 1.89 T and -500 at 85 G,

within the same order of magnitude as Wong. -4s Wong r a s able to acquire an 31R

image with this SSR. such an agreement between results implies that imaging with

Our SSR results may be possible. In order to more properly determine the feasibility

of hyperpolarized 12'Se 1IR imaging, we must take a doser look at the minimum

requirements for .\IR imaging. If Ive assume that the minimum signal-to-noise ratio

criteria for imaging is an SSR per voxel (typically a mm3) of -2, then the SNR val-

ues recorded in Table 4.3 must be divided by a factor of N3I2 for a t~wdirnensional

image a i th an XrN field of view for each slice of the object imaged, where the .N

phase encodes act to signal average the image. Furthermore, because the signal is

also non-replenishable and is depleted with each successive RF pulse, the SNR ni11

usually be conserved through the use of a variable fiip angle pulse sequence to pro-

duce a constant SSR per pulse. The SSR is thus decreased by a factor dependent

on the number of RF pulses applied to the sample. Therefore. imaging sequences

reqiiiring few pulses or a single pulse should be the sequences of choice for hyper-

polarized imaging. The best approach is to therefore decideupon a sequence that

allows the least number of RF pulses and then to decide upon a spatial resolution

necpssary to obtain. at the ver' least. an SSR per pisel of -2.

Eclio-planar imaging (EPI) is an imaging technique that uses a single 90' pulse

to image a coniplete two-dimensional slice of an object. This sequence. ahile pow-

erful. requires a long Ti in order to acquire the echos necessary for the image to

form. -4s well. this sequence requires specialized SMR hardware designed for faster

imaging. \\'hile still largely esperirnental. EPI shows much promise for the future of

SIR imaging. particularly in the area of real-time proton imaging. While real-time

imaging would be considerably more difficult to perform r i t h a non-replenishable

magnetization. EPI. and sequences like it' offer a maximum use of the magnetization

using only a single RF pulse. Assuming that T; is long enough to implement EPI. a

minimum spatial resolution. Ax, can be calculated based upon the minimum SSR

desired per vosel. Consider that the region of homogeneity of the low-field rnagnet

is 10 cm = 100 mm. Therefore. the field of view may not exceed this lirnit oithout

introducing significant image distortion. Assuming that a larger RF coi1 is built to

accommodate a larger sample with similar electronic characteristics to produce a

comparable. if not irnproved. SXR of -500. a spatial resolution of 1 mm2 is selected

CH.4 PTER 5. DISCUSSION 92

with 32 s 32 pixels (i.e. 32 mm x 32 mm FOV) and no slice selection we have an

SSR of:

nhich is very near to the minimum requirement for SIR imaging. If a multiple pulse

sequence is used this SNR must be further d i~ided up by the number of pulses in

the sequence. i.e. a ten pulse sequence will reduce the above SSR to 0.276. As the

SSR estimate is already near the minimum required. an- further reduction rnuçt be

conipensated for by decreasing the number of pixels used for the image or. if keeping

a constant FOI' is a concern, increasing the pisel size. Wong[60] uses the variable

flip angle FLASH (Fast Low-Angle SHot) pulse sequence to measure the gas space

of escised rat lungs. The FLASH sequence can utilize a flip angle between 0" and

DO" but the selection of the angle and the repetition time. TR. will alter the contrast

of tlic iniagc in connection with the Tl relaxation time. Therefore. a grpater flip

ariglc than the one Kong uses. 12'. might not yield a better SXR. As with EPI.

FLASH also requires a long Ti in order to acquire the number of echos necessary

for an image to form.

Iniprowments in T; are espected at low field strengths due to the interaction

b c t w m the field and the magnetic susceptibility deviation. A s Assuming that the

rionuni forrni ty of is characterized by a Gaussian spatial distribution a i t h mean

1, and standard deviation &y, AX will cause decoherence for stationan nuclei

precessing in the resultant varying fields. characterized as a contribution to T; in

the form:

Therefore. it can be seen that the decrease in Bo leads to a decrease in the effects of

magnetic suscepiibility deviation, which include image distortion artifacts, thereby

increasing the T; to a value closer to T2. Further impro~ements to T'. can be obtained

CHA P TER 5 . DISCUSSION 93

by shimming the magnetic field as discussed above. This increase in T; will alsoo

for a given gradient strength, yield an increase in the optimum imaging resolution

at Ion field strengths as described by Callaghan[78]:

Cnder the right conditions, as reported b?* Wong[60], this improvement in S. can

yield a resolution comparable to a high-field system. While increasing T ' is possible,

it is ultiniately limited by the T2 relavation time. T2 is affected by diffusion and

cheniical eschange. which occurs when there is an eschange of the spin state between

regions of differcnt chemical shift resulting in no net loss of energ. from the spin

system. but a loss of phase information. -4s with the diffusion contribution to T2

(Eq. 2 .7 ; ) . t he chemical eschange contribution has a quadratic dependence on the

st at ic field: 1 - x ??B,'.

TFE (3.10)

T herefore. T2 will be longer at loiver field st rengt hs. thus providing furt her encour-

agement regarding the use of gradient echo pulse sequences such as EPI and FLASH.

Another imaging consideration is the construction of a larger RF coil to contain a

larger sample. The increase in size of the coil will require a higher transmitter poner

(Le. B I ) to drive the coil current and therefore si11 produce more noise in the signal.

l i so . due to the geometrical differences of the RF coil and the sample, such as a

rat. the filling factor of the coil will be considerably lower than that of a glas cell.

Therefore. while the larger sample will increase the SSR? the lower filling factor !vin

contribute to a reduction in SSR. This ail1 be countered by employing quadrature

transnitting to reduce the arnount of poner necessary to excite the spins (i.e a lomr

BI) and therefore increasing the SSR. The new coil.should not be solenoidal. as

loading larger samples would be clumsy and problematic. but instead a birdcage coi1

or saddle coil could be implemented. Both of these coil designs are commonly used

CWAPTER 5. DISCUSSION 94

for larger sample MR imaging. The Q of the RF coil can also be increased (or the

coil bandwidth decreased) to narrow the spectral lineridth to increase SSR (Eq.

2.57) up to the limit imposed by T;. Our results show that the low-field RF coil

had a much smaller Q than the high-field coil, a result of the high number of turns

of wire used in the low-field coil which introduced a large resistance in the coil.

SXR can be increased by improving the noise figure of the preamplifier, possibly

through the use of low-noise operational amplifiers or liquid nitrogen cooling. SSR

improvements can also be produced through isotopic enrichment of the xenon and

through increased ,pas pressures. However? these approaches to increasing SSR are

problematic as xerion acts as an anesthetic at high concentrations and because bi-

ologiral systenis such as lung spaces can only tolerate certain levels of gas pressure

before beconiing dangerous to the subject. While, logically. an increase in Bo would

irriprow the SSR. a factor of 2 improvement in the SSR would require an increase

in the field strength by a factor of 4 ( S S R x &"). which in turn requires a p o w r

iricrease of a factor of 4 6 (P x 12 x Bi). requiring a substantial upgrade in the

power supply electronics. Improvements to the SSR can be made by increasing the

polarizat ion t hrough optimizat ion of the laser polarization t ime and ce11 tempera-

t u r c and longer Tl relaxation times (Eq. 2.61), i.e. by decreasing wall relaxation

effects ttirough the use of Surfrasil and the removal of impurities such as osygen

from the cell. Finally, acquiring on-resonance will ensure a maximum obtainable

SSR as well as simplify flip angle calibrations. On-resonance signal acquisition will

require the removal of the zero frequency artifact resulting from the DC offset in the

transmit ter. This can be corrected for electronically speaking, but fine-tuning the

correction will involve post-processing. An algorithm must be dewloped to center

the FID on the zero signal mark without having any set reference. Improsements

such as these are currently being investigated.

Future work involving the low field system constructed will involve gas phase

CHAP TER 5 . DISCUSSION 95

imaging. as discussed above, starting with the sample ce11 used in t hese experiments.

Imaging ri11 require the use of gradient coils, a set of which have been provided but

not yet implemented. Once the ce11 has successfully been imaged, larger, more

cornples samples will be considered. such as excised rat lungs and eventually a living

rat. Beyond gas phase studies? dissolved phase kIR imaging could be explored in

blood plasma and suitable biologically compatible substitutes (such as PFOB) as

described in Chapter 1. Such dissolved phase worli is currently being carried out at

1.89 T iii this laboratory. Relaxation studies for gas and dissolved phase imaging

will be pursued in order to determine the amount of tirne available for senon to

difiùsc into the bloodstream and to reach target organs ( T l ) , and to determine the

alloivahle piilse sequences to be used (&). It is already known that Tl is considerably

skiorter tdieii dissolved in blood plasnia. therefore severel' limiting its targetability.

Honorer. the above arguments indicate that T2 stould be considerably longer a t

l o w r field strengths. A flow system for hyperpolarized 129Se is currently under

construction for hyperpolarized esperiments in our laboratory. Once finished. the

systern will be tailored tonards maximizing its polarization factor through optimizing

the polarization time. the ce11 Rb vapor temperature, and the gas Row rate. Such

a floa system will also lead towards acquiring gas and dissolved phase images while

ernploying signal averaging due to the constant replenishing of the hyperpolarized

gas in the system of interest.

In closing, the SSR results obtained not only are a good match to the accepted

theor' but also. based on the discussion provided, indicate that a sufficient amount

of SSR is available to generate a crude UR image. Image quality ri11 only impro1.e

assuming that the recommended modifications to the lon-field system are imple-

mented. particularly the shimming of the magnetic coil and improved RF coil design.

Transverse relasation times promise to increase at lower field strengths offering the

employment of gradient echo pulse sequences to minimize the loss of magnetization

CHAPTER 5. DISCUSSION 96

through the use of sequences with few or a single RF pulse. Radiation damping,

while not an issue in this work, will undoubtedly become one as the nuclear hyper-

polarization increases and T; lengthens. Based on these results and the vast amount

of room available for their improvement, MR imaging of hyperpolarized '''Se at

Ion- magnetic field strengths (i.e. 85 G) is not only feasible, but highly likely to be

successful.

Appendix A

Low-Field Polarimeter Modifications

The tra~isniitter was rnodified from Saam's[7-!] to provide two carrier frequency ref-

crrrm signals for the quadrature phase detector. This can be seen in Figure -4.1.

A n 8 MHz crystal oscillator is used here and divided by a factor of 4 using a 7473

flip-flop. Further division by a factor of 10 using i-LHCT161 synchronous binary

c-oiiriters which output a 200 kHz signal to two separate Ï4HCTÏ-I Rip-flops results

iii the output of two separate orthogonal 100 kHz square wave signals. labeled 21 and

2 2 . These signals are used as references for the quadrature phase detector shown in

Figure A.?. The two signals trigger two separate llAS319 switches prior to the final

aniplification stage in the receiver. Sote that the resistors on both output channels

have been changed from Saarnk values to accornodate the 5OR input impedance of

the SlIIS.

Figure A . 1 : Modified transmitter circuit. An 8 MHz crystal is divided first using a 7-173 divide by 1 circuit. Further division to 100 kHz is provided by 74HCT161 counters and 74HCT7-l flipflops, where two separate 100 kHz square wave signals are output (21 and 22) 90' out of phase with each other for use as reference signals for the quadrature phase detector .

Figure A..': Quadrature phase detection based on Saam phase detector[74]. The circuit is identical to Saam's with the exception of a second phase detection channel branching off frorii the first OP-27 amplifier. The reference frequencies used to signal the MAX319 switches are provided by the dual channel transmit ter shown in Figure A. 1.

Appendix B

Axial Symmetry in Magnetic Fields

Garrett(711 has given a complete discussion of the magnetic field produced by cur-

rerits in a susteni of conductors with cylindrical symmetry. To describe the spatial

variation of the field it is most convenient to use an espansion in spherical harrnonics.

T h field is completely specified if the field along the axis of symmetry is known.

The coordinate system used to describe the systern involres the use of both cylin-

drical (p . o. z ) coordinates and spherical (r. 0: d) coordinates. Figure 3.2 illustrates

bot11 the asis and plane of symmetry that characterize the coordinate system. In

certain situations there is also a plane of symmetry which is perpendicular to the asis

of symmet ry. In t hese cases it is convenient to take the intersection of the symmetry

asis and the symmetry plane to be the origin of the coordinate system. To describe

the magnetic field Ive shall use the components parallel to and perpendicular to the

axis of symrnetry. Thus Ive can write:

n-here k and p are unit vectors parallel and perpendicular to the sp rne t ry asis.

respectively. Since the system of conductors is axially symmetric? the magnetic field

will not be a function of the azimuthal angle @.

It is convenient to use the scalar potential in expressing the fields due to axiallu

symmetric systems. The potential inside a system of conductors with cylindrical

symmetry is of the form:

I t immediately follons from this potential function that the radial and a ~ i a l fields

are giwn by:

-4s esplairicd in Section 3.1: since r = : ahen 0 = O and Pn(l) = 1' it folloivs that

the field strength dong the symmetry auis is given by:

are the coefficients. This shows that the axial component and al1 of its derivatives at

the origin define the field e~erywhere in the central region. This expansion is valid

throughout a sphere centered at the origin with a radius extending from the origin

to the nearest current-carrying conductor.

Irihomogeneity within the spherical region surrounding the solenoid center is

best considered by examining the dependence of the field on 0. Since for an. n the

maximum value of Pn(cosO) is Pn(l) = 1, the variation of H,(r,B) as a function of r

is greatest for 0 = O. i.e. the cornponents of the field parallel to the symmetry avis

possess the greatest degree of nonuniformity along the asis. The masimum values of

the various expansion terms of the radial field can be s h o m to be of the same order

of magnitude as the axial components, but numerically smaller. As well. the radial

field ail1 be of second order when considering only the magnitude of the field due

to being added in quadrature to the axial component. Therefore, variations in the

field along the symmetry avis are a good indication of the degee of homogeneity of

the coil. Designing a coil for maximum homogeneity can therefore be accomplished

using only Eq. B.5.

For the case of thin solenoids. as they are easier to accurately wind, Eq. B.5 can

be written as Eq. 3.4? repeated here:

47 X$ I 1 - u; H,(L O) = --

10 'Zr,

Since there is a plane of syrnmetry passing through the origiii perpendicular to the

axis. tlicrc are no odd powers of 2 in this expansion. Eq. B.7 can therefore be

reluit t t r i as:

x (33 cos' 0, - 30 cos2 0, + 5) ( ) - . . ]

d i e r e .Y is the number of turns per centimeter. The successire ternis are referred to

as zero order. second order, fourth order, etc. These terms can be remo~ed by using

correct ion windings. i.e. by winding addi t ional coils r i t h conter-rotating currents

and angles 0, such that higher order terms cancel. .An example of a coil constructed

ni t h correction windings is giren by Hanson(721. Alternatively, if optimizing power

consumption is an issue' as it was in our case. correction coils can be discarded (as

they each require their own power supply) in favour of alternative coil designs. Split

solenoid coils can be wound with less windings. less poner and geater hornogeneity

than single solenoids. A split solenoid is considered as a solenoid wirh end turns

at O,! minus a solenoid with end turns at OS2, as s h o m in Fig. 3.3. Therefore. bu

selecting angles O, and such that cos OS1 sin4 = cos sin' OS2, second order

terms can be reduced to zero. Calculations show that OS1 must be less than 63".

In the limiting case when OS1 = OS* = 63', the split solenoid becomes a Helmholtz

pair. For the purposes of simplifying sinding accuracy, a split solenoid design (not

a Helmholtz set) was used. For optimum field homogeneity, Garrett's eight-order

double Helmholtz coi1 arrangement should be used. For further information. see

Garrett [ T l ] and Franzen(731.

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