A Multipurpose MRI phantom based on a reverse Micelle solution

Rochester Institute of Technology

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5-1-1996

A Multipurpose MRI phantom based on a reverse

Micelle solution

Jo Roe

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Recommended Citation

A MULTIPURPOSE MRI PHANTOM BASED ON A REVERSE MICELLE SOLUTION

JoE. Roe

May 1996

A thesis submitted in partial fulfillment of the

requirements for the degree of

Master of Science of Chemistry.

Approved:

Joseph Hornak

Thesis Advisor

Gerald A. Takacs

Department Head

Department of Chemistry

Rochester Institute of Technology

TableofContents

Page

Copyright Release Form

Abstract

Acknowledgements i

ListofFigures ii

ListofTables v

ListofSymbolsandAbbreviations vii

1.0 Introduction 1

2.0 Background 4

2.1 Spin Physics 4

2.2 Nuclear Magnetic Resonance 6

2.3 Magnetic Resonance

Imaging

18

2.4 Magetic Resonance Phantoms 26

2.5 Artifacts in Magnetic Resonance Images 27

2.6 The Reverse Mcelle Solution 30

3.0 Experimental 35

3.1 Introduction 35

3.2 Solution Preparation 36

3.3 Solution Characteristics 38

3.4 Electrical Properties 39

3.5 MagneticProperties 43

4.0 ResultsandDiscussion 55

4. 1 ConcentrationofParamagnetic Ions for

Tj

and

T2

Control intheReverse MicelleSolution 55

4.2 PhysicalPropertiesoftheReverse Micelle Solution 59

4.3 Electrical PropertiesoftheReverse MicelleSolution 65

4.4 Magnetic PropertiesoftheReverse Micelle Solution 69

5.0 Conclusion 91

Copyright Release Form

A MULTIPURPOSE MRl PHANTOM BASED

ON A REVERSE MICELLE SOLUTION

I, Jo E. Roe, hereby grant permission to the Wallace Memorial Library ofRIT to

reproduce my thesis in whole or in part. Any use will not be for commercial use or profit.

Signature

AMULTIPURPOSEMRI PHANTOM BASEDON

AREVERSE MICELLESOLUTION

Abstract

by

Jo E. Roe

Magneticresonance

imaging

(MRI)

phantoms are anthroprogenic objects usedforsystem

performance

testing

of anMR imager. Currentphantomsused

today

containaqueoussolutions of

paramagneticsalts. When

imaged,

thesephantoms produce a_standingwave artifact. Thepresence ofthis

artifact makeitdifficulttodistinguish between inhomogeneities inthe

B]

transmitand receivefieldof an

imaging

coilandthe

imaging

phantom. Thisthesisdescribesa reverse micelle

(RM)

solutionandits

applicabilityforuseinanMR

imaging

phantom. The RMsolution consists ofthreecomponents:

H20,

whichissurrounded

by

the_surfactant,

AOT,

toforma

droplet,

whichissuspendedinthe

hydrocarbon,

anddecane. Volumefractions

(<|>)

of water andAOT from 0.50to0.9 0werestudied. TheRMsolutionis

easytomake_upandishomogeneous. The RMsolution wasfoundtobephase-stableattemperatures

ranging from 0to40Cat certain<(>values. Thedielectricconstant oftheRMsolution washalfthe

dielectricconstant of_{H20. The resistivity}oftheRMsolution was5timesgreaterthanan aqueous

solution of6mMNiCland0. 1 54mMNaCl. The diffusioncoefficientoftheH20andAOTcomponent

increasedas<j>increased. The diffusioncoefficient ofdecane decreasedas<|>increased. The_viscosityof

the RMsolutionincreasedas<|>increased. The viscosityoftheRMsolutionis35timesgreaterthan the

viscosityofH20. The RMsolutions_{containing 0.}

10, 0.25,

and0.50mMMn+2intheaqueousphase

produce overall

T

and

T2

values similartohumantissue. Theaddition of either

3, 5,

or8mMNi+2inthe

aqueous phase oftheRMsolution produces

T

and

T2

values usefulforsystemperformancetesting. The

RMsolution_{containing 8}mM Ni+2

intheaqueousphasedisplayedtheleasttemperaturedependent

T]

and

spectralpeaksofhuman tissue.

Consequently,

theRMsolution phantom couldbeusedto test thefat

saturation

imaging

sequence. Spectral

T

values ofthe H20anddecanecomponent were measured. The

individual

T

valuesdiffered fromtheoverall

T,

values oftheRMsolution,thus, studyingtheeffects of

Acknowledgements

Special ThankstoDr. Joseph Hornakfor

taking

the time toexplainconcepts andexperimentstome. His

patiencein explaining (overand_over)untilIunderstood

(finally)

was_greatlyappreciated. ThankYou.

Specialthanks to_{Dr. Michael Kotlarchyk for attempting}to teachme

University

Physics

I, II,

andIII in

onehourorless. Iam still_spinningfromtheconversation. Specialthanks toDr. Andreas

Langner,

who

hastaughtme sometricks toputinto_mytoolbox. Istilldreamabout some oftheseconcepts. Special

thanks toMr. Wayne

Prentice,

whofoundthebestimager forour mostimportanttestofourRMsolution

phantom. Thank youfor_sharingsomeof your expertise onMR imagerswith us.

Specialthanks toBrian AntalekofKodak Research

Labs,

who providedthediffusionmeasurements ofthe individualRMcomponents. Specialthanks toEdmondKwokofthe

University

of

Rochester,

who

developeda computersoftwareprogramthatenabledustodeterminespectral

T

valuess. Specialthanks

toDevi

Ramanan,

whohelpedgatherand analyzedataatthe

beginning

and endofthisproject. Thanksto Dr. Saara

Totterman,

DirectoroftheMagnetic Resonance

Imaging

Centerat

Strong

Memorial

Hosital,

for allowingustimeontheimager. Thanksto

University

Medical

Imaging

for allowingustimeontheir imager. Thanksto GE MedicalSystemsfor

funding

part ofthisresearch.

Thanksto

Barry, Bev, Bill,

andRonfortheirsupportfromone graduatestudenttoanother. _{Thank you,}

Davidfor

listening

andR-E-A-D-I-N-G forme.

Specialthanksto_myfamily. ThankstoRich_{for giving up many}of your

Friday

nights andto_my

kids,

who never complainedtoo

loudly

when Momwashome late.

ThankstoDr. Tom

Gennett,

whogaveme somegood advice

-"Why

don'tyougo seeDr.

Hornak,

he

may havesome workforyoutodo."

ListofFigures

number page

1. Netmagnetization

(Mm)

ofthespin vectorsin_{astatic magnetic}fieldina

rotatingframeof 8

reference

2. ApplicationofRFpulseor

B!

_{field along}the +x-axisinthe_{rotating frame}of

reference 8

3. Perturbationofthenet spins_awayfrom the+zaxis 9

4. Longitudinalrelaxation of spin vectorsbacktoequilibrium 1 1

5. Themolecularmotionsof either_{nonviscous, slightly viscous,}and viscousliquidat aparticular

frequency

12

6. Themagnetization

(M^)

intothexy-plane afterapplicationofa90RFpulse_alongthe

+x-axis 13

7. Thespin vectorsbegintoprecess atdifferentratesduetoinhomogeneitiesinthe

BQ

field and

variationsinthelocalmagneticfields 13

8. Thespin vectorsare_precessingatdifferentrates andovertimecancel each other 14

9. An_{exponentially}

decaying

sinewave overtime_alongadirection inthe_xy-plane,calledan

FID 16

10. Thespin vectorsbegintoprecessin_{the xy}planeafter a90pulseisappliedinthe+x-axisina

spin-echopulse sequence 16

11. Inthespin-echopulsesequence, thespins areflipped 180

by

theapplication of a second pulse- _a

180

pulse_alongthe +x-axis 17

12. Thespins arerefocusedandwillbegin toprecessatdifferentratesuntil

Mxy

isequaltozero 17

13.

Timing

diagramforspin-echo pulse sequence 18

14. Birdcageheadcoil side view 20

15. Theaxialplane,thecoronal_plane,sagittal plane views of a samplebottle 21

17. Cross-sectiondiagramofa reverse micellein decane 34

18. Cross-sectionalview ofRM inasolution ofdecane 34

19. Diagramofthe_conductivitycellforthedielectricandRFstudies 40

20. Spectra fromtheAOT 44

2 1. Crosssectional view of variabletemperature_apparatus

containing foursamples 48

22. Arrangementofthelarge bottlenextto thesmallbottle inthesupport stand 5 1

23. RMsolutions usedin

Ti

oftheindividualcomponent_study 54

24. Agraph oftheinverseofthe

T

ins"1

versustheconcentration of

Mn+2

57

25. Agraph oftheinverseofthe

T2

ins"1

versustheconcentration of

Mn+2

57

26.

Stability

diagram forRMsolutionscontain

[Mn+2]

=

0.

1, 0.25,

and0.5mM 60

27.

Stability

diagram forRMsolutions contain

[Ni+2]

=

3, 5,

and8mM 61

28. LowresolutionNMRspectraof w-decane 70

29. LowresolutionNMRspectraof_{H20 containing}0.25mM

Mn+2

intheaqueous phase 70

30. LowresolutionNMRspectra of aRMsolution_{containing 0.25}mM

Mn+2

intheaqueous

phase and Rvalueof0.5 71

31. Signalobtainedfroma spin-echo pulse sequenceforanRMsolution_containing8mM

Ni+2 in

theaqueous phase with a<j)value of

0.6,

an aqueous8mMNi+2solutionanddecaneas a

functionof_{varying TE} 72

32. a)

1/T]

ins"1

as afunctionof<(>fortheRMsolution_containing

0.1, 0.25,

0.5 mM

Mn+2 inthe

aqueous phase,

b)

1/T2

ins"1

as afunctionof<j>fortheRMsolution_containing

0.1, 0.25,

0.5

mMMn+2intheaqueous phase 73

33. a)

1/Ti

ins"1

as afunctionof fortheRMsolutions_containing

3,

5,

8mMNi+2intheaqueous

phase,

b)

1/T2

ins"1

asafunctionof <|>fortheRMsolutions_containing

3, 5,

8mMNi+2in the

aqueous phase 74

34.

Ti

as afunctionof<}>andtemperatureforaRMsolution_containing

Mn+2

35.

T2

as afunctionof

$

andtemperatureforaRMsolution_containingMn+2intheaqueous phase

77

36.

T]

as afunctionof<j>andtemperature foraRMsolution_containing Ni+2

intheaqueous phase

78

37.

T2

as afunctionof<j>andtemperatureforaRMsolution_containingNi+2intheaqueous phase

79

38. Normalized

(a)

transmit,

and

(b)

receiveRFmagneticfields fromtheGElowpassquadrature

bodycoil. The fieldsweremeasuredina27cmdiametersphere_containing

(1)

aqueous6mM

Ni+2

with 154mM

NaCl, (2)

RMwitha<|>=_{0.6 (8mM}

Ni+2)

intheaqueous_phase,and

(3)

aqueous 14mMNi+2 83

39. Signal fromsolutionsofaqueous8 mM

Ni+2, decane,

andRMsolution with<|>=

0.6and8mM

Ni+

intheaqueous phase asafuncitonofoffset

frequency

ofthesaturationpulsefromthewater

resonanceinaGE Chemsatspin-echo sequence 86

40. Figure40. Molecularmotions as afunctionof

frequency

modelfortheH20componentofRM

List

of

Tables

number _page

1.

Ti

and

T2

valuesina 1.5Teslamagneticfield 15

2. CharacteristicsoftheRMComponents 32

3. Ionsperreverse micellein differentconcentrations 32

4. Amounts

H20, AOT,

andDecane Needed forPhiValuesin 25mlcontainers 36

5. Volumeanddiameterof_{the small, medium,}andlargephantoms 37

6. Phantom SolutionsandSizes 37

7. DeterminationofthedielectricconstantandRF_conductivity 4 1

8. Solutionsfor dielectricconstant and_{RF conductivity}measurements 41

9. Solutionsusedfor

Q

measurements 43

10.

Imaging

parametersforspectral_study 44

11. Solutions forecho modulationstudies 45

12.

Imaging

parametersforecho modulation studies 45

13.

Imaging

parametersfor

Ti

determination. 46

14.

Imaging

parametersfor

T2

calculation 46

15. _{Solutions for susceptibility}studies 50

16. PhantomsolutionsforTRmapping 52

17.

Imaging

parametersfor_{TR mapping study} 52

18. Solutions for fatsaturationstudies 53

19.

Imaging

parametersfor fatsaturation_study 53

20.

Imaging

parametersfor individualspectral

T

study 54

21.

T!

and

T2

values ofaqueoussolutions oftheparamagneticionMn+2 5 5

22.

T]

and

T2

comparison of

[Mn+2]

solutions andhumantissue 58

25. Dielectricconstant, resistivity,andconductivityvalues 66

26.

Quality

measurementsof several solutionsandhuman_anatomyinanRFcoil 68

27.

T]

and

T2

_stabilityafter sonication ortemperaturechanges 81

28.

Mean,

C

V,

andCI for

T,

and

T2

reproducibility 81

29. Coefficientof variationfor

B]T

and

B1R

fieldsinsidea27cmdiameterphantom 82

30. Spectral Ti's inms oftheH20anddecanecomponents oftheRMsolutionscontaining

Ni+2

87

ListofSymbolsandAbbreviations

AOT aerosolOT

B0

staticmagneticfield

B,

appliedmagneticfield

BlR

appliedreceive magneticfield

Bit

applied magnetictransmitfield

c speed oflightina vaccuum

CFA center

frequency

adjust

[A]

concentrationofspeciesA

cp centipoise

c,

average capacitance

CI 95%confidenceinterval

cv coefficientof variation

D

density

e _permittivity

FID free induction

decay

Y gyromagneticratioforHproton

G,

phase_encodinggradient

Gf

frequency

encodinggradient

Gs

slice selectiongradient

GE General Electric

HPLC highperformance_{liquid chromotography}

ID inside diameter

L

reflectedincidentlight

J joules

K dielectricconstant

k(l,2,3,4,5,67,8)

spin exchangeconstant

K degrees Kelvin

X wavelength

I cell constant

L inductance

Lp

probeinductance

H permeability

M

Molarity

expressedinmoles/liter

Mhz megahertz

Mn+2

manganese+2ion

MW molecular weight

MRI magnetic resonance

imaging

M^

magnetizationin_xyplane

Mz

magnetization vectorinzdirection

M^

initialmagnetization vectorinzdirection

V Larmor

frequency

V resonant

frequency

Vref standard

frequency

Av changeinthe

frequency

ofthebandwidth

TI indexof refraction

n viscosity

NMR nuclearmagneticresonance

^parallel numberof spins aligned paralleltomagneticfield

NS normalsaline solution

OD outsidediameter

?

volumefractionofH20+AOT/H20+AOT+decane <t> shorted cell phase

q charge of anion

Q

factor _{quality factor}

0

netdipolemomentinvolume

(v)

Qcoil

quality factor inan

imaging

coil V<loadcd quality factorofaloaded

imaging

coil NCsample quality factorofa sample

p resistivity

P polarization

R resistance

r distance betweentwocharges

(q)

RF radio

frequency

RG receive gain

RM reverse micelle

RPS revolutions per second

8 chemicalshift

5 skin-depth

slicethk slicethickness

SNR signal-to-noiseratio

T Tesla

T,

spin-lattice relaxationtime

T2

spin-spin relaxationtime

T2* _{inhomgeneousspin-spinrelaxation}time

TE timeof echo

TG transmitgain

TR timeof repetition

V volume

V velocity

o angular

frequency

Z impedanceof cell

1.0 Introduction

The

imaging

modalitycalled magnetic resonance

imaging

(MRI)

is basedontheprinciples of

nuclearmagnetic resonance

(NMR)

[Stark]. While NMR has been_widelyused

by

thechemistforthepast

fifty

years,MRIisa_relativelynewtechniqueinthefieldofmedicine. NMRwasfirst discovered

by

Bloch

andPurcell

independently

in 1940. In 1952.

they

receivedtheNobelprizeforthisdiscovery. Thiswork

was used

by

chemistsina_varietyofapplicationsuntil 1971.whenDamadian foundthatanNMR

parametercalledthespin-latticerelaxationtime,

T,

. was notthesamefor

healthy

anddiseasedtissue. In

1973. Lauterburappliedlinearmagneticfieldgradientstoobtain spaualinformation,whichallowed an

imageof an objecttobeproduced similartoimagesproduced

by

computerized

tomography

[Kean].

These developmentsmadethemedical_communityaware oftheimportanceofthis

imaging

techniquefor

thediagnosisofdisease inthehumanbody. MRIisaradiationless. nondestructive, and noninvasive

technique,whichhasgrowingapplicauonsinthediagnosisofdifferent diseasesinthehuman body.

SinceMRIis usedas adiagnostictooltoproduce_{high quality}anatomicalimagesofthehuman

body,theimager,ortheinstrumentwhich providestheimagesmustbemaintained_periodically Thisis

donetoensurethatthemagneticfieldsandgradients are_{operatingoptimally}togenerate accurateand

clearimages.

Imaging

phantoms,whichareanthroprogenic objects,areemployedas standardsforsystem

performancetesting.

Themost common phantomscurrentlyusedforsystem performance_testingcontain aqueous

solutions of paramagnetic salts. Thistypeof phantom solution produces a_standingwave artifact when

imaged. Thepresence ofthisartifact makes itdifficultto test the

homogeneity

ofthetransmitandreceive

radio

frequency

fieldsof an

imaging

coil. Thethrustofthisresearch wastodeterminethecause ofthe

standingwave artifact andto

develop

a phantom solution whichcontained propertiesthatwouldminimize

or eliminatethe_standingwave artifact.

As previouslymentioned,phantomsareanthroprogenic objects which are usedforsystem

[Tofts]. Thesolution shouldhavea_{high resistivity}to eliminatetheskin-effectartifact

[Bottomley],

and a

high viscositytoprevent convectioncurrentsfrom

forming

inthesolutioninsidethephantom. The

phantom solutionshouldhavespin-lattice relaxationtime_(T, )and spin-spin relaxationtime

(T2 )

values

whichcouldbevariedandarereproducible.

Varying

the

T,

and

T2

valuesofthesolutionwouldallow

ranges which are similartohumanussueor a range usefulforsystem performancetesting. The

T,

and

T2'softhesolution shouldbereproduciblefromone

imaging

siteto thenext regardless oftemperature

fluctuations.

Paststudiesof phantomsinvolve_usingacrylamide gels,hydrogels.agar,andaqueoussolutionsof

paramagnetic salts [DeLuca. Gore]. Eachofthese typesof phantom solutionshavedisadvantages. In

organicmaterials, indirectspin-coupling,or

J-coupling

produces echo modulation whichaffect the

intensity

ofthesignal in an_{image [Hinks]. The standing}waveartifact is present inthephantoms

containinganaqueous solution of paramagnetic salts[Tofts]. Other disadvantagesofthesesolutions are

theirlackofstability,

difficulty

inpreparation,andimpurities Thesesolutionsalsomay beconductive or

ahavelow resistivitywhichproduces a skin-effect artifact.

We haveattemptedtodesigna phantom solution which contains_manyoftheproperties of an

idealphantom solution.Thephantomsolutionthatwe proposeisa reverse micelle

(RM)

solution. The

RMsolutionisanexample of athreecomponent microemulsion. The H20component ofthesolutionis

surrounded

by

thesurfactantcomponent,whichissuspendedinthethirdcomponent,ahydrocarbon.

DeterminationoftheapplicabilityoftheRMsolutionforuse as anMR

imaging

phantom included

studyingthestabilityoftheRMsolution,it's dielectricconstant, resistivity, andviscosity. Further

characterization ofthebehavioroftheRMsolution included studies

determining

thediffusioncoefficients

oftheindividualcomponents,theoverall

T,

and

T2

values at varioustemperatures,andspecUal

T

values

oftheindividualcomponents.

Presented inthisthesisisthebackground

theory

for NMRandMRI.as wellasbackground

material abouttheRMsolution. The

following

sectiondescribethe experimentsthatwere performedto

determinethephysical, electrical. NMRandMRIpropertiesoftheRMsolution. Thephysical properties

properties oftheRMsolutionincludethedielectricconstant, resistivity, andconductivitymeasurements as

wellasthe_abilityofthesolutiontoloadthe

imaging

coil,whichiscalledthe

Q

factor. TheNMR

propertiesoftheRMsolutioninclude themagnetic_{susceptibility}ofthesolutionand spectra ofthe

components oftheRMsolution. AlsoincludedintheNMRsectionistheoverall

T

and

T2

studies and

howthe

Ti

and

T2

valuesareaffected

by

temperature.Thespectral

T

values oftheindividual components

oftheRMsolution concludetheNMRsection. The MRIpropertiesoftheRMsolution containthe

transmitand receivefieldmappingandthefat-saturation

imaging

sequencestudies. Theresults and

discussionsectionareorganizedina similar manner asthe experimentalsection. _{A summary}ofthe

2.0 Background

This backgroundsectioncontainsthe

theory

whichisessentialforunderstanding theresults of

thisthesis.Itcomprisessix main_topics;spinphysics, nuclear magnetic resonance

(NMR),

magnetic

resonance

imaging

(MRI),

the_{MRI phantom,}artifactsinMR

images,

andthereverse micelle

(RM)

solution. Spinphysics relatesNMRto theatomic

level,

whiletheMRIsectionappliesthe

theory

ofNMR

toproduce animageand explains

imaging

parametersforuseintheexperiments. TheMRIphantom

sectionexplainsthepurpose and constructionofaphantom,andtheproblemswhich can occur with

phantomsare explainedintheartifact portion.

Finally,

theRMsegment presents_{information concerning}

the RMsolutionaswell asreasonsitcouldbeuseful as anMRIphantomsolution.

2.1 Spin Physics

Innuclear magnetic_{resonance, the}signal originatesfromthespinsinthenucleus oftheatom

anditsinteractionwithamagneticfield. Froma rathersimplifiedview,theproton and neutron possess a

fundamental propertyof nature calledspin orintrinsicangularmomentum. Theoriginofthespinis

controversialand notwell understood

[Jaffe]

and willnotbediscussed inthis thesis. Itis difficultto

definewhat_exactlyspin

is;

_{therefore, it is}most oftendefinedintermsofthebehavioritexhibitsinan

externallyappliedfield [Schwartz]. Aclassical_{analogy found}in_manytextbookscomparesthespin

angularmomentumtoa_spinning

top

ina gravitationalforce field. Theangular momentum ofa_spinning

top

willnotchangeas

long

asthereisnotorque_actingonthesystem.The

top

continuestospin aboutits

verticalaxis. Onceatorqueorexternal

field,

suchas, gravity,isapplied,theangular momentumofthe

top

isnolongerconstant. Theangular momentum_continuallychangesinthedirectionofthe torque

[Kotiarchyk,

1995]. The spinning

top

nolongerspinsaboutitsaxis,butwillspinina cone-shaped path.

Thisphenomenaof

following

acone-shaped pathistermedprecession[Chakeres].

Inthenucleus,theprotons and neutrons pair_upor aligninthenuclear orbitalsinamanner

similartoelectronsinelectronic orbitals.Whenthespinsofindividualnucleons pair_upand_completely

cancel eachother,thereisno angularmomentum,orthenuclearspinisequaltozero. Whenthe nucleons

donot pairup, thenucleus contains anonzero net spin andthenucleuspossesses spin angular

tells themaximumamount of spinthatthenuclueus contains. Quantummechanically,thespin quantum

numberisa multiplen,of1/2. Then/2 net spinhasa magneticmoment associated withit. Themagnetic

dipolemoment causesthenucleusto_{behave similarly}toasmallbarmagnet with a north and south pole.

Themagneticdipolemomentisavector_{containing both}

direction,

whichisthesense of spin_usingthe

righthandrule andmagnitude,whichisthestrength ofthebarmagnet. Themagneticdipolemoment can

berepresented

by

avector_alongtheaxisof spin withthedipolemoment_pointingfromthesouthpoleto

thenorthpoleofthemagnet[Morgan]. Thenucleuspossesses_manypossible(n+

1)

_energystatesinan

externalmagneticfield. It isthis_propertywhichallowstheresonance phenomenato occur,andproduce

theNMRsignal.

'H

isthemostabundant and simplestisotope foundinthehuman body. Thenucleus consists of a

single protonanditsnetspinis 1/2.

'H

_{is widely}usedinMRIbecause itproducesthestrongestNMR

signal.

In nature, thespin vectorsofthe

'H

protons are_randomlyoriented. Oncethespinvectorsare

placedinastaticmagneticfield

(B0), they

will_{behave similarly}to the_spinning

top

inagravitational

field. Sincethe

'H

protonpossesses aspin of

1/2,

twospin vector orientations canbefound- _parallel and

antiparallelto thestaticexternalmagneticfield. Aparallel orientationoccurswhenthemagneticdipole

moment ofthespin vectors are alignedwiththestatic magneticfield. This isthelower_energy

configurationand most common. Theantiparallel_orientation,wherethemagneticdipolemoment ofthe

spin vectorsare aligned_opposingthestatic magnetic

field,

isa_{higher energy}configuration. _{In nature,}

thereare moreparallelorientedprotons,thus_creatinga net magneticmoment vector orMagnetization

(MJ.

Theratio ofthenumberspinsintheparallel orientation

(N^id)

to thenumberofspinsinthe

antiparallel orientation

(Nmtipiiniiei)

canberepresented

by

theBoltzmannequation:

Nantiparallel

/

Nparallei

=_e

(

1

)

zero,whichmeansall oftheprotons are aligned paralleltothestaticmagneticfield. Asthe temperature

increases,

the thermalmotions ofthemolecules causethe number ofprotonsinthehigherenergy

antiparallelstatetoincreaseuntil

they

are almostequalto thenumber of thoseinthe_{lower energy}state,

andthe ratio approachesunity.

The NMRsignalisproportionalto thedifference between

N^w

and Kmtipmiiei. Sinceatroom

temperaturethe ratioof N^p^ei/

N^iei

1and

Np^iw

-Knu^Li

0,

it isnecessary for NMR

spectroscopytobea_verysensitivetechnique[Dixon].

Thetransitionoftheprotonsinthe_{low energy}parallelstatetothehigher_energyantiparallel

staterequirestheabsorption of a photon ofenergy. The_energyof a photonmust_exactlymatchthe_energy

differencebetweenthe twostatesforthistransitiontooccur. Oncetheprotonisexcitedto thehigher

energy state, itwill returnto the_{lower energy}stateanddoesthis

by

_emittingaphotonof energy.

Theprotonsintheantiparallelstatewillemita photon_onlywhenanother photonisabsorbedand

stimulatestheprotontoemit aphoton. Soone photonof_{energy is}absorbed andtwophotonsare emitted

andtheprotonis leftinthe_{lower energy}state. NMR_{spectroscopy is dependent}onthreephenomena:

1)

theabsorptionof_energy,

2)

the_excitingof thelow_energyprotontoa_{higher energystate,}and

3)

the

return oftheprotontothelow_energystate.

2.2 NuclearMagneticResonance

Ona microscopic

level,

_placingtheprotonsina staticmagneticfieldcausesthespin vectors of

the

]H

protonstobegintoprecess,or spinaboutthezaxisina cone-shapedpath. The Larmor

frequency

(v),

orthe

frequency

atwhich

they

precess,is dependentuponthestrength of the staticmagnetic

field,

BG.

Itcanbewritten:

v=

yB0

(2)

where_y,thegyromagneticratio,istheratio ofthe magneticdipolemomenttoitsspin andisuniquefor

eachtypeof nucleus[Smith]. The Larmor

frequency

is important because itisthe

frequency

at whichthe

A groupofprotons_{experiencing exactly}thesame

B0

field iscalledaspinpacket. Spinpackets

canbeobserved_precessingabouttheapplied magneticfield.

Oncetheprotons are alignedinthestatic

B0 field,

a secondmagneticfield froman_alternatingor

oscillatingradio

frequency

(RF)

pulseisappliedperpendicularto the

B0

field.The

frequency

oftheRF

pulseisattheLarmororprecessional

frequency

ofthe

'H

protons,whichisapproximately 63 MHz ina

1.5 Tesla

B0

field. Attheatomiclevelthisfieldcausestransitionsbetweenthetwoenergystatestooccur

dueto thepresence of photonsattheresonancefrequency. Theprotonsinthelower

(higher)

_energystate

are excitedtothehigher

(lower)

_energystate. Thisphenomenonistermedresonanceand must occurfor

theNMRsignaltobe detected.

Themagnetizationvectorsfromtheindividualspin packets canberepresented_usingan_x,y,and

zcoordinate system. Thexyzcoordinatesystemisaperspectiveof themagnetization vectors called a

frameof reference. In

NMR

a_{rotating frame}ofreferenceisusedtodepictwhat occurstothenet

magnetizationonceit isperturbed

by

the

Bi

field. Inthe_rotatingframeofreference, thexand_yaxes are

rotatingaboutthez axis attheLarmor

frequency

[Stark]. Todifferentiatethe_rotatingframeof reference froma static or

laboratory

frameofreference, thexand_yaxis are primed. Figure1 illustrates howthe

spin vectors ofthe

'H

protonsina_rotatingframeofreference are alignedwiththe +z-axisina static

magneticfield. Figure2showstheapplication of asecondmagneticfield

(B])

fromaRFpulse atthe

Larmorfrequency.

By

conventionin

NMR

the

Bt

field isplaced_alongthe +x-axisinthe_{rotating frame}

Ma

*

B0

y

Figure 1. Netmagnetization

(Mro)

ofthespinvectorsina static magneticfieldina_rotating frameofreference. Thespin vectors are alignedwiththe +z-axisandinthesame directionasthe

B0

field.

AB0

Ma

Figure 2. ApplicationofRFpulseor

Bi

field_alongthe +x-axisinthe_{rotating frame}of

reference.

The appliedRFpulsecausesthe_processingnet spinstoalign_{away from}the

+z-axisas showninFigure 3. Therotation_{away from}the+z-axis dependsonthemagnitudeandduration

z

Mz

B0

^v

Figure 3. Perturbationofthe net spins_{away from} the+zaxis. Thespinswillbegintoprecess

ina cone-shaped path.

IftheRFpulseis leftonfor

long

enough,thenetspinsare rotated90down intothexy-plane.

Oncethis pulseisturned_off,theequilibrium configuration wantstobere-established. Theequilibrium

configurationhaszero_xymagnetization andisaligned withthe+zaxis.The NMRsignalisproduced

by

therelaxationof_{the xy}magnetizationtozero which inducesanelectriccurrentinareceiver coil.

Chemical shift, longitudinalorspin-latticerelaxationtime

(TO,

and_transverse,or spin-spin

relaxationtime

(T2)

arethreeNMRparametersuniquetoeachtypeof nucleus. Theseparametersare

discussed below.

Electrons orbitingaroundthenucleiofmoleculespossess a _moving negativecharge, therefore,a

magneticfield isproduced. Theenvironment oftheelectronsisnotthesameforeachtypeofmolecule

duetodifferentchemical_structures,thus theelectron-induced magnetic_{fields surrounding}theprotons

vary. Whena moleculeisplacedinan external

B0

field,

the magneticfieldfromtheelectronsopposesthe

B0

fieldandshieldstheprotonsfromthe

B0

field. Thiscausesthemagneticfieldatthenucleusto_vary

withtheresonant orLarmor frequency. Thesevariationsin

frequency

makeupthechemical shift

[Chakeres]. Thechemicalshift

($)

inpartsper million of a resonance

frequency,

canbe defined

by

the

following

equation:

=[(v-vref)/vrcf]

where vistheresonance

frequency

and vref isthestandard

frequency

[Morris]. Thechemicalshiftallows

identificationof a molecular compound since eachtypeof chemical proton produces anNMRpeakat a

specificfrequency.

Justastheelectron's magneticfieldaffectsthenucleus,themagneticfieldofanucleus with a

certainchemicalshift affectsanother

nucleus'

magneticfield if itschemical shiftis

different,

andifthe

twonucleihave lessthanthree_{bond lengths separating}them. Thetwonuclei willhavemorethanone

Larmor

frequency

where_energycanbe_{absorbed, thus,}theNMRspectrum will show_splittingofthe

peaks. Thedistance betweenthis_splittingofthepeaksistermed thespin-spin_splittingor

J-coupling

constant andit isa measurein Hzoftheinteraction betweentwonuclei.Asthenumber of nucleiless

thanthreebondlengths away

increases,

thereismore_splittingintheNMRspectralpeak.Morethanone

J-coupling

constant_{may be}presentwhenthisoccurs[Morris].

Anotherinherent NMRparameteristhelongitudinalrelaxation orspin-lattice relaxationtime

(Ti). Recallthat thespin vectorsare aligned_alongthe +zaxisinthe

B0

field. OnceanRFpulseis

applied,thespinvectors rotate_{away from}the+zaxis. Over

time,

thespin vectors will returnto

equilibriumandre-align withthe+z-axisinthe

B0

field. The time ittakesforthisrelaxationofthespin

vectorsfromthenonequilibriumstatebacktoequilibrium occursexponentially,andisthe

T]

time

constant. Themoleculesinthenonequilibriumstatewillgive offits energytoothermolecules andintothe

lattice(inthisthesis,thesolution)inorderfortherelaxationtooccur,

hence,

thetermspin-lattice

relaxation.

T]

'swill_varydueto the

fluctuating

magneticordipolefields fromneighboringmagnetic

nuclei. In

liquids,

the

fluctuating

magneticfield fromthe_neighboringmagneticnuclei, orthe

lattice,

is

Figure 4. Longitudinalrelaxationof spinvectorsbacktoequilibrium. Thespin vectorshave

beenrotated_{away from}the +zaxisand overtimewillre-alignthemselveswiththe

+z-axisat equilibrium.

Therelaxationbehaviorcanbeshown_{mathematically}withtheequation:

Mz=Mm(l-e-,/ri)

(4)

Putsimply,thelongitudinalrelaxationtimeisthetime ittakesthelongitudinalmagnetizationtoreturnto

equilibrium

by

afactorof "e" [Dixon].

Since

Tt

isthelongitudinalrelaxation

time,

T

"' canbedescribedastherelaxation rate. Itisthe

rate of changeofthelongitudinalrelaxationovertime. This isproportionalto thenumber of molecular

motions attheLarmorfrequency. Figure5depictsthemolecularmotions,

J(v),

of a_{nonviscous, slightly}

VISCOUS

J(v)

slightlyviscous

Figure 5. Themolecular motions ofeither_{nonviscous,slightlyviscous,} andviscousliquidat aparticular

frequency

is found

by

intersectionofthe

frequency

withthetypeofliquidand

drawing

a straightlineacrossto thenumber ofmolecular motions.

T

canbepredicted sincethereisan

inversely

proportional_relationshipto themolecular motions and

Ti

.

Another NMRparameteristhe transverseorspin-spinrelaxationtime(T2). Whena90RF

pulseisappliedalongthe+x-axis,thenetspins arerotated_awayfromthe+z-axisandintothexy-planeas

shownin Figure 6. Figure 6 illustrateswhatoccurs oncetheRFpulseisturnedoff. Thespinsbeginto

precessatdifferentratesduetoinherent inhomogeneities inthestatic

Bc

fieldandvariationsinlocal

magneticfieldscaused

by

molecularmotions. Thisproducesatransversemagnetization(Mxy). Thereare

manyspins_precessingatdifferentrateswhich will_eventuallycancel eachother. Thisisshownin Figure

8.Oncethe transversemagnetizationisnolongerpresent,or_{zero, the}spinsbegintorelax

longitudinally

backtoequilibrium_alongthe+z-axis. Thetime ittakesthespinstocancelthetransversemagnetization

*

B0

M

xy

X'

Figure 6. Themagnetization

(M^)

intothexy-plane after applicationof a90RFpulse_along

the+x-axis.

BQ

Figure 7. Thespin vectorsbegintoprecess atdifferentratesduetoinhomogeneitiesinthe

B0

fieldandvariationsinthelocalmagneticfields. Inthe_{rotating frame}of_reference,

theprecessionisshown withthespin vectors

travelling

ina counter-clockwise and

Figure8. Thespinvectorsare_processingatdifferentratesandovertimecancel each_other;

therefore,thetransversemagnetizationbecomeszero.

Mathematically,

thelossoftransversemagnetization caused

by

spininteractionscanberepresented

by

theequation:

Mxy

=Mxyoe-t/T2

(5)

Thespin-spin relaxationtimecan_{be described}asthetime toreducethetransversemagnetization

by

afactor

of"e" [Dixon]. The

T2

isalmost always shorterthan

T,

_causingtransversemagnetizationtodisappear

before longitudinalrelaxationcan occur.

T2

"'

isthetransverserelaxationrate andisproportionalto thenumberofmolecular motions at

andlessthantheLarmorfrequency.

Energy

isnottransferredinthisrelaxation_{process, only}alossof phase

oftheindividualspins occurs. Thelossofphasehappens dueto the themolecular motions_causing

fluctuating

magneticfields[Chakeres].

T2

fromthevariationsinthemagneticfieldsfrom molecular motions and

T2

fromthe

inhomogeneities inthe

B0

fieldcomprisethe

T2*,

ortheinhomogenous

T2

[Morris]. Thetransverse

magnetizationdecaysas afunctionof T2*

Some

Ti

and

T2

valuesforthehuman

body

arelistedbelow inTable 1. Thevalues ofthetissues

differbecausethe

density

and molecular motionsofthe

'H

protons_{vary from}tissuetotissue. The

T,

and

T2

Table 1.

T,

andT2 valuesina1.5 Teslamagneticfield [Fletcher].

Tissue

T, (ms)

T2 (ms)

Cerebralspinalfluid 800-2000

Whitematter 760-1080

Grey

matter 1090-2150

Meninges 500-2200

Muscle 950-1820

Adipose 200-750

110-2000

61-100 61-109 50-165

20-67 53-94

Anincreaseintemperaturecausesanincreaseinthemotion of_{molecules,consequently, the}

Ti

and

T2

valuesare changed.

Usually,

the

Ti

and

T2

willbecomeshorter.

Conversely,

adecrease intemperature

willdecreasethemolecularmotions,andgenerally, the

T]

and

T2

valuesarelonger.

Onemethodof_adjustingthe

T

and

T2

valuesisatechniquecalled paramagneticdoping.

Paramagneticsubstancescontain unpairedelectronswhichmakesthemmoresusceptibletomagnetization

[Stark]. Theunpairedelectronscausethelocalmagnetic_{field surrounding}theprotonstochangeand

dipole-dipoleinteractionsare enhanced[Lufkin]. The

Ti

relaxationtimeof waterinanaqueoussolution of

paramagneticions isshortenedbecausethereisanincreaseinthestrength ofthe_alternatingmagneticfield

oftheparamagnetic

ion,

_therefore,more spins willbeexcited andbeginto_{resonate, producing}anincrease

inthenumberof molecular motions.

T2

relaxationisshorteneddueto theincreased

inhomogeneity

ofthe

magneticfield causingtransversemagnetizationtorelaxat afasterrate[Chakeres]. Someexamples of

paramagneticionsare

Ni+2, Mn+2,

and Cu+2

In

NMR,

thesignalisobtainedfromthe T2*_decay.

An oscillatingcurverepresentsthesignal

fromthetransversemagnetizationafter application of anRFpulse attheLarmorfrequency. OncetheRF

pulseis

discontinued,

theT2* decaystozero. Thisexponentially

decaying

oscillatingwaveiscalledafree

Mx

M/VwW

Figure 9. An_{exponentially}

decaying

oscillating

_waveover_{time along}adirection inthexy-plane. The

decaying

oscillatingwaveiscalled anFID.

TheFTDisconvertedfromthetimedomainto the

frequency

domain

by

a mathematicaltechnique

calledFourier transform. Thistechniqueallows absorptions associatedwith anNMRspectral peaktobe

seenas afunctionofthefrequency. TheamplitudeoftheFIDdeterminestheamplitudeofthespectral

peaks.

Aspin-echo pulse sequenceisone methodof_obtainingsignalfroma sampleinNMR A90 RF

pulseisapplied_alongthe +x-axis_causingthespinstoprecessinthexy-plane asshownin Figure9.

A

B0

Figure 10. Thespin vectorsbegintoprecessinthe_xyplane after a90pulseisappliedinthe

+x-axisina spin-echo pulse sequence.

A180

pulseisnowappliedalongthe+x-axis,thespins areflipped180

aboutthe +x-axis

(along

A

B0

^

Fiarre 11. Inthespin-echo pulsesequence, thespins areflipped180

by

theapplication ofa secondpulse- _a 180

pulse_alongthe+x-axis. Nowthe spinswillconvergeor

refocus.

B0

Fisire 12. Thespinsarc refocusedandwillbegintoprecess atdifferentrates until

M^y

is

equaltozera

90

RF ,180RF

90 RF

Figure13

Timing

diagram forspm-echo pulse sequence

illustrating

theapplicationof a90RF

pulsefollowed

by

a18>

RFpulse andtheFIDand echo signalswhichare generated

by

these RFpulses. TheTEaidTRare adjustable experimental parameters.

The FID fromthe90

RFpulseisshown as wellasthe echoor signalfromthe 180RFpulse.

The repeatingofthepulsesequencefromthe90RFpulseto thenext90RFpulseiscalledtherepetition

time(TR). The time fromthe90RFpulseto themaximum amplitudeoftheechoiscalled thetimeofthe

echo(TE). These timescanbevaried,

depending

ontheNMRexperiment.

Oncethesignalisobtainedfromthe_sample,the

T

and

T2

canbecalculated. The

following

signal

equationfroma spin-echo pulse sequence calculatesthesevalues:

5=

(l-e-ra/ri)(e-TErt2)

(6)

Algorithmsthenfindthebestfitofthesignalequationto thedataand producea

Ti

and

T2

value

[Gong,

Li].

2.3 Magnetic Resonance

Imaging

Magneticresonance

imaging

applies magneticfieldgradients andtheprinciplesof NMRtocreate

animageoftheNMRsignal.

Consequently,

theMRIhardware ismoreelaboratethantheNMRhardware.

MRI hardware includesasuper-conducting magnet,gradientcoils, RFtransmitandreceive_coils,computer

hardware,

imageand_arrayprocessors,andRFandmagneticfieldshields.

The super-conductingmasnetiscomposedof niobium-titanium_alloyandisenclosedinacopper

matrix. Themagnetproducesthenatic external

B0

field.Anadvantage ofthistypeofmagnetis higher

spatialinformationof an imagetobeobtained whilethe RF transmitandreceive coilsdetectthesignaland

allowthecomputer and processorstoproductxhe

image

asweseeiL A

lining

ofaluminumor copper mesh

aroundthemagnetroomprotectstheimagerromoutsideRFelectromagneticinterference. Anironshield

surroundingtheMRIcarerprotects theimayr from distortioncaused

by

ferromagneticmaterials outside

themagnetroom[Morgan].

The abilityoftheMRimagertolocaeandseparate signalsfrom different tissues differentiates

MRIfromonedimensionalNMRspectroscop-. As_{previouslymentioned,}thegradient coils usedin MRI

encodespatialinformatienaboutasampleinnthe signal. Themagneticfieldofthegradientisvaried

linearly

alongeitheran x__y,or zdirection. _{Fir example,}anRFpulseexcites theprotons in a certain

imagingvolume. AsingeFIDisgeneratedhxalltheprotonsbecause

they

experiencethe same magnetic

fieldand are_processinga:the samefrequence Oncea gradientisappliedinthexdirection,themagnetic

fieldtheprotons experienceisvariedduetobarlocationsandthestrength ofthefieldatthatparticular

location. The

frequency

aprecession oftherrotonsisnotthesame andFTDsaregeneratedforeach of

thesefrequencies [Stark). Therearethreefieir.gradients_{sliceselection,phaseencoding,and}

frequency

encoding.

Thesliceselectiongradient

(G,)

isappliedperpendicularlyto thechosen_slice,where rotation

oftheselectedspinsintoohe y-axis and precssioninthexy-planetakesplace. Thisgradientdetermines

thelocationandthicknessoftheslice. Bothnelocationoftheslice andthicknesscanbeadjusted

by

changingthewidthand

frequency

oftheRFpuseor slope ofthegradient,

G,

[Stark]

.

Phase_encodingofthespinpackets ccurswhenthephase_encodinggradient

(G-)

isturnedon

perpendicularlyto

G,

. Applicationof

G$

alon*x causes spinsatcertain

locations,

x, torotateat a

frequency

dependentontie static

B0

fieldatikx

location,

and

G^

fieldstrength. Thespin packetsatthe

differentxlocationswilllaveaparticularphaeanglealongthey-axisand arenowphase encoded.

Thethirdor

frecpency

_encodinggrarient

(Gf)

isapplied_orthogonallyto

G$

andG,.. Application

strength,y

location,

and

Gf

fieldstrength. Thesespins are

frequency

encoded. Theapplicationofthe

G^and

Gf

gradients

help

determinetheresolution of theimage [Stark].

Imaging

coilstransmittheRFpulsesintoand receive signalsfromthesample

being

imaged.

Twocommoncoils of theimageraretheheadand

body

coil. The

body

coilisthelargestofthecoils and

is built intotheboreofthemagnet. IttransmitstheRFpulses andwillreceivetheRFsignalfromthe

sample. Becausethis coilisso

large,

itcauses a poor signal-to-noise ratio

(SNR)

inanimageof asmall

object. The headcoilisa smallertransmitandreceive coil. The SNR is improvedwiththis typeof coil

duetothecloser_proximityofthesmallsample(or anatomy)

being

imaged. Figure 14isa schematic ofa

sideviewoftheheadcoil.

4-B,

B0

1T

Figure14. Birdcage headcoilsideview. The

\\

arecapacitorsplaced onthecoil. A

sample orthehumanheadisplacedinsidetheheadcoilinthedirectionofthe

B0

field.

Therearethreestandard

imaging

planes which are obtainedfromanMRimager. Thesearethe

axial, coronal,and sagittalplaneswith respecttoa

body lying

inthemagnet.Theplaneischosen

depending

on which view ofthesample oranatomyisdesired. Figure 15 illustratestheseplanesthrough a

Axialplane

Coronalplane

Sagittalplane

Figure15. Theaxialplane

(

)

isthe cross-sectionofthissample

bottle,

thecoronal plane

(

)

slicesthe

top

fromthebottomofthesample

bottle,

andthesagittal plane

(---)

slicesthesamplebottle from righttoleft.

2.3.1 Other

imaging

parameters

Thereare several

imaging

parameterswhichcanbeadjustedtoobtainthedesired image

containingtheoptimumcontrast and resolution. Inan

image,

thesignaloriginatesfroma voxel or

volume elementofa sample. Itis defined

by

its locationwithinthemagnet andits dimensions. Voxels

aremostlyrectangularinshape. Eachvoxelcorrespondstoa_pixel,orpictureelement,andthesmallest

partofadigitalimage display. A highersignalfromavoxelcausesthe

intensity

ofthepixeltobe

brighter intheimage. The pixeldatapoints,composingeachsideofthe

image,

arethen placedin

columns androws,oramatrix. Thesizeofthematrixis

typically

128x

256,

192x

256,

or256x256.

The detailsoftheimageareenhancedwhenthereisahighernumber ofpixelsorlargermatrix

MRI isatomographic

imaging

technique. Itcreatestwo dimensionalimagesofthehydrogen

NMRsignalinsidea slicethrough theobject with athickness(thk). Theslicethicknessis dependenton

thegradient strength and

frequency

oftheRFpulse. Theslicethicknesscan_varyfromsubmillimeterto

centimeters, thereforethenumberof_protons,which producesignal,will_varyfromslicethicknesstoslice

thickness.

Usually,

thethinner the slicethicknessthegreaterthe resolutionandimage detail. While

thicker slicesimprovethe

SNR,

_{they decrease}thespatial resolution.

The fieldof view

(FOV)

isthesizeincentimeters oftheareatobe imaged. Thesizeof the

FOV is determined

by

thesize oftheobjecttobe imagedand mustbeaslargeasorlargerthantheimaged

object[Smith]. Thesize ofthevoxelis determined

by

theFOVand slicethickness.

Increasing

theslice

thicknesswhile

keeping

the FOV constant,willincreasethesize ofthevoxel. Thisprocedurecanbe

followedtoimproveSNR levels.

Other

imaging

parameterscanbevaried toproduce greater signalinthe

images,

or optimal

spectralinformation. Thesearethetransmittergain

(TG),

flip

angle, receive gain

(RG), TR

andTE.

The TG determinestheamplitude ofthedelivered RFpulse(Bi). Thisparameter canbevariedtoobtain

an optimal value or90RFpulse. The

flip

angle,oramountof rotation oftheRFpulseintothe xy-plane,

iscontrolled

by

theTG. TheTG is increased_uptoa certainpoint,whichincreasesthe

flip

angle,and

allowsthespinstoberotated90andintothexy-plane.Thisproducesabettersignal intheimage.lithe

TG isincreasedtoomuch,thespinsare rotated past90andlesssignalisproduced.Thecontrastof an

imagecanbealtered

by

_adjustingtheTRandTEvalues. Most often,alonger TEand shorterTRaffords

thebestcontrastinanimage.

2.3.2

Imaging

techniques

Eachtissuehasaunique

T1( T2,

and proton

density

whichproducesthesignalintensities.

Consequently,

theseuniquevalues canbeusedtodifferentiatetissuetypes.Twotypesof_signal,fromthe

differentchemicalshiftsoffatandwater,arepresentinthehumanbody. Sometimes it isusefulto

certaintissuesis increased. For example,thewatersignalintnmorslocated in

fatty

tissue,

canbe

enhanced,allowingthetumortobe more_readily

diagnosed

[GEManual-chemsatsequence].

WhenanRFpulseis_{applied, thefetprotons precess slowerthanthewaterprotons,}

resulting ina

220 Hzseparationbetweentheirspectral jeaks. Thisseparationof

frequency

permitsthesuppression of

thewaterorfatpeaktooccur. The GEctemsattechniquepresaturatesthefatsignal witha

frequency

selectivepulse,priorto thenormal90RFpulseina spin-echo pulsesequence. Thespinsoftheprotons

ofthefatare rotatedintothexy-plane_carsng

Mz

tobeequalto0. Spin-spinrelaxationoccurs_causing

Mx

=

My

=_0forthefat

[H.

Next,

the901RFpulsefromthespin-echo pulsesequenceisapplied.

Assuming

the

T,

offatismuchlargerthaithetimebetweenthesaturation pulse andthe90pulse,only

thespins of thewater arerotatedintothe w-planebecause

M^

of fatshould still equal zero. _{Now only}

thewaterspins areflipped

by

the180

puseandrefocused. Anechoor signalfromthewaterprotonsis

thus recorded. Ifthe

T

ofthefatprotonsisshort, thespinshaverelaxedbacktoequilibrium_alongthe

z-axis. Thespinscannowbeexcited

by

the90RFpulseofthespin echopulse sequence,and somefat

signalcanbeproduced. Thefatsignalisidlongersuppressedcompletely, andthecontrastbetweenthe

waterandfattissueisnot as great. ThisEchnique canbeappliedtowateras

long

asthepresaturation

pulseisthesame precessional

frequency

cfthewater protons andthe

Ti

of waterislongerthanthetime

betweenthesaturation and90pulse.

Magnetizationtransferormagnetization exchangebetween differenttypesofprotons, such asthe

protonsinonecomponent

(A)

andthosenanother component

(B)

of a_solution,affecttheoverall

Ti

ofa

system. Theexchange_pathwaycan occur

by

chemical exchangeorthroughspacedipolarinteractions

[Balaban]. Theantiparallel protonsof orecomponent givesoff a photonattheLarmorfrequency. This

photon_mayexcite a proton of anothercomponentattheLarmor

frequency,

_{changing it from}theparallel

toantiparallelstate.

Therefore,

an_energyexchangebetweenthetwocomponentsoccurs. The_probability

oftheemitted photon_excitingaprotonof mother componentisproportionaltothe squareofthedistance

Candtheexchange ratek betweenthe components. Theoverall

Tj

canbeeither monoexponentialor

multiexponential

depending

onthemagnitude oftheexchangeratesk. Theoverall

T,

of the three

componentsystemcanberepresented

by

a spinbathmodel,Figure 16.

A* B*

Lattice

ks

Figure 16. Threecomponent

(AB,C)

spin-bathmodel. The*_denotes

spinsintheexcited

state. Eachcomponenthas itsownspin-latticerelaxation rate(1/

Ti)

_process,

whichcorrespondsto the

k1(

k2

,and

k3

valueand opensintothelattice. The

exchange rates

kt

and

k5

arethe _energypathwaysbetweentheA*andB*

components. Theexchange rate

k;

and

k7

arethe_energypathwaysbetween

componentsB*andC* No energypathwayis foundbetweencomponentsA*andC*

If the kvalues are

large,

theoverall

Ti

willbemonoexponential. If kvaluesaresmall, the

overall

Tt

willbemultiexponential,thusdependentonthe

Ti

oftheindividualcomponents. Todetermine

whethertheoverall

T,

ismonoexponential ormultiexponential, amagnetization-transferpulse sequence

canbeutilized. Thispulse sequence appliesthecenter

frequency

adjust

(CFA)

variable control ofthe

prescan_mode,where_onlytheslice selection and phase_encodinggradients areturnedon.

T,

datafrom

thesignal ofthespectrum of each componentiscollected

by

_adjustingtheTEvalues. Thisispossible as

Determinationofthekvalues canbe foundthrough the

following

equations and

by

_plottinga curve of

bestfitto thedata.

Initially,

thereare spinsintheexcited state

(A*,

B*, C*)

thatgiveofftheir_energyand relaxback

to theground state

(A,

B,

C). Thiscanbeexpressedinthe

following

manner:

A*

> A+_energy

(7)

B*

>B+_energy

(8)

C* _>C+

energy

(9)

Sincethere arethreecomponents_makingupthesolution,the

following

_energyexchangebetween

components willoccur:

A*₊

B >A+B*

(10)

B*_{+A >B+}A*

(11)

B*₊

C

>B

+C*

(12)

B+C* >B*_+C

(13)

Assuming

firstorderreactionsofequations7through

9,

thechangeintheconcentration oftheexcited

spinsovertimecanbeexpressedas:

dA*/dt=

-k,

[A*]

(14)

dB*/dt=

-k2

[B*]

(15)

dC*/dt=

-k3

[C*]

(16)

where

ki, k2

,k3 , respectively,arefirstorder rate constantsforthespin-latticerelaxationprocessesofthe

individualcomponents. Therates are negative since theconcentration oftheexcitedspinsis

decreasing

inconcentration.

Energy

isexchangedbetweenthecomponentsasdepicted inequations10through 13. Nowthe

reactionbecomesdependentontheconcentration of anotherinthesystemandthereactionissecond

dB*/dt=

-k6[B*][C]

(19)

dC*/dt

=

-k7[C*][B]

(20)

wherethekvalues arethe_{exchange rate constantsbetweencomponents. Iftheconcentration of}

unexcited spins_{is very large}andthereforeremains_constant,theabove equationscanbemodifiedtoformpseudo

firstorder rate equations. Nowtheexchange rateconstantsincludetheconcentrationoftheunexcitied

spins aswell astheexchange ratetoformnewexchangerateconstants. Thereactions canbeexpressed

as:

dA*/dt=

-kg[A*]

(21)

dB* /dt=

-k9

[B*]

(22)

dB*/dt=

-k10[B*]

(23)

dC*/dt=

-k[C*]

(24)

Combining

allthetermstoformcoupleddifferentialequations,theexchange rate constantscan befound. This isexpressedinthe

following

equations:

dA*/dt=

-k1[A*]-ks[A*] +

k9[B*]

(25)

dB* /dt=

-k2 [B*]

-k9

[B*]

-k,0 [B*]

+

kg

[A*]

+

k [C*]

(26)

dC*_{/ dt}=

-k3 [C*]

-k

[C*]

+

k,0

[B*]

(27)

2.4MRIPhantom

Phantomsare_nonlivingobjectswhichhavea_varietyof usesin MRI.

They

are usedfor

evaluatingsystem performance ofthe

imager,

thedevelopmentof pulsesequences,

testing

ofthe_reliability of

T]

and

T2

measurements,and astestobjectsfor tissues

[Kraft,

Gore]. Thephantoms are constructedof differentsizesand shapes

depending

ontheiruse. Thesolutionsinsidethephantomshavebeenmade of

aqueous solutionsof paramagnetic_salts, polyacrylamidegels,agarosegels, gelatin, oils, or other

tissue-mimicking organicsolutions

[DeLuca,

Mitchell]. Themostcommon phantomforsystemperformance

testing

isaspherical phantomcomposedof anaqueoussolution_containg14mM_{NiCl2. The availability}

penetration effect artifact produced

by

theincreased ionicstrength of thesolution. Asa resultthe

transmitand receiveRFmagneticfields

B,R

and

BiT

of an

imaging

coil, andthe

homogeneity

ofthemain

B0

fieldcan not_{be accurately}measured.

2.5 Artifactsin MR images

Artifactsaredistortionsinanimagecaused

by

inhomogeneities

inthestatic

B0

field.

nonuniformities of applied

Bi

field,

variationsinthe_sensitivityof_{the RF coils,}a FOVthatissmaller

than theobject

being

imaged,

and motion oftheobject. Theseartifacts_maycause adecreaseinthe

resolution andcontrastinanimageoradistorted image. Correctionofthewrap-around artifactfromtoo

smalla

FOV,

canbemade

by increasing

theFOVontheimager. The motion artifactiseliminated when

theimagedobjectisheldinplace andnot allowedtomove.Theothertypesofartifactare more

challenginganddifficulttocorrect, since

they

canbecaused

by

inherentproperties oftheimagerandRF

coils.

Therefore,

theuse of a uniform phantomsolutionissignificant_{in understanding}andforcorrecting

theseartifacts.

A_{dielectric standing}waveartifactisproducedinphantoms_containingaqueous solutions of

paramagneticsaltsduetothesolution'shigh dielectricconstant.The dielectricconstant oftheaqueous

solution canberelatedto theindexof refraction of asubstance

(r\{)

throughaseries of calculations. The

indexof refractionis definedinthe

following

equation:

r,i=

c/v;

(28)

where cisthe_velocityoflight inavacuumand_v;,isthe_velocityoflightinamedium/.

Thevelocityof radiation canbe definedas :

c=

vYXXvac

(29)

whereVvacisthe

frequency

ina vacuum andXisthewavelengthina vacuum, and

v,=

v^

(30)

where vis

frequency

inamediumand

X,

isthewavelengthinamedium, Eqn

28,

now becomes:

r|i=

Xi=\/T]i

(32)

The indexof refraction can alsoberelatedtothe_permeabilityandpermittivityofasolution

through thisequation:

Tl.-CHirS*)-"2

(33)

whereuistherelative_permeabilityof a medium

(m

/u),whichis 1 inmostsubstances,exceptmetals,

andet,istherelative_permittivityof a mediumfa/e0)

[

Moore]. Therelative_permittivityisalso called

thedielectricconstantk([Gettys]:

e,=_enK

(34)

For_manynonmetallic_materials,suchasthoseusedinthis

thesis,

u^= _1.

Combining

equations

28.30,

33,

and34yields

h

= c

(k)

-m

Iv

(35)

WhenanRFwavetriestoenter orleavea_phantom,afractionofits

intensity

islost. If

Io

isthe

incident

intensity

and

Ir

thereflection

intensity,

thefractionreflected,

Ir

/

10

, is

Ir/Io

=

(Tu-Tl2)2/

(T,,

+T12)2

(36)

where_tjiandt|2,aretheindexof refractionoftwomediums[Skoog]. Sincethedielectricconstantofthe

aqueoussalt solutioninsidethephantomis

80,

theindex of refractionis9. The indexof refraction of

airis

1,

_makingtheamountofreflectedwaves 64%.

Theelectromagnetic wave

traveling

inthedirectionofthe

Bt

fieldwillchangeafterreflection. It

reflects180outof phase andinthe oppositedirection. Asthewave_{reflects, both}constructive and

destructive interferenceoccurs. Whentheobjecttobe imagedisthesamediameteras one-half of this

wavelength,a_standingwave results.

Thewavelengthinairat63

MHz,

the_operating

frequency

ofthe 1.5T imageris4.7_m,and

whenthispassesintotheaqueoussolutionphantom,thewavelengthisreducedto0.52 m. The27cm

diametersphere ofthe phantom,usedinsystemperformancetesting, isapproximatelyone-half this

wavelength. Themaximumamplitude ofthe

Bt

fieldcaused

by

constructiveinterference willbe XIAfrom

intensity

isgreaterinthat region. Destructive

interference

occurs_alongtheouteredges ofthephantom

resulting inunderflipped spinswitha subsequentdecrease inthesignalintensity.

Consequently,

the

imageofthespherewillappeartohaveabrighter

intensity

inthecenterthanatitsouter edges. This

phenonmenisthe_standingwaveartifact. Theuse of_oils, such_as,vegetableoil,have beenproposedas

alternativetypesofphantom solutionstominimizethe_standingwave artifact

[Tofts,

1993]. Theoilshave

alower dielectricconstantthanwater whichresultsinalongerwavelengththan theaqueoussolutions,

and_{thus, does}notforma_standingwaveinsidethephantom. Theconstructiveanddestructive

interferencefromreflectedwavesinsidethephantomdonot cause a maximum and minimuminthewave

andlargevariationsinthesignal

intensity

oftheimageare not seen.Disadvantagesofoils arethat

they

contain

impurities,

anddonothaveproperties similartohumantissue.

Ina similiar_{manner, the}size ofthephantom canbe

decreased,

whichwill minimizethe

standingwaveartifact.Nowtheconstructiveanddestructive interferencewill notcauseamaxiumumin

thewavewhentheshortenedwavelengthisreflected. The disadvantageof

decreasing

thesize of the

phantomisthatitalsoreducesthedesired large

imaging

volume.

Therefore,

reducingthesize ofthe

phantomand_using oilsforphantom_solutions, produce a phantomthatisless beneficial forsystem

performancetesting.

Ideally,

thephantom solutionshouldloadan

imaging

coil_similarlyto thehumanbody. Inorder

foraphantom_containingan aqueous solution ofparamagneticionstoperforminthesame manner asthe

human

body,

NaClisaddedtoincreasetheionicstrength ofthesolution[Hornak,Smith]. An

imaginary

componentisaddedto thedielectricconstantastheionicstrengthis

increased,

and anRFpenetration or

skin-deptheffectisproduced. Thisskin-deptheffectmaypreventtheRFtransmitterfieldfrom

penetrating theobject.The

flip

angle ofthe

B]

magneticfield is lessthan90

atthecenter ofthe

phantom,causingadecrease intransversemagnetization,therefore, thesignaldetectedfromthecenteris

less. The phantomimagewill appearbrighterattheedges ofthesphere thaninthecenter.Thisiscalled

Convectioncurrents caused

by

thermalgradientsdueto the depositionofRFenergy inaliquid

maycreate an artifact. Theartifactisproducedinthe

following

manner. Asolution_maycontaintwo

regions,forexample,an upperand alower. Asthetemperatureofthe lowerregion ofthesolution

increases,

the _viscosityof thelowerregionis decreased. Oncethe temperaturebetweentheregions

reaches acritical

difference,

theRayleighnumber,the_{lower viscosity}layerpushes upward whilethe

upperlayerwiththeincreased_viscosityflowsto thebottom. Aconvection current emerges. Thispattern

becomes oscillatoryand

finally

_{completely disordered. The}artifactismanifested

by

circulatorypatterns

intheimageofthesolution[Gibbs]. Asthe_viscosityofa solution

increases,

the temperatureneededto

producetheconvectioncurrentswillrise.

Therefore,

whenthe temperatureofthe_energyreleasedis held

constant, theseconvection currents will not appearinasolution with ahigherviscosity.

Totestfor inhomogeneitiesofthe

Bi

transmitand receivefieldsofan

imaging

_coil, these

artifactsmustbeminimal or notpresentinatestphantom. Ifthephantomsolutionitselfcausesartifacts

to occur, itwouldbe difficulttodistinguishtheorigin ofthevariations oftheimage

intensity

fromthe

imaging

coilorthephantom.Insomecases, thismay leavethe

imaging

systematlessthanitsoptimal

operatingperformance.

2.6 Thereversemicellesolution

Areversemicellesolutionoffers_manyadvantages whencomparedtoanaqueoussolution of

paramagneticions foruseinanMRIphantom. Itsphysical properties willbe discussedinthe

following

paragraphs.

Thereverse micelle

(RM)

solutionisan example of awater-in-oilmicroemulsion.

Separating

the

waterfromtheoilisasurfactant which containsahydrophillicandhydrophobicend. Thehydrophillic

polarheadis incontactwiththe water,andsurroundsthewaterina singlelayertoforma water

droplet,

or water pool. The hydrophobicend,a

long

carbon_chain,extends_awayfromthepolarheadandintothe

hydrocarbonoroil. Thesethreecomponents canalsoformanotherphase calledthelamellarphase. In

thisphase,thethreecomponentsareseparatedintosheetsorlayers. Asandwichofthewater

layer,

a

layerofthepolarheadsofthesurfactantant, thehydrophobictailsofthesurfactant,andthen the

decane,

Thephase changeofthe RM to the

lamellar

phaseis duetoanincrease intheattractive

interparticle

interactions

whentheRMconcentrationis

increased

as<)>increasesand

by increasing

the

temperature. Theseattractive

interparticle interactions

cause a phase changefromahomogeneousdroplet

phase,that

is,

theRM phase,toa phase_containingtheRMandlamellarphase,orthecoexistence phase

[Vollmer]. Thecoexistence phase willformthelamellarphase athighertemperatures.

TheparticularRMsolution usedinthis_studyconsistedof_{water, the}hydrocarbon

decane,

and

thesurfactant

bis(2-ethylhexyl)

sulfosuccinate sodium_salt,or aerosoloctyl(AOT). TheAOThasthe

following

chemical composition:

CH2CH3

I

Na+

03S-CH-COO-CH2CHCH2CH2CH2CH3

CH2-COO-CH2CHCH2CH2CH2CH3

CH2CH3

TheNa+_{readily dissolves into}thewaterinsidetheRMwhilethe

S03

_groupcomprisesthepolarhead.

Theradius oftheRMcanbeadjusted

by

_changingthemolarratioofwater-to-_{AOT. Inthis}

study,themolarratioofH20/AOT was heldconstantat

40.8,

orthemass ratioof waterto AOTwas

constant at0.6inallofthesolutions. This fixedmolar_{(or mass)}ratio produced anRMwithamean

radiusof50

A

[Kotlarchyk,1992]. Thephi

(<|>)

_value,orratioofthevolume ofAOTandwaterto the total

volume of

AOT,

water,and

decane,

canbeadjustedtoproduce_varyingconcentrationsofRMs per

volumeina solution.

Therefore,

theamountofdecane present

decreases,

_causingtheconcentration of

RMs toincreaseasthe valueincreases.

Insidethereversemicelle,some ofthese

Na+

ions dissociateintothewater

forming

cationsinside

thewaterpool,

leaving

thepolarheadoftheAOT_negativelycharged.

Strong

hydrogen bonds form

between thepolarheadsoftheAOTandthehydrogenofthewaterinsidetheRM P'Aprano].

Consequently,

thereisalayerof structured or

"bound"

waterof_{approximately 5}

A

thick_alongtheoutside

2.4

A

oftheend ofthetail extendsintothe

hydrocarbon

[Kotlarchyk,

1985]. Thetotalvolumeof a single

RM_{is approximately 5.2x10}'22 ml.

Themolecular_weights,

density

(D),

numberofHatoms ofthe RMofthe threecomponents are

listed in Table 2. Thenumberof

Ni+2, Mn+2,

andNa+inanRMforeach concentrationisrepresentedin

Table 3.

Table 2.

Characteristics

oftheRM

Components

Component M.W.

(g/mol)

D

(g/cm3)

No.ofHatoms

AOT Decane H20 444.57 142.29 18.02 1.2060 0.7300 0.9970 37 22 2

Table 3. Ionsperreverse micelleindifferentconcentrationsoftheaqueous phase

Ion Concentration

(mM)

AveragenumberofionsperRM

Ni+2 8 Ni+2 5 Ni+2 3 Mn+2 0.5 Mn+2 0.25 Mn+2 0.10 Na+ 1340 2.51 1.58 0.95 0.16 0.08 0.03 405

Theconcentration ofNa+fromtheAOTinsideeachreverse micelleis1.34

M,

anddependent

onlyontheconcentration oftheAOT.

Therefore,

405Na+are containedinsideeach oftheRM.

regardless oftheconcentration oftheparamagneticion. Theparamagneticionsarelocatedintheaqueous

phaseofthe RManddonotaffectthesizeand shape oftheRM.

Figure 17displaysacross-sectiondiagramoftheRM_containingwater withaparamagnetic

ion,

AOTanddecane. The hydrophilicpolarheadsoftheAOTencapsulatethewaterwhilethehydrophobic

tailsoftheAOTextendoutintothehydrocarbondecane. Thestructure ofthelatticeofRMs ina solution

correspondstoafaceorbody-centeredcubicfKotlarchyk, 1984]. Figure 18showstheRMs ina solution.