A bifurcated study of spin-lattice relaxation information in nuclear magnetic resonance imaging

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A bifurcated study of spin-lattice relaxation information in nuclear magnetic resonance imaging quantitative analysis with conventional techniques and the unconventional stimulated echo imaging technique
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Spin-lattice relaxation   ( lcsh )
Magnetic resonance imaging   ( lcsh )
Nuclear magnetic resonance spectroscopy   ( lcsh )
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Nuclear Engineering Sciences thesis Ph. D
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Thesis (Ph. D.)--University of Florida, 1985.
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Bibliography: leaves 151-154.
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by William Sattin.
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Typescript.
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A BIFURCATED STUDY OF SPIN-LATTICE RELAXATION INFORMATION
IN NUCLEAR MAGNETIC RESONANCE IMAGING:
QUANTITATIVE ANALYSIS WITH CONVENTIONAL TECHNIQUES AND THE
UNCONVENTIONAL STIMULATED ECHO IMAGING TECHNIQUE








BU

WILLIAM SATTIN






















A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN
PARTIAL FULFILLMENT OF THE REQUIREMENTS
FOR THE DEGREE OF DOCTOR OF PHILOSOPHY



UNIVERSITY OF FLORIDA


1985








































Copyright 1985

bU
William Sattin




























For WendU and Emily, my life


















ACKNOWLEDGMENTS


There are manU people to whom I am indebted for their

assistance in accomplishing this work. Let me begin with my

high school physics instructor, Sedgewick Duckworth. The

love of life through understanding which he instilled within

me shall never waver.

I sincerely appreciate the freedom and guidance offered

me by mU advisor, Dr. Katherine N. Scott. Her door is always

open to me.

I thank Dr. Alan M. Jacobs for seeing me through this

work, literallU, from start to finish. Also, I am grateful

to have had the chance to interact with Dr. E. RaUmond

Andrew, for he embodies the wisdom, wonder, and charm of the

discipline of nuclear magnetic resonance.

The other members of mU committee contributed in a

variety of ways to strengthen this work, as did my fellow

students. At appropriate points in the text I acknowledged

those individuals who made specific contributions.

Special thanks go to the Department of Radiology for

partial financial support. Additional financial support was

supplied bu NIH grant PF1-RR-02278.


















TABLE OF CONTENTS


ACKNOWLEDGMENTS. ............. .. ........ ....... .....

LIST OF TABLES. .................... ............

LIST OF FIGURES................................. ...

ABSTRACT.................................... ........

CHAPTER


PAGE

.. ..iv

....vi

...vii

.... ix


I INTRODUCTION............................... ... 1

II UTILIZATION OF THE SPIN-LATTICE RELAXATION
TIME IN NMR IMAGING............................5

Introduction........ ....................... 5
TheorU of Spin-Lattice Relaxation...............5
Clinical Use of Spin-Lattice Relaxation.........8

III INVESTIGATION INTO T1 DETERMINATION ON A
WHOLE BODY NMR IMAGER..........................10

Introduction....................................10
Methods and Materials........................... 13
Results....................................... 4
Discussion........................................ 5

IV EXPLOITING THE STIMULATED ECHO IN NMR IMAGING..71

Introduction...................................71
TheorU..............................................7
Materials and Methods..........................91
Results........................................ 121
Discussion....................................138

V SUMMARY AND CONCLUSIONS.......................117

REFERENCES.. ...................... .......................151

BIOGRAPHICAL SKETCH.................................... 155
















LIST OF TABLES


NUMBER TABLE PAGE

3-1 Concentration of Copper Sulfate Doped
Water and Resultant Spin-Lattice Relaxation
Time for Phantom Material......................17

3-2 Typical Raw Data Acquired for Tl
Determination.............. ............ ....33

4-1 Four-Step Phase Cycling Used in Stimulated
Echo Imaging .............. ....... ... ..... 101















LIST OF FIGURES


NUMBER TABLE PAGE

3-1 Phantom used for all Tl measurements...........15

3-2 Field mapping apparatus........................

3-3 Spatial homogeneity mapping of the main
magnetic field................. ..... ....... ... 21

3-4 Spatial homogeneity mapping of the
transmitted rf field...........................22

3-5 Color NMR images of phantom....................29

3-6 Examples of fitted data sets Uielding
good T1 estimates.............................35

3-7 Examples of fitted data sets which
Yielded poor T1 estimates......................36

3-8 Sample computer output of data
correlation program............................39

3-9 HUpothetical output of data
correlation program............................42

3-10 Representative data indicating independence
to position in field-of-view...................47

3-11 Representative data indicating independence
to actual Tl value............................. 4B

3-12 Representative data indicating independence
to number of images............................50

3-13 SummarU of results.............................51

3-14 Effect of rf attenuating material upon
measurement precision and accuracU............63

4-1 Basic stimulated echo imaging sequence.........78

4-2 The formation of a primary echo................79

4-3 The formation of a stimulated echo.............86


vii









4-4 The evaluation of a residual gradient..........97

4-5 Effect of residual gradients on image
formation......... ..... ...................... 99

1-6 The extended stimulated echo imaging
sequence........................... ....... 108

'-7 The tip angle reduced TI (TART)
imaging sequence .......................... 112

4-8 The formation of a series of TART images......111

i-9 The stimulated echo-diffusion coefficient
imaging sequence...................................120

4-10 The response to the stimulated echo
sequence........ ..................... ..... 122

4-11 The William Tell phantom.....................124

4-12 The quantitative use of the STE image.........126

4-13 A water-lipid image of a hen's egg............128

4-14 A STE chemical shift image....................130

41-15 An extended STE multiecho series of images....132

4-16 A comparison of the spin echo image and the
primarU echo image............................134

4-17 A series of TART images......................136


viii



















Abstract of Dissertation Presented to the
Graduate School of the University of Florida in Partial
Fulfillment of the Requirements for the Degree of Doctor of
Philosophy



A BIFURCATED STUDY OF SPIN-LATTICE RELAXATION INFORMATION
IN NUCLEAR MAGNETIC RESONANCE IMAGING:
QUANTITATIUE ANALYSIS WITH CONVENTIONAL TECHNIQUES AND THE
UNCONVENTIONAL STIMULATED ECHO IMAGING TECHNIQUE


BU

William Sattin

December 1985



Chairman: Katherine N. Scott
Major Department: Nuclear Engineering Sciences

This work is comprised of two separate investigations,

both related to spin-lattice relaxation, or T1, information

in nuclear magnetic resonance CNMR) imaging. One study

explored the ability of commercially available NMR imagers

to accurately and precisely determine the T1 value of imaged

objects. The specific goal was to evaluate empirically the

advice found in the NMR spectroscopy literature on Tl

determination, and how well this advice applied to NMR

imaging with its unique set qf experimental constraints. The

primary conclusion was that if one wished to obtain a direct

estimate of the actual T1 value in an object which might be









within a spatiallU inhomogeneous radio frequency field, the

most accurate, precise, and time-effective technique to use

was three fast inversion recoverU images, with suitably

chosen values of the inverting time, whose signal

intensities were fitted bu a three-parameter exponential

function.

The other studU concerned itself with the detailed

theory, practical considerations, and possible applications

of the stimulated echo CSTE) in NMR imaging. Whereas

conventional NMR imaging techniques rely upon the spin echo,

which has solelU T2 relaxation weighting unless the NMR

signal is saturated, STE NMR imaging is unique in that the

STE has intrinsic Tl weighting. Possible applications

abound. In addition to generating Tl contrast images, it is

possible to calculate quantitative Tl information from a

series of STE images. Additionally, STE images effectivelU

enhance objects with long Tl values over those with shorter

T1 values, whereas spin echo images do not. Also, it was

demonstrated that the STE easilU integrates into chemical

shift imaging schemes. Of prime interest are two STE imaging

sequences which permit the acquisition of a series of STE

images within one imaging sequence, where each image has

progressively increased T1 weighting. Finally, a method of

in vivo determination of diffusion coefficients is

proposed, which utilizes STE imaging to lessen the effect of

T2 weighting.















CHAPTER I
INTRODUCTION



From modest but promising beginnings in the 1940s and

19SOs, nuclear magnetic resonance (NMR) spectroscopy has

developed into an important research tool. The First

applications of NMR yielded insights into the properties of

the atomic nucleus. EarlU in its history, NMR spectroscopy

was adapted from the sole use bU physicists, to the realm of

chemists, who saw the potential of the chemical shift

phenomenon as a structural probe. This first useful

parameter has now been supplemented by manU other

experimentallU accessible quantities, making NMR a powerful

and versatile technique that Uields information related to

molecular structure, interactions, and dynamics. Most new

applications of NMR have been derived from parallel

improvements in instrumentation and methods, resulting in

applications in physics, chemistry, biology, geology, and

medicine. Particular applications include two-dimensional

fourier transform NMR EAu763, high resolution NMR in

solids EHa763, chemically induced dynamic nuclear

polarization EKa7B3, multiple quantum NMR UVe773, and

NMR imaging ELa733. The conclusions of the present

investigation are particularlU applicable to NMR imaging.









The technique of NMR imaging is one that interests not

onlU scientists, but also nonscientists, for it promises to

provide a safe and noninvasive method for diagnosing

dysfunction or disease in human tissue. Most whole body NMR

imagers in use today detect the NMR signals from the protons

in the object. In in vivo applications the major source of

protons is water. Manu applications of NMR imaging are based

on the fact that different regions of the object Ci.e.

different tissues or organs) have different water contents

and different values of the characterizing times, T1 and T2.

For soft tissue differentiation, where relative water

content is essentially a constant, it is the wide

variability in the values of T1 and T2 which makes possible

images with anatomical detail, and more importantly, images

which contain pathological detail. These images, which

contain pathological detail, are of particular interest

because of the proposal EDa713 that Tl values of water

protons in cancerous or damaged cells are longer than those

of protons in normal cells ELeB13. The present

investigation explored the role of Tl, the spin-lattice

relaxation time, in NMR imaging.

Chapter II offers a brief account of the theory of

spin-lattice relaxation and discusses the impetus for the

present investigation: the dual role of Tl in NMR imaging.

One role of T1 in NMR is qualitative in nature, T1 as a

source of image contrast. The other role is quantitative,

for Tl values have the potential of being diagnostic.









Chapter III explores the ability of commercially

available NMR imagers to accurately and preciselU determine

the T1 value of imaged objects. The specific goal was to

evaluate empiricallU the advice on T1 determination found in

the NMR spectroscopy literature and to see how well it

applied to NMR imaging with its unique set of experimental

constraints. The primary result presented in Chapter III is

concerned with the direct estimate of the actual T1 value in

an object which may be within a spatiallU inhomogeneaus rf

field. The most accurate, precise, and time effective

technique to use is three fast inversion recoverU images,

with suitably chosen values of the inverting time, whose

signal intensities are fitted bU a three-parameter

exponential function.

Chapter IU presents the detailed theorUy, practical

considerations, and, by way of examples, the possible

applications of the stimulated echo CSTE) CHa503 in NMR

imaging. Whereas conventional NMR imaging techniques rely

upon the spin echo, STE NMR imaging incorporates the unique

T1 dependence of the STE. The results reported in Chapter IU

take the form of specific applications of the STE to NMR

imaging. First, it is shown that in addition to generating

T1 contrast images, it is possible to calculate quantitative

T1 information from a series of images. Second, a novel

application of the T1 weighted STE image is demonstrated,

either the enhancement or the suppression of elements in the

object with different T1 values. Third, it is shown that the









STE is easily integrated into chemical shift imaging

schemes. Fourth, two stimulated echo imaging methods are

presented which permit the acquisition of a series of STE

images within one imaging sequence, where each image has

progressively increased T1 weighting. Finally, a method of

in vivo determination of molecular translational

self-diffusion coefficients, which utilizes STE imaging to

lessen the effect of T2 weighting, is proposed.

In the final chapter, Chapter U, a summary of results

is presented, as well as the final conclusions, which

identify the thread which runs through this entire work, a

thread that, at once, connects and binds.















CHAPTER II
UTILIZATION OF THE SPIN-LATTICE RELAXATION TIME
IN NMR IMAGING


Introduction

The two NMR relaxation times, T1 and T2, play a

pivotal role in the understanding of the organization of

biological systems at the molecular level in general, and in

NMR imaging in particular. Differences in proton NMR

relaxation times of normal and pathological tissue are the

key to NMR image contrast and the discrimination of disease,

a fact responsible for their widespread use as diagnostic

parameters in clinical NMR imaging. T1 and T2 directly

affect the selection of imaging pulse sequence timing

parameters, and consequently, the total imaging times and

patient throughput. Also, Tl may influence the choice of the

optimum operational magnetic field strength for NMR imaging,

due to T1's significant variation with frequency EBoBJ3.

Theory of Spin-Lattice Relaxation

A detailed description of the complete theory of

spin-lattice relaxation is beyond the scope of this work,

rather, those elements of the theory crucial to the

understanding of this investigation are presented. Consider

an ensemble of identical, interacting atoms, whose nuclei

contain either an odd number of protons, an odd number of

neutrons, or both. At room temperature, the majority of









nuclei will reside in the lowest energU level, the so called

ground state. In the absence of a magnetic field the nuclear

spin states are degenerate all with the same energy, though

the application of a magnetic field removes this degeneracy.

Additionally, the nuclei will process about the direction of

the applied magnetic field, a concept which is more fully

explained in Chapter IV. RadiofrequencU electromagnetic

radiation stimulation will cause the nuclei to absorb

energy, raising them to an excited state. The nuclei in an

excited state can return to the ground state onlU by

dissipating the excess energy to their surroundings. Return

to the ground state, or relaxation, also requires a

stimulating rf field. The fields causing this spin-lattice

relaxation are provided bU the surrounding nuclear

environment, the so-called lattice. The term, lattice, was

first introduced to describe the positions of molecules in

crystalline solids, but has since been extended to other

phases in addition to the solid phase, and now simply

indicates the magnetic environment of the nuclei.

The rf fields provided by the lattice for relaxation

result from the presence of other magnetic nuclei,

paramagnetic ions and molecules, and molecular magnetism

which is the result of the fast rotation of electronic

charges. The most common source of lattice fields is the

dipole field produced by neighboring magnetic nuclei. For

example, in the water molecule, one of the hydrogen nuclei

produces a magnetic field, thus affecting the adjacent







7

proton. The lattice field must fluctuate to transFer energy

effectively from the excited proton to the lattice. Thus,

these fluctuations must occur at a rate which matches the

transitional Frequency of the excited protons.

In liquids, the Fluctuations in the lattice Field are

the result of molecules undergoing Brownian motion, which

may be either translational or rotational in nature. Both

intramolecular and intermolecular relaxation processes

occur. With intramolecular relaxation, energy is transferred

between nuclei within the same molecule, whereas

intermolecular relaxation involves nuclei of different

molecules. The protons in water and lipid, the primary

sources of protons in the human body, relax predominantly by

the intramolecular dipole-dipole mechanism.

Typically, the average rate at which the molecules

reorient themselves is related to the size of the molecule.

Small molecules, such as water, reorient more quickly than

larger molecules, such as lipids, with correlation times on

-11 -B
the order of 10 and 10 seconds respectively. Indeed, the

large macromolecules, such as DNA and proteins, tumble

rather slowly, with correlation times three or four orders

of magnitude slower than lipid. The Frequency of rotation

for the medium-sized molecules, such as lipids, most closely

corresponds to the transitional Frequency of the excited

protons, at typical nuclear magnetic resonance magnetic

Field strengths. Hence, lipid-based protons will relax

faster than water-based protons, which rotate at a frequency









that is typicallU greater than the transitional frequency of

the protons. SimilarlU, the macromolecules are inefficient

in causing relaxation, for they rotate at frequencies which

are much less than the transitional frequency.

Efficient relaxation correlates to short TI values,

whereas inefficient relaxation results in long Tl values.

For example, in fat, which has a high lipid content, Ti is

typically of the order of a few hundred milliseconds, yet

the TI of pure water is about three seconds. Although free

water relaxes slowly, the water in biological tissue tends

to relax much faster, with typical T1 values of only several

hundred milliseconds. In an attempt to explain this

phenomenon, it was postulated that a fraction of water in

tissues is bound to the surface of proteins EZi573. Hence,

the motion of bound water is reduced, thus more closelU

matching the transitional frequency of the protons. This

enhanced relaxation results in shorter T1 values. In

practice, an equilibrium exists between bound and Free

water. It is thought that this equilibrium is perturbed in

certain pathological conditions, resulting in the clinically

observed elevation in T1 values of certain tumors CDa713.

Clinical Use of Spin-Lattice Relaxation

Although spin densitU images are useful in a number of

clinical situations, there is nearly universal agreement

that images which depend significantlU an the relaxation

parameters T1 and T2 show considerably greater soft tissue

contrast. This increased contrast allows improved










differentiation and recognition of anatomical detail and

helps to demonstrate and assess mass effects EStB53.

The explanation for this increased contrast lies in the

Fact that relaxation times of tissue cover a wider range of

values than the range of proton densities in the same

tissues. For example, at low magnetic field strengths, the

difference in T1 between liver and kidney is over 50%,

whereas the difference in proton density is less than 10%.

Perhaps more important is the large alteration in relaxation

time that occurs in various disease states, even when the

proton density itself is not altered significantly. For

example, tumors often have Tl values which are increased by

200% or 300% compared to the surrounding normal tissue.

The determination of absolute numbers for T1 promises

to aid in tissue specification, although there is still

considerable variability of values being reported from

investigator to investigator. Recently, BottomleU et al.

have collated a vast body of relaxation time information for

the purpose of establishing the range of normal values

CBo8'3. Deficiencies in measurement techniques were

identified as a major source of data irreproducibility.

Additionally, there is significant overlap between normal

and abnormal tissue in some types of pathology, for example,

diffuse liver disease EDoB23. Thus, to date, measured Tl

values are still too variable, and have yet to improve

significantly the tissue specificity of NMR imaging.


















CHAPTER III
INVESTIGATION INTO Tl DETERMINATION ON A
WHOLE BODY NMR IMAGER



Introduction

Proton nuclear magnetic resonance CNMR) imaging mau

yield both qualitative images which are evaluated visually

and quantitative information which is evaluated numerically.

The quantitative information may be used to generate values

of localized in vivo NMR parameters such as the spin

density, the spin-spin relaxation time, T2, and the

spin-lattice relaxation time, T1. The NMR spectroscopy

literature is full of suggestions on how best to determine

these parameters, particularlU T1, in conventional samples

studied by physicists and chemists EGrB3, HaB13.

Similarly, the NMR imaging literature offers a multitude of

suggestions for in vivo T1 determination, based on both

empirical and theoretical arguments EPUB33. The goal of

this work was to evaluate empirically the advice found in

the NMR spectroscopU literature as to how well it applied to

NMR imaging, with its unique experimental constraints.

The pulse programming capabilities of commercial NMR

imagers are tUpicallU limited, yet there are no fewer than

four distinct pulse sequences available which may be used to










provide estimates of the actual in vivo T1: the spin echo

(SE) sequence EHa503, the progressive saturation (PS)

sequence EFr713, the inversion recovery CIR) sequence

EUVo6B3, and the fast inversion recovery (FIR) sequence

CKo773. Each of these sequences has at least two timing

parameters, values of which need to be optimized so as to

reduce the overall error in the determined TI value. In

addition, a rational choice of the number of images to be

generated, the spacing of the variable timing parameters,

and the form of the fitting function must be made with

consideration towards the resultant precision and accuracy

in measurement, and the net imaging time required. Precision

is used in this work to mean the degree of exactness with

which a quantity is stated, while accuracy is used to

indicate the conformity of an indicated value to an accepted

standard value UVa763. A precise T1 estimate is not

necessarily accurate, whereas it is hoped that all accurate

T1 estimates are precise. Furthermore, other constraints of

the system must be incorporated into the decision process,

namely the spatially inhomogeneous rf field, which is the

result of rf coil design and the rf attenuating properties

of the object CBo7B3.

In the present study, experiments were conducted on a

phantom consisting of an array of vials containing

paramagneticallU doped water, whose T1 values spanned the

range of clinical concern. Each previously mentioned

parameter was systematically varied, and single slice images







12

of the phantom were generated while the phantom was first

immersed in air, and second, in a saline solution of

physiological concentration. The effect of the saline

solution was to dissipate the rf energy in a similar Fashion

to the human body, resulting in a spatially inhomogeneous rf

field. The raw data were computer processed, resulting in a

large population of reduced data, upon which correlative

studies were performed.

This investigation produced two principal conclusions.

The primary conclusion was, accepting the assumptions given

in the methods and materials section concerning the phantom

material, that to obtain a direct estimate of the actual Tl

value in an object which may be within a spatially

inhomogeneous rf field, the most accurate, precise, and time

effective technique to use was three FIR images, with

suitably chosen values of the inverting time, TI, fitted by

a three-parameter exponential function. The use of IR images

was equally accurate and precise, but not as temporally

efficient. A second conclusion was that the use of three SE

images, with suitably chosen values of the pulse sequence

repetition time, TR, and fitted by a two-parameter

exponential function can be more precise and time effective

than the FIR technique in estimating T1, but was always much

less accurate. These conclusions may be used a priori to

design the series of images which will yield the most

accurate, precise, and time efficient estimate of an in

vivo T1 value, or they may be used a posteriori to help










evaluate the accuracy of a calculated T1 value from a given

series of images. Examples of each type of application are

given in the results section.

Methods and Materials

NMR Imaging Sustem

All experiments in this investigation were conducted on

a Teslacon whole body NMR imager, manufactured by Technicare

Corporation. The main magnetic field was produced by a six-

coil, air-core, water-cooled resistive electromagnet. The

magnet was nominally operated at 0.15 Tesla, but could be

adjusted by altering the current in the electromagnet. The

clear bore diameter was one meter, allowing access of an

entire human body, with the long axis of the body aligned

with the z direction of the main magnetic field.

The imager used separate rf receiver and transmitter

coils, allowing separate performance optimization. The

transmitter coil was for all intents and purposes a part of

the imager, although it was possible to utilize a myriad of

rf receiver coils. The manufacturer supplied body rf coil

was used for all measurements. This permitted the

investigation to be conducted over a large field of view,

0.75 meters, which facilitated the examination of spatially

dependent variables.

The rf coil used in NMR is part of a resonant circuit,

and it was possible to measure the quality factor, 0, of a

circuit containing the body rf coil, on the bench. A sweep

wave generator, manufactured by Wavetec, was coupled to the








1i

rf coil. The frequency dependent response was monitored with

an oscilloscope, and the Q was determined by



Q f/8f E3-13



where SF was the width of the resonance curve at 70.7% of

the amplitude of the response at the resonance frequency, f

CKrB13. The 0 was determined with the coil both physicallU

unloaded, and loaded with a dielectric material CO.S9% NaCl

aqueous solution). The ratio of the unloaded 0 to loaded 0

was approximatelU 0.7.

The Teslacon imager made use of a DEC PDP 11/2E

computer for pulse sequence programming, data acquisition,

and data processing. Additionally, a FPS floating point

arrau processor aided in data processing. All experiments

were conducted with the standard software supplied by the

manufacturer Csoftware release C), except for modifications

implemented which allowed for continuous data acquisition

with software controlled incremental timing parameters.

Phantom

The phantom used for all measurements was designed to

model certain properties of the human bodU. Due to the

spatial extent of the body it was of interest to examine the

possible effects of spatially dependent parameters, such as

main magnetic field and rf magnetic field inhomogeneities,

upon in vivo spin-lattice relaxation measurements. Hence,

the phantom's geometric design, as seen in figure 3-1,

























































Figure 3-1. Phantom used For all T1 measurements. Inner
structure holds eight vials coaxial with the
main magnetic field while outer structure could
be filled with saline solution.










permitted comparative measurements to be made on identical

samples which were spatially distributed within the imager's

field of view. The external container could be Filled with a

saline solution, immersing the phantom.

The range of T1 values within the body typically spans

From 100 milliseconds to 1000 milliseconds, with a few

singular exceptions (e.g. cerebral spinal fluid). As given

in table 3-1, all experiments were conducted on aqueous

solutions of copper sulfate with varying concentrations,

spanning a T1 range of 70 to 1100 milliseconds.

Three assumptions were made concerning this simple

phantom material. First, the spin-lattice relaxation decay

process was a monotonically decreasing function of time.

Second, the exponential decay had a single time constant.

Third, the noise spectrum was white, Gaussian, and had a

zero mean. The third assumption has been verified for the

NMR imager over a wide range of experimental conditions

ESaB]3.

The actual, or "gold standard" value of Tl for each of

the phantom materials was determined in the following

manner: a single cylindrical glass vial (with a diameter of

1.0 centimeters and a length of 10.0 centimeters)

containing the doped water solution under analysis, was

placed at the position of maximum sensitivity of the rf

transmission coil, and coaxial to the main magnetic Field.

Owing to the small filling factor resulting from the

relatively small sample volume, the receiver gain was






















Table 3-1

Concentration of Copper Sulfate Doped Water and
Resultant Spin-Lattice Relaxation Time for Phantom Material


Material

BCKeU 1)
CCKeu 2)
DCKae 3)
E(KeU 4)
FCKey 5)


Concentration (mM)


5.0
3.5
2.0
1.0
0.5


T1 (msec)


73.214.3
154.013.8
277.B23.1
54i0.457.1
1102.2109.9








18

adjusted to make optimum use of the dynamic range of the

analog-to-digital converters. The imagery was set up to

acquire an IR image, with the pulse sequence repetition

time, TR, set to 10 times the expected T1 value so as to

avoid saturating the signal. All magnetic Field gradients,

required for spatial encoding of the NMR signal, were turned

off. This resulted in the imager being used as a

conventional spectrometer. The inverting time, TI, was

incrementallU varied for over twenty values which spanned

the estimated Tl value. For each value of TI, the Fourier

transform of the time domain signal was observed, and ten

values of maximum amplitude and mean noise were recorded.

The arithmetic means of these values were fitted with a

three-parameter exponential function using the data

reduction routine of the program "NMR", resident on a

Nicolet 11BOE computer ENm823. This procedure was repeated

for each different doped solution on two occasions,

separated by over a year, with the results given in table

3-1.

In addition to effecting the 0 of the rF coil, a

dielectric substance will also dissipate incident rF energy.

An otherwise spatially homogeneous rf field will become

spatiallU inhomogeneous if a dielectric fills the space.

Hence, the mere presence of the body in the NMR imager maU

alter the homogeneity of the transmitted rF Field. The

macroscopic implication of this effect was a variation in

pulse tip angle from point to point within the body. For








19

example, for a given transmitted rf pulse, a region close to

the surface of the body might experience a 180 degree tip

angle, while an interior region, owing to rf attenuation by

the tissue, might experience a 170 degree tip angle. Since

T1 measurement accuracy is often sensitive to missed tip

angles, the problem of a spatially inhomogeneous rf field

was studied as part of this investigation. Figure 3-1 shows

the phantom holder positioned within a large cylindrical

bottle. All experiments were conducted on the phantom within

the empty bottle, and also within the bottle while full of

saline solution of physiological concentration (0.9% NaCl).

The dimensions of the bottle approximated those of a human

abdomen.

Spatial Mapping of Intrinsic Inhomogeneities

Tl is a calculated value, determined from intensity

measurements. Therefore any source of intensity variation

might introduce errors into T1 calculations. Two common

sources were main magnetic field inhomogeneity and rf field

inhomogeneity. Before attempting any experiments, the

intensity of the main magnetic field and rf transmitted

field were spatially mapped utilizing the specially

constructed field mapper depicted in figure 3-2. The results

are presented in figures 3-3 and 3-' respectively.

Since all images were single slice, it was sufficient

to examine the z equal zero plane for main magnetic field

and/or rf transmitted field inhomogeneities. A 56 centimeter

diameter circular piece of lucite with thirty-seven small























































Figure 3-2. Field mapping apparatus. Multiple point source
phantom with specially designed rF receiver coil
shown at center. Designed for measurements in
the transverse plane over a 56 centimeter
diameter circular region.








21










40

30


Figure 3-3. Spatial homogeneity mapping of the main magnetic
field. Each isostrength curve is 2.5 ppm of the
main magnetic field. Measurements were made in
the transverse plane over a 56 centimeter
diameter circular region.






















































Figure 3-4. Spatial homogeneity mapping of the transmitted
rf field. Each isostrength curve is
approximately 0.25% of the field at the central
region. Measurements were made in the transverse
plane over a 56 centimeter diameter circular
region.










vials of doped water embedded within it was placed in the z

equal zero plane. A one centimeter diameter rf receiver coil

was constructed as seen in figure 3-2, which could be

placed in turn over each small vial. The imager was operated

as a spectrometer, with the only detectable source of signal

being the vial over which the special rf coil was situated,

resulting in essentially point source measurements.

To evaluate the main field inhomogeneity, the coil was

placed on the center vial, and the main magnetic field was

adjusted to insure resonance. The coil was then moved

systematically from vial to vial while the registered

deviation from the resonance frequency was recorded. Since

no imaging gradients were in use, there was a one-to-one

correlation between resonance offset and main field

inhomogeneity. Over the useful field of view, a coaxial

circle of thirty centimeters in diameter, the main magnetic

field was homogeneous to approximately 25 parts per million

of the main field. This value was within the manufacturer's

specifications and was deemed experimentally acceptable.

Although this investigation considered the effects of a

spatially inhomogeneous rf field, it was concerned primarily

with spatial variations resulting from rf attenuation by the

object, and not intrinsic, and therefore constant

inhomogeneities of the transmitted rf field. This intrinsic

variation was determined, for documentation purposes, in the

following manner.








2'

The special rf coil was systematically moved from vial

to vial, and while on each vial the main magnetic field

would be slightly altered so as to insure resonance. This

was accomplished simply by altering the current in the

electromagnet. With the resonance condition holding,

numerous intensity measurements were recorded and later

averaged. This procedure was repeated for each vial. After

all intensity values had been recorded, the averaged

intensities were compared to determine the transmitted rf

homogeneity. If each identical point source sample

experienced the same tip angle, then all intensitU values

should have been equal on resonance. Any variation in

intensity was attributed to variation in tip angle. Over the

useful field of view, a coaxial circle about thirty

centimeters in diameter, the transmitted rf field varied by

approximatelU 3.0.

Data Acquisition Methodolougy

The investigation was aimed at determining the most

efficient and accurate method of obtaining actual Tl values

from NMR images, with consideration towards the constraints

a spatiallU inhomogeneous rf field imposses. Nonuniform rf

irradiation was a concern for it results in a spatially

dependent sUstematic error in rf pulse tip angles, and hence

in measured Tl CFr713. Evaluation of four pulse sequences

was conducted, the spin echo (SE), the inversion recovery

CIR), the progressive saturation (PS), and the fast

inversion recovery (FIR). The degree of freedom of the










fitting function dictated the lower bound on the number of

images required for a unique determination of the T1 value,

while the upper bound was investigated as to its dependence

upon pulse sequence utilized, desired accuracy in

measurement, and net imaging time. Similarly, the spacing of

the variable timing parameter was evaluated as a function of

the measurement accuracy and net imaging time for a given

pulse sequence.

For all experiments, a nonlinear least squares fitting

algorithm was used, of the form



SCTP) K CEexpC-TP/T1)3 C3-23



where K and C were constants and SCTP) was the signal

intensity as a function of a timing parameter, TP.

In PS and SE images, Tl weighting was introduced by

saturating the signal with rapid pulsing. Therefore, TP was

the pulse sequence repetition time, TR. The spectroscopy

literature CFr713 suggests using a fitting function with

two degrees of freedom, given by setting C in equation 3-2

equal to K, to determine T1 from either PS or SE images.

T1 information was incorporated into IR images by

inverting the equilibrium magnetization, allowing some time

to pass during which spin-lattice relaxation occurred, and

sampling the remaining magnetization by bringing it into the

transverse plane where detection took place. For IR images,

TP was equal to the inverting time, TI. The NMR spectroscopy







26

literature UVoB83 suggests using a fitting function with

two degrees of freedom, given by setting C in equation 3-2

equal to 2K, for IR images where the inverting pulse was

exactly 180 degrees. When the inverting pulse was missed,

possibly due to a spatially inhomogeneous rf field, the

literature EKo773 suggests the use of a fitting function

with three degrees of freedom, such as equation 3-2.

The FIR images were identical to the IR images, except

that a rapid TR was used, with one result being a reduction

of the total image time. Typically, TR for IR images was

five times T1 or longer, while in FIR images TR was commonly

two to three times Tl. As suggested in the literature

ECa753, this rapid TR requires the use of a fitting

function with three degrees of freedom, such as equation

3-2, whether the inverting pulse was missed or not.

Details of the exact experimental procedure follow. It

should be noted that the specified method was performed for

each of the five phantom samples as given in table 3-1, both

surrounded by air and surrounded by the dielectric saline

solution. This permitted the analysis to span the entire

clinically useful T1 range, and also to evaluate the effects

of missed rf pulse tip angles resulting from an

inhomogeneous rf field. All acquired images were single

slice, at the z equal zero plane, with slice thickness of

one centimeter. The Teslacon imager typically gathered 256

data points in the readout direction and 128 data points in

the phase encoding direction. The displayed image was 512










pixels by 512 pixels which was derived from the stored image

data which was dimensioned 256 bU 256. Hence the data in the

phase encoding direction were interpolated. To avoid the use

of interpolated data, the data acquisition routine was

modified to permit the use of 256 phase encoding gradient

steps. In all experiments the echo time, TE, was maintained

at its shortest value, 30 milliseconds, to minimize

contributions from spin-spin relaxation and molecular

self-diffusion. Two averages were taken for each image.

The PS and SE experiments differed in only two

respects. First, the PS images relied upon the bulk

magnetization's reaching a steadu-state value in the

presence of the rapid pulsing with w/2 rf pulses. It is

suggested that the system reaches this steady-state within

four pulses EFr713, hence all PS images were preceded bU

four pulses prior to image acquisition. Second, PS

experiments Uield consistent values of T1 for TR in the

range of 0.5T1 to 2.OT1, whereas SE experiments yield

consistent values of T1 for TR in the range of 0.5T1 to

3.OT1. Hence, images were collected with TR ranging from its

minimum value, dictated bU the manufacturer to be 50ms, to a

maximum of three times the actual T1. Additionally, a TR

value of 5.0T1 was used to sample the unsaturated initial

magnetization. In total, no less than twenty images were

acquired with varying TR values. In data processing images

with TR less than or equal to 1.5T1 were considered PS

images, and those with TR greater than 1.5T1 were SE images.








28

The IR and FIR experiments, as acquired with the

imager, differed in only two respects. First, the IR images

were acquired assuming that the bulk magnetization was at

its initial equilibrium value prior to the commencement of

the pulse sequence. Therefore, TR for all IR images was set

to at least five times the actual T1 value. This condition

was not required for FIR images, hence the origin of "fast"

in fast inversion recovery, with TR nominally set to twice

the actual T1 value in the FIR images. Second, since the

maximum value of TI must be less than TR, the range of TI

for IR images was from its minimum value, dictated by the

manufacturer to be 25 milliseconds, to Just less than 5.OT1.

In the FIR images, TI ranged from 25 milliseconds to just

less than 2.OT1. In total, no less than ten IR images or ten

FIR images were acquired with varying TI values.

Data Processing Methodology

All images acquired with the Teslacon system were

displayed on a high resolution monochromatic CRT monitor,

with a maximum of 1024 gray levels. It was also possible to

display the images on a high resolution color monitor, as

shown in figure 3-5. Each image was reconstructed, and the

spatiallU dependent signal intensities were displayed on the

CRT monitor for analysis. Reconstruction of the PS and SE

images differed from that of the IR and FIR images.

The imager acquired all raw data using quadrature

detection, effectivelU resulting in each data point's being

defined by a complex number. PS and SE experiments sampled





























































b



Figure 3-5. Color NMR images of phantom. Ca) With eight
identical vials, (b) with all vials surrounded
by saline solution.








30

the magnetization, whose value lay between zero and its

equilibrium value. Since this is a one sided range, all

positive in sign, signal intensities in PS and SE images

were represented by the magnitude of the corresponding

complex number. IR and FIR experiments sampled the

magnetization while it was in the range of plus or minus its

equilibrium value. To retain the signed information, signal

intensities in IR and FIR images were determined and

represented taking into account the phase of the

corresponding complex number.

While in the display mode, quantitative information was

obtained from the image. Signal intensity information was

gathered by positioning a software controlled region of

interest, ROI, about the spatial area of concern. The system

made available the number of pixels enclosed in the ROI, the

mean intensity value of those pixels, and the corresponding

standard deviation. For all images taken with the phantom

designed for this investigation, no fewer than one hundred

pixels were used to defined each vial. The intensity

information from all eight vials in the field of view, and

also the intensity information from a representative region

of background noise, were determined and recorded. These

measurements formed the raw data base on which all

subsequent analysis was conducted.

A Fortran program, which performed a nonlinear least

squares fit without the need for initial guesses of the

fitted values, was written and implemented on a IBM 470










computer sUstem. The general purpose of this program was to

determine the optimal number of images, and the values of

their associated timing parameters, required to accurately

and precisely determine T1 For a given pulse sequence. The

details of how this was accomplished follow.

The program accepted as input the type of pulse

sequence and the signal intensities as a function of the

corresponding timing parameter. This information was given

for each vial, for each different concentration of solution,

and for both immersion in air and immersion in saline

solution. In NMR spectroscopy, where the sample under

investigation maU be examined for any given period of time,

typically ten to thirty data pairs are used in fitting the

empirical data to the theoretically expected function,

resulting in an estimate of T1. In NMR imaging, the time

constraint is more restrictive. Ill patients cannot remain

in the imager for an extended period of time, and the

physician is usually not willing to spend an inordinate

amount of time on a single procedure.

This study aimed to determine whether the acquisition

of two, three, or four images resulted in the most accurate

and precise T1 estimate. If each data set contained, say,

ten data pairs, the analUsis program considered each

possible combination of two data pairs at a time, three at a

time, and four at a time. These two, three, or four data

pairs were then fitted to the appropriate functional form of

equation 3-2 for the given pulse sequence.








32

If a function with three degrees of freedom was

required, then only the combinations involving three and

four data pairs were used. For example, an IR data set,

consisting of ten data pairs and Fitted to both a function

with two degrees of freedom and a function with three

degrees of freedom, generated seven hundred and five fitted

values of T1. Multiplying this by the eight vials, the five

different concentration samples, and the possible immersion

in air or saline resulted in over five thousand estimated T1

values. These estimated values were compared to the actual

Tl value, and also to the estimated Tl value obtained if all

of the data pairs, for example ten, were fitted to equation

3-2. Comparison with the actual T1 tested for precision and

accuracy, while comparison with the estimated Tl tested

simply for precision. It required over five minutes of CPU

time to process all the raw data and transfer in excess oF

twelve megabytes of reduced data.

Table 3-2 presents some typical raw data which were

acquired For Tl determination. The experiment performed was

an inversion recovery experiment, conducted on phantom

material C. The TR and TE values were kept constant at

1250msec and 30msec respectively. Data are presented for

both the phantom material immersed and not immersed in the

saline solution. Column one depicts the values of TI used

For Tl determination, chosen to properly span the actual Tl

value of phantom material C of 154msec. The

region-of-interest derived signal intensities for vials 1












Table 3-2

Typical Raw Data Acquired for T1 Determination


TICmsec)


SI(vial 1)


SICvial 5)


Background


PHANTOM NOT IMMERSED IN SALINE SOLUTION


-13.7
-7.1
4'.1
87.1
119.5
1'8.7
163.6
186.2
223.9


-90.1
-26.1
80.1
173.2
229.5
273.9
326.0
361.1*
'30.0


PH~M~flM TMMFR~Ffl TM


16.3
21.8
27.1
33.7
38. 4
39.8
'0.2
'7.8
51.2


SALINE SOLUTION


24.0
36.0
1B. L
60.0
68.9
78.1
82.7
86.5
95.1


Inversion recovery experiments were conducted on phantom
material C, with TR-1250msec and TE-30msec, resulting in
the stated signal intensities (SI) and background values.


50
75
125
175
225
275
325
400O
1000


0.38
0.12
0.06
-0.26
-0.27
-1.32
1.15
-0.07
0.05


50
75
125
175
225
275
325
400
1000


0.06
-0.33
1.'0
1.90
1.10
1. 0
-0. 74
-2.10
-0.114


...W..M.n.. Tm.... rn TM C.,, TFP zn In








34

and 5 are presented in columns two and three respectively,

in arbitrary units. Uial 1 was in a region of minimum

receiver coil sensitivity, while vial 5 was in a region of

higher sensitivity. Column four contains the background

noise intensity values. Two points of interest are noted.

One, the magnitude of all signal intensities of vial 5 are

greater than the corresponding values for vial 1. This is a

direct result of the receiver coil sensitivity. Second, the

signal intensities For the phantom immersed in the saline

solution vary dramatically from those signal intensities for

the phantom not immersed in the saline solution. A possible

explanation is that the saline solution absorbs a portion of

the transmitted rF power, thus resulting in missed tip

angles at the vials' positions.

Figures 3-6 and 3-7 present examples of fitted curves

to typical data which were acquired for T1 determination.

Figure 3-Sa illustrates the fitting of ten inversion

recovery data sets by a three-parameter exponential

function. The estimated Tl value was 132Bmsec, which

happens to be within 15% of the actual T1 value of 1S'msec.

In the subsequent analysis of this data, only groups of

three data sets and groups of four data sets will be used to

determine T1. Each T1 value determined in this manner will

be compared to both the natural Tl value oF 1t5msec, and

also the estimated T1 value of 132msec.

Figure 3-6b illustrates the fitting of only three out

of the possible ten data sets to a three-parameter














Ti


1328ms


T- 131ms
1


Figure 3-6. Examples of fitted data sets yielding good Tl
estimates. Curve (a) was generated by fitting
all points while Cb) was generated by fitting
only the points denoted by "O".

















xXX X X


S- 61ms


x x




xx T 70ms


b


x x
K K






T- 101ms



0 C


Figure 3-7. Examples of fitted data sets which yielded poor
T1 estimates. Curves Ca), Cb), and (c) were
fitted only to the data points denoted as "0".










exponential function. The three data points used for fitting

are denoted as "0", while the unused data points are

presented as "X". For this particular choice of three data

points, the estimated Ti value is 131msec. Thus, this

particular value is both within 15% of the all points

estimated T1 value of 132msec, and also within 15% of the

natural Ti value of IS5msec. Figure 3-7 presents three other

possible choices of three data sets, Fitted bU a

three-parameter exponential function. In each case, the

estimated T1 value is neither within 15% of the all points

estimated T1 value nor the natural T1 value. These

particular choices of three data sets would be deemed poor.

The different grouping of the data points in figure 3-7a, b,

and c, is an artifact of the curve fitting program, done so

that the full fitted curve might be displayed.

The good choice of three data sets of figure 3-6b, and

the bad choices of figure 3-7 illustrate certain basic

characteristics. The good choice of figure 3-6b depicts

three TI values which span the entire relaxation curve. One

point defines the signal intensity at, essentiallU, time

equal zero. Another TI value results in a signal intensity

corresponding to almost the completlU relaxed state. Finally

the third TI value comes just about at the time the

relaxation curve changes the most. Of course, these are not

the only choices of TI values which resulted in good fits,

indeed, there were manU. One of the purposes of this

investigation was to identify and quantify how much








38

variation could be tolerated from the near ideal

distribution of TI values as depicted in figure 3-Bb.

Obviously, the variations illustrated in figure 3-7 could

not be tolerated. In each case the three TI values were

grouped very near each other, and therefore were unable to

characterize the entire relaxation curve, rather, they only

characterized the small region of the curve where they were

located.

Data Analysis Methodologu

To facilitate analysis of the numerical data, a program

was developed on an APPLE 2-plus microcomputer, which

down-loaded the processed data from the IBM 3330 disk pack,

and permitted graphical display of correlated parameters. An

example of one such output is given in figure 3-B. The

graphical presentation of correlated data allowed for rapid

qualitative data analysis. By this method, conclusions

concerning positional dependence, dependence on the actual

T1 value, optimal number of images required, variation in

accuracy and/or precision in estimated TI value as a

function of phantom immersion in either air or saline

solution, choice of fitting function, and relative merit of

each pulse sequence were efficiently and accurately

determined.

The criterion used in all evaluations was as follows:

for a given set of parameters Ce.g. FIR experiment, actual

T1 of 277.8 milliseconds, vial number three, phantom

immersed in saline solution, using three images, and fitted





















Tl DATA GATHERED ON TESLACON
10Ft RUN=KEY
S UIRL=3
SPSEQ=SE

S7- + PTS=4
C1C -< SALT=YES
S TCOrM=ALL

z 48- :^: Key
40 +:


*20-- :
-- : 5
5% 101 15% 26J 25* >25i
ACCEPTANCE LEVEL











Figure 3-8. Sample computer output of data correlation
program.








O0

by a function with three degrees of freedom), the criterion

was that the estimated T1 value fitted with less than a 15%

relative error to either the actual T1 value or the Tl

estimate obtained by fitting all the data pairs. In

comparing different sets of parameters, what was actually

compared was the percentage of all possible permuted data

pairs which met this criterion. This percentage was denoted

as "range in %" in figure 3-8.

The other features of figure 3-8 are as follow. The

parameter "RUN" refers to which phantom material was used in

the particular run illustrated. The phrase "RUN-KEY" implies

that the plot is an overlay plot of many runs, and that one

is referred to the "Key" which indicates which plotting

character corresponds to which phantom material. The "Key"

indicates that the results of five different phantom

materials are presented on this single plot. "RUN" 1 through

5 corresponds to phantom material B through F.

The parameter "UIAL" indicates from which of the eight

possible vials the data came from. Similarly, "PSEQ"

indicates which pulse sequence was used for the Tl estimate

Ci.e. PS, SE, IR, FIR). "#PAR" refers to the number of

parameters in the fitting function used for Tl

determination, either two or three. "#PTS" refers to the

number of data points fitted to determine Tl. "#PTS" was

either two, three, or four for "#PAR" equal to two, or

"#PTS" was three or four for "#PAR" equal to three. The

parameter "SALT" indicates if the phantom was immersed in










the saline solution ("SALT-YES"), or if the phantom was not

immersed in the saline solution C"SALT-NO"). The parameter

"TCOM" indicates what the estimated T1 was compared to,

either the all points estimated Tl C"TCOM-ALL"), or the

natural T1 ("TCOM-GLD"). Finally, "LEVU
acceptance levels are given on the x axis.

Figure 3-9 is an aid which illustrates how to interpret

the graphical displays of correlated parameters. Figure 3-9a

illustrates a favorable situation. This figure illustrates

that approximately 50% of all experiments resulted in an

estimated T1 value within 5% of the standard value. Indeed,

over 935 of all experiments were within 15% of the standard.

If this hypothetical curve corresponded to an inversion

recovery experiment, then it could be interpreted as

follows. Although many different sets of TI values were

considered, the T1 value which was estimated appeared to

remain relatively constant. Thus, it would not be very

crucial in practice to optimize the choice of the TI values

used to gather data for T1 determination, for so many

different combinations were equally able to generate an

accurate and precise estimate.

Figure 3-9b illustrates a poor situation. In this

figure, less than 5% of all experiments would result in an

estimated T1 value which was within 5% of the standard.

Indeed, it appears that less than 30% of all experiments

would result in estimated T1 values within 25% of the

standard. If this hypothetical curve corresponded to real














T1 ODATA GATHERED ON TESLACON
108

80

80
W 50
S40
S30.
2@
10

5% 10% 15% 20% 25% >25%
ACCEPTANCE LEVEL

a






Tl DATA GATHERED ON TESLRCON
100





54.1






5%: 10- 15% 20% 25% >25%
ACCEPTANCE LEUEL

b



Figure 3-9. Hypothetical output of data correlation program.
Output Ca) depicts a nearly ideal output, while
(b) depicts a poor output.










data it would indicate that just a very few choices of the

timing parameters would result in an acceptable T1 estimate.

Typically, most of the actual curves fell between the two

hypothetical curves of figure 3-9.

Typically, natural biological variation will far exceed

any machine error, hence total measurement errors within 10%

for in vitro experiments are not uncommon EBeB'3.

Indeed, total measurement errors could exceed 10% for in

vivo experiments, where the investigator has less control

over certain biological variables. Although certain

combinations of parameters resulted in estimated T1 values

of high precision Cthe estimated value had much less than a

15% relative error), acceptance at the 15% relative error

level was chosen to coincide with typical in vivo

biological variability.

After the qualitative data analysis based upon the

graphical display of correlated parameters was completed, a

more detailed quantitative analysis was conducted in order

to determine those values of the variable timing parameter

which permitted the most accurate and precise estimate of T1

to be made. A description of the analysis method follows.

First, for a given set of experimental parameters (i.e.

pulse sequence, phantom solution concentration, immersion in

air or saline, particular vial, number of images used for

fit, and the form of the fitting function), the values of

the variable timing parameter which resulted in a fit with

less than 15% relative error were noted. By way of








LHI

illustration, if one of the fixed parameters was the use of

three images, then the analysis culminated in a set of, for

example, one hundred groups of three numbers. Each group of

three numbers was actually three values of the variable

timing parameter CTR for PS and SE images, TI for IR and FIR

images) which resulted in a good fit. Each value was then

scaled to the T1 value which the fit was being compared

to. Next, a linear-multiple-regression analysis CSpB13 was

performed on this set of groups, yielding a regression

equation which related the three values of the variable

timing parameters to each other. This is the

multidimensional analog to the least-squares fit line used

For two dimensional data sets. Hence, for three images, a

least squares fit plane was determined which incorporated the

empirical data into an analytical expression. This

analytical expression could be used a priori in selecting

values of the variable timing parameter, or a posteriori

in evaluating the group of timing parameters used in a

series of images.

Results

There were five basic results of this investigation,

two of which are of primary importance. Some of the results

were of a general nature, such as the dependence of

measurement upon the position within the field of view, and

the variation in the accuracy and precision in the estimated

T1 value as a function of the actual Tl value. Other results

were more specific, such as the determination of how many








15

images acquired with which pulse sequence, and fitted by

which function, resulted in accurate and precise estimated

Tl values, independent of the presence of the rf attenuating

saline solution. Finally, particular results were

quantitative, for example, the linear multiple regression

analysis of the values of the variable timing parameter

which resulted in accurate and precise Tl estimates.

The performance of the PS experiment was so poor in

contrast to the SE, IR, and FIR experiments, for the reasons

offered in the discussion section of this chapter, that it

was discounted as a viable method of T1 determination. The

following results apply only to SE, IR, and FIR experiments.

Representative data are presented in support of all results.

The reproducibility of signal intensities for a given set of

parameters was at all times greater than 95%, and tUpically

greater than 97.5%. The reproducibilitU was determined from

a series of measurements which were all repeated ten times.

Positional Dependence

All estimated Tl values were constant within 15% to the

position within the field of view from which the individual

signal intensities were recorded. That is, although spatial

variations in signal intensity occurred, calculated values

of Tl did not exhibit these variations, within acceptable

experimental limits. The signal intensity variations

resulted from the intrinsic magnetic field inhomogeneity,the

intrinsic transmitted rf field inhomogeneity, and mostly,

the spatiallU inhomogeneous rf receiver coil response.








46

The representative data of figure 3-10 support this

result. Vial three was positioned at the site of maximum

receiver sensitivity, while vial five was located at a

position of poor sensitivity. A comparable percentage of

experiments met the acceptance criterion (fitted Tl value

had less than a 15% relative error) for both vials. Although

similar estimated T1 values were calculated for both vials,

typicallU the standard deviations in the fits for vial five

were larger than those for vial three, owing to the smaller

signal to noise ratio of the intensities at that position.

Dependence Upon Actual Tl Value

The percentage of experiments which met the acceptance

criterion was constant within 15% to the actual T1. That is,

a given set of parameters Cwith the values of the variable

timing parameter suitably chosen for the actual T1)

generated a similar number of good fitting T1 estimates,

independent of the actual T1. Also, for a given set of

parameters characterizing experiments which met the

acceptance criterion, the values of the variable timing

parameter normalized to the actual T1 were constant within

15% to the actual T1. Thus, it was possible to characterize

the optimal values of the timing parameter independent of

T1. The representative data of figure 3-11 support this

result. Each different "RUN" represents a different actual

T1 value of the phantom material. The close grouping of the

data along the "RANGE IN %" axis, as a function of

"ACCEPTANCE LEUEL", indicates the insensitivity to Tl value.








L7





Tl DATA GATHERED ON TESLACON


100
38
90.
80
70
60
50*
-1
40-
30
20'
10


5% 10'% 15%
ACCEPTANCE


20% 25%
LEVEL


T1 DATA GATHERED ON TESLACON

18800 -
90
80..
78 0.
60
58
40 -
30 -


10


5% 10Q 15f
ACCEPTANCE


RUN=KEY
UIRL=5
PSEQ=FIR
#PAR=3
#PTS=4
SRLT=YES
TCOM=ALL
LEU Key
+ : 1
x : 2
S: 3
S: 4
0:5


RUN=KEY
VIAL=3
PSEQ=FIR
#PAR=3
#PTS=4
SALT=YES
TCOM=ALL
LEV Key
+ : 1
x : 2
3
a : 4
0:5


2LEVE 2
LEVEL


Figure 3-10. Representative data indicating independence to
position in field-of-view. (a) Vial 5 output,
(b) identical output for vial 3.


* .5.


*


" '


>25%


.



















T1 DATA GATHERED ON TESLACON


100 RUN=KEY
SUIRAL=3
9 PSEQ=FIR
.\ 80- -- -#PAR=3
70- #PTS=4
SRLT=YES
TCOM=GLD
w 50- LEU z 40- Key
a 30- + : 1
2 x : 2
2 A
IQ + : 4
0 1 I 4 I o 5
5% 10% 15% 20% 25' >25%
ACCEPTANCE LEUEL











Figure 3-11. Representative data indicating independence to
actual TI value.








9IS

Dependence Upon Number of Images

For a given set of parameters, the percentage of

experiments which met the acceptance criterion utilizing a

two-parameter fitting function was constant within 15% to

the acquisition and use of two, three, or four images for T1

estimation. Similarly, the percentage of experiments which

met the acceptance criterion utilizing a three-parameter

fitting function was constant within 15% to the acquisition

and use of three or four images for T1 estimation. That is,

a given set of parameters, with the degree of the fitting

function constant, generated a similar number of good

fitting T1 estimates, independent of the number of processed

images.

There was a corollarU result. As explained previously,

IR experiments were Fitted twice, once by a function with

two degrees of freedom Cgiven bu setting C in equation 3-2

equal to 2K), and once by a function with three degrees of

freedom (given bu equation 3-2). For each form of the

function, all IR experiments were constant within 15% to the

number of images used, although fitting with the

three-parameter function resulted in a substantially higher

percentage of experiments which met the acceptance

criterion.

The representative data of figure 3-12 support these

results. AdditionallU, the results of fitting FIR

experiments with a function with two degrees of freedom are

also presented in figure 3-13.














T1 DATA GATHERED OHN TESLACON


RUN=KEY
VIAL=3
PSEQ=IR
#PAR=3
#PTS=3
SALT=YES
TCOM=GLO
LE(U Key
+ : 1
X 2
0: 3
S: 4
o : 5


5% 10% 15% 20% 25%
ACCEPTANCE LEVEL


T1 DATA GATHERED ON TESLACON


10 : :







40


RUN=KEY
VIA L =3
PSEQ=IR
#PAR=3
#PTS=4
SALT=YES
TCOM=GLD
LEU Key





%


A5C I 15% 20% 25%
ACCEPTANCE LEVEL


Figure 3-12. Representative data indicating independence to
number of images. Ca) Using three images for Tl
determination, Cb) using four images for Tl
determination.


100.
90.
80
70
60
50-
40
30
20-
10.


>25












01 75
0
L-
O
C
0
0
2
aR 25-


Salt
Estimated T,


OiA
r~II

7I


0- Lm
No Salt
Estimated T1


Salt
Natural IT


P0
!~ES


C, M CM CT CM C'
cr w a: a: a:
LL
No Salt
Natural T1


Figure 3-13. Summary of results.


k-
CO 75-

0
0 50-
C
0)
^ 25


_ __










Optimal Sets of Parameters

To obtain a direct estimate of the actual Tl value in

an object which may be within a spatially inhomogeneous rf

field, the most accurate, precise, and time effective

technique to use was three FIR images, with suitably chosen

values of TI, fitted by a three-parameter exponential

function. The use of IR images was equally accurate and

precise, but not as temporally efficient.

Three SE images, with suitably chosen values of TR, and

fitted bU a two-parameter exponential function can be more

precise and time effective than the FIR technique in

estimating Tl, but were alwaUs much less accurate, and prone

to error if an inhomogeneous rf field was present. The

representative data of figure 3-13 support these results.

Optimum Uariable Timing Parameter Values

For each of the three above mentioned optimum sets of

parameters, a linear multiple regression analysis was

conducted on the empirical values of the variable timing

parameters which resulted in estimated Tl values of 15%

relative error or less. For each regression analysis, a

coefficient of linear multiple correlation was determined.

The coefficient maU lie between 0 and 1. The closer it was

to 1, the better was the linear relationship between the

variables, with a value of 1 indicating a perfect

correlation. The closer it was to 0, the worse was the

linear relationship. For all cases, the coefficient of

linear multiple correlation was 0.5 or greater.










The use of three FIR images, fitted bU a three

parameter exponential function, was the optimal method of

estimating the actual T1 value, in the presence of a

spatially inhomogeneous rf field. The relationship between

the three values oF TI in these FIR experiments was



H 1.1 + 0.6M 0.1L E3-33



where the three TI values, H, M, and L were the highest,

middle, and lowest values all scaled to T1 by dividing the

specific timing parameter by the actual T1 value. The

standard error of estimate in H was 0.3, for M it was 0.3,

and for L it was 0.2.

The use of three IR images, fitted by a three-parameter

exponential function, was another method of estimating the

actual TI value, in the presence of a spatiallU

inhomogeneous rf Field. The relationship between the three

values of TI in the IR experiments was



H 1.6 + 1.1M + O.6L E3-43



where the three TI values, H, M, and L were the highest,

middle, and lowest values normalized to the actual T1 value.

The standard error of estimate in H was 1.2, For M it was

0.4, and For L it was 0.3.

A large percentage of SE experiments did not meet the

acceptance criterion when the estimated TI value was










compared to the actual T1 value. However, there was a large

percentage of SE experiments which did meet the acceptance

criterion when the calculated T1 value was compared to the

value of T1 estimated by the fitting of all data pairs. This

indicated that while estimated T1 values from SE images were

not accurate, they were precise. The relationship between

the three values of TR For this set of parameters in the SE

experiment was



H 1.7 + 1.1M 0.3L E3-53



where the three values, H, M, and L were the highest,

middle, and lowest values normalized, in this case, to the

T1 value estimated by fitting all data pairs. The standard

error of estimate in H was 1.1, for M it was 0.7, and for L

it was 0.3.

Discussion

The in vivo determination of T1 values is complicated

by many factors, some of which were addressed by this

investigation.The specific aim of this investigation was to

evaluate empirically the suggestions offered by the NMR

spectroscopy literature on T1 determination and as to how

well they applied to NMR imaging, with its unique set of

experimental constraints.

The NMR spectroscopy literature offered suggestions on

which pulse sequence to use, the number and values of the

variable timing parameter to use, and the form of the










fitting function required to calculate T1 from the

individual signal intensity measurements. The added

constraints imposed by NMR imaging were the Following:

measurements could be obtained from any position within a

large field of view, typical T1 values in the human body

span a range of over an order of magnitude, total imaging

times had to be minimized, and the human body has dielectric

properties which resulted in spatially dependent rF

attenuation.

Positional Dependence

It was determined that all estimated T1 values were

constant within 15% to the position within the field of view

From which the individual signal intensities were recorded.

IF there were no spatial variation in signal intensity (for

fixed experimental parameters), then this would be an

expected result. As demonstrated by the signal intensity

variations in figure 3-5, this was not the case.

The predominant cause of spatial variations in signal

intensity measurements was the spatially inhomogeneous rf

receiver coil response. The half saddle shape of the rF

receiver coil produced an axially asymmetric spatial

response, as seen in figure 3-5. Thus, For a hypothetical

sample that filled the field of view and produced a

constant, homogeneous signal from each position, the

recorded signal intensity would be the constant intensity

convoluted with the rF coil's sensitivity response at that

location. This would influence only K and C of equation 3-2,










and not the exponential time constant. Thus, this

investigation verified experimentally the theoretical

prediction.

This result is significant for the following reason.

Although it is tempting to make a differential diagnosis

based upon differences in signal intensities (e.g. if the

liver is more intense than the spleen then diagnosis A, if

vice versa then diagnosis B), these differences may not be

entirely organic in nature. Variations in calculated Tl

values (for a constant set of imaging parameters) are a more

reliable indicator of true clinical variation.

Dependence Upon Actual T1 Ualue

It was determined that the percentage of experiments

which met the acceptance criterion was constant within 15s

to the actual T1 value, for properlU chosen values of the

variable timing parameter. Since experiments were conducted

over an actual T1 range of approximatelU 100 milliseconds to

1000 milliseconds, this result is valid onlU over this

range. To justify this empirical result, it is necessary to

consider two factors, the physical model of spin-lattice

relaxation, and any instrumentational dependence upon Ti

determination.

Spin-lattice relaxation theory predicts, for such a

simple phantom material (paramagnetically doped water), a

monoexponential relationship between the signal intensity

and the variable timing parameter. The spin-lattice

relaxation rate is directly obtainable from the exponential







57

time constant. This relatively simple relationship holds no

T1 dependent bias. That is, all other factors being equal,

T1 is simply a scaling factor in the exponential argument,

and does not influence the general form of the function.

Thus, the empirical invariance to T1 was to be expected, on

the basis of the physical model.

Although instrumental effects on Tl determination can

have many causes, ranging from rf field production to

computer roundoff errors, there could not be any direct

instrumentational dependence upon Tl, for obviously the

instrument could have no knowledge of the phantom's Tl

value. Thus, any T1 dependent bias would have to have been

indirectly related. Since Tl calculations are based upon

signal intensities and the values of a variable timing

parameter, any direct instrumental bias towards these

parameters will indirectly affect Tl determinations.

The accuracy in defining a timing parameter was

governed by the computer's CPU clock. If we consider a clock

frequency of one megahertz (a value much less than even

modern personal computers, let alone the PDP 11/24), then

timing events could be controlled to within a microsecond.

Since typical values of timing parameters were of the order

of tens or hundreds of milliseconds, it seems unlikely that

incorrectly set timing parameters were a large source of

error in the determination of Tl values.

On the other hand, the signal intensity was influenced

by a myriad of variables, most of which were instrumental in








58

nature. For example, all experiments in this investigation

utilized a single slice mode of acquisition. The use of

multislice acquisition introduced other variables which

influenced signal intensities, if all other factors remained

constant.

Perhaps the greatest instrumental influence upon signal

intensity was the required use of spin echo formation and

imaging magnetic gradients for image signal acquisition.

Conventional Fourier imaging EEdBO3 relies upon the

detection of spin echoes. This did not introduce further

complications in the SE images, but PS, IR, and FIR

experiments conventionally generate a free induction decay

(FID) signal, and not an echo. Indeed, this complication

could explain the poor performance of the PS sequence. The

PS experiment relied upon the net magnetization's reaching a

steady-state value while being subjected to repetitive w/2

rf pulses, but by its very nature a spin echo had a

dynamically varying net magnetization. Although the IR and

FIR experiments do not force the net magnetization to a

steady-state value, altering their pulse sequence to include

echo formation could have been a source of signal intensity

error. The formation of spin echoes required the

magnetization to remain in the transverse plane Cin the

rotating coordinate system) for an appreciable period of

time. This introduced T2 damping of the signal intensity,

and in the presence of magnetic field gradients, damping due

to molecular self-diffusion ESt653.








59

The empirically determined invariance to the actual T1

value is significance for two reasons. First, it permitted

the development of general recommendations concerning the

optimal values of the variable timing parameter. Second, it

indicated that concerns raised about instrumental effects on

T1 determination did not introduce any systematic errors in

measurement, possibly only statistical errors. Thus, the

results of this investigation could be applied to in vivo

T1 determination without loss of accuracy due to any T1

dependence, to the extent that the phantom used in this

investigation modeled the in vivo object.

Dependence Upon Number of Images

It was determined that for a given set of parameters,

and with a fitting function with two degrees of freedom, the

percentage of experiments which met the acceptance criterion

was constant within 15 for the acquisition and use of two,

three, or four images for T1 estimation. Similarly, for a

fitting function with three degrees of freedom, the

percentage of experiments which met the acceptance criterion

was constant within 15% to the acquisition and use of three

or four images for T1 estimation. This result agrees with

the NMR spectroscopy literature, which states that to a

first approximation, the error in estimated T1 values does

not depend upon the number of data pairs used in the

calculation, provided the rms error of the experimental data

was less than one tenth of the signal intensity at time

equal to infinity.









In this investigation, an estimated T1 value was deemed

a good approximation to the actual Tl value if the relative

error was less than 15%. For this acceptance level, onlU

First order effects were of sufficient magnitude to

influence the error in the estimated T1 value. Therefore the

observed invariance to the number of data pairs used in

calculating the spin-lattice relaxation time corresponds to

the NMR spectroscopy literature's suggestion concerning this

point CBeBO3.

This result was of particular significant for the

following reason. In NMR imaging, time is at a premium. This

investigation sought to identify the method of spin-lattice

relaxation time determination which maximized accuracy and

precision, and minimized the total imaging time. One waU to

minimize the total imaging time was to take the least number

of images required to generate mathematically unique and

statistically significant results. Thus, for those

techniques which were fitted bU a function with two degrees

of freedom, two images sufficed, while three were required

for fitting functions with three degrees of freedom.

Since the earliest beginning of NMR imaging, some have

made the suggestion that the best method of in vivo Tl

determination was the fitting of two SE images with a

function with two degrees of freedom EHrB3, Ma793. This

result indicates that, if the signal to noise ratio was

adequate in each image, two images would indeed be the

reasonable number to acquire and process. This does not imply








61

that this method was optimal, but simply that it conformed

to this "least number of images" result. Indeed, results of

this work indicated that although the two image SE method

was optimal in reducing the total imaging time, it was far

from optimal in terms of its accuracy in estimating T1.

The summary of results presented in figure 3-13

contains much information concerning the appropriate choice

of pulse sequence/fitting function for a given situation.

The precision of each sequence was indicated by the

corresponding percent of experiments meeting the acceptance

criteria when the calculated Tl was compared to the

"Estimated T1" value. The least demanding situation was when

the phantom was not immersed in the saline solution. For

this situation all combinations of pulse sequence/fitting

function were essential equal in precision. This was not

true when the phantom was immersed in the saline solution.

In this situation the SE:e method was slightly more precise

than any other method of Tl determination, all of which

shared an essentially equal precision.

Those experiments whose calculated T1 values met the

acceptance criteria when compared to the "Natural T1"

represented methods of determining precise and accurate T1

estimates. For this situation both the IR:e and FIR:2

methods were inadequate, whether the phantom was immersed in

the saline solution or not. Additionally, both the IR:3 and

FIR:3 methods of T1 determination were best, while the SE:2

method performed marginally.










It was of importance to document to what degree a

particular pulse sequence/Fitting function varied from the

"Salt" to "No Salt" case. To facilitate that analUsis the

percent relative difference was calculated from figure 3-13

for both the "Estimated Tl" and "Natural T1" results. The

percent relative difference was determined bU subtracting

the "% Meeting Criteria" of the "Salt" case from the "%

Meeting Criteria" of the "No Salt" case, and then the result

was divided by the "n Meeting Criteria" of the "No Salt"

case. This was done for each pulse sequence/fitting

function, for both the "Estimated Tl" and the "Natural Tl"

results, with the outcomes given in figure 3-14.

IdeallU, a given pulse sequence/fitting function would

perform as well whether the phantom was immersed in the

saline solution or was not immersed in the saline solution.

Since this is the ideal situation, the ideal percent

relative difference would be zero. The SE:2 method of Tl

determination suffered the smallest loss of precision, as

depicted in the "Estimated Tl" result in figure 3-14. The

"Natural Tl" results indicated that the IR:3 was least prone

to losses of accuracy and precision, while the SE:2 and

FIR:3 methods were nearlU as lossless. These results must

not be considered out-of-context. For example, the result

that the SE:e method had a low percent relative difference

for the "Natural Tl" case viewed in conjunction with the

results of figure 3-13 indicated that, in this particular

situation, the SE:S method went from being a poor method of

















I

I

I


I

I

I
I
g


Estimated


C
0



4)
0co
0v30
cO

10
4
*4) 10-
(t
C*


50
C

03




OC
00)
>Z
S-
0 10
Q0


Figure 3-14. Effect of rf attenuating material upon
measurement precision and accuracy.


Natural T


- jjs--










determining accurate and precise Ti values when the phantom

was not immersed in a saline solution, to being a slightly

poorer method when the phantom was immersed in the saline

solution

A Priori Recommendations

All of the results of this investigation dealt with the

determination of the optimal method of in vivo Ti values.

Of primary importance were the results concerned with the

optimal pulse sequence and optimal values of the variable

timing parameter. These particular results may be used a

priori to design an imaging scheme which results in

reliable Tl values, or a posteriori to evaluate the

reliability of a calculated Tl value. The a priori

recommendations follow.

Optimal sets of parameters

The first decision to be made in the design of a TI

imaging series is the choice of pulse sequence. This

decision is based upon three factors, total imaging time,

and the accuracy and precision in T1 determination. The

results indicate that there were three choices, three FIR

images fitted by a three-parameter exponential function,

three IR images fitted by a three-parameter exponential

function, or three SE images fitted by a two-parameter

exponential function.

The FIR series of Tl images had a number of advantages

over the IR or SE series, which made it the recommended

method. First, the method required, at most, half the total










time of the corresponding IR series. Second, it yielded

consistent results, independent of whether the saline

solution was present or not. Finally, it generated estimates

of T1 which were both accurate and precise. This meant that

in vivo T1 values could be obtained directly, without the

need of a calibrated set of measurements.

There were also some disadvantages to the FIR series of

T1 images. First, being an inversion type of experiment,

phase reconstruction of the images was required to make use

of the full dynamic range offered by the technique. In

practice, phase reconstruction is not always easily

accomplished. Second, it did not always offer the minimum

total imaging time. Often, the SE series of images would

result in less total imaging time. Finally, the SE series

often produced more precise measurements of Tl than the FIR

series did. Although the FIR series had some flaws, overall

it was the most rugged method, yielding accurate and precise

estimates of Tl under the most adverse of situations.

The IR series shared many of the attributes of the

recommended FIR series, but had an intrinsic tragic flaw. An

IR image necessitated the use of a long total image time.

This long TR would often clash with the clinical necessity

of speed. An advantage the IR series had over the FIR was

that, due to the extended TR time, less saturation of signal

occurred. Thus, the IR images had slightly more contrast, an

aid for visual evaluation, but no real advantage in the

quantitative analysis required for Tl determination.








66

The enigma of the investigation was the SE method of

spin-lattice relaxation time determination. The SE series

had many advantages. One, it often resulted in the shortest

total imaging time. Two, only simple magnitude

reconstruction was required. Finally, the SE series oftened

attained estimated spin-lattice relaxation time values with

very high precision. Additionally, although not a result of

this investigation, the SE technique is often the clinical

technique of preference, displacing the inversion techniques

consistently. For these reasons, the SE method of

spin-lattice relaxation time determination appears to enjoy

the most widespread use. Additional results of this

investigation indicated that the SE method had some serious

shortcomings, and yielded quality results only in

restrictive situations.

The most important disadvantage of the SE method was

its lack of accuracy in estimating TI values. The SE method

always fared best when its estimated T1 value was compared

to the T1 value determined by fitting all points, rather

than when it was compared to the actual T1 value. Thus, in

vivo Ti values could not reliably be determined directly.

Instead, some type of calibration curve would need to be

generated to permit actual Tl values to be gleaned from SE

estimated T1 values. This conclusion agrees with other

reported investigations into the use of SE images for T1

determination EPyB33.








67

Optimum variable timing parameter values

Once the decision as to which pulse sequence to be

utilized is made, either the SE, IR, or FIR imaging

sequence, it is necessary to specify the values of the

variable timing parameter. For FIR and IR images this is TI,

while for SE images it is TR. To insure optimal accuracy and

precision, the results of the linear multiple regression

analUsis should be used. The derived linear relationships

among the three values of the variable timing parameter for

the FIR, IR, and SE methods have been given in equations

3-3, 3-4, and 3-5 respectively.

There are some general guidelines to be offered as to

how best to use the suggested results a priori. First, the

greater the uncertainty in the T1 value under investigation,

the greater should be the spread in the three values. The

lowest value, L, could be picked to correspond to the

shortest permissible value of the particular timing

parameter. For the instrumentation used in this

investigation, that was 25 milliseconds for TI and 100

milliseconds for TR. The highest value of the timing

parameter, H, would vary depending upon the pulse sequence.

For the FIR and IR methods, H could correspond to some value

close to TR, sau O.STR. The solution is not as straight

forward for the SE method, where there is no fixed timing

parameter of relevance on which to base the choice. In this

case, H should be chosen with consideration towards the

largest value in the expected T1 range.








68

Often it is desired to merge the T1 determining images

with the images desired for visual evaluation. In this case,

one or two of the values for H, 1, or L may be taken to

correspond to the values associated with the images required

for visual evaluation, with the remaining timing parameter

determined by the linear multiple regression equation. For

example, two SE images with the TR values of 500

milliseconds and 1000 milliseconds are desired for visual

evaluation. Additionally, an in vivo T1 determination is

desired of a tissue whose T1 is thought to be about 650

milliseconds. By setting L and M to 0.77 and 1.54,

respectively, and utilizing the linear multiple regression

equation for the SE method, H is determined to be 3.16,

corresponding to a TR value of 2055 milliseconds. Note that

nonsense answers would result, in this particular case, if

the two existing TR values were assigned to L and H, or M

and H. Additionally, if the Tl of concern was thought to be

350 milliseconds, then assigning M to be 0.77, and H to be

1.54 yields the third value of TR as 145 milliseconds. By a

similar process, the optimal values of the timing parameters

in FIR and IR series are determined.

In the manner just described, an optimal method of in

vivo Ti determination may be developed a priori, based

upon the available imaging time, desired accuracy and

precision, and range of T1 under investigation.










A Posteriori Recommendations

It frequently happens that the desire for a

quantitative determination of TI is not expressed until

after the imaging series is completed. If the images were

acquired along the lines of either the FIR, IR, or SE

methods outlined earlier (i.e. three images were acquired,

all with the same number of signal averages), then it would

be possible to generate an estimated Tl value, and with the

aid of the linear multiple regression equations, determine

the reliability of the estimate. The procedure is explained

in the following scenario.

Three inversion type images were acquired, with TE

equal to 30 milliseconds, TR equal to 1500 milliseconds, and

three values of TI equal to 50, 550, and 850 milliseconds.

All images were acquired with four signal averages. A

three-parameter exponential is fitted to the data, and an

estimated Tl value of 700 milliseconds is calculated. The

question is: is this a reasonable Tl value to expect this

series of images to properly characterize, or is it just the

result of some mathematical fitting routine which is

insensitive to certain physical realities?

Since the value of TR is approximately twice the T1

estimate, this series is comparable to the FIR method of T1

determination. The linear multiple regression equation for

the FIR series indicates that the optimal Tl value, for this

set of TI values, is 477 milliseconds. This is obviously not

equal to the estimated value of 700 milliseconds, but the








70

linear multiple regression equation is not without error,

presented in the form of standard error of estimates in L,

M, and H.

By a simple propagation of error analysis of equation

3-3, the standard error of estimate in T1 for the FIR method

of T1 determination, aCT1), may be determined to be 152

milliseconds. Thus, the optimal T1 value to be determined by

the set of TI values used in this example is 477152

milliseconds. The estimated value, 700 milliseconds, is

nearly 1.5 standard errors greater than the optimal mean

value, and it is therefore deemed an unreliable estimate.

This analysis could be conducted as easily for any IR or SE

series of images.



















CHAPTER IV
EXPLOITING THE STIMULATED ECHO IN NMR IMAGING

Introduction

There is an adage that applies equally to all

multipulse NMR experiments which states it is easier to

induce spin echoes than not. Rather than ignore or suppress

these additional echoes in NMR imaging experiments EDuB43,

this investigation sought to glean added information from

them. In particular, this study exploited the unique

properties of the stimulated echo (STE), as first identified

by Hahn EHa503, and further quantified bU Woessner

EWo613. Although new to NMR imaging EFrB5, HaB5, SaBSa,

Sa85b3, stimulated echoes have been successfully applied by

Tanner to the measurement of translational self-diffusion

coefficients ETa703, by Lausch and Spiess to study

infrequent jumps of complex molecules ELaBO, SpB03, and

more recently to analyze slow rotational motions of

molecular solids by Sullivan at al. ESuB23. Furthermore,

other investigators conducting research into stimulated echo

NMR imaging,concurrently with this investigation, have

recently reported their initial findings EFrB5, HaB53.

This investigation is unique in that it is the first to

indicate that stimulated echoes may be applied to NMR







72

imaging, to specifically outline how the stimulated echo may

be applied, and to present actual images utilizing the

specified methods.

In NMR imaging, image contrast from area to area in the

object results predominantly from the differences of the

spin density, the spin-lattice relaxation time, T1, and the

spin-spin relaxation time, T2. With current instruments,

contrast due to relaxation is achieved through the use of

either the spin echo (SE) technique, or an inverting

technique, such as the inversion recovery (IR) sequence. In

particular, T1 weighting is introduced in the SE sequence by

the rapid repetition of the entire pulse sequence, resulting

in signal saturation, while the IR technique introduces Tl

weighting by inverting the equilibrium magnetization,

initially aligned along the positive z axis, and sampling

its recovery with a w/2 rf pulse.

STE imaging introduces T1 weighting into the NMR image

in the following manner. Viewed from the rotating frame of

reference, an initial w/2 rf pulse, at time equal to zero,

rotates the equilibrium magnetization into the transverse

plane. While in the transverse plane, the net magnetization

is reduced due to TE2 relaxation, molecular diffusion and

procession within an inhomogeneous magnetic field. A second

w/2 rf pulse, at time equal to T1, will split the net

magnetization equally into two orthogonal components, one of

which lies in the transverse plane and the other which lies

in the longitudinal plane.







73

The individual isochromats which comprise the net

transverse magnetization will constructively interfere to

form the primary echo (PE) at a time equal to twice 71. The

net longitudinal magnetization will be reduced due to T1

relaxation and molecular self-diffusion. At a time T2 after

the second 90 degree rf pulse, a third 90 degree pulse is

applied which rotates this T1 reduced net longitudinal

magnetization back into the transverse plane, where the

individual isochromats constructively interfere to form the

STE at a time Tl after the third 90 degree rf pulse. It is

precisely this ability to store and retrieve magnetization

along the longitudinal direction, where T1 relaxation

occurs, which makes the application of the STE to NMR

imaging unique.

Conventional Fourier NMR imaging EEdBO3 relies upon

spin echo formation for data acquisition. This investigation

was unique in that it introduced the use of the STE for data

acquisition in NMR imaging. STE imaging, with its unique Tl

dependence, is an ideal technique for T1 contrast imaging.

As indicated, there are two viable methods of T1 contrast

imaging currently in widespread use, the SE and IR

techniques. Although the IR sequence has produced excellent

results, there are a number of distinct drawbacks to its

implementation. For example, one must insure a proper

inverting pulse and use phase sensitive reconstruction to

fully exploit the dynamic range afforded by the technique.

The SE sequence is intrinsically a T2 dependent technique,










hence images acquired with this sequence will frequently

contain a high degree of mixed Tl and T2 contrast. The

results of this investigation indicate that, in many ways,

STE imaging bridges the gap between the accuracy of the IR

technique, and the efficiency of the SE imaging technique.

The results of this investigation took the form of

specific applications of the STE to NMR imaging. First, it

was shown that in addition to generating T1 contrast images,

it was possible to calculate quantitative T1 information

from a series of STE images in which the storage time had

been systematically varied. Second, a novel application of

the T1 weighted STE image was obtained: the enhancement or

suppression of elements in the object with different Tl

values. Third, it was demonstrated that the STE was easily

integrated into chemical shift imaging schemes. Fourth, two

STE imaging methods were developed which permitted the

acquisition of a series of STE images within one imaging

sequence, where each image was progressively weighted by

increasing T1 relaxation damping. Finally, a method of in

vivo determination of molecular translational

self-diffusion coefficients, which utilized the STE's unique

T1 dependence, was proposed.

Theory

Introduction

Echo phenomena have long held a prominent role in

spectroscopy, with applications in various fields spanning

from magnetic resonance to laser spectroscopy. Echoes were








75

detected in NMR for the first time in 1950 by Hahn EHaSO3,

and spin echoes have subsequently been applied in NMR to

various ends, including the measurement of T1 values

ECa5'3, the investigation into molecular diffusion

processes ESt653, the determination of scalar coupling

constants EFr753, the indirect detection of magnetic

resonance CEmBO3, coherence transfer CMa783, and NMR

imaging EEdBO3. Also, the same effects have been exploited

in electron spin resonance Mti723, microwave spectroscopy

CG1763, and in laser optical spectroscopy CKu6S3.

An echo is usually created by exciting the system under

investigation at least twice, where the excitation is often

pulses of electromagnetic radiation. All species in the

system experience the same initial pulse, hence a coherence

is produced. In time, inhomogeneous interactions within the

system act to destroy the coherence. This is accomplished in

NMR by an inhomogeneous magnetic field, by an inhomogeneous

Stark field in microwave spectroscopy, or by the Doppler

effect in optical spectroscopy EMa7B3. A second pulse,

applied at a time T, inverts the accumulated effects of the

inhomogeneous interaction. Thus, the initial coherence is

regained and an echo occurs at a time 2T. Under particular

conditions, portions of the coherence will continue to

defocus, even after the application of the second pulse, and

hence will not participate in echo formation. This component

is dubbed the narcissus, after Narcissus in Greek mythology,

who refused the love of Echo EHa5B3.








76

In 1916, Bloch introduced a phenomenological vector

equation to describe NMR EB1453. It accurately

characterized an isolated particle of spin 1/2 in the

presence of a static magnetic field. Feunman et al. EFe573

have demonstrated that this description is complete, that

is, a geometric representation of the Schroedinger equation

is possible. Also, Pegg et al. [Pel13 have shown this

description to be perfectly rigorous, because the vectors

are equivalent to Heisenberg operators in the Heisenberg

representation of quantum mechanics. It was advantageous to

utilize this graphical method of analysis, and results

derived in this manner are correct without restriction.

Bloch's model of NMR assumed that the magnetization of

bulk material, influenced by a magnetic field, conformed to

the laws of classical electrodynamics. Based on this

premise, a vector differential equation was developed

relating the bulk magnetic moment vector, M, to the applied

magnetic vector field, B, such that



dM/dt rCM x B) EL-13



where r is a proportionality constant called the

gyromagnetic ratio. The geometric interpretation of equation

4-1 is that the magnetic moment rotates about the applied

magnetic field with the frequency n, such that



|a| IrBs Ci-23










This relationship between the precession frequency and the

applied magnetic field is referred to as the Larmor equation.

The frequency n is the Larmor frequency. The Larmor

equation, expressed as in equation 4-2, indicates that the

processional frequency n is proportional to the magnetic

field B, where r is the constant of proportionality.

The Larmor equation may be obtained from an argument

based upon classical physics, as outlined here, or derived

in identical form from a quantum mechanical argument. This

unique property indicates why the classical formulation

offers added insight into the NMR phenomenon. Additionally,

the absence of the Planck constant in the Larmor equation

given in equation 4-2 further justifies the classical

treatment of the resonance phenomenon.

Further support of the classical formulation of the NMR

phenomenon is offered by the correspondence principle of

quantum mechanics EWa533, which is based on the assumption

that quantum theory, or at least its formalism, contains

classical mechanics as a limiting case. This idea was First

expressed by Planck EP1063, when he showed that in the

limit the Planck constant approaches zero, all quantum

theoretic conclusions converge towards classical results.

Formation of the Primary Echo Image

Consider a spin system in thermal equilibrium with its

surroundings, subjected to the rF pulse and magnetic field

gradient experiment displayed in figure 4-1. In the

graphical representation of figure 4-2a, the initial























IF..I- -


A, A,
Ix I--I I--I__


Figure 4-1. Basic stimulated echo imaging sequence.


Gx

Gy
G...............
















































I
I-





IIIx \
B,(90) )




d
















X


I
i `











I


Figure q-2. The formation of a primary echo.










equilibrium magnetization of the spin system, MI, is

depicted as being initially aligned along the z direction,

coaxial with the main magnetic field. The net magnetization

is rotated into the plane transverse to the main magnetic

field by the transmission (Tx) of a 90 degree, or w/E rf

pulse applied as shown in figure 4-2b. It is assumed that

the rf pulse is of frequency nCp) and width tCp), such that

tCp) is small compared to T1 and T2, and excites the entire

chemical shift frequency bandwidth equally. If, for example,

the rf pulse has a phase A equal to 90 degrees Ci.e. along

the positive x direction as depicted in figure *-2b), then

the transverse magnetization will initially be aligned with

the negative y direction, in the rotating frame of

reference.

The rotating frame of reference refers to a set of axes

which are rotating about the z axis, the direction of the

main applied magnetic field. The z axis of the rotating

frame is parallel to the z axis of the laboratory Frame of

reference, as defined by the main applied magnetic field.

The two rotating axes orthogonal to the z axis rotate with

an angular speed equal to the effective component of the rf

magnetic field. The rotating axis in the direction of the rf

magnetic field is referred to as the in-phase component,

while the other axis is the out-of-phase component. The

rotating frame of reference is a useful construction for two

reasons. One reason is that the phenomenological vector

equation which describes NMR takes on a simpler form when








81

expressed in terms of the rotating frame of reference. Also,

a simpler physical picture of events is possible when

considered in the rotating frame of reference.

For a given nucleus, theory indicates that resonance

occurs at a single frequency, dictated by the main magnetic

field strength as in equation '-2. In practice, resonance

takes place over a range of frequencies determined by the

inhomogeneity of the main magnetic field throughout the

sample. Therefore, the object may be considered to be

comprised of an ensemble of magnetic moments, whose

resonance frequencies are symmetrically distributed about

the Larmor frequency, n. Figure 4-2c illustrates the free

precession Ci.e. Larmor type precession and not rf pulse

induced rotation) of all these isochromats during the time

interval 1l. Since figure 4-2c depicts the dynamics of the

magnetization in a frame of reference rotating at frequency

n, the isochromatic moment pairs maintain a symmetry about

the U direction, but rotate in opposite directions. This is

indicated in figure '-2c in the following manner. The light

gray regions represent a range of isochromats which deviate

less from a than do the range of isochromats represented by

the dark gray, that is, the light gray region processes

slower than the dark gray region, in this frame of

reference. In each case, solid area versus hatched area

indicates positive versus negative deviation from n.

Within this time interval 71, pulsed linear magnetic

field gradients are applied as in the conventional fourier










imaging technique [EdB03. The preparatory readout gradient

is embodied in the effective x gradient, CGx), whereas By

and Gz are employed for phase encoding. The effect of these

pulsed magnetic Field gradients is the spatial encoding of

the NMR signal in a precise manner. If one, two, or three

orthogonal pulse field gradients are used for image

formation, then a one, two or three dimensional Fourier

transform of the time domain NMR signal will result in an

image where signal intensity is a function of one, two, or

three spatial dimensions. Obviously, z direction

discrimination could also be achieved with a selective w/2

rf pulse applied in the presence of a slice selective Gz

CHo773.

After the time interval Tl, a second 90 degree rf pulse

is applied, as indicated in figure 4-2d. Whereas prior to

the second rf pulse all magnetization was lying in the

transverse plane Cassuming negligible T1 relaxation during

the interval l1), after the second rf pulse the net

magnetization has components in the longitudinal plane as

well as the transverse plane. Figure 4-2e illustrates the

transverse component oF the net magnetization immediately

following the second rf pulse, obtained by simply projecting

the net magnetization of figure 4-2d onto the transverse

plane. Since prior to the second rf pulse all magnetization

was lying in the xy plane, all magnetization after the

second pulse lies in the xz plane (if the rf pulse is

applied along the positive x direction as indicated), hence








83

the projection of the net magnetization onto the transverse

plane, immediatelU following the second rf pulse, lies

completelU on the x axis.

The intrinsic properties of the isochromats have not

been altered by this magnetization gymnastics. The sense and

speed of free procession in the transverse plane for the

isochromats following the second rf pulse is identical to

the sense and speed of free procession prior to the second

rf pulse Ci.e. as indicated in figure 'i-2c). Hence, from

time rl on, the isochromats will freelU process as in figure

'-2f. From time T1 to time 271 the isochromat vectors will

interfere amongst themselves, with maximum constructive

interference occurring at time 2T1. This constructive

interference constitutes a primary echo (PE), with maximum

amplitude at time 271, and so named to distinguish it from

the spin echo which results from a w/2-T-w rf pulse

sequence. The maximum amplitude of the PE at time 2T1,

MCPE), is given bU


2
M(CPE) MisinOlsin C(2/2)expC-2Tl/T2)fCG,D,T1) 1C-33


where Mi is the equilibrium magnetization, 01 is the tip

angle of the ith pulse, and fCG,D,71) corresponds to the

diffusional damping resulting from molecular diffusion in

the presence of magnetic field gradients. For a constant

steady magnetic field gradient, fCG,D,-1) is given by

22 3
exp-C2/3)Dr 6 r71 where 6 is the magnetic field gradient








BLi

and D is the translational self diffusion coefficient. It

should be noted that pulsed magnetic field gradients have

been used in this investigation, hence the functional form

of fCG,D,rl) will be different ESt653. The two cases are

identical, in the limit, as we pass from pulsed to

continuous application of the gradient.

As illustrated in figure 1-1, the Gx readout gradient

is imposed, centered about the time 2T1, to frequency encode

the PE with x direction spatial dependence. Additionally,

the receiver CRx) is gated open during this same time, to

permit acquisition CA) of the spatially encoded PE. If all

pulses are ideal w/2 rf pulses, then the PE image is

identical to the image produced by conventional spin echo

imaging, except for a factor of one half in signal

intensity. This reduction in the signal to noise ratio would

be intolerable unless it is possible to recover it, or reap

some compensating benefit. Fortunately the other half of the

magnetization is not dissipated, rather it has been stored

as longitudinal magnetization by the second w/2 rf pulse.

Formation of the Stimulated Echo Image

It can be shown that the solution to the Bloch equation

in the rotating frame EB1463 takes on the form



MxCt+tp) MxCt) CL-L3

My(t+tp) My(t)cose MzCt)sine E4-53

MzCt+tp) My(t)sine + MzCt)cose EC-63










in response to a rf pulse about the x axis commencing at

time t and of width tp, corresponding to a tip angle of 0

degrees. In this representation the rotating portion of the

net magnetization is decomposed into two orthogonal

components. Mx is taken to be in phase with respect to the x

axis rotating frame of reference, while MU is 90 degrees out

of phase. Of prime interest is equation 1-6, which

characterizes the longitudinal magnetization, and in

particular its dependence on MyCt). Since the spin system is

initially in thermal equilibrium, MyCt-0) 0. Hence, by

equation 4-6, MzCt-tp) 0 for an ideal w/2 rf pulse. As

applied to the experiment of figure 4-1, the implication is

that during the interval 71, Mz simply approaches the

equilibrium magnetization, if the affect of relaxation is

considered.

If T1 is of the order of T2 or less, then MyCt-rl) is

surely nonzero. That is, at time 71 we will have appreciable

transverse magnetization. Therefore the second w/2 rf pulse,

in addition to inducing the PE, will also produce net

longitudinal magnetization, that is, zCEt-7l+tp] is

nonzero. This becomes quite apparent when a graphical

analysis is conducted.

Figure 4-3a is simply the graphical representation of

the net magnetization immediately following the second w/2

rf pulse of figure 4-1. Indeed, figure 4-3a is identical to

figure 4-2d. Whereas we considered the transverse projection

of this net magnetization in order to describe the formation



































a b



Li. Y


Figure 4*-3. The formation of a stimulated echo.








87

of the PE, we now consider the longitudinal component of the

net magnetization immediately following the second rf pulse,

illustrated in figure 4-3b. For the duration of T2 the

longitudinal magnetization is affected solely by

spin-lattice relaxation. Furthermore, even the readout

pulsed magnetic field gradient for the PE image does not

influence the longitudinal magnetization.

The third 90 degree pulse, which comes at the end of

the 72 interval, simply rotates the stored longitudinal

magnetization back to the transverse plane, as depicted in

figure l-3c. The intrinsic properties of the isochromats

have not been altered by the additional magnetization

gymnastics. Indeed, the sense and speed of free precession

in the transverse plane for the isochromats following the

third rf pulse is identical to the sense and speed of free

precession prior to the second rf pulse, which is indicated

in figure 4-2c. Hence, after the application of the third rf

pulse, the isochromats will freely process as in figure

'-3c. Since the only time this magnetization was influenced

by the inhomogeneous main magnetic field was during the

interval 71, the isochromat vectors will interfere amongst

themselves during the interval r2, with maximum constructive

interference occurring at a time 71 after the third rf pulse,

for T2>Tl. This constructive interference constitutes the

stimulated echo (STE), with maximum amplitude at a time 71

past the application of the third rf pulse. Thus, the

maximum amplitude of the STE at a time Tl1 after the third rf










pulse, MCSTE), is given by



MCSTE) 1/2MisinOesin92sinO3expE-C2Tl/T2 + T2/T1)3 *

fCB,D,Tl,T2) Ct-73



where 01 is the ith rf pulse, and FCG,D,Tl,T2) is the

diffusional damping term for the STE. For a constant steady

magnetic field gradient, fCG,D,Tl,T2) is given by

2 2 3 2
expC-C2/3)Dr 6 (fl +T1 TE2), and is modified for pulsed

magnetic field gradients ETa703.

The relaxation damping term tells the history of the

magnetization that went into the STE's formation. Since

spin-lattice relaxation occurred only within the interval

T2, the magnetization must have been stored along the

longitudinal direction during that interval. Likewise, the

magnetization can be traced to the transverse direction for

both the 71 interval between the first and second rf pulse,

and also for a time 71 subsequent to the third rf pulse, for

a total time of T2 influence amounting to 271.

As illustrated in figure '-1, the Gx readout gradient

is imposed, centered about a time Tl after the third rf

pulse, to frequency encode the STE with x direction spatial

dependence. Additionally, the receiver CRx) is gated open

during this same time, to permit acquisition (A) of the

spatially encoded STE. If each e1 was an ideal w/2 rf

pulses, and ignoring relaxation and diffusional damping, it

is noted from equation 4-7 that MCSTE) is proportional to








BS

(1/2)MI. This is the other factor of one half we noted

earlier after the formation of the PE. Whereas the

conventional spin echo imaging experiment Uields a single

image whose intensity is proportional to Mi, the stimulated

echo imaging sequence maU yield two images, each

proportional to (1/2)Mi, and each in spatial registration

with the other. The utilitU of these images lies not in this

proportionality, but rather in the unique Tl dependence of

the STE image. Applications which further extend and exploit

this Tl dependence are presented later in this chapter.

Formation of Secondaru Echoes

As was previously outlined, the rf pulse sequence given

in figure 4-1 mill yield both the primary echo and the

stimulated echo. AdditionallU, the application of the three

w/2 rf pulses may yield up to three other secondary echoes,

for a total of five echoes resulting from three rf pulses.

The origins of these secondary echoes are as follows.

The same echo formation mechanism which results in the

primarU echo after the application of the first two rf

pulses may also cause the formation of two of the three

secondarU echoes. If we consider the three rf pulses taken

two at a time, then there are three unique combinations, the

first and second pulses, the first and third pulses, and the

second and third pulses. Each combination will result in an

echo, with the first case simplU being the primary echo. The

second case results in an echo at a time T1+72 after the

third rf pulse, and the third case results in an echo at a








90

time T2 after the third rf pulse. Each of these echoes will

have different T2 weighting, dependent upon the time the

magnetization spends in the transverse direction.

The final secondary echo is derived from the PE. At

time 71 after the second rf pulse the PE has an amplitude

maximum. That is, at this time, the coherence imparted by

the first rf pulse has been regained. Indeed, there is as

much coherence amongst the isochromats which comprise the PE

at time 71 after the second rf pulse as there was

immediatelU following the first rf pulse, ignoring the

coherence lost due to relaxation and the diffusion process.

Therefore, for all intents and purposes, the PE at time Ti

after the second rf pulse behaves as if it was transverse

magnetization just after the application of a rf pulse.

Thus, after the time T1 past the second rf pulse, the

isochromats which comprise the PE will begin to lose

coherence until the third rf pulse acts to refocus them,

resulting in an echo at a time 2-T71 after the third rf

pulse.

Thus, the application of three rf pulses may result in

as many as five echoes. Each of these echoes could be used

for image formation, although the simplicity of the PE and

the unique Tl dependence of the STE make these two echoes

ideal for image formation. The addition of a fourth rf pulse

results in the formation of eighteen echoes, and an example

based upon this extended sequence is given late in the

chapter.