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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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Sattin, William, 1957-
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x, 155 leaves : ill., (some col.) ; 28 cm.

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Estimate reliability ( jstor )
Image contrast ( jstor )
Imaging ( jstor )
Magnetic fields ( jstor )
Magnetism ( jstor )
Magnetization ( jstor )
Magnets ( jstor )
Nuclear magnetic resonance ( jstor )
Signals ( jstor )
Tarts ( jstor )
Dissertations, Academic -- Nuclear Engineering Sciences -- UF
Magnetic resonance imaging ( lcsh )
Nuclear Engineering Sciences thesis Ph. D
Nuclear magnetic resonance spectroscopy ( lcsh )
Relaxation (Nuclear physics.) ( lcsh )
Spin-lattice relaxation ( lcsh )
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bibliography ( marcgt )
non-fiction ( marcgt )

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Thesis:
Thesis (Ph. D.)--University of Florida, 1985.
Bibliography:
Bibliography: leaves 151-154.
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Typescript.
General Note:
Vita.
Statement of Responsibility:
by William Sattin.

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Copyright [name of dissertation author]. Permission granted to the University of Florida to digitize, archive and distribute this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder.
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A BIFURCATED STUDY OF SPIN-LATTICE RELAXATION INFORMATION
IN NUCLEAR MAGNETIC RESONANCE IMAGING:
QUANTITATIUE ANALYSIS WITH CONUENTIONAL TECHNIQUES AND THE
UNCONUENTIONAL STIMULATED ECHO IMAGING TECHNIQUE
By
WILLIAM SATTIN
A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIUERSITY OF FLORIDA IN
PARTIAL FULFILLMENT OF THE REQUIREMENTS
FOR THE DEGREE OF DOCTOR OF PHILOSOPHY
UNIUERSITY OF FLORIDA
1985


Copyright 19B5
by
William Sattin


For Uendy and Emily, my life


ACKNOWLEDGMENTS
There are many people to whom I am indebted For their
assistance in accomplishing this work. Let mB begin with my
high school physics instructor, Sedgewick Duckworth. The
Iovb of life through understanding which he instilled within
me shall never waver.
I sincerely appreciate the Freedom and guidance oFFBred
me by my advisor, Dr. Katherine N. Scott. Her door is always
open to me.
I thank Dr. Alan M. Jacobs For seeing me through this
work, literally, From start to Finish. Also, I am grateFul
to have had the chance to interact with Dr. E. Raymond
Andrew, For he embodies the wisdom, wonder, and charm oF the
discipline oF nuclear magnetic resonance.
The other members oF my 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 spBCiFic contributions.
Special thanks go to the Department oF Radiology Far
partial Financial support. Additional Financial support was
supplied by NIH grant P41-RR-OEB70.


TABLE OF CONTENTS
PAGE
ACKNOWLEDGMENTS iv
LIST OF TABLES vi
LIST OF FIGURES vii
ABSTRACT ix
CHAPTER
I INTRODUCTION 1
II UTILIZATION OF THE SPIN-LATTICE RELAXATION
TIME IN NMR IMAGING 5
Introduction 5
Theory of Spin-Lattice Relaxation 5
Clinical Use of Spin-Lattice Relaxation 0
III INVESTIGATION INTO T1 DETERMINATION ON A
WHOLE BODY NMR IMAGER 10
Introduction 10
Methods and Materials 13
Results 44
Discussion 54
IV EXPLOITING THE STIMULATED ECHO IN NMR IMAGING..71
Introduction 71
Theory 74
Materials and Methods SI
Results 1E1
Discussion 130
V SUMMARY AND CONCLUSIONS 147
REFERENCES 151
BIOGRAPHICAL SKETCH
155


LIST OF TABLES
NUMBER TABLE PAGE
3-1 Concentration of Copper Sulfate Doped
Ulater and Resultant Spin-Lattice Relaxation
Time for Phantom Material 17
3-2 Typical Raw Data Acquired for T1
Determination 33
4-1 Four-Step Phase Cycling Used in Stimulated
Echo Imaging 101
vi


LIST OF FIGURES
NUHBER TABLE PAGE
3-1 Phantom used For all T1 measurements 15
3-2 Field mapping apparatus 20
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 yielding
good T1 estimates 35
3-7 Examples oF Fitted data sets which
yielded poor T1 estimates 36
3-B Sample computer output oF data
correlation program 39
3-9 Hypothetical 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 T1 value 46
3-12 Representative data indicating independence
to number oF images 50
3-13 Summary oF results 51
3-14 EFFect oF rF attenuating material upon
measurement precision and accuracy 63
4-1 Basic stimulated echo imaging sequence 7B
4-2 The Formation oF a primary echo 79
4-3 The Formation oF a stimulated echo B6
vii


4-4 The evaluation of a residual gradient 97
4-5 Effect of residual gradients on image
formation 99
4-6 The extended stimulated echo imaging
sequence 109
4-7 The tip angle reduced TI CTART)
imaging sequence 112
4-B The formation of a series of TART images 114
4-9 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 uater-lipid image of a hens egg 128
4-14 A STE chemical shift image 130
4-15 An extended STE multiecho series of images.... 132
4-16 A comparison of the spin echo image and the
primary 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 CONUENTIONAL TECHNIQUES AND THE
UNCONUENTIONAL STIMULATED ECHO IMAGING TECHNIQUE
Bg
William Sattin
December 1385
Chairman: Katherine N. Scott
Major Department: Nuclear Engineering Sciences
This work is comprised of two separate investigations,
both related to spin-lattice relaxation, or Tl, information
in nuclear magnetic resonance CNMR) imaging. One study
explored the ability of commercially available NMR imagers
to accurately and precisely determine the Tl 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 of experimental constraints. The
primary conclusion was that if one wished to obtain a direct
estimate of the actual Tl value in an object which might be
ix


within a spatially inhomogeneous radio Frequency Field, the
most accurate, precise, and time-BFFective technique to use
was three Fast inversion recovery images, with suitably
chosen values oF the inverting timB, whose signal
intensities were Fitted by a three-parameter exponential
Function.
The other study concerned it3elF with the detailed
theory, practical considerations, and possible applications
oF the stimulated echo CSTE) in NMR imaging. Uhereas
conventional NMR imaging techniques rely upon the spin echo,
which has solely TS relaxation weighting unless the NUR
signal is saturated, STE NMR imaging is unique in that the
STE has intrinsic T1 weighting. Possible applications
abound. In addition to generating T1 contrast images, it is
possible to calculate quantitative T1 inFormation From a
series oF STE images. Additionally, STE images eFFectively
enhance objects with long T1 values over those with shorter
T1 values, whereas spin echo images do not. Also, it was
demonstrated that the STE easily integrates into chemical
shiFt imaging schemes. OF prime interest are two STE imaging
sequences which permit the acquistion 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 diFFu3ion coeFFicients is
proposed, which utilizes STE imaging to lessen the eFFect oF
TS weighting.
x


CHAPTER I
INTRODUCTION
From modest but promising beginnings in the 1940s and
1950s, nuclear magnetic resonance CNflRl spectroscopy has
developed into an important research tool. The First
applications of NNR yielded insights into the properties of
the atomic nucleus. Early in its history, NdR spectroscopy
was adapted from the sole use by 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 many other
experimentally accessible quantities, making NP1R a powerful
and versatile technique that yields information related to
molecular structure, interactions, and dynamics, dost new
applications of NdR have been derived from parallel
improvements in instrumentation and methods, resulting in
applications in physics, chemistry, biology, geology, and
medicinB. Particular applications include two-dimBnsional
Fourier transform NdR CAu75D, high resolution NdR in
solids CHa76D, chemically induced dynamic nuclear
polarization CKa7BD, multiple quantum NdR CUe77D, and
NdR imaging CLa73D. The conclusions of the present
investigation are particularly applicable to NdR imaging.
1


a
The technique of NflR imaging is one that interests not
only scientists, but also nonscientists, For it promises to
provide a safB and noninvasivB method For diagnosing
dysFunction or disease in human tissue. Most whole body NI1R
imagers in use today detect the NflR signals From thB protons
in the object. In in vivo applications the major source oF
protons is water. Many 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 12.
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 CDa71J that T1 values oF watBr
protons in cancerous or damaged cells are longer than those
oF protons in normal cells CLeBlD. 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 Tl in NMR is qualitative in nature, Tl as a
source oF image contrast. The other role is quantitative,
For Tl values have the potential oF being diagnostic.


3
Chapter III explores the ability of commercially
available NflR imagers to accurately and precisely determine
the T1 value of imaged objects. ThB specific goal mas to
evaluate empirically the advice on T1 determination found in
the NflR spectroscopy literature and to see how well it
applied to NhR 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 spatially inhomogeneous rf
field. The most accurate, precise, and time effective
technique to use is three fast inversion recovery images,
with suitably chosen values of the inverting time, whose
signal intensities are fitted by a three-paramBter
exponential function.
Chapter IU presents the detailed theory, practical
considerations, and, by way of examples, the possible
applications of the stimulated echo CSTE) CHa50J in NMR
imaging. Whereas conventional NflR imaging techniques rely
upon the spin echo, STE NflR 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 NflR
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


4
STE is Basily 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 TE 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 far 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, T1 may influence the choice of the
optimum operational magnetic field strength for NMR imaging,
due to Tls significant variation with frequency CBoB4D.
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
5


E
nuclei will reside in the lowest energy 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 I 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 only 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 by 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. ThB 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. ThB latticB FiBld 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 -0
the order of 10 and 10 seconds respectively. Indeed, thB
large macromolecules, such as DNA and proteins, tumble
rather slowly, with correlation timBS three or four orders
of magnitude slower than lipid. The frequency of rotation
for the medium-sizBd 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 waterbased protons, which rotate at a frequency


B
that is typically greater than the transitional frequency of
the protons. Similarly, the macromoleculBS are inefficient
in causing relaxation, for they rotate at frequencies which
are much less than the transitional frequency.
Efficient relaxation correlates to short T1 values,
whereas inefficient relaxation results in long T1 values.
For example, in fat, which has a high lipid content, T1 is
typically of the order of a few hundred milliseconds, yet
the T1 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 CZ57D. Hence,
the motion of bound water is reduced, thus more closely
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 CDa711.
Clinical Use of Spin-Lattice Relaxation
Although spin density images are useful in a number of
clinical situations, thBrB is nearly universal agreement
that images which depend significantly on the relaxation
parameters T1 and T2 show considerably greater soft tissuB
contrast. This increased contrast allows improved


a
differentiation and recognition of anatomical detail and
helps to demonstrate and assess mass Bffects CStB53.
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 T1 values which are increased by
200* or 300* compared to the surrounding normal tissuB.
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, Bottomley et al.
have collated a vast body of relaxation time information for
thB purpose of establishing the range of normal values
CBo843. Deficiencies in measurement techniques were
identified as a major source of data irrBproducibility.
Additionally, there is significant overlap between normal
and abnormal tissue in some types of pathology, for example,
diffuse liver disease CDoB23. Thus, to date, measured T1
values are still too variable, and have yet to improve
significantly the tissue specificity of NMR imaging.


CHAPTER III
INVESTIGATION INTO T1 DETERMINATION ON A
WHOLE BODY NMR IMAGER
Introduction
Proton nuclear magnetic resonance CNMR) imaging may
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, TB, and the
spin-lattice relaxation time, T1. The NMR spectroscopy
literature is full of suggestions on how best to determine
these parameters, particularly Tl, in conventional samples
studied by physicists and chemists CGrB3, HaBlD .
Similarly, the NMR imaging literature offers a multitude of
suggestions for in vivo Tl determination, based on both
empirical and theoretical arguments CPy83]. The goal of
this work was to evaluate empirically the advice found in
the NMR spectroscopy literature as to how well it applied to
NMR imaging, with its unique experimental constraints.
The pulse programming capabilities of commercial NMR
imagers are typically limited, yet there are no fewer than
four distinct pulse sequences available which may be used to


11
provide estimates of the actual in vivo Tl: the spin echo
CSE) sequence CHa50D, the progressive saturation CPS)
sequence CFr71D, the inversion recovery CIR) sequence
COoBSD, and the fast inversion recovery (FIR) sequence
CKa77). Each of these sequences has at least tuo timing
parameters, values of which need to be optimized so as to
reduce the overall error in the determined Tl 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 thB conformity of an indicated value to an accepted
standard value CUa7Bl. A precise Tl estimate is not
necessarily accurate, whereas it is hoped that all accurate
Tl estimates are precise. Furthermore, other constraints of
thB 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 CBo7BD.
In the present study, experiments were conducted on a
phantom consisting of an array of vials containing
paramagnetically doped water, whose Tl 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 T1
value in an object which may bB 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 Tl, 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 Tl value, or they may be used a posteriori to help


13
evaluate the accuracy cf 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 System
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 thB z direction of the main magnetic fiBld.
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, Q, of a
circuit containing the body rf coil, on the bench. A sweep
wave generator, manufactured by Ulavetec, was coupled to the


14
rf coil. The frequency dependent response was monitored with
an oscilloscope, and the Q was determined by
Q f/6f C3-1D
where 6f was the width of the resonance curve at 70.73s of
the amplitude of the response at the resonance frequency, f
CKrBll. The was determined with the coil both physically
unloaded, and loaded with a dielectric material (0.33s NaCl
aqueous solution!. The ratio of the unloaded to loaded
was approximately 0.7.
The Teslacon imager made use of a DEC PDP 11/S4
computer for pulse sequence programming, data acquisition,
and data processing. Additionally, a FPS floating point
array processor aided in data processing. All experiments
were conducted with the standard software supplied by the
manufacturer (software 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 body. Due to the
spatial extent of the body it was of interest to examine the
passible effects of spatially dependent parameters, such as
main magnetic fiBld and rf magnetic field inhomogeneities,
upon in vivo spin-lattice relaxation measurements. Hence,
the phantoms geometric design, as seen in figure 3-1,


15
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.


16
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 Ce.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 simplB
phantom material. First, the spin-latticB 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
CSaB1!] .
The actual, or "gold standard value of T1 for each of
the phantom materials was determined in the following
manner: a single cylindrical glass vial Cwith 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


17
Table 3-1
Concentration of Copper Sulfate Doped Water and
Resultant Spin-Lattice Relaxation Time for Phantom Material
Material
Concentration CmM)
T1 (msec)
BCKey
1)
5.0
73.2114.3
CCKey
2}
3.5
154.013.8
DC Key
3)
E. 0
277.8123.1
ECKey
4)
1.0
540.457.1
FCKey
5 )
0.5
1102.21103.!


18
adjusted to make optimum use of the dynamic range of the
analog-to-digital converters. The imager 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 NflR signal, were turned
off. This resulted in the imager being used as a
conventional spectrometer. The inverting time, TI, was
incrementally varied for over twenty values which spanned
the estimated Tl value. For Bach 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-paramBter exponential function using the data
reduction routine of the program NHR, resident on a
Nicolet 11B0E computer CNm82J. This procedure was repeated
for each different doped solution on two occasions,
separated by over a year, with thB results given in table
3-1.
In addition to effecting the of the rf coil, a
dielectric substance will also dissipate incident rf energy.
An otherwise spatially homogeneous rf fiBld will become
spatially inhomogeneous if a dielectric fills the space.
Hence, the mere presence of the body in the NMR imager may
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 misset 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 bottlB while full of
saline solution of physiological concentration C0.93i NaCl).
The dimensions of the bottlB approximated those of a human
abdomen.
Spatial flapping of Intrinsic InhomogBneities
T1 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 3-8. The results
are presented in figures 3-3 and 3-4 respectively.
Since all images were single slice, it was sufficient
to examine the z equal zero planB for main magnetic fiBld
and/or rf transmitted field inhomogeneities. A SB centimeter
diamBter circular piece of lucite with thirty-seven small


20
FigurB 3-2. Field mapping apparatus, Flultiple 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
FigurB 3-3. Spatial homogeneity mapping of the main magnetic
Field. Each isostrength curve is 2.5 ppm of the
main magnetic Field. Measurements uere made in
the transverse plane over a 56 centimeter
diameter circular region.
ra
ail


22
Figure 3-4. Spatial homogeneity mapping of the transmitted
rf Field. Each isostrength curve is
approximately 0.25?i of the Field at the central
region. Measurements were made in the transverse
plane over a 56 centimeter diameter circular
region.


23
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 bB
placed in turn over each small vial. The imager was operated
as a spectrometer, with thB 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 manufacturers
specifications and was deBmed experimentally acceptable.
Although this investigation considered the effects of a
spatially inhomogeneous rf fiBld, 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.


24
The special rF coil urns 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 intensity values
should have been equal on resonance. Any variation in
intensity was attributed to variation in tip angle. Over the
useFul FiBld oF view, a coaxial circle about thirty
centimeters in diameter, the transmitted rF Field varied by
approximately 3.0%.
Data Acquisition Methodology
The investigation was aimed at determining the most
eFFicient and accurate method oF obtaining actual T1 values
From NriR images, with consideration towards the constraints
a spatially inhomogeneous rF Field imposses. NonuniForm rF
irradiation was a concern For it results in a spatially
dependent systematic error in rF pulse tip angles, and hence
in measured T1 CFr71D. Evaluation oF Four pulse sequences
was conducted, the spin echo CSE), the inversion recovery
CIR), the progressive saturation CPSD, and the Fast
inversion recovery CFIR). The degree oF Freedom oF the


25
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, dBsired 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
SCTP3 K CCexpC-TP/Tl)3 C3-23
where K and C were constants and SCTP3 was the signal
intensity as a function of a timing parameter, TP.
In PS and SE images, T1 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 timB, TI. The NNR spectroscopy


E6
literature CU0B8D suggests U3ing a fitting function with
tuio degrees of freedom, given by setting C in equation 3-E
equal to EK, for IR images inhere the inverting pulse uias
exactly 1B0 degrees. When the inverting pulse was misset,
possibly due to a spatially inhomogeneous rf field, the
literature CKo77D suggests the use of a fitting function
with three degrees of freedom, such as equation 3-E.
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 T1. As suggested in the literature
CCa751, this rapid TR requires the use of a fitting
function with three degrees of freedom, such as equation
3-E, whether the inverting pulsB was misset or not.
Details of the exact experimental procedure follow. It
should be noted that thB specified method was performed for
each of the five phantom samples as given in table 3-1, bath
surrounded by air and surrounded by the dielectric saline
solution. This permitted thB analysis to span the entire
clinically useful T1 range, and also to evaluate thB effects
of misset rf pulse tip angles resulting from an
inhomogeneous rf field. All acquired images were single
slice, at the z equal zero planB, with slice thickness of
onB centimeter. The Teslacon imager typically gathered E5B
data points in the readout direction and 1EB data points in
the phase encoding direction. The displayed image was 51E


e7
pixels by 512 pixels which was derived from the stored image
data which was dimensioned 255 by 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 takBn for each image.
The PS and SE experiments differed in only two
respects. First, thB PS images relied upon the bulk
magnetizations reaching a steady-state value in the
presence of the rapid pulsing with rr/2 rf pulses. It is
suggested that the system reaches this steady-state within
four pulses CFr711, hence all PS images were preceded by
four pulses prior to image acquisition. Second, PS
experiments yield consistent values of T1 for TR in the
range of 0.5T1 to 2.0T1, whereas SE experiments yield
consistent values of T1 for TR in thB range of 0.5T1 to
3.0T1. Hence, images were collected with TR ranging from its
minimum value, dictated by 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.


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 thB commencement of
the pulsB sequence. Therefore, TR for all IR images mas set
to at least five times thB 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 5.0T1.
In the FIR images, TI ranged from 25 milliseconds to Just
less than 2.0T1. 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
spatially 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, effectively resulting in each data points being
defined by a complex number. PS and SE experiments sampled


29
Figure 3-5. Color NMR images of phantom. Ca) With eight
identical vials, (bl with all vials surrounded
by saline solution.


30
the magnetization, whosB value lay bBtuieen zero and its
equilibrium value. Since this is a one sided range, all
positive in sign, signal intensities in PS and SE images
mere represented by the magnitude oF thB corresponding
complex number. IR and FIR experiments sampled thB
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 phasB 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 Bight 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.
ft 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


31
computer system. The general purpose of this program uias 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 NflR spectroscopy, where the sample under
investigation may 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 Tl. In NflR 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 Tl estimate. If each data set contained, say,
ten data pairs, the analysis 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
T1 value, and also to the estimated T1 value obtained iF all
oF the data pairs, Far example tBn, were Fitted to equation
3-2. Comparison with the actual T1 tested For precision and
accuracy, while comparison with the estimated T1 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 T1 determination. The experiment pBrFormed 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 thB 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


33
Table 3-2
Typical Raw Data Acquired for T1 Determination
TI(msec) SICvial 13 SICvial 51 Background
PHANTOM NOT IMMERSED IN SALINE SOLUTION
50
-43.7
-90.4
0.3B
75
-7.1
-26.4
0.12
125
44.1
80.1
0.06
175
B7.4
173.2
-0.26
225
119.5
229.5
-0.27
275
14B.7
273.9
-1.32
325
163.5
326.0
1.15
400
1B6.2
361.4
-0.07
1000
223.9
430.0
0.05
PHANTOM IMMERSED
IN SALINE SOLUTION
50
16.3
24.0
0.06
75
21.8
36.0
-0.33
125
27.4
4B.4
1.40
175
33.7
60.0
1.90
225
3B.4
68.9
1 .10
275
39. B
78.1
1.40
325
40.2
82.7
-0.74
400
47.8
86.5
-2.40
1000
51.2
95.1
-0.44
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


34
and 5 are presented in columns two and three respectively,
in arbitrary units. Uial 1 mas 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.
Qne, 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
thB phantom not immersed in the saline solution. A possible
explanation is that the saline solution absorbs a portion of
thB transmitted rf power, thus resulting in misset 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 3-6a illustrates the fitting of ten inversion
recovery data sets by a thrBB-parameter exponential
function. The estimated T1 value was 1328msec, which
happens to be within 1B\ of the actual T1 value of 154msec.
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 T1 value of 154msec, and
also the estimated T1 value of 132msec.
Figure 3-6b illustrates the fitting of only three out
of the passible ten data SBts to a three-parameter


35
Figure 3-6. Examples ef Fitted data sets yielding goad T1
estimates. Curve Cal was generated by Fitting
all points while Cb) was generated by Fitting
only the points denoted by


36
X x
Figure 3-7. Examples of Fitted data sets which yielded poor
T1 estimates. Curves Ca), (b), and Cc) were
Fitted only to the data points denoted as "0.


37
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
paints, the estimated T1 value is 131msec. Thus, this
particular value is both within 15\ of the all points
estimated T1 value of 132msec, and also within 155: of the
natural T1 value of 154msec. Figure 3-7 presents three other
possible choices of three data sets, fitted by a
three-parameter exponential function. In each case, the
estimated T1 value is neither within 155: of the all paints
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. DnB
point defines the signal intensity at, essentially, time
equal zero. Another TI value results in a signal intensity
corresponding to almost the completly relaxed state. Finally
the third TI value comes Just about at the time thB
relaxation curve changes thB most. Of course, these are not
the only choices of TI values which resulted in good fits,
indeed, there were many. Dne of the purposes of this
investigation was to identify and quantify how much


30
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 uiere unable to
characterize the entire relaxation curve, rather, they only
characterized the small region oF the curve where they were
located.
Data Analusis Methodology
To Facilitate analysis oF the numerical data, a program
was developed on an APPLE E-plus microcomputer, which
down-loaded the processed data From the IBH 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
TI 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
TI oF E77.0 milliseconds, vial number three, phantom
immersed in saline solution, using three images, and Fitted


33
TI OfiT GATHERED ON TESLACON
Figure 3-8. Sample computer output of data correlation
program.


40
by a function with three degrees of freedom), the criterion
was that the estimated T1 value fitted with Ibss than a 1S'<
relative error to either the actual T1 value or the T1
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 fallow. 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 refered to the Key which indicates which platting
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 thB eight
passible vials the data came from. Similarly, PSEQ
indicates which pulse sequence was used for the T1 estimate
Ci.e. PS, SE, IR, FIR). #PAR refers to the number of
parameters in the fitting function used for T1
determination, either two or three. #PTS refers to the
number of data points fitted to determine T1. #PTS was
either two, three, or four for #PAR equal to two, or
#PTS was three or four for #PAR equal to three. ThB
parameter "SALT indicates if the phantom was immersed in


41
the saline solution C SALT-YES5, or if the phantom was not
immersed in the saline solution ("SALT-NO). The parameter
TC0f1 indicates what the estimated T1 was compared to,
either the all points estimated TI C "TCOM-ALL), or the
natural TI C "TCOfl-GLD). Finally, LEO< X indicates that the
acceptance IbvbIs 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 95* 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 SBts oF TI values were
considered, the Tl 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 Tl 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 Tl value which was within 5* oF the standard.
Indeed, it appears that less than 30* oF all experiments
would result in estimated Tl values within 25* oF the
standard. IF this hypothetical curve corresponded to real


R H H E I N r H G
42
T1 DTR GATHERED ON TESLRCON
a
T1 DTR GTHEREO OH TESLhCON
b
Figure 3-9. Hypothetical output of data correlation program.
Output Cal dBpicts a nearly ideal output, while
Cbl dBpicts a poor output.


43
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 CBe04D.
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 Brror), acceptance at the 15% relative error
level was chosen to coincide with typical in vivo
biological variability.
After the qualitative data analysis based upon thB
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 Ci.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


44
illustration, if one of the fixed parameters mas 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 thBn
scaled to the Tl value which the fit was being compared
to. Next, a linear-multiplB-regression analysis CSpBID was
performed on this set of groups, yielding a regression
equation which related thB 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 incoporated 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 thB accuracy and precision in the estimated
Tl 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
T1 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 T1 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 arB presented in support of all results.
The reproducibility of signal intensities for a given set of
parameters was at all timBS greater than 95*, and typically
greater than 97.5*. The reproducibility was determined from
a series of measurements which were all repeated ten times.
Positional Dependence
All estimated T1 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 T1 did not exhibit these variations, within acceptable
experimental limits. The signal intensity variations
resulted from the intrinsic magnetic field inhomogenBity,the
intrinsic transmitted rf field inhomogeneity, and mostly,
the spatially inhomogeneous rf receiver coil response.


46
The representative data of figure 3-10 support this
result. Uial 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 CfittBd T1 value
had less than a 15* relative error) for both vials. Although
similar estimated T1 values were calculated for both vials,
typically the standard deviations in the fits for vial five
were larger than those for vial thrBB, owing to the smaller
signal to noise ratio of the intensities at that position.
Dependence Upon Actual T1 Ualue
The percentage of experiments which met the acceptance
criterion was constant within 15* to the actual Tl. That is,
a given set of parameters Cwith the values of the variable
timing parameter suitably chosen for the actual Tl)
generated a similar number of good fitting Tl estimates,
independent of the actual Tl. 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 Tl were constant within
15* to the actual Tl. Thus, it was possible to characterize
thB optimal values of the timing parameter independent of
Tl. The representative data of figure 3-11 support this
result. Each different RUN represents a different actual
Tl 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.


47
T1 DATA GATHERED OH TESLACON
a
T1 DATA GATHERED ON TESLACON
b
Figure 3-10. Representative data indicating independence to
position in Field-of-vieuj. Ca) Uial 5 output,
(b) identical output for vial 3.


48
TI DATA GATHERED OH TESLACON
RUN=KEY
UIAL=3
PSEQ=FIR
#PAR=3
#PTS=4
SALT=YES
TCOM=GLD
LEUO
Key
+ : 1
x : 2
o- : 3
: 4
o : 5
* 10* 15* 28* 25* >25*
ACCEPTANCE LEUEL
Figure 3-11. Representative data indicating independence to
actual TI value.


43
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 thrBB-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 corollary result. As explained previously,
IR experiments were fitted twice, once by a function with
two degrees of freedom Cgiven by setting C in equation 3-E
equal to EK), and once by a function with three degrees of
freedom Cgiven by equation 3-E). 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 3-1E support these
results. Additionally, the results of fitting FIR
experiments with a function with two degrees of freedom are
also presented in figure 3-13.


50
TI DATA GATHERED ON TESLACON
a
TI DflTfi GATHERED ON TESLACON
b
Figure 3-12. Representative data indicating independence to
number of images. Cal Using three images for T1
determination, Cb) using four images for T1
determination.


Meeti
a? 25 =
Salt
Estimated T<
I 1
I? S
CM 04 CO 04 CO
LU CC '
CO . U.
Salt
1
Natural T
1
w ¡Z
No Salt
Estimated T,
co
u. u.
No Salt
Natural T,
1
Figure 3-13. Summary of results


5E
Optimal Sets oF Parameters
To obtain a direct estimate of the actual T1 valuB in
an abject uihich 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 by a two-parameter exponential function can be more
precise and time effective than the FIR technique in
estimating Tl, but were always much less acurate, and prone
to error if an inhomogeneous rf field was present. The
representative data of figure 3-13 support these results.
Optimum Oariable Timing Parameter Ualues
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 may 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.


53
The use of three FIR images, fitted by 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 C3-31
whBre the three TI values, H, n, and L were the highest,
middle, and lowest values all scaled to TI by dividing the
specific timing parameter by the actual TI value. The
standard error of estimate in H was 0.3, for n 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 spatially
inhomogeneous rf field. The relationship between the threB
values of TI in the IR experiments was
H 1.6 + 1.in + 0.6L C3-41
where the three TI values, H, M, and L were the highest,
middle, and lowest values normalized to the actual TI value.
The standard error of estimate in H was 1.2, for H 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


54
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 + l.in 0.3L C3-5D
where the three values, H, tl, and L were the highest,
middle, and lowest values normalized, in this case, to the
Tl value estimated by fitting all data pairs. The standard
error of BstimatB in H was 1.1, for fl it was 0.7, and for L
it was 0.3.
Discussion
The in vivo determination of Tl 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 NhR
spectroscopy literature on Tl determination and as to how
well they applied to NMR imaging, with its unique set of
experimental constraints.
The N1R spectroscopy litBraturB offered suggestions on
which pulse sequence to use, the number and values of the
variable timing parameter to use, and the form of the


55
Fitting Function required to calculate T1 From the
individual signal intensity measurements. The added
constraints imposed by NflR imaging were the Following:
measurements could be obtained From any position within a
large Field aF 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 ISk 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 CFor
Fixed experimental parameters), then this would be an
expected result. As demonstrated by the signal intensity
variations in Figure 3-5, this was not thB 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 coils sensitivity response at that
location. This would inFluence only K and C oF equation 3-B,


56
and not the exponential time constant. Thus, this
investigation verified experimentally thB theoretical
prediction.
This result is significant for the following reason.
Although it is tempting to make a differential diagnosis
bassd upon differences in signal intensities Ce.g. if thB
liver is more intense than the spleen then diagnosis A, if
vice versa then diagnosis B), these differences may not bB
entirely organic in nature. Uariations in calculated T1
values Cfor 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 155i
to the actual T1 value, for properly chosen values of the
variable timing parameter. Since experiments were conducted
over an actual T1 range of approximately 100 milliseconds to
1000 milliseconds, this result is valid only over this
range. To justify this empirical result, it is necessary to
consider two factors, the physical model of spin-lattice
relaxation, and any instrumBntational dependence upon T1
determination.
Spin-lattice relaxation theory predicts, for such a
simple phantom material Cparamagnetically doped water), a
monoexponential relationship between thB signal intensity
and the variable timing parameter. The spin-lattice
relaxation rate i3 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 thB exponential argument,
and does not inFluence the general Form oF thB Function.
Thus, the empirical invariance to T1 was to be expected, on
the basis oF the physical model.
Although instrumental eFFects on T1 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 phantoms Tl
value. Thus, any Tl 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 thesB
parameters will indirectly aFFect Tl determinations.
The accuracy in deFining a timing parameter was
governed by the computers CPU clock. IF we consider a clock
Frequency oF one megahertz Ca 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 uisrs instrumental in


58
nature. For example, all experiments in this investigation
utilized a single slice mode of acquisition. ThB use of
multislice acquisition introduced other variables uihich
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 CEdBOJ 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
CFID) signal, and not an echo. Indeed, this complication
could explain the poor performance of the PS sequence. The
PS experiment relied upon the net magnetizations reaching a
steady-state value while being subjected to repetitive tr/2
rf pulses, but by its very nature a spin echo had a
dynamically varying net magnetization. Although thB 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 planB Cin the
rotating coordinate system) for an appreciable period of
time. This introduced TE damping of the signal intensity,
and in the presence of magnetic field gradients, damping due
to molecular self-diffusion CSt65D.


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 usBd 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.


BO
In this investigation, an estimated T1 value was deemed
a good approximation to the actual T1 value if the relative
Brror uias Ibss than 155i. For this acceptance level, only
First order effects mere of sufficient magnitude to
influence the error in the estimated T1 value. Therefore thB
observed invariance to the number of data pairs used in
calculating the spin-lattice relaxation time corresponds to
the NUR spectroscopy literatures suggestion concerning this
point CBeQOD.
This result uas of particular significant for the
following reason. In NUR 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. OnB way 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 by 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 NHR imaging, some have
made the suggestion that the best method of in vivo T1
determination was the fitting of two SE images with a
function with two degrees of freedom CHrB3, ha7SD. This
result indicates that, if the signal to noise ratio was
adequate in each image, two images would indeed be the
resonable number to acquire and process. This does not imply


El
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 tBrms 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 T1 was compared to the
"Estimated Tl 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:2 method was slightly more precise
than any other method of Tl determination, all of which
shared an essentially equal precision.
Those experiments whose calculated Tl values met the
acceptance criteria when compared to the "Natural Tl
represented methods of determining precise and accurate Tl
estimates. For this situation both the IR:2 and FIR:2
methods were inadequate, whether the phantom was immersed in
the saline solution or not. Additionally, bath the IR:3 and
FIR:3 methods of Tl determination were best, while the SE:2
method performed marginally.


62
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 analysis the
percent relative diFFerence was calculated From Figure 3-13
For both the Estimated Tl and Natural Tl results. The
percent relative diFFerence was determined by subtracting
the Meeting Criteria oF the Salt case From the 5i
Meeting Criteria oF the No Salt case, and then the result
was divided by the Meeting Criteria oF the No Salt"
case. This uias done For Bach pulse sBquence/Fitting
Function, For both the Estimated Tl and the Natural Tl
results, with the outcomes given in Figure 3-14.
Ideally, a given pulse sequence/Fitting Function would
perForm as well whether the phantom was immersed in the
salinB solution or was not immersed in the saline solution.
SincB this is thB 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 lasses oF accuracy and precision, while the SE:2 and
FIR:3 methods were nearly as lossless. These results must
not be considered out-oF-context. For example, the result
that the SE:2 method had a low percent relative diFFerence
Far the Natural Tl case viewed in conjunction with the
results oF Figure 3-13 indicated that, in this particular
situation, the SE:2 method went From being a poor method oF


% Relative Difference Between
No Salt and Salt
63
50
CM
CM
CO
CM
CO
LXJ
oc
cr
cc
oc
CO
U_
li-
Estimated Tj
CM
CM
CO
CM
CO
UJ
OC
oc
oc
OC
CO
LL
u_
Natural
Figure 3-14. Effect of rf attenuating material upon
measurement precision and accuracy.


64
determining accurate and precise T1 values when the phantom
uas 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 T1 values.
Of primary inportance mere 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 T1 values, or a posteriori to evaluate the
reliability of a calculated T1 value. The a priori
recommendations follow.
Optimal sets of parameters
The first decision to be made in the design of a T1
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 T1 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


B5
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 thB 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, thB SE series
often produced more precise measurements of T1 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 T1 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 thB FIR was
that, due to the extended TR time, Ibss saturation of signal
occurred. Thus, the IR images had slightly more contrast, an
aid for visual evaluation, but no real advantage in thB
quantitative analysis required far T1 determination.


E6
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
VBry high precision. Additionally, although not a result of
this investigation, the SE technique is often thB clinical
technique of preference, displacing the inversion techniques
consistently. For these reasons, the SE method of
spin-lattice relaxation time determination appears to enjoy
thB most widespread usb. Additional results of this
investigation indicated that the SE method had some serious
shortcomings, and yielded quality results only in
restrictive situations.
ThB most important disadvantage of the SE method was
its lack of accuracy in estimating T1 values. The SE method
always fared best when its BstimatBd 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 T1 values could not reliably be determined directly.
Instead, some type of calibration curve would need to be
generated to permit actual T1 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 CPyB31.


67
Optimum variable timing parameter values
Once the decision as to which pulse sequence to he
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
analysis should bB 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 Tl 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 E5 milliseconds for TI and 100
milliseconds for TR. The highest value of the timing
parameter, H, would vary depending upon thB pulse sequence.
For the FIR and IR methods, H could correspond to some value
close to TR, say 0.9TR. ThB solution is not as straight
forward for the SE method, where there is no fixed timing
parameter of relavance on which to base the choice. In this
case, H should be chosen with consideration towards the
largest value in the expected Tl range.


60
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, fl, 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 n 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 n
and H. Additionally, if the T1 of concern was thought to be
350 milliseconds, thBn assigning fl 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 T1 determination may be developed a priori, based
upon the available imaging time, desired accuracy and
precision, and range of T1 undBr investigation.


63
6 Posteriori Recommendations
It Frequently happens that the desire For a
quantitative determination oF T1 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 Ci.e. three images mere acquired,
all with the same number oF signal averages), then it mould
be possible to generate an estimated T1 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 mere 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 wbtb acquired with Four signal averages. A
thrBB-parameter exponential is FittBd 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 Tl
estimate, this series is comparable to the FIR method oF Tl
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,
fl, and H.
By a simple propagation of Brror analysis of equation
3-3, the standard error of estimate in T1 For the FIR method
of T1 determination, aCTll, may be determined to be 152
milliseconds. Thus, the optimal T1 value to bB determined by
the set of TI values used in this example is 4771152
milliseconds. The estimated value, 700 milliseconds, is
nearly 1.5 standard errors greater than thB 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 IU
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 CDuB4D,
this investigation sought to glean added information from
them. In particular, this study exploited the unique
properties of the stimulated echo CSTE1, as First identified
by Hahn CHa50J, and further quantified by Uoessner
CUI06II Although new to NMR imaging CFr85, HaBS, SaB5a,
Sa85bJ, stimulated echoes have been successfully applied by
Tanner to the measurement of translational self-diffusion
coefficients CTa70D, by Lausch and Spiess to study
infrequent Jumps of complex molecules CLaBO, SpBOl, and
more recently to analyze slow rotational motions of
molecular solids by Sullivan et al. CSuBBJ. Furthermore,
othBr investigators conducting research into stimulated echo
NMR imaging,concurrently with this investigation, have
recently reported their initial findings CFrBS, HaBSD.
This investigation is unique in that it is the first to
indicate that stimulated echoes may be applied to NMR
71


7£
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, thB spin-lattice relaxation time, Tl, and the
spin-spin relaxation time, TE. With current instruments,
contrast due to relaxation is achieved through the use of
either the spin echo CSE) technique, or an inverting
technique, such as the inversion recovery CIR5 sequence. In
particular, Tl 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 thB equilibrium magnetization,
initially aligned along the positive z axis, and sampling
its recovery with a rr/E rf pulse.
STE imaging introduces Tl weighting into the NhR image
in the following manner. UiBwed from the rotating frame of
reference, an initial tt/E rf pulse, at time equal to zero,
rotates the equilibrium magnetization into the transverse
plane. While in the transverse plane, the nBt magnetization
is reduced due to TE relaxation, molecular diffusion and
precession within an inhomogeneous magnetic field. A second
tt/E rf pulse, at time equal to rl, 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 CPE) at a time equal to twice r1. The
net longitudinal magnetization will be reduced due to T1
relaxation and molecular self-diffusion. At a time rS after
the second 90 degree rf pulse, a third 90 degree pulse is
applied which rotates this T1 reduced net longitudinal
magnetization back into thB transverse planB, where the
individual isochromats constructively interfere to form the
STE at a time rl 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 CEdBOJ 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 NflR imaging. STE imaging, with its unique T1
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,


74
hence images acquired with this sequence will Frequently
contain a high degree of mixBd T1 and TE 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 timB had
been systematically varied. Second, a novel application of
the T1 weighted STE image was obtained: the enhancement or
suppression of Blements in the object with different T1
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 STEs 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
dBtBctsd in NflR For thB first tima in 1950 by Hahn CHa50D,
and spin Bchoss havs subssqusntly bBBn appliBd in NMR to
various snds, including ths msasurBmsnt of TI valas
CCa54D, ths invBstigation into molacular diffusion
procsssas CSt65D, ths dBtarmination of scalar coupling
constants CFr751, thB indirect detection of magnstic
rasonancB EEmBOD, coharance transfer Cf1a7B3, and NflR
imaging CEdBOD. Bisa, the same affects have been exploited
in electron spin resonance CN72D, microwave spectroscopy
CG176D, and in laser optical spectroscopy CKCuBHD.
An Bcho 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 inital pulse, hence a coherence
is produced. In time, inhomogeneous interactions within the
system act to destroy the coherence. This is accomplished in
NflR by an inhomogeneous magnetic field, by an inhomogeneous
Stark field in microwave spectroscopy, or by the DopplBr
effect in optical spectroscopy Cf1a78D A second pulse,
applied at a time t, inverts the accumulated effects of the
inhomogeneous interaction. Thus, thB initial coherence is
regained and an echo occurs at a time Bt. 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 CHa58D.


76
In 1946, Bloch introduced a phenomenological vector
equation to describe NMR CB146D. It accurately
characterized an isolated particle of spin 1/E in the
presence of a static magnetic Field. Feynman et al. CFe57D
have demonstrated that this description is complete, that
is, a geometric representation of the Schroedinger equation
is possible. Also, PBgg et al. CPeBlD havB shown this
description to be perfectly rigorous, because the vectors
are equivalent to Heisenberg operators in thB 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.
Blochs model of N1R 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, n, to the applied
magnetic vector field, B, such that
dn/dt rcn x B) C4-ih
where T 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 fiBld with the frequency n, such that
C4-ED


77
This relationship between the precession Frequency and thB
applied magnetic Field is reFered to as the Larmor equation.
The Frequency n is thB Larmor Frequency. The Larmor
equation, expressed as in equation 4-2, indicates that the
prBcessional Frequency n is proportional to the magnetic
Field B, where T 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 NfIR phenomenon. Additionally,
thB absence oF the Planck constant in the Larmor equation
given in equation 4-B Further JustiFies the classical
treatment oF the resonance phenomenon.
Further support oF the classical Formulation oF the NHR
phenomenon is oFFerBd by the correspondence principle oF
quantum mechanics CUa53D, 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 CP106], 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


7B
Tx
Gx
Gy
Gz
Rx
A
o
A
o
Figure 4-1. Basic stimulated echo imaging sequence.


73
Figure 4-2. The Formation of a primary echo.


00
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 CTx) oF a 00 degree, or w/E rF
pulse applied as shown in Figure i-Eb. It is assumed that
the rF pulse is oF Frequency nCp) and width tCp), such that
tCp) is small compared to T1 and TE, and excitBS the entire
chemical shiFt Frequency bandwidth equally. IF, Far example,
the rF pulse has a phase A equal to 90 degrees Ci.e. along
the positive x direction as depicted in Figure i-EbD, 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. ThB z axis oF thB 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 rBFerBd to as thB 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 NflR takes on a simpler Form when


B1
expressed in terms of the rotating frame of reference. Also,
a simpler physical picture of events is possible uihen
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 4-5. In practice, resonance
takes place over a range of frequencies determined by thB
inhomogeneity of the main magnetic fiBld throughout the
sample. Therefore, thB object may bB considered to bB
comprised of an ensemblB of magnetic moments, whose
resonance frequencies are symmetrically distributed about
the Larmor frequency, n. Figure 4-5c illustrates the free
precession Ci.e. Larmor typB precession and not rf pulse
induced rotation) of all these isochromats during the time
interval t1. Since figure 4-5c depicts the dynamics of the
magnetization in a frame of reference rotating at frequency
n, thB isochromatic moment pairs maintain a symmetry about
the y direction, but rotate in opposite directions. This is
indicated in figure 4-5c in the following manner. The light
gray regions represent a range of isochromats which deviate
less from n 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 rl, pulsed linear magnetic
field gradients are applied as in the conventional fourier


BE
imaging technique CEdBOJ. The preparatory readout gradient
is embodied in the effective x gradient, CGx), whereas Gy
and Gz are employed for phase encoding. The effect of thesB
pulsed magnetic field gradients is the spatial encoding of
the NMR signal in a precise manner. If one, two, or threB
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 tt/E
rf pulse applied in the presence of a slice selective Gz
CHo771.
After the time interval r1, a second 30 degree rf pulse
is applied, as indicated in figure 4-Ed. Whereas prior to
the second rf pulse all magnetization was lying in the
transverse plane Cassuming negligible T1 relaxation during
the interval -rl), after the second rf pulse the net
magnetization has components in the longitudinal plane as
well as the transverse plane. Figure 4-Ee illustrates the
transverse component of the net magnetization immediately
following the second rf pulse, obtained by simply projecting
the net magnetization of figure 4-Ed 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 Cif the rf pulse is
applied along the positive x direction as indicated), hence


03
the projection of the net magnetization onto the transverse
plane, immediately Following the second rf pulse, lies
completely on the x axis.
The intrinsic properties of the isochromats have not
been altered by this magnetization gymnastics. The sense and
speed of free precession in the transverse plane for the
isochromats fallowing the second rf pulse is identical to
the sense and speed of Free precession prior to the second
rf pulse Ci.e. as indicated in Figure 4-2c). Hence, From
time rl on, the isochromats will FrBBly precBss as in Figure
4-2F. From time rl to time 2t1 the isochromat vectors will
interfere amongst themselves, with maximum constructive
interference occuring at time 2t1. This constructive
interference constitutes a primary echo CPE), with maximum
amplitude at time 2rl, and so named to distinguish it From
the spin echo which results from a Tr/2-T-Tr rf pulse
sequence. The maximum amplitude of the PE at time 2rl,
nCPE), is given by
2
HCPE) n¡sinOlsin C02/2)expC-2t1/T2)FCG,D,rl) C4-3D
where Mi is the equilibrium magnetization, 9i is the tip
angle of the ith pulse, and FCG,D,t1) corresponds to the
diffusional damping resulting From molecular diffusion in
the presence of magnetic field gradients. For a constant
steady magnetic field gradient, F(G,D,t1) is given by
2 2 3
expf-C2/3)Dr G rl }, where G is the magnetic field gradient


B4
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 CSt651. The two cases are
identical, in the limit, as we pass from pulsed to
continuous application of the gradient.
As illustrated in figure 4-1, the Gx readout gradient
is imposed, centered about the time Erl, 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 BncodBd PE. If all
pulses are ideal tt/2 rf pulses, then the PE imagB is
identical to thB image produced by conventional spin echo
imaging, except for a factor of one half in signal
intensity. This reduction in thB signal to noise ratio would
be intolerable unless it is passible 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 tt/2 rf pulse.
Formation of the Stimulated Echo Image
It can be shown that the solution to the Bloch equation
in the rotating frame CB146D takes on the form
HxCt+tp) nxCt)
C 4-41
flyCt+tp) riy(t)cos9 rizCt)sin9
C 4-51
MzCt+tp) riy(t)sin9 + f1zCt)cos9
C4-6D


B5
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, fix is taken to be in phase with respect to the x
axis rotating frame of reference, while My is 90 degrees out
of phase. Of prime interest is equation 4-6, which
characterizes the longitudinal magnetization, and in
particular its dependence on flyCt). Since the spin system is
initially in thermal equilibrium, tlyCt-0) 0. Hence, by
equation 4-6, HzCt-tp) 0 for an ideal tt/E rf pulse. As
applied to the experiment of figure 4-1, the implication is
that during the interval rl, flz simply approaches the
equilibrium magnetization, if the affect of relaxation is
considered.
If t1 is of the order of TE or less, thsn f1y(tTl) is
surely nonzero. That is, at time t1 we will have appreciable
transverse magnetization. Therefore the second ir/E rf pulse,
in addition to inducing the PE, will also produce net
longitudinal magnetization, that is, MzCt-rl+tpU 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 tt/E
rf pulse of figure 4-1. Indeed, figure 4-3a is identical to
figure 4-Ed. Whereas we considered the transverse projection
of this net magnetization in order to describe the formation


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


07
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 thB readout
pulsed magnetic field gradient for the PE image does not
influence the longitudinal magnetization.
The third 90 degree pulsB, which comes at the end of
the t2 interval, simply rotates the stored longitudinal
magnetization back to the transverse plane, as depicted in
figure 4-3c. 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 precess as in figure
4-3c. Since the only time this magnetization was influenced
by the inhomogeneous main magnetic field was during the
interval t1, the isochromat vectors will interfere amongst
themselves during the interval t2, with maximum constructive
interference occuring at a time t1 after the third rf pulse,
for t2>t1. This constructive interference constitutes the
stimulated echo CSTE), with maximum amplitude at a time t1
past the application of the third rf pulse. Thus, the
maximum amplitude of the STE at a time t1 after the third rf


88
pulse, flCSTE), is given by
tlCSTE) 1/Srii sin01sin92sin93expC-C2t1/T2 + tE/T1)D *
fCG,D,rl,t2) C4-7D
where 0i is the ith rf pulse, and FCG,D,t1,t2 is the
diffusional damping term for the STE. For a constant steady
magnetic field gradient, FCG,D,t1,t2) is given by
2 2 3 2
expf-(2/3)Dr G CtI +rl t2)1, and is modified for pulsed
magnetic field gradients CTa703.
The relaxation damping term tells the history of thB
magnetization that went into the STEs 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 rl interval between the first and second rf pulse,
and also for a time rl subsequent to the third rf pulse, for
a total time of T2 influence amounting to 2rl.
As illustrated in figure 4-1, the Gx readout gradient
is imposed, centered about a time rl after the third rf
pulse, to frequency encode the STE with x direction spatial
dependence. Additionally, the receiver (Rx) is gated open
during this same time, to permit acquistion (A) of the
spatially encoded STE. If each 9i was an ideal tt/2 rf
pulses, and ignoring relaxation and diffusional damping, it
is noted from equation 4-7 that nCSTE) is proportional to


83
Cl/2)Mi. This is ths other Factor of one half we noted
earlier after the formation of the PE. Whereas the
conventional spin echo imaging experiment yields a single
image whose intensity is proportional to Hi, the stimulated
echo imaging sequence may yield two images, each
proportional to Cl/2)f1i, and each in spatial registration
with thB other. The utility of these images lies not in this
proportionality, but rather in the unique T1 dependence of
the STE imagB. Applications which further extend and exploit
this T1 dependence are presented later in this chapter.
Formation of 5econdaru Echoes
As was previously outlined, the rf pulse sequence given
in figure 4-1 will yield both the primary echo and the
stimulated echo. Additionally, the application of the three
rr/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
primary echo after the application of the first two rf
pulses may also cause the formation of two of thB three
secondary echoes. If we consider the three rf pulses taken
two at a timB, then there are three unique combinations, thB
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 simply bBing the primary echo. The
second case results in an echo at a time t1+t2 after the
third rf pulse, and the third case results in an echo at a


Full Text
I
&•
/'
Ci
I \

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
By
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 19B5
by
William Sattin

For Uendy and Emily, my life

ACKNOWLEDGMENTS
There are many people to whom I am indebted For their
assistance in accomplishing this work. Let mB 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 my advisor, Dr. Katherine N. Scott. Her door is always
open to me.
I thank Dr. Alan M. Jacobs For seeing me through this
work, literally, From start to Finish. Also, I am grateFul
to have had the chance to interact with Dr. E. Raymond
Andrew, For he embodies the wisdom, wonder, and charm oF the
discipline oF nuclear magnetic resonance.
The other members oF my 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 spBCiFic contributions.
Special thanks go to the Department oF Radiology Far
partial Financial support. Additional Financial support was
supplied by NIH grant P41-RR-OEB70.

TABLE QF CONTENTS
PAGE
ACKNOWLEDGMENTS iv
LIST OF TABLES vi
LIST OF FIGURES vii
ABSTRACT ix
CHAPTER
I INTRODUCTION 1
II UTILIZATION OF THE SPIN-LATTICE RELAXATION
TIME IN NMR IMAGING 5
Introduction 5
Theory of Spin-Lattice Relaxation 5
Clinical Use of Spin-Lattice Relaxation 0
III INVESTIGATION INTO T1 DETERMINATION ON A
WHOLE BODY NMR IMAGER 10
Introduction 10
Methods and Materials 13
Results 44
Discussion 54
IV EXPLOITING THE STIMULATED ECHO IN NMR IMAGING..71
Introduction 71
Theory 74
Materials and Methods SI
Results 1E1
Discussion 130
V SUMMARY AND CONCLUSIONS 147
REFERENCES 151
BIOGRAPHICAL SKETCH
155

LIST OF TABLES
NUMBER TABLE PAGE
3-1 Concentration of Copper Sulfate Doped
Ulater and Resultant Spin-Lattice Relaxation
Time for Phantom Material 17
3-2 Typical Raw Data Acquired for T1
Determination 33
4-1 Four-Step Phase Cycling Used in Stimulated
Echo Imaging 101
vi

LIST OF FIGURES
NUHBER TABLE PAGE
3-1 Phantom used For all T1 measurements 15
3-2 Field mapping apparatus 20
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 yielding
good T1 estimates 35
3-7 Examples oF Fitted data sets which
yielded poor T1 estimates 36
3-B Sample computer output oF data
correlation program 39
3-9 Hypothetical 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 T1 value 40
3-12 Representative data indicating independence
to number oF images 50
3-13 Summary oF results 51
3-14 EFFect oF rF attenuating material upon
measurement precision and accuracy 63
4-1 Basic stimulated echo imaging sequence 7B
4-2 The Formation oF a primary echo 79
4-3 The Formation oF a stimulated echo B6
vii

4-4 The evaluation of a residual gradient 97
4-5 Effect of residual gradients on image
formation 99
4-6 The extended stimulated echo imaging
sequence 10B
4-7 The tip angle reduced TI CTART)
imaging sequence 112
4-B The formation of a series of TART images 114
4-9 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 imagB 126
4-13 A uater-lipid image of a hen’s egg 128
4-14 A STE chemical shift image 130
4-15 An extended STE multiecho series of images.... 132
4-16 A comparison of the spin echo image and the
primary 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 CONUENTIONAL TECHNIQUES AND THE
UNCONUENTIONAL STIMULATED ECHO IMAGING TECHNIQUE
Bg
William Sattin
December 1385
Chairman: Katherine N. Scott
Major Department: Nuclear Engineering Sciences
This work is comprised of two separate investigations,
both related to spin-lattice relaxation, or Tl, information
in nuclear magnetic resonance CNMR) imaging. One study
explored the ability of commercially available NMR imagers
to accurately and precisely determine the Tl 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 of experimental constraints. The
primary conclusion was that if one wished to obtain a direct
estimate of the actual Tl value in an object which might be
ix

within a spatially inhomogeneous radio Frequency Field, the
most accurate, precise, and time-BFFective technique to use
was three Fast inversion recovery images, with suitably
chosen values oF the inverting timB, whose signal
intensities were Fitted by a three-parameter exponential
Function.
The other study concerned it3elF with the detailed
theory, practical considerations, and possible applications
oF the stimulated echo CSTE3 in NMR imaging. Uhereas
conventional NMR imaging techniques rely upon the spin echo,
which has solely TS relaxation weighting unless the NUR
signal is saturated, STE NMR imaging is unique in that the
STE has intrinsic T1 weighting. Possible applications
abound. In addition to generating T1 contrast images, it is
possible to calculate quantitative T1 inFormation From a
series oF STE images. Additionally, STE images eFFectively
enhance objects with long T1 values over those with shorter
T1 values, whereas spin echo images do not. Also, it was
demonstrated that the STE easily integrates into chemical
shiFt imaging schemes. OF prime interest are two STE imaging
sequences which permit the acquistion 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 diFFu3ion coeFFicients is
proposed, which utilizes STE imaging to lessen the eFFect oF
TS weighting.
x

CHAPTER I
INTRODUCTION
From modest but promising beginnings in the 1940s and
1950s, nuclear magnetic resonance CNflRl spectroscopy has
developed into an important research tool. The First
applications of NNR yielded insights into the properties of
the atomic nucleus. Early in its history, NdR spectroscopy
was adapted from the soIb use by physicists, to the realm of
chemists, who saui the potential of the chemical shift
phenomenon as a structural probe. This first useful
parameter has now been supplemented by many other
experimentally accessible quantities, making NP1R a powerful
and versatile technique that yields information related to
molecular structure, interactions, and dynamics, dost new
applications of NdR have been derived from parallel
improvements in instrumentation and methods, resulting in
applications in physics, chemistry, biology, geology, and
medicinB. Particular applications include two-dimensional
Fourier transform NdR CAu75D, high resolution NdR in
solids CHa76D, chemically induced dynamic nuclear
polarization CKa70D, multiple quantum NdR CUe77D, and
NdR imaging CLa73D. The conclusions of the present
investigation are particularly applicable to NdR imaging.
1

a
The technique of N(1R imaging is one that interests not
only scientists, but also nonscientists, For it promises to
provide a safe and noninvasivB method For diagnosing
dysFunction or disease in human tissue. Most whole body NI1R
imagers in use today detect the NflR signals From thB protons
in the object. In in vivo applications the major source oF
protons is water. Many 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 12.
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 CDa71J that T1 values oF watBr
protons in cancerous or damaged cells are longer than those
oF protons in normal cells CLeBlD. 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 Tl in NMR is qualitative in nature, Tl as a
source oF image contrast. The other role is quantitative,
For Tl values have the potential oF being diagnostic.

3
Chapter III explores the ability of commercially
available NflR imagers to accurately and precisely determine
the T1 value of imaged objects. ThB specific goal mas to
evaluate empirically the advice on T1 determination found in
the NflR spectroscopy literature and to see hout well it
applied to NhR 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 spatially inhomogeneous rf
field. The most accurate, precise, and time effective
technique to use is three fast inversion recovery images,
with suitably chosen values of the inverting time, whose
signal intensities are fitted by a three-paramBter
exponential function.
Chapter IU presents the detailed theory, practical
considerations, and, by way of examples, the possible
applications of the stimulated echo CSTE) CHa50D in NMR
imaging. Whereas conventional NflR imaging techniques rely
upon the spin echo, STE NflR imaging incorporates the uniquB
T1 dependence of the STE. The results reported in Chapter IU
take the form of specific applications of the STE to NflR
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

4
STE is Basily 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 TE 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 far their widespread use as diagnostic
parameters in clinical NMR imaging. T1 and TB directly
affect the selection of imaging pulse sequence timing
parameters, and consequently, the total imaging times and
patient throughput. Also, T1 may influence the choice of the
optimum operational magnetic field strength for NMR imaging,
due to Tl’s significant variation with frequency CBoB4D.
Theoru 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 ensembls 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
5

E
nuclei will reside in the lowest energy 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 I 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 only 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 by 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. ThB latticB Field must Fluctuate to transFar 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, uihich
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 -0
the order oF 10 and 10 seconds respectively. Indeed, thB
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-sizBd 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

a
that is typically greater than the transitional frequency of
the protons. Similarly, the macromoleculBS are inefficient
in causing relaxation, for they rotate at frequencies which
are much less than the transitional frequency.
Efficient relaxation correlates to short T1 values,
whereas inefficient relaxation results in long T1 values.
For example, in fat, which has a high lipid content, T1 is
typically of the order of a few hundred milliseconds, yet
the T1 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 CZÍ57D. Hence,
the motion of bound water is reduced, thus more closely
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 CDa71D.
Clinical Use of Spin-Lattice Relaxation
Although spin density images are useful in a number of
clinical situations, thBrB is nearly universal agreement
that images which depend significantly on the relaxation
parameters T1 and T2 show considerably greater soft tissuB
contrast. This increased contrast allows improved

a
differentiation and recognition of anatomical detail and
helps to demonstrate and assess mass Bffects CStB53.
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 T1 values which are increased by
200* or 300* compared to the surrounding normal tissuB.
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, Bottomley et al.
have collated a vast body of relaxation time information for
thB purpose of establishing the range of normal values
CBo843. Deficiencies in measurement techniques were
identified as a major source of data irrBproducibility.
Additionally, there is significant overlap between normal
and abnormal tissue in some types of pathology, for example,
diffuse liver disease CDoB23. Thus, to date, measured T1
values are still too variable, and have yBt to improve
significantly the tissue specificity of NMR imaging.

CHAPTER III
INVESTIGATION INTO T1 DETERMINATION ON A
WHOLE BODY NMR IMAGER
Introduction
Proton nuclear magnetic resonance CNMR) imaging may
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, TE, and the
spin-lattice relaxation time, T1. The NMR spectroscopy
literature is full of suggestions on how best to determine
these parameters, particularly Tl, in conventional samples
studied by physicists and chemists CGr83, HaBlD.
Similarly, the NMR imaging literature offers a multitude of
suggestions for in vivo Tl determination, based on both
empirical and theoretical arguments CPy83]. The goal of
this work was to evaluate empirically the advice found in
the NMR spectroscopy literature as to how well it applied to
NMR imaging, with its unique experimental constraints.
The pulse programming capabilities of commercial NMR
imagers are typically limited, yet there are no fewer than
four distinct pulse sequences available which may be used to

11
provide estimates of the actual in vivo Tl: the spin echo
CSE) sequence CHa50D, the progressive saturation CPS)
sequence CFr71D, the inversion recovery CIR) sequence
COoBSD, and the fast inversion recovery (FIR) sequence
CKa77). 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 Tl 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 thB conformity of an indicated value to an accepted
standard value CUa7Bl. A precise Tl estimate is not
necessarily accurate, whereas it is hoped that all accurate
Tl estimates are precise. Furthermore, other constraints of
thB 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 CBo7BD.
In the present study, experiments were conducted on a
phantom consisting of an array of vials containing
paramagnetically doped water, whose Tl 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 T1
value in an object which may bB 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 Tl, 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 Tl value, or they may be used a posteriori to help

13
evaluate the accuracy cf 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 thB z direction of the main magnetic fiBld.
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, Q, of a
circuit containing the body rf coil, on the bench. A sweep
wave generator, manufactured by Ulavetec, was coupled to the

14
rf coil. The Frequency dependent response was monitored with
an oscilloscope, and the Q was determined by
Q - F/6 F C3-1D
where 6F was the width oF the resonance curve at 70.73s oF
the amplitude oF the response at the resonance Frequency, F
CKrBll. The â–¡ was determined with the coil both physically
unloaded, and loaded with a dielectric material (0.33s NaCl
aqueous solution!. The ratio oF the unloaded â–¡ to loaded â–¡
was approximately 0.7.
The Teslacon imager made use oF a DEC PDP 11/54
computer For pulse sequence programming, data acquisition,
and data processing. Additionally, a FPS Floating point
array processor aided in data processing. All experiments
were conducted with the standard soFtware supplied by the
manuFacturer (soFtware 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 body. Due to the
spatial extent oF the body it was oF interest to examine the
passible eFFects oF spatially dependent parameters, such as
main magnetic FiBld and rF magnetic Field inhomogeneities,
upon in vivo spin-lattice relaxation measurements. Hence,
the phantom’s geometric design, as seen in Figure 3-1,

15
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.

16
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 Ce.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 simplB
phantom material. First, the spin-latticB 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
CSaB4D.
The actual, or "gold standard” value of T1 for each of
the phantom materials was determined in the following
manner: a single cylindrical glass vial Cwith 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

17
Table 3-1
Concentration of Copper Sulfate Doped Water and
Resultant Spin-Lattice Relaxation Time for Phantom Material
Material
Concentration CmM)
T1 (msec)
BCKey
1)
5.0
73.2114.3
CCKey
2}
3.5
154.0±13.8
DC Key
3)
E. 0
277.8123.1
ECKey
4)
1.0
540.4±57.1
FCKey
5 )
0.5
1102.21103.!

18
adjusted to make optimum use of the dynamic range of the
analog-to-digital converters. The imager 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 NflR signal, were turned
off. This resulted in the imager being used as a
conventional spectrometer. The inverting time, TI, was
incrementally varied for over twenty values which spanned
the estimated Tl value. For Bach 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-paramBter exponential function using the data
reduction routine of the program ”NHR”, resident on a
Nicolet 11B0E computer CNm82J. This procedure was repeated
for each different doped solution on two occasions,
separated by over a year, with thB results given in table
3-1.
In addition to effecting the â–¡ of the rf coil, a
dielectric substance will also dissipate incident rf energy.
An otherwise spatially homogeneous rf fiBld will become
spatially inhomogeneous if a dielectric fills the space.
Hence, the mere presence of the body in the NHR imager may
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 misset 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 bottlB while full of
saline solution of physiological concentration C0.93i NaCl).
The dimensions of the bottlB approximated those of a human
abdomen.
Spatial flapping of Intrinsic InhomogBneities
T1 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 3-8. The results
are presented in figures 3-3 and 3-4 respectively.
Since all images were single slice, it was sufficient
to examine the z equal zero planB for main magnetic fiBld
and/or rf transmitted field inhomogeneities. A SB centimeter
diamBter circular piece of lucite with thirty-seven small

20
FigurB 3-2. Field mapping apparatus, Flultiple 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
FigurB 3-3. Spatial homogeneity mapping of the main magnetic
Field. Each isostrength curve is 2.5 ppm of the
main magnetic Field. Measurements uere made in
the transverse plane over a 55 centimeter
diameter circular region.
r2
Mil

22
Figure 3-4. Spatial homogeneity mapping of the transmitted
rf Field. Each isostrength curve is
approximately 0.25of the Field at the central
region. Measurements were made in the transverse
plane over a 56 centimeter diameter circular
region.

23
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 thB 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 deBmed experimentally acceptable.
Although this investigation considered the effects of a
spatially inhomogeneous rf fiBld, 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.

24
The special rf coil urns 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 intensity values
should have been equal on resonance. Any variation in
intensity was attributed to variation in tip angle. Over the
useful fiBld of view, a coaxial circle about thirty
centimeters in diameter, the transmitted rf Field varied by
approximately 3.0k.
Data Acquisition Methodology
The investigation was aimed at determining the most
efficient and accurate method of obtaining actual T1 values
From NHR images, with consideration towards the constraints
a spatially inhomogeneous rf field imposses. Nonuniform rf
irradiation was a concern for it results in a spatially
dependent systematic error in rf pulse tip angles, and hence
in measured T1 CFr71D. Evaluation of four pulse sequences
was conducted, the spin echo CSE), the inversion recovery
CIR), the progressive saturation CPS3, and the fast
inversion recovery CFIR). The degree of freedom of the

25
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, dBsired 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/TDD C3-2D
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, T1 weighting was introduced by
saturating the signal with rapid pulsing. Therefore, TP was
the pulse sequence repetition time, TR. The spectroscopy
literature CFr71) 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 timB, TI. The NNR spectroscopy

E6
literature CU0B8D suggests U3ing a fitting function with
tuio degrees of freedom, given by setting C in equation 3-E
equal to EK, for IR images inhere the inverting pulse uias
exactly 180 degrees. When the inverting pulse was misset,
possibly due to a spatially inhomogeneous rf field, the
literature CKo77D suggests the use of a fitting function
with three degrees of freedom, such as equation 3-E.
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 T1. As suggested in the literature
CCa751, this rapid TR requires the use of a fitting
function with three degrees of freedom, such as equation
3-E, whether the inverting pulsB was misset or not.
Details of the exact experimental procedure follow. It
should be noted that thB specified method was performed for
each of the five phantom samples as given in table 3-1, bath
surrounded by air and surrounded by the dielectric saline
solution. This permitted thB analysis to span the entire
clinically useful T1 range, and also to evaluate thB effects
of misset rf pulse tip angles resulting from an
inhomogeneous rf field. All acquired images were single
slice, at the z equal zero planB, with slice thickness of
onB centimeter. The Teslacon imager typically gathered E5B
data points in the readout direction and 1EB data points in
the phase encoding direction. The displayed image was 51E

27
pixels by 512 pixels which was derived from the stored image
data which was dimensioned 255 by 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 takBn for each image.
The PS and SE experiments differed in only two
respects. First, thB PS images relied upon the bulk
magnetization’s reaching a steady-state value in the
presence of the rapid pulsing with rr/2 rf pulses. It is
suggested that the system reaches this steady-state within
four pulses CFr711, hence all PS images were preceded by
four pulses prior to image acquisition. Second, PS
experiments yield consistent values of T1 for TR in the
range of 0.5T1 to 2.0T1, whereas SE experiments yield
consistent values of T1 for TR in thB range of 0.5T1 to
3.0T1. Hence, images were collected with TR ranging from its
minimum value, dictated by the manufacturer to be 50ms, to a
maximum of three times the actual Tl. 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.

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 thB commencement of
the pulsB sequence. Therefore, TR for all IR images mas set
to at least five times thB 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 5.0T1.
In the FIR images, TI ranged from 25 milliseconds to Just
less than 2.0T1. 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
spatially 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, effectively resulting in each data point’s being
defined by a complex number. PS and SE experiments sampled

29
a
b
Figure 3-5. Color NMR images of phantom. Ca) With eight
identical vials, (bl with all vials surrounded
by saline solution.

30
the magnetization, whosB value lay betuieen 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 thB corresponding
complex number. IR and FIR experiments sampled thB
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 phasB 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.
ft 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

31
computer system. The general purpose of this program uias 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 NflR spectroscopy, where the sample under
investigation may 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 Tl. In NflR 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 Tl estimate. If each data set contained, say,
ten data pairs, the analysis 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-S 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 passible immersion
in air or saline resulted in over Five thousand estimated T1
values. These estimated values were compared to the actual
T1 value, and also to the estimated T1 value obtained iF all
oF the data pairs, Far example tBn, were Fitted to equation
3-2. Comparison with the actual T1 tested For precision and
accuracy, while comparison with the estimated T1 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 T1 determination. The experiment pBrFormed 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 thB 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

33
Table 3-2
Typical Raw Data Acquired for T1 Determination
TI(msec) SICvial 13 SICvial 51 Background
PHANTOM NOT IMMERSED IN SALINE SOLUTION
50
-43.7
-90.4
0.38
75
-7.1
-26.4
0.12
125
44.1
80.1
0.06
175
B7.4
173.2
-0.26
225
119.5
229.5
-0.27
275
14B.7
273.9
-1.32
325
163.5
326.0
1.15
400
1B6.2
361.4
-0.07
1000
223.9
430.0
0.05
PHANTOM IMMERSED
IN SALINE SOLUTION
50
16.3
24.0
0.06
75
21.8
36.0
-0.33
125
27.4
48.4
1.40
175
33.7
60.0
1.90
225
38.4
68.9
1 .10
275
39.8
78.1
1.40
325
40.2
82.7
-0.74
400
47.8
86.5
-2.40
1000
51.2
95.1
-0.44
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

34
and 5 are presented in columns two and three respectively,
in arbitrary units. Uial 1 mas 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.
Qne, 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
thB phantom not immersed in the saline solution. A possible
explanation is that the saline solution absorbs a portion of
thB transmitted rf power, thus resulting in misset 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 3-6a illustrates the fitting of ten inversion
recovery data sets by a three-parameter exponential
function. The estimated T1 value was 132±8msec, which
happens to be within 15* of the actual T1 value of 154msec.
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 T1 value of 154msec, and
also the estimated T1 value of 132msec.
Figure 3-6b illustrates the fitting of only three out
of the passible ten data SBts to a three-parameter

35
Figure 3-6. Examples ef Fitted data sets yielding goad T1
estimates. Curve Cal was generated by Fitting
all points while Cb) was generated by Fitting
only the points denoted by

36
X x
Figure 3-7. Examples of Fitted data sets which yielded poor
T1 estimates. Curves Ca), (b), and Cc) were
Fitted only to the data points denoted as "0”.

37
exponential function. The three data points used for fitting
are denoted as ”Q”, while the unused data points are
presented as ”X". For this particular choice of three data
points, the estimated T1 value is 131msec. Thus, this
particular value is both within 15\ of the all points
estimated T1 value of 132msec, and also within 155: of the
natural T1 value of 154msec. Figure 3-7 presents three other
possible choices of three data sets, fitted by a
three-parameter exponential function. In each case, the
estimated T1 value is neither within 155: of the all paints
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. DnB
point defines the signal intensity at, essentially, time
equal zero. Another TI value results in a signal intensity
corresponding to almost the completly relaxed state. Finally
the third TI value comes Just about at the time thB
relaxation curve changes thB most. Of course, these are not
the only choices of TI values which resulted in good fits,
indeed, there were many. One of the purposes of this
investigation was to identify and quantify how much

30
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 Analusis Methodology
To Facilitate analysis oF the numerical data, a program
was developed on an APPLE E-plus microcomputer, which
down-loaded the processed data From the IBH 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
TI 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.
ThB criterion used in all evaluations was as Follows:
For a given set oF parameters Ce.g. FIR experiment, actual
TI oF E77.0 milliseconds, vial number three, phantom
immersed in saline solution, using three images, and Fitted

33
Figure
T1 OATH GATHERED ON TESLACON
3-8. Sample computer output of data correlation
program.

40
by a function with three degrees of freedom), the criterion
mas that the estimated T1 value fitted uiith Ibss than a 15k
relative error to either the actual T1 value or the T1
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 k" 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 refered to the ’’Key” which indicates which platting
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 thB eight
passible vials the data came from. Similarly, "PSEQ”
indicates which pulse sequence was used for the T1 estimate
Ci.e. PS, SE, IR, FIR). ”#PAR” refers to the number of
parameters in the fitting function used for T1
determination, either two or three. ”#PTS” refers to the
number of data points fitted to determine T1. ”#PTS” was
either two, three, or four for ”#PAR” equal to two, or
"ttPTS” was three or four for ”#PAR" equal to three. ThB
parameter "SALT” indicates if the phantom was immersed in

41
the saline solution C’’SALT-YES” ) , or if the phantom was not
immersed in the saline solution C’’SALT-NO”). The parameter
”TCON” indicates what the estimated T1 was compared to,
either the all points estimated TI (’’TCOM-ALL”), or the
natural TI C"TCOM-GLD”). Finally, ”LEO acceptance IbvbIs 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 95* 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
Fallows. Although many diFFerent SBts oF TI values were
considered, the Tl 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 Tl 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 Tl value which was within 5* oF the standard.
Indeed, it appears that less than 30* oF all experiments
would result in estimated Tl values within 25* oF the
standard. IF this hypothetical curve corresponded to real

R H H G E I N R ñ H G
42
Figure
T1 DñTR GÑTHERED ON TESLRCON
a
T1 DñTR GñTHEREO ON TESLÑCON
b
3-9. Hypothetical output of data
Output Cal dBpicts a nearly
Cb) dBpicts a poor output.
correlation program,
ideal output, while

43
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 CBe04D.
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 Brror), acceptance at the 15% relative error
level was chosen to coincide with typical in vivo
biological variability.
After the qualitative data analysis based upon thB
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 Ci.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

44
illustration, if one of the fixed parameters mas 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 thBn
scaled to the Tl value which the fit was being compared
to. Next, a linear-multiplB-regression analysis CSpBID was
performed on this set of groups, yielding a regression
equation which related thB 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 incoporated 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 thB accuracy and precision in thB estimated
Tl 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
T1 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 T1 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 arB presented in support of all results.
The reproducibility of signal intensities for a given set of
parameters was at all timBS greater than 95*, and typically
greater than 97.5*. The reproducibility was determined from
a series of measurements which were all repeated ten times.
Positional Dependence
All estimated T1 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 T1 did not exhibit these variations, within acceptable
experimental limits. The signal intensity variations
resulted from the intrinsic magnetic field inhomogBnBity,the
intrinsic transmitted rf field inhomogeneity, and mostly,
the spatially inhomogeneous rf receiver coil response.

46
The representative data of figure 3-10 support this
result. Uial three mas 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 CfittBd T1 value
had less than a 15* relative error) for both vials. Although
similar estimated T1 values were calculated for both vials,
typically the standard deviations in the fits for vial five
were larger than those for vial thrBB, owing to the smaller
signal to noise ratio of the intensities at that position.
Dependence Upon Actual T1 Ualue
The percentage of experiments which met the acceptance
criterion was constant within 15* to the actual Tl. That is,
a given set of parameters Cwith the values of the variable
timing parameter suitably chosen for the actual Tl)
generated a similar number of good fitting Tl estimates,
independent of the actual Tl. 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 Tl were constant within
15* to the actual Tl. Thus, it was possible to characterize
thB optimal values of the timing parameter independent of
Tl. The representative data of figure 3-11 support this
result. Each different ’’RUN” represents a different actual
Tl 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.

47
T1 DATA GATHERED ON TESLACON
a
T1 DATA GATHERED ON TESLACON
b
Figure 3-10. Representative data indicating independence to
position in Field-oF-vieuj. Ca) Uial 5 output,
(b) identical output for vial 3.

48
TI DATA GATHERED OH TESLACON
RUN=KEY
UIAL=3
PSEQ=FIR
#PflR=3
#PTS=4
SALT=YES
TCOM=GLD
LEUOÍ
Key
+ : 1
x : d
♦ : 3
â–¡ : 4
o : 5
¡y. 10V 15'; 2QZ 25’: >25’4
ACCEPTANCE LEUEL
Figure 3-11. Representative data indicating independence to
actual TI value.

49
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 thrBB-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 corollary result. As explained previously,
IR experiments were fitted twice, once by a function with
two degrees of freedom Cgiven by setting C in equation 3-2
equal to 2K), and once by a function with three degrees of
freedom Cgiven by equation 3-E). 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. Additionally, the results of fitting FIR
experiments with a function with two degrees of freedom are
also presented in figure 3-13.

50
TI DATA GATHERED OH TESLACOH
a
TI DfiTfi GATHERED ON TESLACON
b
Figure 3-1S. Representative data indicating independence to
number of images, (a) Using three images for T1
determination, Cb) using four images for T1
determination.

Figure 3-13. Summary oF results.
% Meeting Criteria
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1001
Salt Salt
Estimated T, Natural T.
% Meeting Criteria
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llllllllllllllllllllllllllllllllllllllll
1R: 2
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m

52
Optimal Sets oF Parameters
To obtain a direct estimate of the actual T1 valuB in
an object uihich 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 by a two-parameter exponential function can be more
precise and time effective than the FIR technique in
estimating Tl, but were always much less acurate, and prone
to error if an inhomogeneous rf field was present. The
representative data of figure 3-13 support these results.
Optimum Variable Timing Parameter Ualues
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 may 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.

53
The use of three FIR images, fitted by 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 + 0.6n - 0.1L C3-31
whBre the three TI values, H, n, and L were the highest,
middle, and lowest values all scaled to TI by dividing the
specific timing parameter by the actual TI value. The
standard error of estimate in H was 0.3, for H 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 spatially
inhomogeneous rf field. The relationship between the threB
values of TI in the IR experiments was
H - 1.6 + 1.lH + 0.6L C3-41
where the three TI values, H, M, and L were the highest,
middle, and lowest values normalized to the actual TI value.
The standard error of estimate in H was 1.2, for n 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

54
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 + l.in - 0.3L C3-5D
where the three values, H, tl, and L were the highest,
middle, and lowest values normalized, in this case, to the
Tl value estimated by fitting all data pairs. The standard
error of BstimatB in H was 1.1, for fl it was 0.7, and for L
it was 0.3.
Discussion
The in vivo determination of Tl 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 NhR
spectroscopy literature on Tl determination and as to how
well they applied to NMR imaging, with its unique set of
experimental constraints.
The NÍ1R spectroscopy litBraturB offered suggestions on
which pulse sequence to use, the number and values of the
variable timing parameter to use, and the form of the

55
Fitting Function required to calculate T1 From the
individual signal intensity measurements. The added
constraints imposed by NflR imaging were the Following:
measurements could be obtained From any position within a
large Field aF 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 1S\ 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 CFor
Fixed experimental parameters), then this would be an
expected result. As demonstrated by the signal intensity
variations in Figure 3-5, this was not thB 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,

56
and not the exponential time constant. Thus, this
investigation verified experimentally thB theoretical
prediction.
This result is significant for the following reason.
Although it is tempting to make a differential diagnosis
bassd upon differences in signal intensities Ce.g. if thB
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. Uariations in calculated T1
values Cfor 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 155i
to the actual T1 value, for properly chosen values of the
variable timing parameter. Since experiments were conducted
over an actual T1 range of approximately 100 milliseconds to
1000 milliseconds, this result is valid only 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 T1
determination.
Spin-lattice relaxation theory predicts, for such a
simple phantom material Cparamagnetically doped water), a
monoexponential relationship between thB signal intensity
and the variable timing parameter. The spin-lattice
relaxation rate i3 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 thB exponential argument,
and does not inFluence the general Form oF thB Function.
Thus, the empirical invariance to T1 was to be expected, on
the basis oF the physical model.
Although instrumental eFFects on T1 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 Tl 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 thesB
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 Ca 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 uisrs instrumental in

50
nature. For example, all experiments in this investigation
utilized a single slice mode of acquisition. ThB use of
multislice acquisition introduced othBr variables uihich
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 CEdBOJ 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
CFID) 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 tr/2
rf pulses, but by its very nature a spin echo had a
dynamically varying net magnetization. Although thB IR and
FIR experiments do not farce 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 planB 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 CSt65D.

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 usBd 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.

BO
In this investigation, an estimated T1 value was deemed
a good approximation to the actual T1 value if the relative
Brror uias Ibss than 155i. For this acceptance level, only
First order effects mere of sufficient magnitude to
influence the error in the BstimatBd T1 value. Therefore thB
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 CBeQOD.
This result uas 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. OnB way 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 by 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 T1
determination was the fitting of two SE images with a
function with two degrees of freedom CHrB3, Ha7SD. This
result indicates that, if the signal to noise ratio was
adequate in each image, two images would indeed be the
resonable 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 tBrms 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 T1 was compared to the
"Estimated Tl” 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:2 method was slightly more precise
than any other method of Tl determination, all of which
shared an essentially equal precision.
Those experiments whose calculated Tl values met the
acceptance criteria when compared to the "Natural Tl”
represented methods of determining precise and accurate Tl
estimates. For this situation both the IR:2 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 Tl determination were best, while the SE:2
method performed marginally.

B2
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 analysis the
percent relative diFFerence was calculated From Figure 3-13
For both the ’’Estimated Tl” and ’’Natural Tl” results. The
percent relative diFFerence was determined by subtracting
the Meeting Criteria” oF the ’’Salt” case From the ”5i
Meeting Criteria” oF the ”No Salt” case, and then the result
was divided by the Meeting Criteria” oF the ”No Salt"
case. This was done For Bach pulse sBquence/Fitting
Function, For both the ’’Estimated Tl” and the ’’Natural Tl”
results, with thB outcomes given in Figure 3-14.
Ideally, a given pulse sequence/Fitting Function would
perForm as well whether the phantom was immersed in the
salinB solution or was not immersed in the saline solution.
SincB this is thB 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 lasses oF accuracy and precision, while the SE:2 and
FIR:3 methods were nearly as lossless. These results must
not be considered out-oF-context. For example, the result
that the SE:2 method had a low percent relative diFFerence
Far the ’’Natural Tl” case viewed in conjunction with the
results oF Figure 3-13 indicated that, in this particular
situation, the SE:2 method went From being a poor method oF

% Relative Difference Between
No Salt and Salt
63
50
CM
CM
CO
CM
CO
LXJ
oc
cr
cc
oc
CO
U_
li-
Estimated Tj
CM
CM
CO
CM
CO
UJ
OC
oc
oc
CC
CO
LL
u_
Natural Tj
Figure 3-14. Effect of rf attenuating material upon
measurement precision and accuracy.

64
determining accurate and precise T1 values when the phantom
uas 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 T1 values.
Of primary inportance mere 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 T1 values, or a posteriori to evaluate the
reliability of a calculated T1 value. The a priori
recommendations follow.
Optimal sets of parameters
The first decision to be made in the design of a T1
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 T1 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

G5
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 thB 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, thB SE series
often produced more precise measurements of T1 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 T1 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 thB FIR was
that, due to the extended TR time, Ibss saturation of signal
occurred. Thus, the IR images had slightly more contrast, an
aid for visual evaluation, but no real advantage in thB
quantitative analysis required far T1 determination.

E6
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
VBry high precision. Additionally, although not a result of
this investigation, the SE technique is often thB clinical
technique of preference, displacing the inversion techniques
consistently. For these reasons, the SE method of
spin-lattice relaxation time determination appears to enjoy
thB most widespread usb. Additional results of this
investigation indicated that the SE method had some serious
shortcomings, and yielded quality results only in
restrictive situations.
ThB most important disadvantage of the SE method was
its lack of accuracy in estimating T1 values. The SE method
always fared best when its BstimatBd 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 T1 values could not reliably be determined directly.
Instead, some type of calibration curve would need to be
generated to permit actual T1 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 CPyB31.

67
Optimum variable timing parameter values
Once the decision as to uihich pulse sequence to he
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
analysis should bB 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 Tl 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 E5 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, say 0.9TR. ThB solution is not as straight
forward for the SE method, where there is no fixed timing
parameter of relavance on which to base the choice. In this
case, H should be chosen with consideration towards the
largest value in the expected Tl range.

60
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, fl, 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 n 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 n
and H. Additionally, if the T1 of concern was thought to be
350 milliseconds, thBn assigning fl 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 T1 determination may be developed a priori, based
upon the available imaging time, desired accuracy and
precision, and range of T1 undBr investigation.

63
6 Posteriori Recommendations
It Frequently happens that the desire for a
quantitative determination of T1 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 Ci.e. three images were acquired,
all with the same number of signal averages), then it mould
be possible to generate an estimated T1 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 mere acquired, mith TE
equal to 30 milliseconds, TR equal to 1500 milliseconds, and
three values of TI equal to 50, 550, and 850 milliseconds.
All images merB acquired mith Four signal averages. A
thrBB-parameter exponential is FittBd 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 Tl
estimate, this series is comparable to the FIR method of Tl
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,
fl, and H.
By a simple propagation of Brror analysis of equation
3-3, the standard error of estimate in T1 For the FIR method
of T1 determination, aCTlD, may be determined to be 152
milliseconds. Thus, the optimal T1 value to bB determined by
the set of TI values used in this example is 4771152
milliseconds. The estimated value, 700 milliseconds, is
nearly 1.5 standard errors greater than thB 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 IU
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 CDuB4D,
this investigation sought to glean added information from
them. In particular, this study exploited the unique
properties of the stimulated echo CSTE1, as first identified
by Hahn CHa50J, and further quantified by Uoessner
CUI06II . Although new to NMR imaging CFr85, HaBS, SaB5a,
Sa85bJ, stimulated echoes have been successfully applied by
Tanner to the measurement of translational self-diffusion
coefficients CTa70D, by Lausch and Spiess to study
infrequent Jumps of complex molecules CLaBO, SpBOl, and
more recently to analyze slow rotational motions of
molecular solids by Sullivan et al. CSuBBJ. Furthermore,
othBr investigators conducting research into stimulated echo
NMR imaging,concurrently with this investigation, have
recently reported their initial findings CFrBS, HaBSD .
This investigation is unique in that it is the first to
indicate that stimulated echoes may be applied to NMR
71

7£
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, thB spin-lattice relaxation time, Tl, and the
spin-spin relaxation time, TE. With current instruments,
contrast due to relaxation is achieved through the use of
either the spin echo CSE) technique, or an inverting
technique, such as the inversion recovery CIR5 sequence. In
particular, Tl 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 thB equilibrium magnetization,
initially aligned along the positive z axis, and sampling
its recovery with a rr/E rf pulse.
STE imaging introduces Tl weighting into the NhR image
in the following manner. UiBwed from the rotating frame of
reference, an initial tt/E rf pulse, at time equal to zero,
rotates the equilibrium magnetization into the transverse
plane. While in the transverse plane, the nBt magnetization
is reduced due to TE relaxation, molecular diffusion and
precession within an inhomogeneous magnetic field. A second
tt/E rf pulse, at time equal to rl, 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 CPE) at a time equal to twice r1. The
net longitudinal magnetization will be reduced due to T1
relaxation and molecular self-diffusion. At a time rS after
the second 90 degree rf pulse, a third 90 degree pulse is
applied which rotates this T1 reduced net longitudinal
magnetization back into thB transverse planB, where the
individual isochromats constructively interfere to form the
STE at a time rl 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 NflR imaging CEdBOJ 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 NtlR imaging. STE imaging, with its unique T1
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,

74
hence images acquired with this sequence will Frequently
contain a high degree of mixBd T1 and TE 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 timB 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 T1
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
dBtBctsd in NflR For thB first tima in 1950 by Hahn CHa50D,
and spin Bchoss havs subssqusntly bssn appliBd in NMR to
various ands, including tha measurement of T1 values
CCa5HD, the investigation into molecular diffusion
processes CSt65D, the determination of scalar coupling
constants CFr751, thB indirect detection of magnetic
resonance EEmBOD, coherence transfer Cf1a7B3, and NflR
imaging CEdBOD. Bisa, the same effects have been exploited
in electron spin resonance CNÍ72J, microwave spectroscopy
CG176D, and in laser optical spectroscopy CKu643.
An Bcho 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 inital pulse, hence a coherence
is produced. In time, inhomogeneous interactions within the
system act to destroy the coherence. This is accomplished in
NflR by an inhomogeneous magnetic field, by an inhomogeneous
Stark field in microwave spectroscopy, or by the Doppler
effect in optical spectroscopy Cf1a78D . A second pulse,
applied at a time t, inverts the accumulated effects of the
inhomogeneous interaction. Thus, thB initial coherence is
regained and an echo occurs at a time Bt. 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 CHa58D.

76
In 1946, Bloch introduced a phenomenological vector
equation to describe NMR CB146D. It accurately
characterized an isolated particle of spin 1/E in the
presence of a static magnetic Field. Feynman et al. CFe57D
have demonstrated that this description is complete, that
is, a geometric representation of the Schroedinger equation
is possible. Also, Pegg et al. CPeBlD havB shown this
description to be perfectly rigorous, because the vectors
are equivalent to Heisenberg operators in thB 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 NHR 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, n, to the applied
magnetic vector field, B, such that
dn/dt - rcn x B) C4-ih
where T 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 fiBld with the frequency n, such that
C4-ED

77
This relationship between the precession Frequency and thB
applied magnetic Field is reFered 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 T 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 NfIR phenomenon. Additionally,
thB absence oF the Planck constant in the Larmor equation
given in equation 4-B Further JustiFies the classical
treatment oF the resonance phenomenon.
Further support oF the classical Formulation oF the NdR
phenomenon is oFFerBd by the correspondence principle oF
quantum mechanics CUa53D, 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 CP106], 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

7B
Tx
GX
gy
GZ
Rx
A
o
A
D
FigurB 4-1. Basic stimulated echo imaging sequence.

73
Figure 4-2. The Formation of a primary echo.

80
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 CTx) oF a 80 degree, or tr/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 TE, and excites the entire
chemical shiFt Frequency bandwidth equally. IF, Far example,
the rF pulse has a phase A equal to 80 degrees Ci.e. along
the positive x direction as depicted in Figure ‘i-Eb), 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. ThB z axis oF thB 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 rBFerBd to as thB 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 NflR takes on a simpler Form when

B1
expressed in terms of the rotating frame of reference. Also,
a simpler physical picture of events is possible uihen
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 4-5. In practice, resonance
takes place over a range of frequencies determined by thB
inhomogeneity of the main magnetic fiBld throughout the
sample. Therefore, thB object may bB considered to be
comprised of an ensemblB of magnetic moments, whose
resonance frequencies are symmetrically distributed about
the Larmor frequency, n. Figure 4-5c illustrates the free
precession Ci.e. Larmor typB precession and not rf pulse
induced rotation) of all these isochromats during the time
interval rl. Since figure 4-5c depicts the dynamics of the
magnetization in a frame of reference rotating at frequency
n, thB isochromatic moment pairs maintain a symmetry about
the y direction, but rotate in opposite directions. This is
indicated in figure 4-5c in the following manner. The light
gray regions represent a range of isochromats which deviate
less from n 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 rl, pulsed linear magnetic
field gradients are applied as in the conventional fourier

BE
imaging technique CEdBOJ. The preparatory readout gradient
is embodied in the effective x gradient, CGx), whereas Gy
and Gz are employed for phase encoding. The effect of thesB
pulsed magnetic field gradients is the spatial encoding of
the NMR signal in a precise manner. If one, two, or threB
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 tr/2
rf pulse applied in the presence of a slice selective Gz
CHo771.
After the time interval r1, a second 30 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 -rl), after the second rf pulse the net
magnetization has components in the longitudinal plane as
well as the transverse plane. Figure 4-Ee illustrates the
transverse component of the net magnetization immediately
following the second rf pulse, obtained by simply projecting
the net magnetization of figure 4-Ed 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

03
the projection of the net magnetization onto the transverse
plane, immediately Following the second rf pulse, lies
completely on the x axis.
The intrinsic properties of the isochromats have not
been altered by this magnetization gymnastics. The sense and
speed of free precession in the transverse plane for the
isochromats fallowing the second rf pulse is identical to
the sense and speed of Free precession prior to the second
rf pulse Ci.e. as indicated in Figure 4-2c). Hence, From
time rl on, the isochromats will FrBBly precBss as in Figure
4-2F. From time rl to time Erl the isochromat vectors will
interfere amongst themselves, with maximum constructive
interference occuring at time Erl. This constructive
interference constitutes a primary echo CPE), with maximum
amplitude at time Erl, and so named to distinguish it From
the spin echo which results from a tt/E-t-tt rf pulse
sequence. The maximum amplitude of the PE at time Erl,
nCPE), is given by
E
HCPE) - n¡sinOlsin (02/2)expC-2t1/T2)FCG,D,rl) C4-3D
where Mi is the equilibrium magnetization, 9i is the tip
angle of the ith pulse, and F(G,D,t1) corresponds to the
diffusional damping resulting From molecular diffusion in
the presence of magnetic field gradients. For a constant
steady magnetic Field gradient, F(G,D,t1) is given by
E E 3
expC-C2/3)Dr G rl }, where G is the magnetic Field gradient

B4
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 CSt651. The two cases are
identical, in the limit, as we pass from pulsed to
continuous application of the gradient.
As illustrated in figure 4-1, the Gx readout gradient
is imposed, centered about the time Erl, 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 BncodBd PE. If all
pulses are ideal tt/E rf pulses, then the PE imagB is
identical to thB image produced by conventional spin echo
imaging, except for a factor of one half in signal
intensity. This reduction in thB signal to noise ratio would
be intolerable unless it is passible 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 tt/E rf pulse.
Formation of the Stimulated Echo Image
It can be shown that the solution to the Bloch equation
in the rotating frame CB146D takes on the form
HxCt+tp) - nxCt)
C 4-41
flyCt+tp) - riy(t)cos9 - rizCt)sin9
C 4-51
MzCt+tp) - riy(t)sin9 + rizCt)cos9
C4-6D

B5
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 thB rotating portion of the
net magnetization is decomposed into two orthogonal
components, fix is taken to be in phase with respect to the x
axis rotating frame of reference, while fly is 90 degrees out
of phase. Of prime interest is equation 4-6, which
characterizes the longitudinal magnetization, and in
particular its dependence on flyCt). Since the spin system is
initially in thermal equilibrium, tlyCt-0) “ 0. Hence, by
equation 4-6, HzCt-tp) - 0 for an ideal tt/E rf pulse. As
applied to the experiment of figure 4-1, the implication is
that during the interval rl, flz simply approaches the
equilibrium magnetization, if the affect of relaxation is
considered.
If t1 is of the order of TE or less, thsn f1y(t“Tl) is
surely nonzero. That is, at time t1 we will have appreciable
transverse magnetization. Therefore the second ir/E rf pulse,
in addition to inducing the PE, will also produce net
longitudinal magnetization, that is, MzCt-rl+tpU 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 rr/E
rf pulse of figure 4-1. Indeed, figure 4-3a is identical to
figure 4-Ed. Whereas we considered the transverse projection
of this net magnetization in order to describe the formation

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

07
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 thB readout
pulsed magnetic field gradient for the PE image does not
influence the longitudinal magnetization.
The third 90 degree pulsB, which comes at the end of
the t2 interval, simply rotates the stored longitudinal
magnetization back to the transverse plane, as depicted in
figure 4-3c. 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 precess as in figure
4-3c. Since the only time this magnetization was influenced
by the inhomogeneous main magnetic field was during the
interval t1, the isochromat vectors will interfere amongst
themselves during the interval t2, with maximum constructive
interference occuring at a time t1 after the third rf pulse,
for t2>t1. This constructive interference constitutes the
stimulated echo CSTE), with maximum amplitude at a time t1
past the application of the third rf pulse. Thus, the
maximum amplitude of the STE at a time t1 after the third rf

88
pulse, flCSTE), is given by
tlCSTE) - 1/Srii sin01sin92sin93expC-C2t1/T2 + tE/T1)D *
FCG,D,rl,t2) C4-7D
where 0i is the ith rF pulse, and F(G,D,t1,t2í is the
diFFusional damping term For the STE. For a constant steady
magnetic Field gradient, FCG,D,t1,t2) is given by
2 2 3 2
expC-(2/3)Dr G CtI +t1 t2)1, and is modiFied For pulsed
magnetic Field gradients CTa703.
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 rl interval between the First and second rF pulse,
and also For a time rl subsequent to the third rF pulse, For
a total time oF T2 inFluence amounting to 2rl.
As illustrated in Figure 4-1, the Gx readout gradient
is imposed, centered about a time rl aFter the third rF
pulse, to Frequency encode the STE with x direction spatial
dependence. Additionally, the receiver (Rx) is gated open
during this same time, to permit acquistion (A) oF the
spatially encoded STE. IF each 9i was an ideal tt/2 rF
pulses, and ignoring relaxation and diFFusional damping, it
is noted From equation 4-7 that I1CSTE) is proportional to

83
Cl/2)f1i. This is the other Factor of one half we noted
earlier after the formation of the PE. Whereas the
conventional spin echo imaging experiment yields a single
image whose intensity is proportional to Hi, the stimulated
echo imaging sequence may yield two images, each
proportional to Cl/2)f1i, and each in spatial registration
with thB other. The utility of these images lies not in this
proportionality, but rather in the unique T1 dependence of
the STE imagB. Applications which further extend and exploit
this T1 dependence are presented later in this chapter.
Formation of 5econdaru Echoes
As was previously outlined, the rf pulse sequence given
in figure 4-1 will yield both the primary echo and the
stimulated echo. Additionally, the application of the three
rr/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
primary echo after the application of the first two rf
pulses may also cause the formation of two of thB three
secondary echoes. If we consider the three rf pulses taken
two at a timB, then there are three unique combinations, thB
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 simply bBing the primary echo. The
second case results in an echo at a time t1+t2 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 timB the
magnetization spends in the transverse direction.
The final secondary echo is derived from the PE. At
time t1 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 rl after the second rf pulse as there was
immediately following thB first rf pulse, ignoring the
coherence lost due to relaxation and the diffusion process.
Therefore, for all intents and purposes, thB PE at time rl
after the second rf pulse behaves as if it was transverse
magnetization Just after the application of a rf pulse.
Thus, aftBr the time rl 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 timB t2-t1 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 T1 dependence of the STE make these two echoes
ideal for imagB formation. ThB 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.

31
Materials and Methods
The NMR Imaper/Spectrometer Sustems
All proton NMR experiments were conducted on one of two
NMR imager/spectrometer systems. The majority of experiments
uerB performed on a Nicolet CGE-NMR) NT-BO spectrometer
located in thB Department of Radiology at the University of
Florida. A single experiment, the TART imaging sequence, was
conceived and developed at the University of Florida, but
was implemented on a prototype General Electric CSI
imager/spectrometer located in the applications lab of
General Electric NMR Instruments, Fremont, California.
The Nicolet CGE-NMR) NT-80 spectrometer was coupled
with an Oxford 00/310 MR superconducting magnet operated at
1.09T, with a clear bore diameter of 31 centimeters.
Transient gradient pulsBs were generated with the Oxford
2320 room temperature shim power supply, which was modified
by J.R. Fitzsimmons and R.G. Thomas so as to improve its
temporal response time. The power supply was under the
direct control of the Nicolet 293C pulse programmer, so as
to allow pulse control of the x, y, and z gradients.
Controlling software was written in Nicolet 1200 assembly
language by T.H. Mareci, M.D. Cockman, and R.G. Thomas. The
DAC outputs to x, y, and z were dependent upon the state of
six TTL inputs, two for each direction so as to allow pulse
sequences to be implemented which required the sign of the
magnetic gradient pulse to be reversed in the course of the
experiment. These six TTL inputs, U, A, U, C, Ul, and H

92
(corresponding to x, y, and z respectively) could be gated
on during any pulse or time delay in the imaging pulse
sequence.
Imaging pulse sequences tuerB generated directly with
the available pulse sequence generating software resident on
thB Nicolet system, once the pulsBd magnetic gradient
controlling hardware/software was implemented. Additional
assembly language software was developed by H.D. Cockman to
permit the sequential incrementation of the pulsed magnetic
fiBld gradients, required for the Fourier imaging technique
used in this investigation.
The NicolBt spectrometer uses a twenty bit word length,
hence single precision data acquisition resulted in twenty
bit deep data. In conjunction with N.D. Cockman, an assembly
language routine was developed which scaled the twenty bit
deep data to five bits (permitting image display with
thirty-two gray levels), and transfered the scaled data over
a RS232 transmission line to a Cromemco Z-2D computer for
image processing and display. The image processing and
display software was developed by L.T. Fitzgerald. All
images presented, except those associated with the TART
experiment, were acquired and processed in a like manner,
unless otherwise noted. The images generated with the TART
experiment were acquired and processed with the resident
hardware and software which was standard on the General
Electric CSI imager/spectrometer.

93
Residual Gradients
As outlined in the previous section, the stimulated
echo imaging scheme of figure 4-1 has, as its backbone, the
rf pulse sequence ir/E-Tl-ir/E-TE-n/E. A PE image is obtained
at a time rl after the second tt/E rf pulse, with relaxation
weighting expC-Erl/TE). The STE image is obtained at a time
rl after the third tr/E rf pulse, with its relaxation
weighting given by expC-Erl/TE^expC-rE/Tl). Since the
spatial encoding is identical for the PE image and the STE
image, the two are in spatial registration, though residual
gradients may act in a manner which alters this
registration, as to be explained.
Consider the effect of residual gradients in the
following gedanken experiment. Phase encoding pulsed
magnetic field gradients are applied within the interval t1
of the basic STE imaging sequence as depicted in figure 4-1.
Ideally there would be no residual gradients present, that
is, there would be no field gradient once the current pulse
which produced the phase encoding gradient had died down.
Now consider the effect of a residual gradient which remains
even after the current pulse ceases. All isochromats in the
interval rl will experience a phase shift B as a result of
the phase encoding pulsed gradient. At time rl, half the
magnetization is rotated to the longitudinal direction, and
thus is no longer influenced by field gradients. The
remaining transverse magnetization experiences a phase
reversal of sorts at time rl, which accounts for the

34
formation of the PE. If there is a residual gradient, the
transverse isochromats will rephase in its presence,
resulting in an additional phase shift of dCPED. The stored
longitudinal magnetization is not influenced by the residual
gradient until it is brought back to the transverse plane,
where it rephases to form the STE. If a residual gradient is
present, there will bB an associated additional phase shift
of dCSTE).
Both bJCPE) and 0CSTE1 are negative relative to B, for
they were incurred after a phase reversing rf pulse, and
J dCPE)| is greater than |dCSTED|, since the magnitude of a
residual gradient is typically a monatonically decreasing
function of time. Consequently, the PE experiences a total
phase shift which is less than that of thB STE by
jdCPE)-0(STE)|. Since ideally there is a one-to-one mapping
of total phase shift to spatial location, the different
total phases of the PE image and the STE image result in
different spatial mappings along the phase encoding
direction. That is, since the total phase of the PE is less
than that of the STE, the apparent extent of the phase
encoded direction will be less in the PE image than in the
STE image. For Bxample, paints separated by 10 centimeters
in the STE image, along the phase encoded direction, might
be depicted as having only an apparent 8 centimeter
separation in the phase encoding direction of the PE image.
Since the readout direction is essentially unaffected by the
residual gradient, the aspect ratio for all STE images will

95
be, ideally, one, while For the PE images the aspect ratio
will vary as a function of the magnitude of the residual
gradient, and the time it is influential on the transverse
magnetization. In all images presented, except those
corresponding to the TART experiment, the phase encoding
direction is displayed along the horizontal direction, or y
direction.
To evaluate the residual gradient problem on the NT-00
spectrometer, the following experiment was conducted. A
single one centimeter diamBter vial of paramagnetically
doped water was centered in the rf coil of the spectrometer.
The magnet was then shimed with the sample in place,
resulting in an approximate 10 ppm line width. A pulse
sequence was developed, and implemented, to evaluate the
duration and extent of the residual gradient.
The pulse sequence consisted of six steps. The first
step was simply a time delay, set equal to one second so as
to insure the entire sequence was not so rapidly repeated as
to cause signal saturation. The second step was the
application of a pulsed magnetic field gradient of 0.10
mT/m, for a duration of two seconds. This duration was
chosen so as to insure that the Field gradient had
sufficient time to reach its full magnitude. The next step
in the sequence was a variable timing delay, which was
incremented From 05 milliseconds to 705 milliseconds in 05
milliseconds increments, with a single inital value of one
microsecond. At the end of this variable time delay, the

36
Fourth step in the sequence commenced, a 30 degree rf pulse,
with the next step simply the opening of the receiver gate.
The sixth and Final step in the sequence was a time delay
equal to thB total acquisition time, as dictated by the
sweep width and the data acquisition black size. This
permitted the receiver gatB to remain open for the
acquisition of the Free induction decay CFID1 resulting From
the 30 degree rf pulse.
The significance of the experiment was as follows.
Obviously, if there was no pulsed magnetic field gradient
applied in step two, the signal intensities of the Fourier
transformed FIDs would not be dependent upon the variable
timB dBlay of stBp three. Similarly, if thBrB was a gradient
applied in step two, but its magnitude was reduced to zero
prior to the application of the rr/2 rf pulse, then the
resultant signal intensities from the transformed FIDs would
still not be dependent upon the variable time delay of step
three. Rather, consider the case where a gradient is applied
in step two, and its magnitude had not reduced to zero prior
to the application of the it/2 rf pulse. This is what is
meant by a residual gradient, and in this case thB
corresponding signal intensities of the transformed FIDs
will be reduced. Thus, by incrementing the variable time
delay it was possible to temporally map out the extent of
the residual gradient. The plot of signal intensity as a
function of the variable time delay is given in figure 4-4.

Signal Intensity
(arbitrary units)
37
0
2 4 6 8101214
Delay Time (sec X 10-2)
Figure 4-4. The evaluation of a residual gradient.

90
It was apparent from the results of this experiment
that there was a residual gradient present after application
of a pulsed fiBld gradient, and its effect was significant
for nearly 120 milliseconds. Since the magnitude of the
field gradient used in this experiment was typical of the
values used in the STE imaging experiments, and since the
time extent of the residual gradient was comparable to the
time scale used in the experiments, it was concluded that
the problem of residual gradients could not be ignored in
this investigation.
Figure Ht—5 illustrates the effect which the residual
gradient has upon image formation. As outlined earlier, the
effect of residual gradients was upon the spatial mapping in
the phase encoding direction. The images are of two, one
centimeter diameter vials filled with paramagnetically doped
water. The images are displayed as intensity contour plots,
rather that gray scale images. Horizontal is the phase
encoding direction and vertical is the readout direction.
The image in figure 4-5a was formed from transverse
magnetization in the presence of a residual gradient for 100
milliseconds, while the image in figure *i-5b was in the
presence of the residual gradient for 250 milliseconds, and
figure 4-5c for 350 milliseconds.
As predicted, the more time the transverse
magnetization spends in the presence of the residual
gradient, the less is the apparent separation of the vials
in the phase encoding direction. Indeed, in the limit where

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

100
the integrated effect of the residual gradient Just balances
that of the phase encoding gradient, there would be no
effective phase encoding gradient, and hence no spatial
separation in thB image along the phase encoding direction.
Phase Cycling
A drawback to the STE imaging sequence as described is
its insensitivity to signed phase information. Because there
is only pure amplitude modulation of the signal as a
function of the gradients applied during the interval t1, it
would normally be necessary to SBt thB Tx frequency outside
the spectral frequency range, employ single phase detection,
and use only one sided phase encoding gradients to avoid
aliasing. Fortunately a simple modification afforded by
phase cycling of thB rf puIsbs and the receiver circumvented
this problem by converting the amplitude modulation into
phase modulation.
The two step phase cycling, used in conjunction with
quadrature detection, consisted of the first two acquistions
as depicted in table 4-1. Here, A, B, C, and D refer to the
phase of the rf pulses and the receiver, as illustrated in
figure 4-1. Nagayamo et al. have used a closely related
phase cycling procedure in spin echo correlated spectroscopy
CNa7BJ.
The first two phase cycling stBps select the echo
component of the transverse magnetization over the narcissus
component. If either the main field inhomogeneity or the
readout gradient was of sufficient magnitude to suppress the

ru m 3*
101
Acquisition
1
Table 4-1
Faur-StBp Phase Cycling Used in
Stimulated Echo Imaging
A
Phase
B
(degree)
C
D
0
0
0
0
270
0
0
90
100
0
0
100
90
0
0
270

102
narcissus component, then the two step cycle would not be
needed, for only the echo component would be available for
acquisition. Recall, the narcissus component is comprised of
magnetization which continues to defocus even after the
phase reversing pulse has been applied. The defocus of the
narcissus would be advanced if the inhomogenBity of the
magnetic field is enhanced, and a magnetic field gradient
may be considered as Just a large field inhamogeneity. Thus,
the narcissus component would have dBfocused to essentially
zero whan the time came to acquire the echo. For this
scenario, the two step phase cycling would be superfluous.
Although the two step phasB cycling sequence was
adequate, often it was extended to four steps in order to
suppress artifacts resulting from longitudinal magnetization
recovery during the interval t1 CBaBlJ. The four step
phase cycling is illustrated in its entirety in table 4-1.
The phases of B and C are arbitrary, as long as they remain
equal and constant throughout the entire experiment. For a
properly adjusted instrument, and with all rf pulses being
slice selective, the last two phase cycling stBps in table
4-1 could be ignored. Indeed, under suitable conditions, STE
imaging could bB conducted with a single step, without the
need to phase cycle.
In practice, an additional spoiling pulsed magnetic
field gradient was applied immediately following the primary
echo’s readout gradient, and prior to the third tt/2 rf
pulse, along Gx. This reduced artifacts in the stimulated

103
echo image by eliminating the three other possible
overlapping secondary echoes which may occur after the third
rf pulse. Since the STE’s magnetization is stared along the
longitudinal direction during the time interval t2, the
spoil pulse dispersed only the transverse magnetization
which would have gone on to create additional secondary
echoes subsequent to the third rf pulse.
Image Acquisition
Unless otherwise noted, all images acquired with the
NT-80 spectrometer/imager were done so in a like manner.
Although figure 4-1 indicates that 6z phase encoding was
possible in the STE imaging sequence, none was performed in
practice. This resulted in z direction averaged images Cinto
the page). The reason for this was to save time and data
storage space, and does not reflect any inherent limitation
of the imaging system. The Gx readout gradient was 0.5 mT/m,
and was applied for 32ms. There were 64 equal steps of the
Gy phase encoding gradient, ranging from 0.5 to -0.5 mT/m,
each applied for 16ms, excluding any contribution from
residual gradients. The data matrix for each image consisted
of 128 X 64 complex data points. The field-of-view was 10 X
10 centimeters, corresponding to a resolution of 1.5
millimeters in the y direction and 0.75 millimeters in the x
direction. Four averages were done to take advantage of the
four step phase cycling given in table 4-1. The tt/2 rf pulse
width was 260 microseconds. All pulse sequence repetition
times were set so as to avoid signal saturation effects.

104
All images displayed corresponding to the TART
experiment were acquired in thB following manner. The two
dimensional images were acquired with a Field of view of 15
X 15 centimeters, and a slice thickness of E millimeters.
Each imagB forming echo was defined with a data block size
of 51E data points. There werB E5B equal phase encoding
steps. This resulted in a final image matrix of 51E X 51E
paints, after zero filling in both directions.
Experiments
Seven experiments which exploited the unique properties
of the stimulated echo in NÍ1R imaging were conducted. These
experiments covered a wide spectrum of application.
Presented in this section are the methods of using STE
imaging to perform T1 contrast imaging, quantitative T1
imaging, water-lipid contrast imaging, chemical shift
imaging, multiecho STE imaging, and diffusion coefficient
weighted imaging.
Experiment one: T1 contrast imaging
To demonstrate the T1 contrast imaging capabilities of
the STE imaging sequence, the basic imaging sequence given
in figure 4-1 was used, in conjunction with the phase
cycling scheme of table 4-1. ThB image phantom consisted of
a red Delicious apple with a one centimeter vial of copper
sulfate doped distilled water embedded in its center. A
short rl value was used to emphasize the poor T1 contrast of
the PE image, while the long rE value emphasized T1
differences dramatically in the STE image.

105
Experiment two: quantitative T1 imaging
In addition to T1 contrast imaging, STE imaging permits
the quantitative measurement of T1 values. It can be shown
that the diffusional damping of the STE, FCG,D,rl,r5), is
functionally dependent on rl to second and third order, for
both constant and pulsed magnetic field gradients CHa50,
Ta70D). Hence, an analysis of equation 4-7 yiBlds the
result that for rl very small, a plot of the logarithm of
the stimulated echo’s maximum amplitude versus t2 will yiBld
a straight linB whose slope is a measure of T1. If the
effect of diffusion is not completely negligible, such that
corrections for higher order in rl must be made, then a
better value of T1 can be obtained by noting that for rl
much less than rE, the stimulated echo’s maximum amplitude
decreases with rE as expC-T2/TCeff, where the effective
relaxation time TCeff), is given by
1/TCeff) - 1/T1 + g(G,D,rl) C4-8D
with gCG.D.rl) being the diffusional contribution to second
order in t1. This term, for a constant steady gradient, is
EE E
given by gCG,D,rl) - T G DtI , while the functional formed
of gCG.D.Tl) for pulsed magnetic field gradients is
different, though thB rl squared dependence is maintained
CTa701. Hence, a plot of 1/TCeff) against rl squared
yields a straight line whose intercept on the ordinate
yields the value of T1.

106
Experiment three: water—lipid contrast imaging
A novel application of the T1 weighted STE image is
Bither the enhancement or thB suppression of elements in thB
object with different T1 values. In a conventional spin echo
image of an object with various T1 elements, the longer T1
elements may be suppressed by saturation of the signal via
rapid pulse sequence repetition times. In contrast, with STE
imaging it is possible to suppress the shorter T1 elements
via T1 weighting. This capability of STE imaging was clearly
demonstrated by imaging a hen’s egg, where the difference in
the T1 values between the albumen and yolk (corresponding to
a water dense and a lipid dense element, respectively)
allowed for easy visualization of this STE image property.
Experiment four: chemical shift imaging
The STE is easily integrated into chemical shift
imaging schemes. Any existing chemical shift imaging
technique, which currently makes use of echo formation
Cf1a83I), could benefit from the unique properties of STE
imaging. Chemical shift STE imaging was conducted on a
phantom consisting of a vial of water and a vial of oil,
spatially separated in the y direction, but not the x
direction. No readout gradient was employed so as to retain
chemical shift information, and the x direction was the
phase encoded direction.
Experiment five: extended STE multiecho imaging
The three ir/E rf pulse STE imaging sequence given in
figure 4-1 was extended to a T1 weighted multiecho imaging

107
sequence as depicted in Figure 4-6. The addition of a fourth
ir/2 rf pulse results in the formation of up to thirteen
additional tertiary echoes CTE5, six of which have a T1
dependence in their relaxation damping term CU06ID.
The practical factors which entered into the decision
as to which TE to use For imaging were as fallows. With the
possible production of sa many echoes, it was important to
locate one which could be isolated from the other echoes. By
the proper choice of the time intervals rl, t2, and t3, it
was possible to create some echoes which did not overlap
others. Additionally, it was desired to be able to acquire
the PE, the STE, and a TE all within a single pass of the
imaging sequence. Hence, since the formation of the PE and
STE require tt/2 rf pulses, the TE chosen For echo formation
could not have a cosine tip angle dependent term, as is seen
in equation 4-3 which fallows.
Of primary concern was the relative intensity of the
echo. For any given echo, there were three factors which
acted to reduce the echo signal intensity, the tip angle
dependence, the relaxation damping, and the damping due to
diffusion in an inhomogeneous magnetic field. Although there
were certain definite applications of the tip angle
dependence term, this investigation was concerned primarily
with exploiting the applications inherent in the relaxation
damping term. HencB, it was advantageous to imags with
echoes that had a tip angle dependence as close to one as
possible. Although the diffusion damping term was of

100
Tk
-0-4}
G,
gv r7-!
Gz—g
R«
.V -c
-0-
Figure 4 B. The extended stimulated echo imaging sequence.

109
interest, it mas the form of the relaxation damping term
which finally dictated which echo was to be used for image
formation. It was desirable to use a TE with as simple a
relaxation damping term as passible.
All these conditions were fulfilled by the TE whose
maximum occurs at a time tE-tI after the application of the
fourth tt/B rf pulse, whose amplitude at that time, MCTE), is
given by
B
MCTE) - -Cl/B)rii sineisin C0B/B)sin03sin04 *
expC-C2T2/T2+T3/Tli:fCG,D,t1,t2,t3) C4-9D
where Hi is the equilibrium magnetization, 0i represents the
tip angle of the ith pulse, TE is the spin-spin relaxation
time, T1 the spin-lattice relaxation time, and
fCG,D,rl,tB,t3) corresponds to the diffusional damping
CUoGlD, where G represents the magnetic field gradients
and D thB translational self-diffusion coefficient. The time
intervals rl, rB, and t3 are defined as in figure 4-6.
This echo is a tertiary stimulated echo, resulting from
the storage of the primary echo magnetization by the third
rf pulse. The fourth rf pulse rotates this stored
magnetization into the transverse plane for echo formation
and detection. Using all tt/B rf pulses, the PE, STE, and TE
were all produced and available for image formation via the
execution of a single imaging pulse sequence.
In practice, the software which was resident on the
imager/spectrometer permitted the acquisition of only two

1 10
echoes during a single sequence, hence the sequence had tc
be repeated twice so as to acquire all three echoes. The
entire sequence was used each time, so this limitation did
not have any effect upon the results. This problem has been
resolved by the recent addition of more flexible data
acquisition software.
Experiment six: TART multiecho imaging
The extended STE multiecho imaging sequence resulted in
a series of images, each progressively weighted with
spin-lattice relaxation. Although the underlying concept was
correct, some of the intrinsic problems with the technique
acted to limit its usefulness. For example, with so many
echoes being generated in one pass of the sequence it often
was difficult to insure that there was no overlapping of
undesired echoes with desired echoes. This problem would be
compounded if the sequence was extended to five, or more,
rr/E rf pulses.
Fortuitously, another method of forming a series of T1
weighted images was suggested by earlier work in the
observation of T1 relaxation CFrBBl and zero quantum
coherence CBaBOD. In both these cases, the spin system was
manipulated into a given state, and the subsequent time
evolution of the system was monitored with a series of
sampling rf pulses, sufficiently weak so as to minimize
their perturbing effect on the evolving spin system.
It wa3 possible to apply the storage and retrieval
properties of the STE (along the longitudinal direction) to

Ill
an advantage in multiecho T1 imaging. Described earlier, and
illustrated in figure 4-3, the application of the first two
tr/2 degree rf pulses in the STE imaging sequence resulted in
storing magnetization along the longitudinal direction
Cfigure 4-3bl. In the basic STE imaging sequence, all of
this longitudinal magnetization was rotated into the
transverse plane after a T1 weighted interval t2, to form
the STE image. As indicated in equation 4-7, the echo
amplitude is dependent upon the sine of the third rf tip
angle. Indeed, if an ideal tt/2 rf pulse was used, then the
resultant tip angle dependence was simply unity. Fundamental
to the understanding of the TART sequence is the fact that,
although the first two rf pulses of the basic STE imaging
sequence resulted in a net longitudinal magnetization, therB
was no reason that this entire magnetization had to have
been brought into the transverse plane all at once by the
third rf pulse. Indeed, it was possible to bring only a
portion of the magnetization into the transverse plane by
using tip angles less than or equal to SO degrees.
Figure 4-7 is the tip angle reduced TI CTART) imaging
sequence. In this version of the sequence, slice selection
was determined by the first SO degree rf pulse, applied in
the presence of a magnetic field gradient, and was selective
perpendicular to the z axis. The phase of thB first rf
pulse, A, and the phase of the receiver, B, were cycled in
the same manner as the rf pulse and receiver phases in the
basic STE imaging sequence. Following convention, the time

lie
90° 90°
a,
a,
a,
a.
tx O
g>
_tvj—\ /—l_/—\
Tl
* y \ :
,n__a
a
A
-0—if—a.
RX
m
*f* H
TE/2 TE/2
< M H H » H M •*
TE/2 TE/2 TE/2 TE/2
RT
------tt -*<
Figure 4-7. The tip angle reduced TI CTART) imaging
sequence.

113
From the first rf pulse to the maximum amplitude of the PE
mas denoted as TE, thus the time between thB first and
second rf pulses was TE/2. All phase encoding was performed
during this initial interval TE/2, therefore thB PE and the
resultant series of STE images were in spatial registration.
In contrast with the basic STE imaging sequence where a
single SO degree rf pulse was used to form a single STE
image, the TART imaging sequence used a series of rf pulses,
whose tip angles were SO degrees or less, to form a series
of T1 weighted STE images. The reduced tip anglB rf pulses
were denoted by al, a2, 4-7. The T1 recovery time, from the second SO degree rf
pulse to the rf pulse with tip angle ai, was denoted as RTi.
Thus, the ith STE image had a T1 weighting given by
expC-RTi/T1).
The utility of the TART imaging sequence lies in thB
fact that, with the correct choice of RTi values, the entire
spin-lattice relaxation curve was sampled during a single
pass of the imaging sequence, with each sampling point
corresponding to one of the STE images in the series. The
fact that each STE shared a common T2 dependence, given by
exp(-TE/T2J, aided in simplifying the resulting echo
amplitude expressions, although the expressions were
complicated by the fact that each STE had a different
trigonometric dependence upon the rf tip angles.
This complication was eliminated in the following
manner. Figure 4-0 illustrates the use of four nonequal,

114
Figure 4-8
The Formation of
a
series of TART images

115
reduced tip angles to generate a series of four STE images
which were identical in tip angle dependence and T2
relaxation weighting, differing solely in T1 weighting.
Figure 4-Ba is the longitudinal component of magnetization
immediately after the second rf pulse of figure 4-7. Indeed,
figure 4-Ba is identical to figure 4-3h. If ideal w/2 rf
pulses were used for the first two rf pulses, and T2
relaxation during the interval t1 is ignored, then this
component is simply Cl/2)Mi. Thus the application of the
first tip angle reduced rf pulse, with tip angle al, will
rotate into the transverse plane a quantity of magnetization
equal to C l/2)f1i sinal, leaving a quantity (l/2)Hi cosotl in
the longitudinal plane. This is illustrated in figure 4-Bb.
The procedure is repeated, as in figure 4-Bc, when the
second tip angle reduced rf pulse with tip angle a quantity of magnetization C l/25f1i cosalsina2 into thB
transverse plane, leaving a quantity C 1/2)Mi cosoclcosa2 of
magnetization along the longitudinal direction. Figures 4-Bd
and 4-Be illustrate the application of the third and fourth
reduced tip angle rf pulses. This procedure may be
generalized to the application of n reduced tip angle rf
pulses, where the quantity of magnetization rotated into the
transverse plane, now including the relaxation terms but
ignoring diffusional effects, is given by
n-1
Sn -Cl/2)m sinanC \r cosai )expC-(TE/T2 + RTn/Tl)]
i -1
C4-10D

1 IE
uiharB Sn is the maximum signal intensity of the nth STE. All
other terms have been previously defined.
Equation 4-10 is comprised of four seperate factors.
One factor is the term dependent upon the total longitudinal
magnetization available prior to the application of any
reduced tip angle rf pulses, simply C1/21MÍ. This factor is
the same far each STE image in the series. A second factor
which is the same for each STE in the series is the TB
relaxation damping term. A third factor, the T1 relaxation
damping term, is different for Bach STE image in the series,
by design, far this is the source of image to image
contrast. The final factor in equation 4-10 is the tip angle
dependence. Although fundamentally different for each STE
image, it was possible to adjust the values of the reduced
tip angles in a manner which resulted in identical tip angle
dependence in each STE image. This is graphically displayed
in figure 4-8, where the tip angles are such that a constant
amount of transverse magnetization is produced with each
application of a tip angle reduced rf pulse, ignoring T1
relaxation. Thus, when each STE in the series is formed, as
depicted in figure 4-8f, the only difference in each image’s
maximum amplitude is the different exponential T1 weighting.
Althought a qualitative argument based on figure 4-0
indicates that each successive reduced tip angle must be
greater that the previous one (for the quantity of
longitudinal magnetization diminishes with each rf pulse,
yet it is desired to keep the quantity of induced transverse

117
magnetization a constant), it is passible to quantitatively
determine the specific values of the reduced tip angles
required.
There are two key points to consider in the development
of a quantitative expression for the values of the reduced
tip angles which will result in each STE image of the series
having the same tip angle dependence. The first point is the
most obvious, it is necessary to set the trigonometric form
of the tip angle dependence of the nth STE equal to the
trigonometric form of the tip angle dependence of the
Cn-l)th STE. For example, if n equals four, then setting
sin relationship sino<4 - tana3. The generalized recursive
relationship is given by
aCn-1) - arctantsinaCn)J C4-11J
where a(n) and aCn-1) are the nth and (n-l)th reduced tip
angles, respectively.
Equation 4-11 is useful in assessing the relationship
amongst the reduced tip angles, but it does not suggest any
specific values. The second key point to consider is the
fact that, since the nth STE image is the last of the
series, a iy/2 rf pulse should be used so as to rotate all
the remaining longitudinal magnetization into the transverse
plane. Thus, this inital (actually, final) condition, in
conjunction with the recursive relation of equation 4-11,
will yield all the reduced tip angles required. Listed in

na
decreasing order, the first ten reduced tip angles are; 90
degrees, 45 degrees, 35.SB degrees, 30 degrees, 36.57
degrees, 34.09 degrees, 33.31 degrees, 30.70 degrees, 19.47
degrees, and IB.43 degrees. Obviously, this list could be
extended for any value of n, although the practical
limitation is the available signal to noise ratio of the STE
image. It is interesting to note that these values are
invariant to the value of n. That is, the five reduced tip
angles of a n equal five series are the same as the last
five reduced tip angles in a, for example, n equal fifty
series. The same recursive relationship has been developed
by Mansfield CMaB4D for use in a different application.
The TART experiment was performed on a phantom of seven
vials filled with water, and doped with copper sulfate to
various concentrations. The vials were 3.5 centimeters in
diameter, and were stacked so that only the wall thickness
separated them. The T1 values of the vials are given in
table 4-3, in the following section. Oial seven contained a
gel solution to reduce its T3 value. Thus, any unexpected T3
dependent weighting in the TART sequence would result in
signal intensity variations, in the images of vial seven,
which could not be explained by T1 weighting. The value of
TE was 15 milliseconds, and each RTi was incremented in
steps of 50 milliseconds, with an initial value of 50
milliseconds. The entire pulse sequence was repeated every
715 milliseconds.

na
Experiment seven: diffusion coefficient mapping
In addition to characterizing an object by its
relaxation times, T1 and T2, and its chemical shift, NflR
experiments afford the opportunity to characterize the
molecular translational self-diffusion coefficient of the
sample. Qne may utilize the T1 dependence of the STE image
indirectly to aid in spatially mapping the diffusion
coefficient. Recently reported methods of in vivo
diffusion coefficient measurement CTaBS, WeB43 rely upon
the w/E-t-w spin echo imaging technique. Since in vivo, T1
is typically greater than TE, the relative effect of
relaxation on signal intensity might be lessened by
observing the diffusional attenuation of the STE rather than
that of the PE in the tí/E-tI-tí/E-tE-tí/E sequence, or the
spin echo in the tt/E-t-ty sequence. A proposed imaging
sequence is presented in figure 4-S.
The modification to the basic STE imaging sequence of
figure 4-1 is the addition of diffusive pulsed magnetic
field gradients, shown in figure 4-B as a part of Gz.
Assuming the influence of any constant background field
gradient is negligible, the effect of the diffusive
gradients is given by
E E E
F C G , D , S , A ) “ expC-T G DS CA-5/351 C4-1EJ
with 6 and A depicted as in figure 4-3, where A -Al for the
PE image and A -££ for the STE image. Hence, thB T1
dependence of thB STE facilitates diffusion coefficient

1E0
Rx
The stimulated echo-difFusion coefficient
imaging sequence.
Figure 4-9.

121
determination by permitting a greater range in a 2 values. In
sequences where relaxation damping is strictly T2 dependent
Ce.g. spin echo imaging, primary echo imaging), relaxation
effects often dominate the diffusional Bffect. This is of
primary concern in systems which undergo restricted
diffusion CWo63D, for example living cells CTa68), when
it is desired to extend the diffusion effect to the maximum.
Results
Introduction
The time domain response of a spin system to three tt/2
rf pulses is given in figure 4-10. This is simply the
stimulated echo rf pulse sequence, without applied pulsed
magnetic field gradients, generated with the NT-00
spectrometer and presented herB for illustrative purposes
only. Fallowing the notation of figure 4-10, Ca) is the
response to the first tt/2 rf pulse applied at time zero,
with a FID fallowing immediately. 0 second tt/2 rf pulse was
applied after a time interval rl equal to 400 milliseconds,
with a FID fallowing immediately. This response is noted as
Cb) in figure 4-10. A PE was formed at time 2rl, 000
milliseconds from time equal zero, and is indicated in
figure 4-10 as Cc). At a time t2 equal to 675 milliseconds
after the second rf pulse, a third tt/2 rf pulse is applied,
with a FID following immediately. This response is noted as
Cd) in figure 4-10. A STE was formed at a time rl after the
third rf pulse, 1475 milliseconds from time equal zero, and
is noted in figure 4-10 as Ce). Three other secondary echoes

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

123
are formed, denoted in figure 4-10 as Cf), Cg), and (h). The
corresponding times were, 2r2 C1350 milliseconds from time
equal zero), t1+2t2 C1750 milliseconds from time equal
zero), and 2Ct1+t2) (2150 milliseconds from time equal
zero!.
One problem associated with STE imaging is highlighted
in figure 4-10. It should be noted that the STE is not
temporally isolated from the secondary echo which formed at
time 2t2. Artifacts would be introduced into a STE image
based upon this particular STE. It was possible to adjust
the values of rl and t2 so as to isolate the STE, but this
approach would result in restricting the timing parameters
to certain values. As mentioned earlier, in practice a
spoiling magnetic field gradient pulse was applied after the
formation of the PE, but prior to the application of the
third rf pulse. This spoil pulse eliminated all transverse
magnetization prior to the application of the third rf
pulSB, thus no secondary BchoBS were formBd.
Experiment one: T1 contrast imaging
Figure 4-11 presents typical results from a basic STE
imaging sequence. The phantom shown in figure 4-lla is a red
Delicious apple with a one centimeter diameter vial of
copper sulfate doped distilled water embedded in its center,
dubbed the ’’William Tell phantom.” Figure 4-llb is the PE
image CtI - 20 milliseconds), and figure 4-llc is the STE
image Crl - 20 milliseconds, t2 - 586 milliseconds).

124
b
c
Figure 4-11. The UJilliam Tell phantom. Ca) au naturel. (b)
the PE image, Cc) and the STE image.

125
Owing to a short t1 value, the doped water and apple
Flesh did not vary greatly in intensity in the PE image.
Host of the variation in intensity within the image was due
to volume averaging, except for the region of low intensity
directly beneath the water vial. This appeared to be the
region of low Flesh density where the seeds reside. The
source of high intensity at the base of the apple was not
known with certainty, but could be the result of a bruise.
ThB T1 of the doped water solution was determined to be
513±17 milliseconds by an inversion recovery sequence
utilizing a composite tt pulse without applied gradients. In
a similar Fashion the T1 of apple FlBsh was determined to be
less than 200 milliseconds. This spread in T1 values was
dramatically demonstrated in figure 4-llc by the STE image.
Experiment two: quantitative T1 imaging
In addition to T1 contrast imaging, STE imaging
permitted quantitative measurements of T1 values as outlined
earlier. Figure 4-12 depicts the results of quantitative T1
imaging with stimulated echoes. The phantom consisted of
three one centimeter diameter vials of copper sulfate doped
water. The top right vial had a T1 of 25013 milliseconds,
the bottom left vial had a T1 of 33313 milliseconds, and the
bottom right vial had a T1 of 512117 milliseconds. These T1
values were determined individually by an inversion recovery
sequence utilizing a composite ir pulse, without applied
magnetic Field gradients.

126

1E7
Figure 4-lBa is the PE image CtI - EO milliseconds),
while Figures 4-l£b thru 4-1EF are STE images of the same
phantom, each acquired with a different tE value Crl - EO
milliseconds, t£ - 100, E50, 500, 1000, and 1500
milliseconds respectively). The T1 value for the bottom left
vial was determined in two ways, based upon the maximum
signal amplitudes of the image of that vial in each of the
STE images. The first method, plotting the logarithm of the
STE’s maximum amplitude versus t£, yielded a value For T1 of
3BE±E milliseconds. This calculated value represented less
than a Five percent relative error when compared to the
actual T1 value. As outlined earlier, a more precise
calculated value of T1 could be determined if the effects of
diffusion were considered, in the manner of equation 4-B.
When the data were analyzed in the manner specified in the
text following equation 4-B, a calculated value for T1 of
3BB±E milliseconds was obtained, which represented less than
a three percent relative error when compared with the actual
T1 value. These results were within acceptable experimental
limits.
Experiment three: water-lipid contrast imaging
Figure 4-13 is a water-lipid T1 contrast image of a
hen’s egg, by STE imaging. Figure 4~13b is the PE image CtI
- E0 milliseconds), and figure 4-13c is the STE image Crl
“SO milliseconds, tE “ IBB milliseconds). Consider figure
4-13c, where the high intensity signal is from the egg’s
albumen Cthe water dense element), the circular region of

12B
image.

129
low intensity is From the egg’s yolk (the lipid dense
element), and the ’’missing” semicircular portion near the
bottom is the egg’s air sac. The magnitude of the readout
gradient used in both Figures 4-13b and 4-13c was 0.5 mT/m,
which was insuFFicient to overcome the lipid chemical shiFt
From the yolk CDÍ84D, mast apparent in the PE image. This
shiFt appears in the readout direction Cvertical) oF Figure
4-13b, but is suppressed in Figure 4-13c due to the
relatively short T1 oF the lipid component oF the yolk.
Additionally, Figure 4-13b suFFers From a distorted aspect
ratio, owing to the inFluence oF residual gradients. Hence,
the phase encoding direction Chorizontal) is reduced in
Figure 4-13b relative to Figure 4-13c.
Experiment Four.- chemical shiFt imaging
Figure 4-14 is an example oF STE chemical shiFt
imaging. The phantom used in this experiment, depicted in
Figure 4~14a, consisted oF two, one-centimeter diameter
vials separated spatially in the y direction but not the x
direction. DnB vial was Filled with vegetable oil having a
T1 oF 20412 milliseconds, as determined by an inversion
recovery experiment with a composite tt pulse, without
applied magnetic Field gradients. The second vial contained
a mixture oF distilled water and deuterated water, having a
TI oF 2.010.1 seconds, determined in a like manner. The
dButerated water was addBd to reduce thB signal amplitude,
so that the unsaturated signal intensities oF the two vials
were similar.

130
Y
b
c
Figure 4-14. ñ STE chemical shift image, (al The phantom,
Cbl the PE image, Cel and the STE image.

131
To retain chemical shift information Calong the cs axis
as depicted in figure 4-14}, no readout gradient was
employed. The x direction urns phase encoded (depicted as the
x axis in figure 4-141. The images are displayed as stacked
plots of spectra. The PE image Crl - 20 milliseconds),
figure 4-14b, demonstrates the near equal intensities of the
two vials for short t1, and the 3.5 ppm relative chemical
shift. In the STE image CtI - 20 milliseconds, t2 - 250
milliseconds) of figure 4-14c, the oil image is suppressed
due to the large difference in T1 between the water and oil.
Each image was scaled to maximum peak intensity.
Experiment five: extended STE multiecho imaging
Figure 4-15 illustrates the results of the extended STE
multiecho imaging sequence, as given in figure 4-5. The
phantom consisted of three, one centimeter diameter vials of
copper sulfate doped water. The top right vial had a T1 of
250±S milliseconds, the bottom left vial had a T1 value of
393±3 milliseconds, and the bottom right vial had a T1 of
512±17 milliseconds. All T1 values were determined by an
inversion recovery experiment utilizing a composite tt pulse,
without applied magnetic field gradients.
Figure 4-15a is the PE image Crl - 20 milliseconds),
figure 4-15b is the STE image Crl - 20 milliseconds, t2 -
148 milliseconds), and figure 4-15c is the TE image Crl - 20
milliseconds, t2 - 148 milliseconds, and t3 - 548
milliseconds). Note the T1 contrast imposed on the STE image
and the TE image as a function of t2 and t3, respectively.

b
c
Figure 4-15. An extended STE multieche series of images. Cal
The PE image, Cb) the STE image, Cel and the TE
image.

133
The aspect ratio of the STE image was one, For residual
gradient influence along the phase encoding direction
(horizontal) was negligible for this echo. Both the PE image
and the TE image were influenced along the phase encoding
direction by residual gradients. The amount of influence was
a Function of how much time the magnetization, which was
used in echo formation, spent in the transverse direction
after initial phase encoding within the rl interval, and the
magnitude of the residual gradient during this time. The
influence was greatest on the TE image, for although the PE
spent a time t1 Cequal to SO milliseconds) in the transverse
direction while in the presence of a residual gradient, the
TE spent a time tE Cequal to 14B milliseconds) in the
transverse direction in the presence of the residual
gradient. IndBBd, the time spent by the TE overlapped that
of the PE. All images were scaled identically.
Experiment six: TART multiecho imaging
Figure 4-16 is a comparison of the images obtained with
the conventional spin echo imaging sequence, and that
obtained from thB PE of the TART sequence. The images are
presented as signal intensity contour plots. As predicted by
equation 4-3, the signal to noise ratio of the PE image is
reduced by a factor of two compared to that of the spin echo
image. The images in figure 4-16, and all othBr images
presented which were generated with the TART sequence, were
phase encoded in the x direction Chorizontal), and with the
read out gradient applied along the y direction (vertical).

134
Figure 4-16. A comparison of the spin echo image and the
primary echo image. Cal The spin echo image,
Cbl and the primary echo image.

135
The T1 weighted series of STE images generated by the
TART sequence are depicted in Figure 4-17. The images are
presented as signal intensity contour plots. The recovery
time, RT, progressed From 50 milliseconds in Figure 4-17a,
to 200 milliseconds in Figure 4-17d, in 50 millisecond
increments.
Qualitatively, thB T1 weighted series aF STE images
represented the available contrast diFFerence due to
variations in spin-lattice relaxation rates. The
quantitative nature aF the intensity variations in the TART
imaging series is represented in table 4-2. The First column
oF the table gives the T1 value determined Far each vial by
an inversion recovery experiment, where eight data paints
were Fitted to a three parameter exponential curve. Each
vial was measured separately by positioning the vial at the
center oF the rF coil, and operating the CSI unit as a
spectromBtBr, without applied magnetic Field gradients.
Column two is simply the standard error in these T1 values
estimated with thB inversion recovery technique.
Column three oF table 4-2 gives the T1 values
determined For each vial by Fitting the signal intensities
From the Four STE images to a two parameter exponential
curve. The intensity values were determined by averaging
pixels over a Fixed size region within the image boundaries
oF each vial. Column Four is simply the standard error in
these T1 values estimated with the TART imaging sequence.

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

137
Table 4-5
Calculated T1 Ualues From Phantom in TART Experiment
Uial
T1 Ualues Cmsec)
IR Standard TART
error
Standard
error
1
115
±0.7
103
±E. 9
a
63
±0.09
66
±1 .S
3
58
±0.04
61
±0.9
4
63
±0 . OE
65
±E. 3
5
115
±0.7
117
±7.0
6
64
±0 . E
63
±1 .6
7
E46
±1.7
EE7
±9.8

130
Experiment seven: diffusion coefficient mapping
As indicated in Figure 4-4, there mas an appreciable
residual gradient present after thB application of a pulsed
magnetic Field gradient. Its influence on image quality was
predominately qualitative, resulting in nonunity aspect
ratios. Unfortunately, the residual gradient was sufficient
to render quantitative diffusion coefficient mapping
impractical, although an example of qualitative diffusion
coefficient contrast imaging has recently been presented by
others Ct1e85D, which utilized an imaging sequence
identical to that in figure 4-9.
Discussion
Exploiting stimulated echoes in NHR imaging involved
the judicious use of the ability to store and retrieve
information along the longitudinal direction, afforded by
the stimulated echo. The results of this investigation took
the form of specific examples which prudently used this
unique property of thB STE in NHR imaging. First, it was
shown that in addition to generating T1 contrast images, it
was passible 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 accessed; the enhancement or
suppression of elements in the object with different T1
values. Third, it was demonstrated that the STE was easily
integrated into chemical shift imaging schemes. Fourth, two
STE methods were developed which permitted the acquisition

139
of a series gF 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 to lessen the effect of
T2 relaxation, was proposed. A detailed disscussion of each
of these results follows.
Experiment One: T1 Contrast Imaging
The PE and STE images of the William Tell phantom
illustrated in figure 4-11 indicate that stimulated echo
imaging not only works, but also works well to produce T1
contrast images. It is worthwhile to elaborate on the
unexpected high intensity regions in the images. In both the
PE and STE image, there was a high intensity region at the
base of the apple, hypothesized to be a bruise. Also, there
is a region of high intensity surrounding the position where
the cylindrical vial was located. Since the resolution of
the image was 1.5 X 0.75 millimeters, and since edges were
well defined in spite of volume averaging, it seems likely
that the region of high intensity surrounding the vial was
not a structual component of the apple, and it is suggested
to be associated with apple flesh which was bruised while
forcing the vial through the apple. The reason bruised apple
flesh would result in increased signal intensity is
explained by the Following.
The full wrath of the Bloembergen, Purcell and Pound
CB14B1 theory of relaxation need not be brought to bear

140
against this problem, rather, Just one simple result of the
theory. The result is that the spin-lattice relaxation rate
is proportional to the correlation time re, in the extreme
narrowing situation. This result, coupled with the fact that
a mare mobile solution has a lower tc, suggests a reason why
bruised applB flesh resulted in increased signal intensity.
An apple is predominately made up of water, although
the flesh is quite cellular in nature, offering a natural
restriction to molecular mobility. When the apple flesh is
bruised, that is, when the cellular structure is broken
down, the molecular mobility increases. This increased
mobility results in a lower tc, and in turn results in an
increase T1 value. Hence, bruised regions have longer T1
values, and would therefore appear increased in intensity
over the surrounding unbruised regions.
Although the STE in figure 4-llc admirably displayed T1
contrast, the relaxation damping of the stimulated echo is
not solely determined by Tl, for there is a expC-Prl/TPl
dependence also. To obtain a ’’pure” Tl mapped image, simple
post acquisition processing is required. It may be noted
that the ratio of the STE’s maximum, given by equation 4-7,
to the PE’s maximum, given by equation 4-3, MCSTE/PE), is
given by
2
ncSTE/PE) - C1/P)C sin9Psin93/sin C9P/P)DexpC-Tp/Tl) *
rCG,D,rl,tP)
C4-13D

141
where all the terms have been previously defined, with
rCG.D.rl.rE) being the ratio of the diffusional damping of
the STE to that of the PE. For ideal ir/2 rf pulses and
negligible diffusional damping, MCSTE/PE) equals
expC-t2/T11, assuming thB pulsB sequence repetition time is
sufficiently long so as to avoid additional T1 dependence
via saturation. Hence, images with strictly T1 contrast
could readily be generated from a single pass of the STE
imaging sequence and appropriate post acquisition data
manipulation. Furthermore, it is noted that MCSTE/PE) is
functionally independent of 81, making it insensitive to
changes in 91.
Experiment Two: Quantitative T1 Imaging
The results of this experiment indicate that STE
imaging is not only capable of T1 contrast imaging, but that
the STE imaging sequence may be as quantitative as the
conventional inversion recovery or spin echo techniques.
Indeed, STE imaging has some advantages over the
conventional techniques which yield calculated T1 values.
The conventional inversion recovery imaging sequence
introduces T1 weighting into the image by inverting the
equilibrium magnetization, taken to be positive initially,
along the negative z axis. The magnetization is sample by a
SQ degree rf pulse as it relaxas along the z axis from the
negative to the positive. Conventional state of the art NdR
imagers handle this situation in one of two ways. Some
instruments offer the capability of retaining this signed

142
information by performing a phase sensitive type of image
reconstruction. This procedure is, at best, difficult to
optimize when the object imaged is so diverse as the human
body. The second option offered is a simple magnitude
reconstruction of the image, where all signed information is
lost. This approach, although simple to implement, could
result in confusion when regions of the object which are
equal in intensity but opposite in sign are displayed as
identical. Since in STE imaging all T1 weighting is one
sided CB.g. all positive), the simple magnitude
reconstruction suffices to display all available T1
information without ambiguity.
Experiment Three: Water—Lipid Contrast Imaging
The images of figure 4-13 illustrate a unique feature
of STE imaging, the ability to suppress the shorter T1
elements in an abject by T1 weighting.
Conventional SE imaging techniques introduce T1
weighting by saturating the signal. That is, the sequence is
repeated so rapidly that therB is little timB between
repetitions for T1 relaxation. Thus, those elements with
short T1 values are able to return to their equilibrium
value prior to the next repetition of the sequence, whereas
those elements with longer T1 values are destined, Just as
Sisyphus was CHa5SJ, to never fully regain their
equilibrium value before the pulsB sequence starts over.
Thus, elements with longer T1 values are suppresed, whereas
elements with shorter T1 values are seemingly enhanced.

143
In contrast, the simple expC-rB/Tll weighting of the
STE image results in the suppression of shorter T1 elements,
while longer T1 elements are seemingly enhanced. For
example, consider the case where t2 is 150 milliseconds, and
two different elements exist in the object, one with T1
equal to 100 milliseconds, and the other with a T1 of 1000
milliseconds. Based solBly upon this difference in T1
values, with all else being equal, the longer T1 element
would appear nearly four times as intense as thB shorter T1
element. The clinical utility of this characteristic of STE
imaging has yet to be explored. However, since many
abnormalities, and in particular malignancies, have longer
T1 values, this raises tantalizing possibilities.
Experiment Four: Chemical Shift Imaging
It has been demonstrated, in figure 4-14, that the
stimulated echo imaging technique is sufficently flexible so
as to permit its incorporation into any existing chemical
shift imaging scheme which relies upon spin echo formation.
Not only may the basic stimulated echo sequence be used in
chemical shift imaging, but so may either of the two
multiecho stimulated echo sequences presented in this
investigation. Additionally, quantitative analysis of T1
could easily be done for each of the chemically shifted
components as outlined previously. Extension of this
technique to nuclei other than hydrogen would be beneficial,
for example, phosphorus, where T1 is often much longer than
T2 CHo75D.

144
Experiment Five: Extended STE flultiecho Imaging
In contrast with the basic STE sequence, the extended
STE multiecho sequence allows for greater T1 contrast For a
given imaging time, and offers a convenient method of T1
estimation. The spin echo multipulse sequence affords
similar advantages For TE contrast imaging. The T1 weighted
multiecho imaging scheme has the added advantage that, in
addition to the train of T1 weighted images, the TE weighted
PE image is also produced. Thus, this singls sequence yields
a TE dominated image, and a series of T1 weighted images,
all in spatial registration. This would be quite useful in
medical applications, where typically a spin echo image with
a short echo time is useful for anatomical differentiation,
and images with high T1 contrast are useful in pathological
diff erentiation.
Experiment Six: TART Hultiecho Imaging
The TART imaging sequence provides both a series of STE
images progressively weighted with T1 relaxation and
constant TE weighting, and also a TE dominated PE image.
Both the spatial resolution and the total imaging times are
comparable to the conventional NHR imaging techniques.
Although clinical utility has yet to be realized, the
flexibility of the technique promises wide applications. For
all the virtues of TART imaging, there is one major vice,
the reduction in the signal to noise ratio of the TART
images over the corresponding spin echo image.

145
NHR imaging makes available a myriad of information
concerning the object under investigation. Unfortunately,
there is always a trade off involved, thB most common one
being the trade off between derived information on the one
hand, and imaging time and signal to noise ratio on the
other. Typically, if one wants to glean additional
information from a spin system, either additional time must
be spent or a reduction in the signal to noise ratio must be
tolerated. This is precisely the situation in TART imaging.
Additional T1 information is obtained through the series of
STE images, but only by paying the price of a reduced signal
to noise ratio.
The signal to noise ratio of the PE and the series of
STE images may be quantified and compared to the signal to
noise ratio of thB conventional spin echo image. If the
equilbrium magnetization is Mi, then, ignoring relaxation
and diffusional damping, the maximum amplitude of the spin
echo image is simply Mi. This is the ruler by which we
measure the PE and STE images of the TART sequence.
As indicated in equation 4-3, the maximum amplitude of
the PE image, ignoring relaxation and diffusional damping
and assuming ideal ir/2 rf pulses, is (l/2)Mi . Thus, the PE
image, which has the same relaxation weighting as the
conventional spin echo image, has a signal to noise ratio
reduced by a factor of two. The other half of the signal to
noise is available for STE image production.

146
IF only a single STE image is produced, then it3 signal
to noise ratio is simply a half of that For the spin echo
image. IF the stored longitudinal magnetization is used to
create a series of STE images, as in the TART sequence, then
thB available Cl/23ni is vectorially divided amongst each
STE image. Since, in the TART imaging sequence, Bach STE has
the identical tip angle dependence, this Factor is properly
given by sinal, simply the tip anglB dependence of the first
STE image in the series. Recall, the vector sum of all the
STE images in the series, neglecting relaxation and
diffusion damping, must be equal to Cl/2)ni. For a series of
n images, the vector sum of all the STE image’s maximum
amplitudes, EH, is given by
2 2 2
EM - CCl/2)HisinalD +CCl/2)Misina2cosalD +
n-1 2
... +C Cl/2)f1i sinanC cosaiH C4-14D
i -1
which may be simplified, as noted, by realizing each reduced
tip angle term equals the first reduced tip angle term,
sinal. Thus, Efl equals the square root of nC Cl/2)f1i sinall .
Since Ef1 must bB equal to (l/2)ni , sinal must be inversely
equal to the square root of n. Thus, since sinal is the
reduced tip angle factor for all the STE images in a TART
sequence with n images, it may be said that the signal to
noise ratio of each image is reduced by a factor of the
square root of n. A similar result was expressed by
flansfield CMaB4D for a different application.

CHAPTER U
SUMMARY ANO CONCLUSIONS
The emphasis of this work was two-fold. One, the
accurate and precise determination of the spin-lattice
relaxation time with a conventional state-of-the-art NMR
imager, and two, the application of the stimulated echo
CSTE1, with its unique T1 dependence, to NMR imaging.
It was shown that under certain conditions it is
passible to obtain an accurate and precise estimate of T1
with a commercial NMR imager. The most reliable method
involved the acquisition of thrBe fast inversion recovery
images, with suitably chosen values of the inverting time as
given in equation 3-3. If the signal intensities from these
images are fitted to a three-parameter monoexponential
function, then an estimated T1 value was determined which
was insensitive to whether the object was in an
inhomogeneous rf field or not. The source of the field
inhomogeneity may be the rf coil itself, or the rf
attenuating properties of the human body which act to
perturb the transmitted rf field.
Additionally, it was also shown that three spin echo
images, with suitably chosen values of the pulse sequence
repetition time as given in equation 3-5, could be used for
T1 estimation. In this case, the signal intensities
147

14B
would be fitted to a two-parameter monoexponential function.
Obtaining estimated T1 values in this fashion could be more
precise and timB efficient than the fast inversion recovery
technique, but was always much less accurate.
The results of this work had additional value in that
they could be applied a priori to aid in designing an
Bntire imaging scheme which would result in reliable T1
estimates, or the results could be used in an a posteriori
fashion, to evaluate the reliability of a calculated T1
value.
Although wide in scope and exacting in execution, this
investigation did have same necessary errors of amission. By
limiting the forms of the fitting functions to those
suggested by the NflR spectroscopy literature, certain
refinements unique to imaging mere not considered CPy83D.
Additionally, two-paint estimates of T1 values based upon
mixtures of inverting and noninverting techniques were not
considered CLÍB5D. Never-the-less, the conclusions of this
investigation are correct and usBful, as long as they are
utilized within the context of the study.
This work was also unique for it introduced the use of
the stimulated echo for data acquisition in 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 stimulated echo images, in
which the storage time had been systematically varied. Also,
a novel application of the T1 weighted STE was demonstrated:

143
the enhancement or suppression of elements in the object
with different T1 values. Additionally, it was demonstrated
that the stimulated echo could be integrated into chemical
shift imaging schemes. Perhaps of most significance were the
two STE imaging methods presented which permitted the
acquisition of a series of STE images within one imaging
sequence, where each imagB is progressively weighted with
increasing T1 relaxation damping. Stimulated echo imaging
was also shown to have the potential to be a method of in
vivo determination of molecular self-diffusion
coefficients.
STE imaging has certain characteristics which makes it
a welcomed addition to NMR imaging. Since all STE sequences
use tip angles of 90 degree or less, the instantaneous and
integrated rf power deposition in the human body is less
than in comparable SE imaging techniques, with no loss in
the net signal-to-noise ratio. This feature indicates that
STE imaging techniques might be ideal for imaging at higher
frequencies, where the body is a more efficient antenna.
Since the STE may be used wherever the spin echo is
currently used in NflR imaging, the spatial resolution and
the total imaging time may be the same as for a conventional
image. Additionally, STE imaging lends itself to multislice
imaging. Thus, multislice and T1 weighted multiecho STE
images could be acquired much as multislice and multiecho
spin echo images are currently acquired.

1E0
Both of thesB investigations, although different in
emphasis, uiere formulated based upon the same fundamental
premise, that it was possible to use the microscopic
properties of matter as investigative tools with which to
examine the macroscopic properties of matter. Indeed, it is
Just this fact, that the phenomenon of NHR is based on
interactions with the atomic nucleus, which gives NHR
imaging the potential to be one of the most important probes
yet devised with which to examine matter. Other
investigative techniques which rely upon interactions with
the electron energy levels of an atom have the potential to
alter the chemical, or biochemical environment of the object
under investigation. NMR imaging is unique in that it only
slightly perturbs the nuclear Bnergy levels of an atom,
although the price paid is that the information gleaned is
done so with relatively poor sensitivity. It is thought that
the conclusions of these investgations into spin-lattice
relaxation in NNR imaging have contributed to a more
efficient use of the information which NHR imaging is able
to supply.

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BIOGRAPHICAL SKETCH
William Sattin, born in 1957, is the son of Eduard and
Sallie Sattin. After attending four elementary schools, two
Junior high schools, and three high schools, he graduated
From his secondary schooling in 1S75, and entered the
Univeristy of Miami in the same year. Tired of switching
schools, he stayed at the University of Miami for seven
years, receiving a Bachelor of Science degree in physics in
1970, a Master of Science degree in physics in 1980, and a
Master of Science degree in radiological sciences in 1902.
Interspersed with all this education he experienced the
happiest day of his life in 1980, when he took Wendy Albin
for his bride. Seeking greener pastures, he enrolled at the
University of Florida in 1982, to pursue a Doctor of
Philosophy degree with emphasis on nuclear magnetic
resonance imaging. A most extraordinary set of circumstances
have recently left him a father, to Emily Albin Sattin, aged
three months.
155

I certify that I have read this study and that in my
â–¡pinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality, as
a dissertation for the degree of Doctor of Philosophy.
K. N.
Katherine N. Scott, Chairman
Associate Professor of Nuclear
Engineering Sciences
I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality, as
a dissertation for the degree of Doctor of Philosophy.
Alan fl. Jacal
Professor of Nuclear Engineering
Sciences
I certify that I have read this study and that in my
â–¡pinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality, as
a dissertation for the degree of Doctor of Philosophy.
E. Raymond Andrew
Professor of Nuclear
Sciences
Engineering
I certify that I have read this study and that in my
â–¡pinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality, as
a dissertation for the degree of Doctor of Philosophy.
Engineering

I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality, as
a dissertation for the degree of Doctor of Philosophy.
J
James R. Brookeman
Associate Professor of Physics
I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality, as
a dissertation for the degree of Doctor of Philosophy.
Thomas H. flared
Assistant Professor of Radiology
This dissertation mas submitted to the Graduate Faculty of
the College of Engineering and to the Graduate School and
was accepted as partial fulfillment of the requirements for
Dean, Graduate School

UNIVERSITY OF FLORIDA
3 1262 08554 1380






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