Title: Magnetic resonance imaging and spectroscopy for the study of translational diffusion
CITATION PDF VIEWER THUMBNAILS PAGE IMAGE ZOOMABLE
Full Citation
STANDARD VIEW MARC VIEW
Permanent Link: http://ufdc.ufl.edu/UF00100727/00001
 Material Information
Title: Magnetic resonance imaging and spectroscopy for the study of translational diffusion applications to nervous tissue
Physical Description: Book
Language: English
Creator: Bossart, Elizabeth L
Publisher: State University System of Florida
Place of Publication: <Florida>
<Florida>
Publication Date: 1999
Copyright Date: 1999
 Subjects
Subject: Magnetic resonance imaging   ( lcsh )
Diagnostic imaging   ( lcsh )
Physics thesis, Ph. D   ( lcsh )
Dissertations, Academic -- Physics -- UF   ( lcsh )
Genre: government publication (state, provincial, terriorial, dependent)   ( marcgt )
bibliography   ( marcgt )
theses   ( marcgt )
non-fiction   ( marcgt )
 Notes
Summary: ABSTRACT: In all stages of trauma and disease in the brain and spinal cord, it is important to know the amount of the physical damage, how far the damage will extend, and how the structural changes relate to the final amount of functionality. Though it is fairly straightforward to measure this damage ex vivo through histological sectioning, assessment of internal physical damage in vivo has been difficult to do. The innovation of magnetic resonance (MR) imaging, in particular the measurement of water diffusion, has been an important step towards quantifying structural changes in living systems. Water diffusion, once considered a single diffusion rate (or single diffusion rate tensor) process, appears to be a multiple diffusion rate process. To the limits of the gradients available (300 mT/m), two unique diffusion regimes have been seen in fixed CNS tissue: a fast diffusing component and a slow diffusing component. Others have speculated that the fast and slow diffusing components in tissue represent diffusion in the extracellular and intracellular spaces, respectively. The aim of these studies was to find the best tissue preparation for ex vivo measurements, determine the best model with which to fit diffusion studies done on CNS tissue, and to provide a basic understanding of the information contained in the fast and slow diffusion compartments. These measurements should provide a solid background for future in vivo experiments, allowing a better understanding of the information provided by the fast and slow diffusion components. This will be useful for understanding the role of diffusion in normal tissue and for quantifying changes due to trauma, which could lead to better diagnostic techniques in the future.
Summary: KEYWORDS: diffusion, diffusion tensor, intracellular, extracellular, magnetic resonance, MR, fixation
Thesis: Thesis (Ph. D.)--University of Florida, 1999.
Bibliography: Includes bibliographical references (p. 129-136).
System Details: System requirements: World Wide Web browser and PDF reader.
System Details: Mode of access: World Wide Web.
Statement of Responsibility: by Elizabeth L. Bossart.
General Note: Title from first page of PDF file.
General Note: Document formatted into pages; contains xiv, 137 p.; also contains graphics.
General Note: Vita.
 Record Information
Bibliographic ID: UF00100727
Volume ID: VID00001
Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
Resource Identifier: oclc - 45265814
alephbibnum - 002484312
notis - AMJ9926

Downloads

This item has the following downloads:

bossart ( PDF )


Full Text










MAGNETIC RESONANCE IMAGING AND SPECTROSCOPY
FOR THE STUDY OF TRANSLATIONAL DIFFUSION:
APPLICATIONS TO NERVOUS TISSUE















By

ELIZABETH L. BOSSART


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


1999




























For Juan















ACKNOWLEDGMENTS


The work in this thesis could not have been accomplished without the help of a

great many people it is truly a collaborative effort. First and foremost, I would like to

thank Dr. Tom Mareci for his help, time and patience over the last few years. Working

with him, I learned a lot about research, and a lot about myself. I would also like to thank

Dr. Steve Blackband for all his counsel and support. Among other things both scientific

and personal, through him I learned when to relax. I would also like to thank Dr.

Raymond Andrew for his encouraging words and advise throughout my graduate career.

His kind words always made me smile.

I would like to thank several people in the lab and around the Brain Institute for

their help in my endeavors. I would like to acknowledge Ron Smith in the Neurosurgery

department of the UF Brain Institute for providing the human brain samples. I would like

to thank Drs. Ed Wirth, Paul Reier and Doug Anderson for their input on and expertise

with the neuroanatomy. With their help I managed to learn more biology than I ever

thought I would know. Also want to acknowledge Ed's help in reading over a couple of

chapters of my thesis and giving me his opinion. I would also like to thank Drs. Ben

Inglis and Dave Buckley. My discussions with them helped make clear many of my

ideas. I would also like to thank Ben Inglis, Jim Rocca and Dan Plant for helping me

learn many of the more practical things about NMR, like how to run the equipment. My

appreciation goes to Xeve Silver for his patience with the "stupid biology questions" I

iii









was constantly asking, for his aid in mixing up solutions, and for doing a lot of the animal

handling. My appreciation also goes to Emma Mercer for all her help with animal

handling. Without her, many of the normal studies and injury studies could not have

been completed. Thanks also go to Emma for providing the artwork in Appendix B and

for proof reading a couple of thesis chapters. I would also like to acknowledge Dr. Abbas

Zaman in the University of Florida Engineering Research Center for not only allowing

me to use his viscometer, but showing me how to use it as well. For their suggestions,

encouragement, and friendship I would like to thank Cecile Mohr, Alan Freeman and Jon

Bui.

I would also like to acknowledge five people without whom I might never have

made it through graduate school. First I would like to thank my parents, Marilynn and

William Bossart, for not setting limits on what I could do. Their support has been

invaluable. Next, I want to recognize my sister Cathy. Through her I learned what it

means to be a survivor. I would also like to acknowledge Koren Okuma. Through the

years her friendship has meant more to me than I know how to say. She has been there

for the ups and the downs and consistently reminded me how to laugh. Last, but not

least, I want to thank Juan Villar for standing by my side, loving me and encouraging me.

His love and support have helped to make the time go by more smoothly. I know this has

not been easy for him, but it has made things easier for me.















TABLE OF CONTENTS
page


A C K N O W L E D G M E N T S ..................................................................................................iii

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

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

LIST O F A BBREV IA TION S ................................................................... ................ xi

A B S T R A C T ..................................................................................................................... x iii

CHAPTERS

1 IN TR O D U CTIO N ......... .. ..................................... ........................... .. ............ 1

Introduction to R elaxation.. .................................................................... .............. 3
D description of T R elaxation.................................. ....................... .............. 4
D description of T2 R elaxation.................................. ....................... .............. 5
Relaxation Processes ....................... ............ ..............................6
E change P rocesses ..... .. ........................................ ........................ .. . ......... 6
D ip olar Interaction s ..... .. ........................................ ......................... . ...... ..... 8
Q uadrupolar Interactions......................................... ......................... .............. 8
Chem ical Shielding A nisotropy ....................... .............................................. 8
S calar R elax action ............................................................................................. 9
Introduction to D iffu sion ............................................ ............................ ............. 9
The Solution to the Bloch-Torrey Equation...................................... .............. 10
D ata C o llectio n ..................................................................................................... 1 1
C alculating b V alues ... .. ........................................ ....................... . . ..... ..... 12
M multiple L inear R egression ..................................... ....................... .............. 15
Problem with the Mono-Exponential Form .............. ................................... 17
M ultiexponential D iffu sion ......................................................................................... 2 1
P orous M edia T heory ................................................................ ..... ...... ......... .. 2 1
An Analytical Model of Restricted Diffusion................................................. 23
M ultiexponential M odel ........................................ ......................... .............. 25
Study D directions .......................................................................................................... 27

2 FIX A TION EFFECTS ..... ................................................................. .............. 30

Materials and Methods ..... ............ ............................................ 32
R elaxation M easurem ents in Solution .............................................. .............. 32


v









Im aging M easurem ents in Tissue...................................................... .............. 33
R e su lts ................. .... .................................................. ..................................... 3 4
Fixative Solution M easurem ents....................................................... .............. 34
Tissue M easurem ents ..... .. ............................... ...................................... 35
D iscu ssio n ............................................................................................................... . .. 3 7

3 RELAXATION AND DIFFUSION MEASUREMENTS ON FIXED HUMAN
B R A IN SA M P L E S ................................................................... ................. ... 44

M materials and M ethods ... ...................................................................... .............. 46
Sam ple Preparation ..... .. ................................ .......................... ......... ..... 46
N M R M easurem ents .. .................................................................... .............. 47
P o st-P ro cessin g ..................................................................................................... 4 8
R e su lts .............. ........................................................................................ . .......... 4 9
D iffusion Tensor M easurem ents ....................................................... .............. 49
T2 R elaxation M easurem ents ....................... ................................................ 52
D iscu ssio n ............................................................................................................... . .. 5 3

4 MULTIEXPONENTIAL DIFFUSION TENSOR IMAGING OF NORMAL RAT
SPINAL CORD ....................... .. .......... .............................. 56

M materials and M ethods ...... .. ................................. .......................... .............. 57
Sam ple Preparation .............................................. .................. .. .. .. .......... 57
Diffusion Tensor Measurements and Post Processing .................................... 57
R e su lts ......................................................................................................... ............ 5 8
D iscu ssio n ............................................................................................................... . .. 6 7

5 MULTIEXPONENTIAL DIFFUSION TENSOR IMAGING OF NORMAL AND 1-
MONTH POST INJURY RAT SPINAL CORDS ............... ................................... 70

M materials and M ethods .... ... ......................................... ....................... ......... ..... 7 1
Sam ple Preparation ..... .. ................................ ........................................ 71
N M R Experim ents ...... .. ..................................... ........................................ 72
R esu lts ....................... ................................................................................ . . . 73
N orm al R at Spin al C ord ........................................................................................ 77
R at Spinal Cord 1-M onth Post Injury ............................................... .............. 85
D iscu ssio n ............................................................................................................... . .. 9 0













vi









6 SUMMARY AND CONCLUSIONS................................................................. 94

G L O S S A R Y .................................................................................................................... 1 0 0

APPENDICES

A C O M PU TER C O D E ..... .................................................................. .............. 104

B P U L SE SE Q U E N C E S ............................................................................................... 125

C RAT SPINAL CORD ANATOMY AT VERTEBRAL LEVEL LI ..................... 127

L IST O F R E F E R E N C E S ................................................................................................ 129

BIO GRAPH ICA L SK ETCH ................................................................ .............. 137







































vii















LIST OF TABLES


Table page


2-1. Measured SNR in gray and white matter regions of the spinal
cord for various tissue preparations ...................... ............... 31

2-2. Relaxation rates in GM/WM for different tissue preparations .............. 35

3-1. Diffusion rates found for various types of fitting routines ....................... 50

3-2. T2 relaxation rates and volume fractions for GM and WM samples ............... 52

3-3. Diffusion volume fractions with and without the T2 contribution ................ 53

4-1. Diffusion rates for the regions if rat spinal cord shown in Figure 4-1 d .......... 61














LIST OF FIGURES


Figure page

1-1. Sim ple pulse sequence exam ple ....................................................... 13

1-2. Natural log of the signal intensity vs. b value graphed for b to 1500 s/mm2 ..... 18

1-3. Natural log of the signal intensity vs. b value for simulated data ................. 20

1-4. Natural log of the signal intensity vs. b value graphed for b to 10000 s/mm2 .... 20

1-5. Natural log of the signal intensity vs. b value for a region of interest
in the rat spinal cord ......................................................... 29

2-1. Graph of 1/T1 vs. concentration ......................................... ........... 34

2-2. Graph of 1/T2 vs. concentration .......................... ........... 36

2-3. Graph of dynamic viscosity vs. concentration .......................... ............ 36

2-4. Fast diffusion rate component vs. slice position graphs for regions of
interest in fixed rat spinal cords measured in PBS ............................. 38

2-5. Slow diffusion rate component vs. slice position graphs for regions of
interest in fixed rat spinal cords imaged in PBS ............................ 39

3-1. The natural log of the signal intensity vs. b value graph for brain white matter .. 45

3-2. The natural log of the signal intensity vs. b value graph for brain gray matter ... 45

4-1. Zero diffusion-weighted images .......................... ........... 58

4-2. The full biexponential diffusion tensor ............... .................... 59

4-3. The color diffusion tensor trace .......................... ........... 64

4-4. The grayscale diffusion tensor trace .......... ....................... 65

4-5. The anisotropy/isotropy images .......................... ........... 66










5-1. Diffusion trace images 7 mm rostral to the epicenter of injury ................... 74

5-2. Diffusion trace images at the epicenter of injury ....................... .............75

5-3. Diffusion trace images 7 mm caudal to the epicenter of injury ................... 76

5-4. Anisotropy/isotropy images 7 mm rostral to the epicenter of injury ............. 78

5-5. Anisotropy/isotropy images at the epicenter of injury ............................ 79

5-6. Anisotropy/isotropy images 7 mm caudal to the epicenter of injury ............. 80

5-7. Graphs showing the fast and slow diffusion rate trace vs. slice position for
normal and injured rat spinal cords ............... ..................... 82

5-8. Graphs showing the fast and slow fractional anisotropy vs. slice position for
normal and injured rat spinal cords ......................... ...... .......... 83


5-9. Graphs showing the fast and slow volume ratio vs. slice position for
normal and injured rat spinal cords .......... ......................... 84















LIST OF ABBREVIATIONS


ADC : apparent diffusion coefficient

ADT : apparent diffusion tensor

Bo : the magitude of the main magnetic field

B1 : the magnitude of the applied magnetic field

by : b value in the i, j direction with respect to the gradient directions, where i, j = x, y or
z

cTR : color scale diffusion tensor trace

Dij : diffusion in the i, j direction with respect the gradient directions, where i, j = x, y, or
z


I [D D (TR(D))I2
3 i=x,y,zj=x,y,z
FA : fractional anisotropy, FA = -

1= x,y,zJ= x,y,z
7: gyromagnetic ratio

GM : gray matter


gTR : grayscale diffusion tensor trace, (Dx + Dyy + Dzz) /3

M (r, t) : the nuclear magnetization transverse to the static magnetic field; M+ = Mx+ iMy

Mo : equilibrium magnetization

Mi(t) : the net magnetization in the transverse plane, perpendicular to the magnetic field
B0, at time t

MR : magnetic resonance

MRI: magnetic resonance imaging










Mz(t) : magnetization along the longitudinal magnetic field at time

NA : number of averages

NMR : nuclear magnetic resonance

PBS : phosphate buffered saline solution

RF : radio frequency

SNR : signal:to:noise ratio

Tc : correlation time; the order of time it takes a molecule to turn through 1 radian, or the
time for a molecule to move through a distance comparable to it's dimensions

T : tortuosity

TE: echo time

TR: repetition time

Deter min ant(D)
VR : volume ratio, VR =
[TR(D) / 3]3

WM : white matter

co : Larmor frequency; coo = 7 Bo














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

MAGNETIC RESONANCE IMAGING AND SPECTROSCOPY
FOR THE STUDY OF TRANSLATIONAL DIFFUSION:
APPLICATIONS TO NERVOUS TISSUE

By

Elizabeth L. Bossart

August 1999

Chairman: T.H. Mareci
Major Department: Physics

In all stages of trauma and disease in the brain and spinal cord, it is important to

know the amount of the physical damage, how far the damage will extend, and how the

structural changes relate to the final amount of functionality. Though it is fairly

straightforward to measure this damage ex vivo through histological sectioning,

assessment of internal physical damage in vivo has been difficult to do. The innovation

of magnetic resonance (MR) imaging, in particular the measurement of water diffusion,

has been an important step towards quantifying structural changes in living systems.

Water diffusion, once considered a single diffusion rate (or single diffusion rate

tensor) process, appears to be a multiple diffusion rate process. To the limits of the

gradients available (300 mT/m), two unique diffusion regimes have been seen in fixed

CNS tissue: a fast diffusing component and a slow diffusing component. Others have

speculated that the fast and slow diffusing components in tissue represent diffusion in the

extracellular and intracellular spaces, respectively.









The aim of these studies was to find the best tissue preparation for ex vivo

measurements, determine the best model with which to fit diffusion studies done on CNS

tissue, and to provide a basic understanding of the information contained in the fast and

slow diffusion compartments. These measurements should provide a solid background

for future in vivo experiments, allowing a better understanding of the information

provided by the fast and slow diffusion components. This will be useful for

understanding the role of diffusion in normal tissue and for quantifying changes due to

trauma, which could lead to better diagnostic techniques in the future.

















CHAPTER 1
INTRODUCTION


Observations of soft tissues in vivo were difficult prior to the advent of 1H

magnetic resonance imaging (MRI; Bottomley, 1982; Callaghan, 1991; Hinshaw & Lent,

1983; Lauterbur, 1973). However MRI techniques were needed to quantify the

differences between normal and abnormal tissue. Among the techniques that have been

used to show contrast in biological tissues are the more conventional T, relaxation and T2

relaxation methods (Akber, 1996; Becerra et al., 1995; Bottomley et al., 1984; Moseley et

al., 1984; Willcott, 1984), and more recent translational water diffusion (Callaghan, 1991;

Le Bihan et al., 1993; Moseley et al., 1990; Stejskal, 1965; Stejskal & Tanner, 1965;

Torrey, 1956). For the measurement of changes due to diffuse injury (i.e. stroke or

edema that causes cell swelling), Ti- and T2-weighted images show very few changes

from normal tissue (Becerra et al., 1995; Moseley et al., 1990; Pierpaoli et al., 1996). In

these cases, translational water diffusion imaging better characterizes the changes from

normal tissue (Ford et al., 1994; Kirsch et al., 1991; Moseley et al., 1990; Pattany et al.,

1997; Pierpaoli et al., 1996; van Gelderen et al., 1994).

Translational water diffusion has been used to define solid porous media samples

(Borgin et al., 1996; Ek et al., 1994; Helmer et al., 1995; Latour et al., 1993; Latour et al.

1994; Mitra et al., 1993; Mitra et al., 1992) and to look at biological tissues (Basser et al.,

1994a & 1994b; Basser et al., 1993; Inglis et al., 1997; Kirsch et al., 1991; Moseley et al.,









1990; Norris et al., 1994; Pattany et al., 1997; Pierpaoli et al., 1996; Szafer et al., 1995a

and 1995b). Measurements of diffusion coefficients both in vivo and in vitro have aided

in elucidating structure in tissues such as brain and spinal cord (Basser et al., 1993;

Basser et al., 1994b; Chenevert et al., 1990; Ford et al., 1994; Gulani et al., 1997; Inglis

et al., 1997; Kirsch et al., 1991; Le Bihan et al., 1993; Moseley et al., 1990; Ono et al.,

1995; Pattany et al., 1997; Pierpaoli & Basser, 1996; Pierpaoli et al., 1996; Szafer, et al.

1995a & 1995b; Thompson et al., 1987; van Gelderen et al., 1994). By taking a series of

diffusion-weighted images, it is possible to calculate the apparent diffusion coefficient

(ADC) for water molecules moving in the direction of the applied diffusion-weighted

gradients. ADC images have been measured for many tissues (Norris et al., 1994; Szafer

et al., 1995a & 1995b; Pattany et al., 1997). However, if the tissue being looked at is

anisotropic, the ADC values are dependent on the orientation of the structure with respect

to the gradient axes. Because imaging gradients will cause some diffusion cross-terms,

an ADC is only an approximation of a complete apparent diffusion tensor (ADT). A full

ADT map of a tissue gives an indication of the fiber tract orientations within the tissue

(Basser et al., 1993; Basser et al., 1994b; Inglis et al., 1997; Kirsch et al., 1991; Moseley

et al., 1990; Pierpaoli et al., 1996). ADC and ADT mapping have been used extensively

to characterize both brain and spinal cord tissue (Basser et al., 1993; Basser et al., 1994b;

Inglis et al., 1997; Kirsch et al., 1991; LeBihan et al., 1993; Moseley et al., 1990;

Pierpaoli et al., 1996).

Diffusion-weighted imaging and spectroscopy are two of the methods thought to

give an indication of function in both pre- and post- injury spinal cords. ADC and ADT

maps of these tissues both in vivo, in vitro and ex vivo have been studied to this end. In









order to compare ex vivo and in vivo measurements of diffusion, more must be

understood about the effects that fixation has on tissue samples. To understand the

fixation effects better, relaxation measurements should be made both on fixative solutions

and on fixed tissue. The measurements on fixative and fixed tissue should aid in the

understanding of how fixation changes the tissue, leading to a better understanding of the

diffusion in fixed tissue. The diffusion maps may be able to give some understanding of

the underlying tissue structure and processes, but first more must be understood about the

diffusion of water through a tissue. In particular, a better understanding is needed of how

relaxation, compartmentalization, exchange and anisotropy effects the diffusion within

tissues.

This introduction begins by outlining different relaxation processes (including

spin-lattice relaxation T1, and spin-spin relaxation T2), and explaining some of the

mechanisms that affect those relaxation processes. Next, the steps necessary to create an

apparent diffusion tensor will be described, followed by a sketch of the inherent problems

in the monoexponential model created by Stejkal and Tanner. The current models that

are used to fit diffusion data are presented and analyzed. From this discussion comes the

presentation of what must be elucidated in order to have a complete model of diffusion in

biological tissue. Finally, a brief outline of the studies done will be presented.


Introduction to Relaxation

Before getting too far into the descriptions of relaxation, one thing should be

noted. In this work a symbol B (e.g. Bo) will be called the magnetic field. Although

calling B the magnetic field is not unusual, it is actually a misnomer. In fact, B is the

magnetic flux density, or magnetic inductance, through a material, and is given by the









equation B = p(H + M) where p. is the permeability of the material, M is the

magnetization of the material, and H is the magnetic field strength. Getting back to

relaxation, a resonant radio frequency (RF) pulse effects a spin system by disturbing it

from its thermal equilibrium state. Equilibrium can be restored via several types of

relaxation processes. The following pages will contain a summary of two relaxation

processes, T1 relaxation and T2 relaxation, then describing some of the mechanisms that

cause changes in these relaxation rates (i.e. T2* relaxation, dipole-dipole interactions,

exchange).


Description of Ti Relaxation

T1, "spin-lattice," or longitudinal relaxation is characterized by the return of the

net magnetization to the ground state (i.e. the state where the net magnetization is along

the main magnetic field) from the high-energy state induced by a RF pulse. For a set of

mutually independent nuclei coupled to a thermal bath, T1 relaxation can be defined as

dMz (Mz -Mo)
_- [1-1]
dt Ti

with the solution

Mz(t)= Mz(0)e-t/Tl + MO(1-e-t/T ) [1-2]

where Mo is the equilibrium magnetization along the longitudinal magnetic field Bo

(which is assumed to be along the z-axis), and Mz(t) is the magnetization along the

longitudinal magnetic field at time t. This means that at time t = TI, approximately 63%

of the magnetization has returned to the ground state. The spin system is considered to

be fully relaxed in the longitudinal direction after 3 to 5 T1 periods has passed.









T1 relaxation is magnetic field strength dependent and is fastest when the nuclear

motion, or tumbling rate, matches the Larmor frequency (coo). At this tumbling rate, T1

reaches its characteristic minimum. The Larmor frequency is the precessional frequency

of a nucleus in a magnetic field. It is governed by the equation coo = y Bo where y is the

gyromagnetic ratio for the nucleus and Bo is the strength of the magnetic field. As the

strength of the magnetic field increases, so does the Larmor frequency. When the Larmor

frequency increases, the characteristic T1 minimum gets longer. Therefore, the higher the

magnetic field, the longer it takes for a nucleus to relax in Ti.


Description of T2 Relaxation

For a perfectly homogeneous magnetic field, Bo, the decay of magnetization in the

x-y plane is governed by T2, "spin-spin," or transverse relaxation. T2 relaxation is

characterized by adjacent spins in high and low energy states exchanging energy without

losing that energy to the surrounding lattice. For a set of mutually independent nuclei

coupled to a thermal bath, T2 relaxation can be defined as

dMi Mi
[1-3]
dt T2

with solution

Mi(t) = Mi(0)e-t/T2 [1-4]

where i = x or y and Mi(t) is the net magnetization in the transverse plane (along the i-

axis), perpendicular to the magnetic field Bo, at time t. This means that after time t = T2,

the net magnetization in the transverse plane has been reduced by approximately 63%.

As with longitudinal relaxation, the spin system is considered to be fully relaxed in the

transverse plane after 3 to 5 T2 periods has passed.









In practice, however, the Bo field is inhomogeneous. This means that in different

parts of the sample the nuclei experience disparate magnetic fields, causing the nuclei to

process at slightly different frequencies. The result is a signal loss due to the dephasing

of individual magnetizations. The consequence of the dephasing is a loss in transverse

magnetization at a rate that is greater than that due to T2 relaxation alone (i.e. the free

induction decay, FID, disappears more rapidly than it would due to T2 relaxation alone).

This loss is known as T2* relaxation and is characterized by the following equation


1- +(yAB) [1-5],
T2 T2

where AB is the inhomogeneous variation in the magnetic field. T2* relaxation results in

an inhomogeneous broadening in the MR spectrum, or severe distortions in MR images

when the data is taken at a narrow bandwidth (Callaghan, 1993). Unlike the irreversible,

homogeneous broadening due to T, and T2 relaxation processes, this type of broadening

is ordered and can be "undone" by the use of an appropriate pulse sequence.

Like TI, T2 is magnetic field dependent. Transverse relaxation time is always less

than or approximately equal to the longitudinal relaxation time. For pure water, the two

relaxation times for 'H NMR are approximately equal, but for biological tissues T2 is

almost always less than Ti.


Relaxation Processes


Exchange Processes

Protons in water molecules experience two types of interactions: (1) dipolar

interaction with protons on the same molecule and (2) intermolecular interaction from

protons in neighboring molecules (Kaplan & Fraenkel, 1980; Andrew, 1958; Callaghan,









1993). These interactions fluctuate as the water molecule diffuses via rotational and

translational motions. For free water, the rotational correlation time (the time it takes for

the molecule to turn through a radian) is much shorter than the Larmor period (1/coo

where coo = 7Bo), so the line width is extremely narrow and T1i T2. An impurity in the

water, such as oxygen, will act as a relaxation center for the water. The dipolar

interaction between the proton and the impurity ionic moment is modulated by the

relative motion between the water and the ion. This interaction causes a shortening of the

relaxation times T1 and T2.

Water molecules closely associated with larger molecules or solid surfaces (i.e.

bound water) will tumble more slowly. The slower rotational motion leads to a reduction

in T1 and T2 relaxation times. This shortening continues until the correlation time (i.e.

the time it takes a molecule to turn through 1 radian, or the time for a molecule to move

through a distance comparable to it's dimensions; Andrew, 1958) for the dipolar

fluctuation is approximately equal to the Larmor period (Tco 1/coo). When the correlation

time for the dipolar fluctuation equals the Larmor period, T1 relaxation reaches its

characteristic minimum.

Water molecules in close proximity to solid surfaces and slowly moving

macromolecules will have their proton relaxation rates thoroughly affected. Slowing of

reorientational motion in water will inevitably lead to an altered proton relaxation for this

phase. Translational diffusion induces an exchange of molecules between the bound and

free phases. Rotational motion in the bound phase can be quite slow (i.e. correlation

times are much longer than the Larmor period), so divergence of T1 and T2 relaxation

occurs with T1 becoming significantly longer than T2.











Dipolar Interactions

The intrinsic magnetic moment associated with each nuclear spin dipole exerts a

large influence on its neighbors via the magnetic field produced by this dipole acting on

the dipole moments of remote spins (Callaghan, 1993; Tycko, 1994; Kaplan & Fraenkel,

1980; Wasylichen, 1987). For solids, where inter-nuclear distances are fixed, this process

dominates the line shape. In all liquids except the most viscous, the tumbling motion of

the molecules is rapid, and the dipolar interaction strength is comparatively weak.

Therefore, the dipolar interactions do not contribute to the broadening of the line shape.

However, for viscous liquids, where tumbling is slower, dipolar interactions begin to take

effect, shortening T2.


Quadrupolar Interactions

A nucleus with spin > 1/2 possesses an electric quadrupole moment (Wasylichen,

1987; Tycko, 1994). The quadrupole moment is collinear with the magnetic dipole

moment for the nucleus. For these nuclei, the interaction between the nuclear quadrupole

moment and fluctuating electric field gradients provide a source for nuclear relaxation.

In fact, for these nuclei, quadrupolar interactions are the principal contributor to spin

relaxation.




Chemical Shielding Anisotropy

Atomic or molecular electron clouds interact with nuclear spin angular

momentum (Callaghan, 1993; Wasylichen, 1987). These interactions characterize the

local electronic environment for an atom or molecule. The principle influence of the









surrounding electron cloud is magnetic shielding which results when electronic orbitals

are perturbed by an applied magnetic field. This phenomenon results in chemical

screening or shielding. The local field of a nucleus with less than tetrahedral symmetry

will be dependent on the orientation of the molecule in the applied magnetic field.

Reorientation of the molecule results in a fluctuation of the field at the nucleus, providing

a source for relaxation.



Scalar Relaxation

The finest structural details observed in the liquid state NMR spectroscopy are

from scalar spin-spin coupling or J coupling (Wasylichen, 1987). Indirect interaction

between two nuclei, I and S, is mediated by the electrons present in the molecular orbital.

Nuclear spin causes a slight polarization in the electron cloud. This electron

delocalization is transmitted to neighboring molecular nuclei, leading to the spin-spin

interaction. Fluctuations in the magnetic field at some nucleus I arise due to one of two

interactions. Either the coupling between the nuclei is time dependent due to rapid

chemical exchange (scalar relaxation of the first kind), or one nucleus has a T1 relaxation

time that is short compared to the inverse of the scalar coupling between the nuclei

(scalar relaxation of the second kind). Scalar coupling of the second kind is often a

reason for T2 being much less than T1.


Introduction to Diffusion

Now that relaxation mechanisms have been treated, it is time to treat translational

water diffusion. In diffusion, particles move from one location to another as a result of

random motion due to thermal or equilibrium processes. Using magnetic resonance, this








random process can be tracked. In the following discussion, a background of diffusion

will be presented, followed by the methods used to collect and process MR diffusion-

weighted data. Afterwards, the shortcomings of the monoexponential diffusion

formulation are presented, and some competing descriptions are explored.



The Solution to the Bloch-Torrey Equation
The Bloch-Torrey equation gives a generalized treatment of diffusion and flow

through a sample due to magnetic fields (Torrey, 1956; Callaghan, 1991). In the case of

isotropic diffusion and spatially independent velocities, this equation reduces to

aM, (r, t) M+(r, t) \\
M(,t) iyr-gM+(r,t)- + DV 2M(r,t)- V vM(r,t) [1-6]
dt T2

where D is the diffusion, v is the velocity of spins due to flow, and M+(r, t) is the nuclear

magnetization transverse to the static magnetic field. This is written in complex notation

as M+ = Mx+ iMy. The solution for this equation has the form

M+ (r, t) = S(t) exp iyr .f g(t')dt']exp [1-7].

Putting this solution back into the Bloch-Torrey equation, it is found that

(t)= [- Dy2 ( g(t')dt')2 + iyv. (Jg(t')dt')]S(t) [1-8].


This differential equation has the solution

S(t)= S(0)exp Dy2 'g(t )2dt exp i v g(t")dt)dt'] [1-9].

In order to look exclusively at diffusion, consider the case where there is no flow

through the sample, i.e. when v = 0. That is, the following equation needs to be solved









S(t) = S(0) exp Dy2 f g(t")dt" dt' [1-10].

This is generally rewritten as

S(t) = S(0)e-bD [1-11]

where the diffusion-weighting coefficient, b, is defined as

b =y 2 '(f "g(t")dt" )2dt' [1-12].

The Bloch-Torrey equation changes when the diffusion is considered to be

anisotropic. If diffusion is anisotropic, the Bloch-Torrey equation becomes

aM+ M+
-iyr gM+ +V. D-VM+ VvM+ [1-13]
at T2

and the solution to the equation when there is no flow becomes (Callaghan, 1991)


S(t)k =S(0)exp I bijkDij [1-14]
i=x,y,zj=x,y,z

where the k subscript indicates the particular gradient strength used to get the signal. The

i and j subscripts on the b and D indicated the direction of the gradients, and the

diffusion-weighting coefficient, by, is now defined as

b j= y gi(t)dt" gj(t)dt" t' [1-15].


Data Collection

In solving the anisotropic form of the Bloch-Torrey equation, a solution was

found that was dependent on b and D, both of which are matrices. If an instantaneous

picture of Di and Dji (where i i j) could be taken, then it is possible that Dj would not

equal Dji. However, an instantaneous picture cannot be taken, and through averaging Di









can be assumed to be equal to Dji. With this assumption, the solution to the Bloch-Torrey

equation becomes

bxxkDxx + byykDyy +b zzkDzz
S(t)k = S(0)exp -+ 2(bxykDxy + bxzkDxz + byzkDyz [1-16]


There are seven unknowns in this equation: S(0) and the six diffusion coefficients, Dij. In

order to solve this equation the data should be taken with the gradients on in seven

different directions. The directions normally chosen are x, y, z, x = y, x = z, y = z, and x

= y = z (or x = y, x = -y, x = z, x = -z, y = z, y = -z, and x = y = z). The direction of

diffusion can be calculated by looking at diffusion in each of these seven directions.

Theoretically these seven unknowns could be found using only seven data points

(one point in each of the seven directions) and the corresponding seven calculated b

values. This is not the best way however since every minor variation in the data would

cause problems in fitting the data to the equation above. To aid in getting a better fit to

the value of the diffusion rate D, three or more data points are taken in each direction.

Each signal intensity, Sk, is taken at different gradient strengths such that every point has

a different b value. This allows the value of diffusion to be quantified more accurately.

In many of the data sets five different gradient strengths were used in each direction.

This gives a total of thirty-five data points and thirty-five times six b values.


Calculating b Values

After the data has been collected, a fit must be made to find the diffusion

constants in each direction. Before a fit can be made, the b values for each direction must

be found. As was stated previously, the b value is given by Eq. [1-15]. A simple

example will be utilized to illustrate the method used to calculate the b values. For the








sequence where an RF pulse is followed by one positive and one negative gradient

(Figure 1-1) the following is defined:

( IGk fortk t tk+ 8k
k) 0 otherwise

F(t, k) = ftk k g(t', k)dt' [1-18],
tk

(bj) = TE F(t,k)F(t, )t [1-19],

(bij = (bijk [1-20],

so bij = bji [1-21]

where k, i indicate the timing of the sequence (in this case k, = 1, 2 or first gradient

pulse in the sequence, second gradient pulse in the sequence) and i, j indicate the



RF


g(t,k)t G i t2 -G




A J< A "
TE

Figure 1-1. Simple pulse sequence example.


direction. Each term must be added together to get the total b value

bii = (bii)bI + (bii)22 + (bii)12 + (bii)21 = (bii) + (bii)22 + 2(bii)12 [1-22].

Solving all the above equations for the simple example provided gives a final b value of









b = 72G282(A-8/3) [1-23].

This answer is the same as others have found using the Heaviside functions (Hinshaw &

Lent, 1983; Torrey, 1956), however the method described here is simpler for more

complex pulse sequences than the method described previously.

What has been described so far may be easily applied to simple pulse sequences.

In order to apply this method to more complex pulse sequences, the effect of RF pulses

within the time sequences must be taken into account (Bodenhausen et al. 1984; Mareci,

1988). One way to do this is to look at RF pulses in terms of coherence transfer

pathways. The coherence order is the difference in the magnetic quantum number of two

eigenstates. Coherence transfer pathways are defined by the value of the coherence

order, pi, after the RF pulse. In a system of isolated spins with spin quantum number 1/2,

the coherence order can take on the values -1 < pi < 1. An echo will form during an

interval, n, due to precession in the main field only if

n
Xpiti =0 [1-24]
i=l

where Ti is the duration of the ith interval. In the same way, an echo is formed due to an

applied gradient field when the following condition is satisfied for Eq. [1-18],


npkF(8k,k)= 0 [1-25].
i=l

The coherence order can be included by modifying Eq. [1-17] (Yang et al., 1994) so that

(tk)JpkG(t) fortk g(t, k) = k k k k [1-26].
0 otherwise









With the inclusion of the coherence order, b values can be calculated from any pulse

sequence easily since the specification of the coherence order at each point in the

sequence accounts for the effect of the RF excitation sequence.


Multiple Linear Regression

In order to quantify the rate of diffusion in each of six different directions, the

following set of equations must be solved


S(t=S(O)exp bkDi

1 xx
2 yy [1-27]
3 = zz
i =< k = 1,...,n
4 =xy
5 = xz
6= yz

once the data has been taken and the b values have been calculated (as before, k indicates

a particular gradient strength) (Stejskal, 1965). Keep in mind that the values bij where i

#j are actually multiplied by 2 in order to appear like Eq. [1-16] (e.g. b'4 = bxy + byx =

2bxy). The first thing that must be done to make this problem simpler is to create a linear

equation by taking the natural log of both sides of Equation [1-27]. That means

6
y(t)k =0 bikDi + k [1-28]
i=l

where y(t)k = ln(S(t)k), yo = ln(S(0)) and k is the uncorrelated random uncertainty for

measured data points (Montgomery, 1976). The intercept should be redefined as y'o in

order to take into account the average value of b

6
y =yo- XbDi [1-29]
i=l









where


b bik [1-30].
n k=l

Using this definition for the intercept, the linear equation becomes

6
Yk =YO- (bik-bi i+) k [1-31].
i=1

This can be written in matrix form as

y =b'a+ Z [1-32]

where y and e are vectors of size 1 x n, a is a vector of size 1 x 7, and b' is a matrix of

size 7 x n. The matrix b' is
1.0 ( b'I- I) ( b' 1) ... (b b' I1
1= .0 (b'-b'2) (b -b2) (b -b2 [1-33]


1.0 (b' -b'n) (b -b'2n) (b' -b'n)


and the vector a is

Transpose() = [y' D1 D2 D3 D4 D5 D6] [1-34].

A least squares fit is performed to find the values for a. For the least squares fit

n 2
L= ek =CTI =(y-b'a) (y-b') [1-35].
k=1

The derivative of L with respect to a is set equal to zero in order to find the optimum

values of a. This means

L = 0 = -2bTy + 2bYTbo' [1-36].









b Tb', = bTy [1-37].

Solving for cx gives the equation in its final form


a b= (Tb bTy [1-38].

The solution to this equation is analytical, and a routine written in IDL

(Interactive Data Language Research Systems Incorporated) will rapidly process the

entire diffusion tensor (64 x 64 matrix, 5 b values in 7 directions) in about half a minute

on an SGI Onyx computer.


Problem with the Mono-Exponential Form

To date, most diffusion weighted images have been taken with b values in the

range of 0 to 1500 s/mm2 (Basser et al., 1994a and 1994b; Basser et al., 1992; Kirsch et

al., 1991; Moseley et al., 1990; Norris et al., 1994; Pattany et al. 1997; Pierpaoli et al.,

1996; Szafer et al., 1995a and 1995b). This is due to the fact that most clinical MR

systems are limited in their gradient strengths. These diffusion measurements seemed to

indicate that diffusion is a monoexponential phenomenon, as can be seen in Figure 1-2.

This monoexponential model was described for liquids by Stejskal and Tanner (Stejskal,

1965; Stejskal & Tanner, 1965). The curve in Figure 1-2 was generated from actual data

taken on a sample of human corpus callosum. With the use of better and stronger

gradient systems in both clinical and non-clinical MR systems, diffusion measurements

are being taken with b values up to 40000 s/mm2 (Assaf & Cohen 1998; Bossart et al.,

1999a and 1999b; Borgin et al., 1996; Buckley et al., 1999; Bui et al., 1999; Ek et al.,

1994; Helmer et al., 1995 and 1999; Inglis et al., 1997; Kraemaer et al., 1999; Latour et







18


al., 1993; Latour et al., 1994; Mitra et al., 1993; Mitra et al., 1992; Mulkern et al., 1999;

Niendorf et al., 1996; Pfeuffer et al., 1999; Stanisz et al., 1997; van Zijl, et al., 1991).


In (Signal Intensity) vs b value
For Gradients in the z direciton


4.8


4.7


451I


0.0 300.0 600.0 900.0 1200.0 1500.0
b value (s/mm^2)

Figure 1-2. Natural log of the signal intensity vs. b value graphed for b to 1500 s/mm2.


Inglis et al. (1997) made some diffusion measurement in spinal cord with b values

up to ~ 10000 s/mm2. The diffusion values found from these measurements were much

smaller than those previously reported. A closer look showed that the data curved much

more than would be expected for monoexponential character. This led to the speculation

that the system might more closely approximate a biexponential curve of the form


S(t)k =S(0)(f) exp I I bijkDi(f)
= i=x,y,zj=x,y,z


+S(0)(s)exp bijkDij(s)
Si=x,y,zj=x,y,z


[1-39].


' Peak height data
---- y = 128.7 exp(-0.000194 b)


'-.,


**ss *


. .









In this equation the f and s subscripts stand for fast and slow diffusion rates, respectively.

In order to get an idea about what happens when a mono-exponential curve fit is

used on biexponential data, biexponential data was generated using a simplification of

Eq. [1-39], namely

S(t)k = S(0)(f) exp(- bkD(f)) + S(0)(s) exp(- bkD(s)) [1-40]

with all values of b, D and S(0) set to given values. The data generated a curve of the

form in Figure 1-3. This curve looks like actual measured data from a human corpus

callosum sample (shown in Figure 1-4). A monoexponential fit to the whole data set

gives very inaccurate results. Instead the data was fit by breaking it up into three regions:

a region of small b values (0 to 1000 s/mm2) where the natural log of the data appears to

be a straight line, a region of large b values (6000 to 10000 s/mm2) where the natural log

of the data also appears to be a straight line, and a region between those two where the

data is obviously better fit to a curved line. The two regions where the data appears to be

straight were fit using a monoexponential curve of the form

S(t)k = S(0)exp(-bkD) [1-41]

where the b values were calculated and the S(t)k values were the generated data point.

Next, the calculated fits to the straight regions were used as a starting point for a non-

linear regression analysis of the curve, this time fitting the entire curve using Eq. [1-40].

The monoexponential fit to the region of high b values gave a diffusion value very close

to that found by the biexponential fit, therefore fitting a monoexponential curve to this

region is a fairly accurate estimate. The monoexponential fit for the region of low b

values, however, is at least a factor of two smaller than answer found by using the

biexponential fit. This suggests that the diffusion values given by investigators working










In(Signal Intensity) vs. b value
Simulated data


2000.0


4000.0


6000.0


8000.0


10000.0


b value (s/mm2)
Figure 1-3. Natural log of the signal intensity vs. b value for simulated data.


In (Signal Intensity) vs b value
For Gradients in the z direction

Peak height data (human brain white matter)
---- y = 128.7 exp(-0.000194 b)
Iy- y = 81.9 exp(-0.000032 b)
-- y = 119.8 exp(-0.000095 b)
* y = 50.1 exp(-0.000552 b) + 79.3 exp(-0.000028 b)


2000.0


4000.0


6000.0


8000.0


10000.0


b value (s/mm^2)
Figure 1-4. Natural log of the signal intensity vs. b value graphed for b to 10000 s/mm2.


simulated data
---- y=92.55exp(-0.000039b)
---- y=99.76exp(-0.000099b)
-- y=82.35exp(-0.000023b)
y=20.01exp(-0.00005b)+80.00exp(0.00002b)


.. -S.
.'
.. .-.

'S .h~ -


-S


4.4 1


4.0 L
0.


0


'4.
e--
S4.5


g) 4.4
.--
--


4.2


4.1


4.0
0.


0









in the b value range of 0 to 1000 s/mm2 may not be accurate if the actual diffusion rate is

a biexponetial. The diffusion values should be higher than one would anticipate from

looking at such a limited range of data.

Exploring the biexponential behavior of the data is the next task. In the following

three sections, different models will be discussed that propose to fit the curvilinear data.

Each model has its positive and negative aspects, but each is incomplete. These aspects

of the models will be described and explored briefly.



Multiexponential Diffusion


Porous Media Theory

Solid-boundary porous-media theory uses the time-dependent diffusion

coefficient of the fluid in the interstitial spaces of the medium, D(t), to give structural

information for the medium (Borgin et al., 1996; Ek et al., 1994; Helmer et al., 1995;

Latour et al., 1993; Latour et al., 1994; Mitra et al., 1992; Mitra et al., 1993). At short

times (i.e. (Dot)1/2 << pore size, where Do is the free diffusion coefficient) the diffusion is

given by (Helmer et al., 1995)

D(t) 4 A
Do 9I V- DOt +O(Dot) [1-42]

where A and V are the pore surface area and pore volume respectively. In the long time

limit


im -D(t) [1-43]
t>oDo T

where T is the tortuosity, or connectivity of the medium. In the intermediate region a

Pade approximate is used to interpolate between the two regions (Latour et al., 1993).









This model has been demonstrated to work very well for solid systems that have

liquids or gases filling their interstitial spaces. Many of the experiments performed to fit

this model varied diffusion time instead of gradient strength. Usually the experiments

run on tissue vary gradient strength and leave the time constant. This makes the

experiments a bit difficult to compare with the tissue measurements. Latour et al. (1993)

used this model to fit data from water in the "pores" of a monosized sphere pack (spheres

a diameter of 96 jpm), and water in packed human red blood cells (1994). Helmer et al.

(1995) extol the virtues of this model in its suggestion that the curvilinear appearance of

the diffusion rate vs. b value data is due to geometrical structure within the sample rather

than the number of distinct compartments within the sample. However, they do not

attempt to fit their biological tissue data (sampling from non-necrotic and necrotic

regions of a tumor) to this model. That suggests some difficulty in applying this model to

tissues. Tissues are not just porous, but have semipermeable membranes that allow the

passage of some substances through but not others. This implies that the cell membrane

is impermeable to all solutes except for very small, uncharged molecules. So diffusional

motion through biological tissue is not as simple as in porous media.

Inside the cell, the diffusion rate is slowed due to water molecules running into

proteins, organelles and other substances contained within the cell. The diffusion rate

outside of the cell will be slowed by the closeness of the cells to one another, similar to

the manner in which the diffusion rate was changed by moving around the packed beads.

Both rates should be modified by exchange between the cells and the surrounding

extracellular space, and the exchange rate will be effected by the permeability of the

membrane in question. The porous media theory does not take into account the









cytoskeletal structures or other substances within the cells, nor does it include exchange.

As well as this theory works for solid substances, it is not clear that it will work for

biological systems because of these aforementioned facts.



An Analytical Model of Restricted Diffusion

The second model was created by Stanisz et al. (1997 and 1998) to look at

restricted diffusion in bovine optic nerve using a three pool model. The model has two

intracellular compartments (spherical and ellipsoidal cells) and one extracellular

compartment. One of the assumptions made in this model is that the diffusion rates for

the two intracellular compartments are equal in magnitude, and the intracellular diffusion

rate is different than the extracellular diffusion rate. This model has three analytical

parts: (a) water motion in the extracellular spaces; (b) restricted diffusion inside cells;

and (c) exchange between the intracellular and extracellular compartments.

The diffusion rate in the extracellular compartment is found by


DEAPP D [1-44]
T

which is the same equation as was given for the long-time behavior in porous-media

theory (Helmer et al., 1995). The tortuosity is orientation dependent. This accounts for

anisotropy in the observed data.

The intracellular diffusion rate is modeled using a one-dimensional

approximation. The model is for restricted diffusion within an infinite parallel

membrane. The equation for the diffusion rate is (Stanisz et al., 1997)









1- cos(yG5 j)

1 (yGS J)2
APP 1
b + 4(,G J ) exp 2 7 2DI 2 l(l) cos ) [1-451

n 2 ((G 2-()2 n)2


where t is the average restricted distance the diffusing species experiences within a cell

of type J = S (spheres), T ellipsoidss).

The exchange rate, K, between the intracellular compartment and the extracellular

compartment is found by multiplying the membrane permeability, P, by the surface-to-

volume ratio A/V. This exchange rate is used by the modified Bloch equations which

were extended according to Karger et al. (1988) to be

dMT 2G22DTAPPMT -KTMT +KEME [1-46]
dt

dt -y2G22D Ms KsMs +KEME [1-47]
d tM
dME = -2G22DEAPPME -KEME + KMS +KTMT [1-48]
dt

with the appropriate initial conditions. Here, E represents the extracellular compartment,

S represents the spherical intracellular compartment and T represents the ellipsoidal

intracellular compartment. Using a Monte Carlo simulation, nine parameters are fit into

the three parts of this model. These nine parameters are the intracellular diffusion rate

(DI), the long and short axes of the ellipsoidal cells (aT(-L) and aT(||)), the diameter of the

spherical cells (as), the volumes of each cell type (VT and Vs), the membrane

permeability of each cell type (PT and Ps), and the extracellular diffusion rate (DE).









There are a few problems with this model. Stanisz et al. (1997) fit the parameters

to within only 15% using this model. The model seems to fit well at smaller b values, but

the larger the b value, the worse the fit seems to get. That means that the model does not

fit the data quite well enough. Their errors probably stem from two major sources: (a)

the long-time diffusion model used for the extracellular space and (b) the one-

dimensional model used to characterize the diffusion in the intracellular space. The long-

time diffusion model is the same as is used in porous media theory, and the drawbacks of

that model were explained in the previous section. As before, exchange between the

intracellular and extracellular spaces will change how well this model fits the data. The

one-dimensional model used to define diffuison in the intracellular space is inaccurate

because of the infinite parallel barrier approximation that was used. This may be a

reasonable approximation for water travelling down the long axis of an ellipsoid, but it

will not fit as well for water travelling in the small spherical cells, or along one of the

minor axes of the ellipsoid. Also, this model takes into account only very regular shaping

of the cells. Cells are very irregularly shaped, and filed with structures and substances

with which water interacts. True biological systems do not have such regular shapes.



Multiexponential Model

The final model was introduced by Karger et al. (1988) and was reiterated by

Niendorf et al. (1996). Of late, this model has gained popularity, and has been used in

presentations at a few meetings (Bossart et al., 1999a and 1999b; Bui et al., 1999; Helmer

et al., 1999; Kraemer et al., 1999; Mulkern et al., 1999; Pfeuffer et al., 1999). When the

system under consideration is composed of different subregions, then the observed signal









attenuation can be given by a superposition of the contributions from individual

subregions

S(b) = fi exp(- bDi) [1-49].
i

For tissues it can be assumed that the two compartments are an intracellular

compartment and an extracellular compartment. Exchange between the two

compartments occurs on a time scale related to the mean lifetime (Tin(ex)) of water

molecules in a compartment. In the short diffusion time limit (t << tin(ex)) the signal is

just a linear superposition of two monoexponentials (Neindorf et al., 1996)

S(b)
S(b) = fin exp(- bDin)+ fex exp(- bDex) [1-50].


At the long diffusion time limit (t >> Tin(ex)), complete exchange occurs between

the two compartments and the signal attenuation will show a monoexponential

dependence

S(b)
S(b) = exp(- b(finDin +fexDex)) [1-51].


In the intermediate range, the signal attenuation appears as the sum of two

monoexponentials as in the short time limit

S(b)
-= fin exp(- bDin)+ fex exp(- bDex) [1-52];


however, the volume fractions (f'in(ex)) and the diffusion rates (D'in(ex)) in the intermediate

time periods become mixtures of the rates found in the short time limit due to the

exchange of water between the two compartments (Karger et al., 1988). The only thing

lacking in this model is an accounting of the anisotropy. Tensor data taken by our group









and by other groups shows that there is anisotropy in some biological samples, otherwise

there would be no difference between the diffusion images along the diagonal of the

tensor. That is to say, the x, y and z images would be exactly the same and the off-

diagonal elements would be zero if the tissue were isotropic. Perhaps the anisotropy

comes from the geometry of the sample, or perhaps it comes from the variety of

substances impeding the diffusion through the tissue sample.



Study Directions

The purpose of this study is to verify that the biexponential model proposed by

Karger et al. (1988) is an accurate one, to adjust the model to take into account anisotropy

in tissues, and to find the roles that compartmentalization, exchange and relaxation play

in diffusion behavior. Although the model proposed by Stanisz et al. (1997 and 1998)

retains some of the characteristics of the Karger model (e.g. assuming distinctly different

diffusion rates in the extracellular and intracellular spaces), it does not seem to fit the data

as closely as the model proposed by Karger et al. (1988). The biexponential model is a

very good two-compartment model with exchange. This model fits well to mono-

directional data taken in rat spinal cord and human corpus callosum (Figures 1-4 and 1-

5). However, as stated before, the model does not adequately explain anisotropic

diffusion in tissues. Also, given large enough diffusion gradients, three or more diffusion

coefficients have been seen. Assaf and Cohen (1998) describe observing a system that

seems to fit the sum of three exponential terms when the gradients are large enough. The

question to answer is whether those different diffusion rates are due to different

compartments or if it is due to other factors. Therefore, the following series of studies are

proposed to aid in determining if this really is a good multicompartment model, to









determine how exchange effects the apparent diffusion rate, and to determine how the

anisotropy fits into the model.

1. TI and T2 relaxation studies of fixative solutions and the effect fixative solutions have

on relaxation in biological tissues were done. These studies will aid in determining

how tissue preparation affects the ex vivo tissue results. It will also help to determine

the best tissue preparation method for comparison with in vivo studies, as well as for

doing histological comparisons.

2. T2 relaxation and diffusion spectroscopy studies were done on human white and gray

matter brain samples. Human brain samples were chosen because nearly

homogeneous tissue samples can be cored from the human brain. The data taken from

brain white and gray matter samples could compare qualitatively with the white and

gray matter in the spinal cord. Pulsed gradient spin-echo spectroscopy was done

because complete data can be taken much more rapidly than with imaging. Also, T2

relaxation imaging experiments are inherently diffusion weighted due to the imaging

gradients used, making the deconvolution of diffusion and relaxation much more

difficult than with spectroscopy studies.

3. Diffusion imaging studies in normal rat spinal cord were done. These studies could

confirm or deny some of the ideas presented in the previous studies on the brain

samples, as well as give the first images of the two different diffusion compartments.

4. Comparison studies of diffusion in normal and injured rat spinal cord were done.

These studies further explore the meaning of the two diffusion compartments, as well

as give some further confirmation of ideas presented in the previous studies.










It is the hope that this process gives a more complete model of diffusion in biological

tissues. This will be useful for understanding the role of diffusion in normal tissue and

for quantifying changes due to trauma, and maybe lead to better diagnostic techniques.



In(Signal Intensity) vs b value
Rat Spinal Cord Gray Matter


5.4 Data from Region of Interest
5.2 -- y=1.04exp(-0.000128b)
5.2 -- y=1.13exp(-0.000612b) + 0.399exp(-0.000037b)
5.0 ,--- y=1.53exp(-0.000439b)
5.0 -- y=0.404exp(-0.000037b)
4.8 -

S4.6 ',

.| 4.4-
S 4.2 ,

4.0 ,.

3.8 -
3.6 .

0.0 3000.0 6000.0 9000.0 12000.0 15000.0
b value (s/mm2)
Figure 1-5. Natural log of the signal intensity vs. b value for a region of interest in the rat
spinal cord.















CHAPTER 2
FIXATION EFFECTS


Relaxation measurements have been made on both fixed and "fresh" (or unfixed)

tissues ex vivo in order to determine the effects that death and fixation have on tissue as

observed using 'H NMR (Akber, 1996; Baba et al., 1994; Bottomley, et al. 1984; Carvlin

et al., 1989; Fischer et al., 1989; Gyorffy-Wagner et al., 1986; Kamman et al., 1985;

Moseley et al., 1984; Nagara et al., 1987; Pattany et al., 1997; Thickman et al., 1983;

Tovi & Ericsson, 1992; Willcott, 1984). Such measurements provide a greater

understanding of how in vitro and ex vivo tissue studies relate to in vivo tissue studies.

These relaxation experiments on tissue samples in vitro and ex vivo have shown that

tissue death and fixation have a very large effect on the T2 relaxation times and a less

pronounced effect on the T, relaxation time. However, these early studies did not explore

the reasons for these relaxation changes or the signal-to-noise ratio (SNR) differences

observed between fixed and unfixed tissue samples.

In this study, experiments were performed to find the best tissue preparation for

imaging in vitro. The SNR measurements presented in Table 2-1 show that tissue

preparation has a huge effect on the SNR. Each measurement was performed on a single

sample of this type. The SNR for each tissue preparation was calculated from images

taken at 600 MHz with the following parameters: TR = 3 s, TE = 36 ms, matrix = 128 x









128, and NA = 2. The SNR was determined to be very poor for fixed samples that were

imaged in the fixative solution. It was also determined to be poor in fixed samples that

were poorly perfused (i.e. lightly fixed and containing blood). However, unfixed samples

and fixed samples that were washed with phosphate buffered saline (PBS) had an

improved SNR when imaged in PBS. It has been shown that the T2 relaxation shortens

rapidly in the first few hours after excision (Thickman et al., 1983; Nagara et al., 1987;

Carvlin et al., 1989; Fischer et al., 1989; Tovi & Ericsson, 1992; Baba et al., 1994).

Therefore, it is not possible to use unfixed samples for long experiments because the

tissue constantly degrades and measurements will be unstable over the course of an

image acquisition. To observe tissue samples ex vivo or in vitro, the best sample

preparation will be one that prevents degradation during the time of the measurements,

maintains sufficient SNR for the relevant calculations to be performed on the data, and

most closely resembles the in vivo tissue.



Table 2-1. Measured SNR in gray and white matter regions of the spinal cord for
various tissue preparations.
Tissue preparation GM WM
SNR SNR

unfixed rat spinal cord imaged in PBS 49.1 45.8
4% formaldehyde fixed rat spinal cord 3.7 3.0
imaged in 4% formaldehyde
4% formaldehyde fixed rat spinal cord 150.1 102.3
imaged in PBS
4% formaldehyde fixed injured rat 9.3 6.4
spinal cord imaged in 4% formaldehyde
4% formaldehyde fixed injured rat 148.2 79.6
spinal cord imaged in PBS
4% formaldehyde fixed, poorly 9.8 4.4
perfused rat spinal cord imaged in 4%
formaldehyde
4% formaldehyde fixed, poorly 105.4 63.7
perfused rat spinal cord imaged in PBS











For multiexponential T2 and multicompartment diffusion experiments, it is

important to have a high SNR (> 60). If the SNR is too low, fitting the data to non-linear

curves is difficult and inconclusive. It is important to understand why these SNR

changes occur in order to avoid these difficulties. The relaxation rates of varying

concentrations of fixative solutions were measured in order to interpret the differences

seen between imaging tissue in fixative solution and PBS. Afterwards, the relaxation rate

for a spinal cord tissue sample fixed with 4% paraformaldehyde solution was measured

both in fixative and in PBS.


Materials and Methods


Relaxation Measurements in Solution

Relaxation times were measured for solutions of formaldehyde (CH20) and

gluteraldehyde (OCH(CH2)3CHO) at concentrations of 1, 2, 4 and 8 percent. They were

also performed on full, half and quarter Karnowsky's solution (full Karnowsky's solution

= 5% gluteraldehyde + 4% formaldehyde). All measurements were performed using a

600 MHz Varian spectrometer with the samples at physiological pH (7.2) and at a

temperature of 250 C. Ti measurements were made using an inversion recovery

sequence, and T2 measurements were made using the Carr-Purcell-Meibloom-Gill

(CPMG) sequence (see Appendix B for the pulse sequences). Each sample spectrum was

performed only once with eight averages.









Imaging Measurements in Tissue

The water relaxation measurements in tissue were acquired using an imaging

spin-echo sequence. Repetition time (TR) was arrayed for the T1 measurements, and

echo time (TE) was arrayed for the T2 measurements. These water relaxation

measurements were performed on a single tissue sample with four averages. To provide

the tissue sample, a rat was transcardially exsanguinated with saline solution and heparin,

then perfused with a 4% formaldehyde solution. Water relaxation measurements were

performed on the water within the fixed cord in immersed in fixative solution. The tissue

was then washed with PBS 4 times over a 36 hour period, placed in fresh PBS, and the

water relaxation measurements were repeated.

Finally, rat spinal cord tissue was prepared by exsanguinating in vivo with saline

solution, followed by perfusion with one of three different fixative solutions prior to

removal from the animal: 4% formaldehyde (n = 3), half Karnowsky's (n = 3) and full

Karnowsky's solution (n = 3). A total of 9 diffusion experiments were performed. Each

tissue sample was taken from the same spinal cord location, at T13. Following fixation,

these cords were washed with PBS three times over a 36 hour period, and placed in fresh

PBS. A full biexponential diffusion experiment, as described in the Materials and

Methods section of Chapter 4 and Chapter 5, was then performed on these cords at 600

MHz. Numerical data was calculated at specific regions of interest in the cord to find out

if the fixative preparation changes the observed diffusion rates. After the experiments, all

tissue samples were replaced in the fixative solution.












Results


Fixative Solution Measurements

The presence of fixative in water slightly decreases its Ti relaxation time (Figure

2-1) and greatly reduces its T2 relaxation time (Figure 2-2). The Ti and T2 relaxation

rates increase linearly with increasing concentration. The graph of Ti relaxation rate vs.

concentration (Fig. 2-1) shows that while Ti relaxation rates change very little with

fixative concentration, there is a definite relationship. This increase is greater for



1/T, vs. Concentration

0.360 ....-*
Formaldehyde s
0.350 Gluteraldehyde ,-
A Karnowsky's solution ,

0.340 ,


0.330 .


0.320 .---


0.310


0.300 '*' *
0.0 2.0 4.0 6.0 8.0 10.0

% Concentration
Figure 2-1. Graph of 1/T1 vs. concentration.
Graphs shown for formaldehyde, gluteraldehyde and Karnowsky's solution.


Karnowsky's solution than it is for the formaldehyde and gluteraldehyde solutions. The

relationship between Ti and fixative concentration may be due to an increase in the

viscosity of the solution (Andrew, 1958) as polymerizing agents such as a fixative is









added. To test this hypothesis, the viscosity of each fixative solution was measured at

250 C using a capillary viscometer. The results of the viscosity measurements are shown

on the graph of viscosity vs. fixative concentration in Figure 2-3. The trends seen in the

slopes of the lines on Figure 2-3 are the same as the trends seen in the lines on Figure 2-1

(i.e. Karnowsky's solution vs. concentration has the steepest slope and formaldehyde

solution vs. concentration has the shallowest slope). The large effect that fixative has on

the T2 relaxation rate of water is most likely due to chemical exchange processes going

on in the solution.



Tissue Measurements

The relaxation rates observed in both the gray matter (GM) and the white matter

(WM) of the rat spinal cord samples show that washing the sample does not significantly

change T1 (Table 2-2). However, washing increases the T2 by about 40% in both gray

and white matter. Since this is the case, it would appear that the short T2 measured in

fixed tissue imaged in the fixative may be due to free fixative exchanging with free water

in the tissue. Therefore, the relaxation rates of the fixed spinal cord tissue are dependent,

in part, on the solution surrounding the tissue.



Table 2-2. Relaxation rates in GM/WM for different tissue preparations.
GMTi WMTi GMT2 WM T2
Tissue preparation (ms) (ms) (ms) (ms)
4% formaldehyde fixed rat spinal 159 245 22 18
cord imaged in 4% formaldehyde
4% formaldehyde fixed rat spinal 178 253 32 28
cord imaged in PBS










1/T2 vs. Concentration


150.0





100.0


'()


50.0




o---B-
0.0
0.0 2.0


4.0 6.0 8.0


% Concentration

Figure 2-2. Graph of l/T2 vs. concentration.
Graphs shown for formaldehyde, gluteraldehyde and Karnowsky's solution.




Dynamic Viscosity vs. Concentration


2.0 4.0 6.0 8.0


10.0


% Concentration
Figure 2-3. Graph of dynamic viscosity vs. concentration.
Graphs shown for formaldehyde, gluteraldehyde and Karnowsky's solution.


10.0


A-









Figures 2-4 and 2-5 show graphs of the fast and slow diffusion rates vs. slice

position for rat spinal cords fixed in three different solutions. The data on each graph

was averaged from measurements on three different spinal cords, for a total of nine rat

spinal cords used for these measurements. The regions of interest used are indicated in

Figure 4-1d, with the exception of the lateral funiculus. The lateral funiculus would be

located between the dorsal lateral funiculus and ventral lateral funiculus on that figure.

These graphs show that the fast and slow apparent diffusion rates observed appear

dependent on the tissue preparation. For the fast diffusion rate graphs, the diffusion rates

are similar in all parts of the cord for fixation with 4% formaldehyde. When fixed with

half Karnowsky's solution, the fast diffusion rates much more spread out from one

another. With full Karnowsky's solution, the diffusion rates are close to one another

again, but the order of fastest to slowest is different than before. Although there are

changes in the fast diffusion rate graphs, the changes are larger in the slow diffusion rate

graphs, where the split between GM and WM changes radically when different fixation

processes are used. A GM/WM split is obvious in both the 4% formaldehyde fixed cords

and the half Karnowsky's solution fixed cords, with the split being larger in the cords

fixed with half Karnowsky's solution. This split disappears when full Karnowsky's

solution is used to fix the spinal cord.


Discussion

It has been shown that changes in the relaxation rate are directly proportional to

changes in viscosity (Andrew, 1958). The changes in T1 relaxation rate appear to be

consistent with changes in viscosity for the various solutions measured, as seen in the

trends of the slopes in Figures 2-1 and 2-3. As stated in Chapter 1, the spins will be fully












a) Fixed with 4% Formaldehyde b) Fixed with Half Karnowsky's Solution
800 800

750 750

I 700 700 ,

650 650

600 ,---- 600 ----- ----......

) 550 5 550 ----- .--
.----"- '--

50 1 2 3 4 5 6 7 50 1 2 3 4 5 6 7
Slice Position Slice Position
c) Fixed with Full Karnowsky's Solution
800

W- 750
S'\ *--* Dorsal Funiculus (WM)
u-700 Dorsal Horn (GM)
-+--^ *--*Lateral Funiculus (WM)
S650 --oVentral Funiculus (WM)
o 60 -----.- -- ...-.. ,Ventral Horn (GM)

C 550

500
0 1 2 3 4 5 6 7
Slice Position
Figure 2-4. Fast diffusion rate component vs. slice position graphs for regions of interest in fixed rat spinal cordsmeasured in PBS.
a) Fixed with 4% formaldehyde. b) Fixed with half Karnowsky's solution. c) Fixed with full Karnowsky's solution.














a) Fixed with 4% Formaldehyde


b) Fixed with Half Karnowsky's Solution


0 1 2 3 4
Slice Position


5 6 7


c) Fixed with Full Karnowsky's Solution
140

120 "

E 100
3 ------ -.
80 "-..
Ca -- ----- .


0 1 2 3 4
Slice Position


1 2 3 4
Slice Position


*--e Dorsal
H-- Dorsal
--+ Lateral
o-- -Ventral
A Ventral


Funiculus (WM)
Horn (GM)
Funiculus (WM)
Funiculus (WM)
Horn (GM)


5 6 7


Figure 2-5. Slow diffusion rate component vs. slice position graphs for regions of interest in fixed rat spinal cords imaged in PBS.
a) Fixed with 4% formaldehyde. b) Fixed with half Karnowsky's solution. c) Fixed with full Karnowsky's solution.


*--4-
S4-~- -.
---k-- -
-*--


- i J. A.




-
-


~


5 6 7


I "i" J









relaxed at approximately 5 times the T1 relaxation time. The relaxation rate for pure

water is approximately 3 s at 600 VMHz, but the fixed tissue samples presented here have

much shorter relaxation rates of approximately 0.5 s. Therefore, full T1 relaxation of the

spins occurs with a TR of approximately 2.5 s. This shortening of T1 relaxation rate

makes it possible to measure the observed signal intensities without T1 dependence.

For the fixative solutions, the shortened T2 relaxation rate is probably due to

chemical exchange. Both formaldehyde and gluteraldehyde are molecules that

polymerize in water, cross-linking the water into a more solid matrix (Hahnenstein et al.,

1994 and 1995; Hopwood 1972; Kawahara et al., 1992; Jayakrishnan and Jameela, 1996;

Prento 1995). The chain length and reaction kinetics are dependent on the pH,

concentration and temperature of the solution. In solution, formaldehyde exists as an

equilibrium mixture of free formaldehyde, a small amount of methylene glycol and the

polymer poly-[oxymethylene] glycol (Hahnenstein et al., 1994 and 1995). Each species

of this solution is highly reactive, though the new bonds formed can be easily broken and

reformed. In solution, gluteraldehyde exists as small amounts of free aldehyde, mono-

and dihydrated monomeric gluteraldehyde, in equilibrium with monomeric and polymeric

cyclical hemiacetals, and various ca, j3-unsaturated polymeric aldehydes (Hopwood, 1972;

Jayakrishnan and Jameela, 1996). The prominent reactive species for gluteraldehyde in

solution are the ca, j3-unsaturated polymeric aldehydes. The other polymeric species

formed have a lower reactivity. In both of these solutions, the exchange of water

molecules in and out of these polymer chains, as well as the hydrogen bonds forming

between the water and the polymers, acts as a relaxation sink, as discussed in Chapter 1

(in the section called Exchange Processes). Therefore, the T2 relaxation time is









significantly reduced from that of water alone. This is similar to the observation made by

Kennan et al. (1996) in polyacrylamide gels of varying cross-link density. The observed

response of the T1 and T2 relaxation curves for the polyacrylamide gels were similar to

those seen here for various concentrations of formaldehyde and gluteraldehyde. That is,

the greater the number of polymers in solution and the stronger their cross-linking

capability, the greater the drop in T2 relaxation rate.

Formaldehyde and gluteraldehyde fix tissues by cross-linking proteins,

glycoproteins, nucleic acids and polysaccharides, thereby "fixing" their structure and

preventing them from breaking down (Helander, 1994; Hopwood, 1972). Both

formaldehyde and gluteraldehyde fix tissue rapidly. Formaldehyde fixation bonds in

tissue are reversible; they have been shown to break down over time when placed in

solutions not containing the fixative (Helander, 1994; Hopwood, 1972). Gluteraldehyde

solutions react with a wider variety of chemical substances in tissue than gluteraldehyde.

This means that tissue fixed in gluteraldehyde is more solidly bound than tissue fixed in

formaldehyde. Gluteraldehyde creates bonds that are unlikely to break down over time

when the sample is placed in solutions which do not contain the fixative. However,

because formaldehyde is a small molecule and its solution has fewer non-reactive

species, it penetrates and fixes the tissue more rapidly than gluteraldehyde solutions

(Hopwood, 1972). This slow penetration of gluteraldehyde into tissues is why

gluteraldehyde, even though it gives a much stronger fix to the tissue, is rarely used on its

own. Instead it is used with a faster fixative, like formaldehyde, in combinations such as

Karnowsky's solution. In these fixative solutions, the formaldehyde rapidly penetrates









the tissue and fixes it to prevent further degradation. Over time, the gluteraldehyde then

replaces the weaker formaldehyde bonds, creating a much more stable tissue sample.

As observed in Figures 2-4 and 2-5, when the tissue is perfused with a different

fixative, the observed diffusion rates changes, even if these tissue samples have been

washed. This is probably due to the different bonds that formaldehyde and

gluteraldehyde create in the tissue. Since formaldehyde bonds are weaker than

gluteraldehyde bonds, the tissue perfused with formaldehyde alone probably more closely

approximates the in vivo case than solutions containing higher amounts of

gluteraldehyde. The relationship between fixative and diffusion rate is probably due to

the structural changes that occur inside the cell due to fixation.

In the experiments to determine the best tissue preparation method for imaging,

the extremely shortened T2 relaxation rate resulted in reduced SNR. The excessive

shortening ofT2 observed in fixed tissue measured in fixative solution can be partially

attributed to free fixative solution in the interstitial spaces of the tissue. T2 shortening

effects of fixative solution can be counteracted, to some extent, by washing the tissue

with PBS (minimizing the amount of free fixative in the tissue) and imaging the tissue in

fresh PBS.

There seemed to be no tissue degradation or fixation reversal during relatively

short time period that the tissue sample was immersed in PBS. Even after being washed,

the T2 relaxation rate is still fairly fast compared to T2 rates seen in vivo, which are

generally twice as long. In order to avoid large amounts of signal loss, the TE must be

chosen as short as possible. Unfortunately, due to the limits of the gradients used here,






43


the TE chosen for diffusion measurements generally must be on the order of the T2

relaxation rate, making T2 a large contributor to signal loss in these measurements.















CHAPTER 3
RELAXATION AND DIFFUSION MEASUREMENTS
ON FIXED HUMAN BRAIN SAMPLES


As seen in Chapter 1, at low diffusion gradient weightings (b < 1000 s/mm2), the

diffusion appears to be a single diffusion rate or a single diffusion rate tensor (Fig. 1-3).

At higher gradient weightings, the data points can no longer be fitted to a single diffusion

rate or single diffusion rate tensor (Figs. 3-1 and 3-2). Instead, the data seems to be

comprised of multiple diffusion rates or a multicomponent diffusion rate tensor. Towards

the gradient limits (b z 15000 s/mm2), two unique diffusion components were seen in

brain and spinal cord tissue: a fast and a slow compartment. These compartments have

been ascribed to the extracellular and intracellular spaces, respectively (Karger et al.,

1988; Neindorf et al., 1996; van Zijl et al., 1991).

Data acquired by non-NMR methods have shown that the volume

fractions for the extracellular space and intracellular space is approximately 0.20 and

0.80, respectively (Nicholson & Sykova, 1998; Sykova, 1997). To test the hypothesis

that the fast component represents extracellular water and the slow component represents

intracellular water, this ratio was taken to be the standard for comparison. In the

biexponential fits (Figure 3-1 and 3-2), the volume fractions differ from the expected

volume fractions. This could be because the two compartments being visualized by

diffusion are not the extracellular and intracellular compartments, or that there are other











In(Signal Intensity) vs. b value
Human Corpus Callosum
4.7 ,I
peak height data
4.. y = 37.5exp(-0.000589b) + 62.5exp(-0.0000172b)
-- y = 95.2exp(-0.000232b)
4.5 ---y = 55.0exp(-0.0000162b)
---y = 81.3exp(-0.0000941b)
4.4



4.2- \ .



S4.0 1 -- % % %,

3.9 \ ,-


3.8 I-

3.7 .. ^ "
0.0 5000.0 10000.0 15000.0
b value (s/mm2)
Figure 3-1. The natural log of the signal intensity vs. b value graph for brain white matter.



In(Signal Intensity) vs. b value
Human Cortical Gray Matter

4.64 s peak height data
4 y = 43.3exp(-0.0004315b) + 56.7exp(0.0000290b)
4.4 y = 93.8exp(-0.0001486b)
4.2 ---y = 18.2exp(-0.0000282b)
---- y = 39.4exp(-0.000098b)
4.0 -
c 3.8 -
c 3.6

L) 3.4 -
-E 32 -'


0.0 5000.0 10000.0 15000.0
b values (s/mm^2)
Figure 3-2. The natural log of the signal intensity vs. b value graph for brain gray matter.









factors that effect the volume fractions calculated. Some of the parameters which may

change the observed volume fractions are relaxation weighting, in particular T2 (Chapter

2), water exchange between compartments, restriction, and proton density differences

between each compartment.

To investigate the origin of these two compartments, diffusion tensor and T2

relaxation measurements were performed with NMR spectroscopic methods on small

homogeneous samples of post-mortem, excised, fixed human corpus callosum (white

matter) and human cortical gray matter. These two samples were chosen for later

comparison with white matter and gray matter in the spinal cord. Spinal cord tissue itself

was not used because it is difficult to core a homogeneous sample from the spinal cord.

Diffusion tensor experiments were performed on these samples using echo times and

diffusion times similar to what would be used in Chapters 4 and 5 for the diffusion tensor

measurements. Also, a multiexponential measurement of T2 relaxation rates allowed the

relaxation to be taken out of the volume fractions found by the diffusion tensor

measurements.


Materials and Methods


Sample Preparation

The cadaver was flushed using a 10% formaldehyde solution, and then perfused

with a 4% solution of formaldehyde mixed with glycerin. The brain was then excised

and stored in 70% ethanol. Cylindrical sections approximately 3 mm in length and 4 mm

in diameter were cored from the corpus callosum (WM) and the cortical gray matter

(GM) of the brain. The samples were soaked in PBS for 6 hours, then sealed in a 5 mm









NMR tube to prevent dehydration. There was no buffer solution surrounding the tissue

samples.


NMR Measurements

'H spectra for each sample of human brain tissue were acquired on a Bruker

Avance 600 MHz spectrometer (14.1 T magnet, 54 mm bore) using a commercially

available 5 mm, three-axis, actively-shielded gradient probe capable of generating 50

G/cm per axis. The samples were maintained at 200 C throughout the NMR

measurements.


T2 relaxation measurements

T2 relaxation measurements were obtained using the Carr-Purcell-Meibloom-Gill

sequence (CPMG; see Appendix B for the sequence), with TR = 8 s and NA = 8. To

enable calculation of more than one relaxation rate, eighteen time points were taken

between TE = 2 ms and TE = 1000 ms.


Diffusion tensor measurements

ADT spectra were obtained using the method described by Basser, et al. (1992;

1994a; 1994b; Basser, 1995; Basser & Pierpaoli, 1996). For the diffusion experiments,

diffusion-weighting gradients were applied along the gradient-winding directions x, y, z,

x = y, x = z, y = z, and x = y = z. To obtain the diffusion-weighted (DW) spectra of

human brain tissue, forty different gradient weightings were applied in each direction.

Gradient strengths were chosen so that the b values would be linearly spaced between 0

and 15000 s/mm2. To acquire the spectra, the acquisition parameters were TR = 3 s, TE

= 36 ms, 8 = 9 ms, A = 20 ms, and NA = 4.












Post-Processing


T2 relaxation spectra

The peak heights of each spectrum from the T2 relaxation data were fit to a

biexponential curve of the form

Sij = Soa exp(- TE / T2a)+ Sob exp(- TE/T2b) [3-1],

where TE is the echo time, T2a(b) the long (short) relaxation times, and SOa(b) is the signal

fraction for T2a(b). As with the diffusion data, this fit was performed using a gradient-

expansion algorithm (IDL, Research Systems Incorporated).


Diffusion tensor spectra

The matrix of b values, bij (i, j = x, y, z) (Mattiello et al., 1994), was determined

for each DW spectrum in IDL. All gradient auto- and cross-terms were taken into

account with the exception of terms involving the imaging phase-encoding gradient,

which was assumed to be zero, i.e. its central value. To obtain a robust biexponential fit,

estimates of the fast and slow diffusion rates were made by separately fitting the peak

heights for the low and high ranges of b. Accordingly, the low (b = 0 to 1000 s/mm2) and

high (b = 6000 to 10000 s/mm2) diffusion-weighted series were fit to the

monoexponential curve in Eq. [1-16] using a multivariate linear regression (Montgomery,

1976). These estimated diffusion rates and the calculated relaxation rates were used as

starting points for fitting the whole data set to the biexponential curve of the form given

in Eq. [1-39], and to a biexponential curve that includes the T2 relaxation weightings:










S= So(f) exp(-TE/T2a )exp bijDij(f)
1 J [3-2]
+ So(s) exp(- TE/ T2b)exp -i bijDij(s)


where the subscripts f and s denote fast and slow components of diffusion, respectively,

and i, j = x, y, z. This fit was performed on the peak heights using a gradient-expansion

algorithm (IDL, Research Systems Incorporated, See Appendix A for examples of the

computer code).


Results


Diffusion Tensor Measurements

Figures 3-1 and 3-2 show the natural logarithm of signal intensity vs. b value for

gray matter (GM) and white matter (WM), respectively, with gradients applied along the

z direction. Table 3-1 lists the So and the diffusion rate values for a monoexponential fit

to the low diffusion-weighting regime (b = 0 to 1000 s/mm2), the high diffusion-

weighting regime (b = 8000 to 15000 s/mm2), the whole data set, and a biexponential fit

to the whole data set. In the high b regime, most of the signal from the fast diffusing

fraction is lost, so the diffusion rates calculated are similar to the slow component values

found by the biexponential fit. In the low b regime, however, there is a significant

contribution from both diffusion rates, so values found by monoexponential fits are

generally a factor of 2 to 3 smaller than the fast component diffusion values found by the

biexponential fit. Nevertheless, these values provide a good starting point for use in a

non-linear curve fitting routine.









A monoexponential curve was fit to the entire b range (0 to 15000 s/mm2). This

monoexponential fit is shown as a dot-dashed line on the graphs in Figures 3-1 and 3-2.

These lines clearly do not fit the data, though the fits have fairly low X2 values (0.012).

Using this fit, the mean WM diffusion value was found to be 87.8 Pm2/s, and the mean

GM diffusion value was found to be 98.4 pm2/s. The differences between the dashed and

the dot-dashed line in Figures 3-1 and 3-2 give an indication of how the monoexponential

fit changes as the maximum b value increases. Fitting to a monoexponential curve gives

smaller diffusion rates for increasing b value because the slow component of diffusion

contributes an increasing amount, making the diffusion rate appear to be smaller.

Although a monoexponential curve fits the data taken for b values of approximately 0 to

1000 s/mm2, it will not properly fit data when higher b values are used. At higher b

values, the X2 may indicate a good fit even when a visual inspection of the data at a single

pixel shows that to be untrue. Therefore, a different model is needed.


Table 3-1. Diffusion rates found for various types of fitting routines.
Monoexponential Fit Biexponential Fit

B =0 to 1000 b = 6000 to b = 0 to 10000 GM WM
s/mm2 10000 s/mm2 s/mm2
GM WM GM WM GM WM Fast Slow Fast Slow
So 93.8 95.2 22.2 55.0 39.1 81.3 43.3 56.7 37.5 62.5
Dxx 226.7 148.9 34.9 8.1 97.9 82.4 478.9 27.6 361.7 9.1
Dw 167.7 167.2 39.4 11.9 109.2 86.9 496.5 41.0 406.6 12.5
Dzz 148.6 231.9 28.2 16.2 98.0 94.1 431.5 29.0 589.0 17.2
D, 86.6 17.0 2.0 1.4 16.4 6.7 87.2 5.6 29.6 1.7
Dxz 140.7 32.7 1.7 2.4 16.6 8.4 82.3 6.3 51.0 2.8
Dz 134.4 16.4 2.7 4.9 17.5 5.5 80.7 6.8 11.9 4.5
TR 181.0 182.7 31.7 12.1 98.4 87.8 468.9 32.5 452.4 13.0









The solid line in each graph is derived from the zero-diffusion-weighting values

(Sof and Sos) with the fast and slow Dzz values from the full tensor fit to Eq. [1-37]. The

diffusion values and zero-diffusion-weighting values found using the biexponential fit are

given in Table 3-1. The data points (Figures 3-1 and 3-2) follow the solid curves very

closely (in the x and y directions as well, not shown), indicating the biexponential fitting

routine gives an accurate fit to the tensor. For white matter, the fast component average

diffusivity (gTR, where gTR = (Dxx + Dyy + Dzz) / 3) is 452.4 pm2/s and the slow

component average diffusivity value is 13.0 pm2/s. For gray matter, the fast component

average diffusivity is 468.9 pm2/s and the slow component average diffusivity is 32.5

[Pm2/s. The diffusion rates found by a monoexponential fit to the entire curve are

approximately a factor of 5 smaller than the fast diffusion component, and approximately

a factor of 2.5 larger than the diffusion values found by the monoexponential fit to the

low b value regime.

The fractional contribution of fast and slow diffusion regimes to the total signal

intensity can be found by dividing each of the zero-diffusion weighting values (Sof and

Sos) by the sum of the two values. In the brain white matter, the fast component

contributes a volume fraction of approximately 0.375 and the slow component

contributes a volume fraction of approximately 0.625 to the total signal intensity. In the

brain gray matter, the fast component contributes a volume fraction of approximately

0.433 and the slow component contributes a volume fraction of approximately 0.567 to

the total signal intensity. As stated in the introduction, these differ from the expected

values of approximately 0.20 for the fast and 0.80 for the slow component. To eliminate









the contribution of T2 relaxation to these diffusion volume fractions, T2 relaxation

measurements were performed and taken into account.



T2 Relaxation Measurements

The T2 relaxation data was best fit by two relaxation rates: a long and a short

relaxation rate. The T2 relaxation rates found for both the GM and the WM samples, and

the So values for each, are found in Table 3-2. Both T2 relaxation rates are longer for the

GM than for the WM. Also, the difference between the two relaxation rates is larger for

the GM than for the WM.



Table 3-2. T2 relaxation rates and volume fractions for GM and WM samples.
Sample Soa SOb T2a T2b
GM 26.7 73.3 663.2 48.4
WM 14.8 85.2 255.3 31.9


In both GM and WM, the volume fractions for the long and the short T2 relaxation rates

are similar to the values expected to be found in the extracellular and intracellular spaces,

respectively (Sykova, 1997). This implies that the T2 relaxation values could represent

the water species present in these spaces. Assuming that the species with the long (short)

relaxation time is the same species as the fast (slow) diffusing species, the relaxation

rates can be removed from the diffusion via Eq. 3-2. After doing this deconvolution, the

volume fractions given in the diffusion experiment are approximately the volume

fractions seen in the T2 relaxation measurements (Table 3-3).









Table 3-3. Diffusion volume fractions with and without the T2 contribution.
Diffusion volume fraction Diffusion volume fraction
with T2 contribution without T2 contribution
Sample Sof Sos Sof Sos
GM 43.3 56.7 27.7 72.3
WM 37.5 62.5 18.3 82.7


Discussion

Single exponential diffusion rates and diffusion rate tensors have been measured

in central nervous system (CNS) tissues for a variety of human and animal subjects

(Chenevert et al., 1990; Ford et al., 1994; Guliani et al., 1997; Inglis, et al., 1997; Le

Bihan et al., 1993; Moseley et al., 1990; Pierpaoli & Basser, 1996; Pattany et al., 1997;

Pierpaoli et al., 1996; Thompson et al., 1987; van Gelderen et al., 1994). Diffusion rates

in normal GM and WM are, on average, similar in humans and animals. In most of these

studies, the maximum b value used was 1000 s/mm2 (Chenevert et al., 1990; Ford et al.,

1994; Le Bihan et al., 1993; Moseley et al., 1990; Pierpaoli & Basser, 1996; Pattany et

al., 1997; Pierpaoli et al., 1996; Thompson et al., 1987; van Gelderen et al., 1994). The

diffusion rate trace values in these studies approximate 300 Pm2/s in GM and 650 [Pm2/s

in WM. These values are both larger than the diffusion rates found by doing a

monoexponential fit to the brain data taken at b = 0 to 1000 s/mm2. The WM values are

similar to the fast diffusion rate values found by doing a biexponential fits to the entire

data set, and the GM rates are about a factor of two smaller. Because of this unexpected

result, it was necessary to look closer at the previous studies. Two major differences

stand out between this study and ones done previously: i) the diffusion times (TD) are

longer than those in this study, and ii) the echo times (TE) are longer (by a factor of two

or more) than those used in this study.









Although diffusion time may not play a significant role in the observed

differences, echo time most likely does. The T2 relaxation rate measurements done on

the brain tissue samples showed that T2 relaxation is biexponential. From the volume

fractions found here, and by observations made by others (van Dusschoten et al., 1995;

Stanisz & Henkelman, 1998), the two rates can be ascribed to the extracellular space and

the intracellular space, with the longer T2 relaxation rate being extracellular and the

shorter T2 relaxation rate being intracellular. By revisiting the assumption that the fast

diffusing species has a long T2 and the slow diffusing species have a short T2, then at

long TE the fast diffusing species will contribute more to the overall signal intensity than

the slow diffusing species. The diffusion trace rates found previously appear to support

this supposition (Chenevert et al., 1990; Ford et al., 1994; Le Bihan et al., 1993; Moseley

et al., 1990; Pierpaoli & Basser, 1996; Pattany et al., 1997; Pierpaoli et al., 1996;

Thompson et al., 1987; van Gelderen et al., 1994). The data in these experiments was

taken at echo times ranging from 70 to 110 ms. The echo times were a minimum of 2

times the short T2 relaxation rate in WM and a minimum of 1.5 times the short T2

relaxation rate in GM., So the slowly diffusing component taken at these long TE values

makes little, if any, contribution to the WM, and a slightly greater contribution to the GM

By taking the T2 relaxation time contribution out of diffusion volume fractions,

the diffusion volume fractions come close to the expected 0.20 and 0.80 for extracellular

and intracellular spaces, respectively. Since the two T2 components appear to represent

the extracellular and the intracellular spaces, and the spaces that the T2 components

represent seem to match the spaces the diffusion components represent, the diffusion

components may also represent the extracellular and intracellular compartments. Also,









because taking the T2 relaxation contribution away from the diffusion volume fractions

gives volume fractions close to the expected values, other mechanisms may have less of a

contribution to the changes in volume fractionation than the relaxation, at least for fixed

tissue. For example, exchange is very slow, if there is any exchange at all. So, for fixed

tissue, it may be possible to completely separate the extracellular spaces from the

intracellular spaces, making it possible to image intracellular and extracellular

compartments. In this case, the Sof and Sos images will be the relaxation-weighted images

of the extracellular and intracellular compartments, respectively, and the fast and slow

diffusion rate tensor images will show, specifically, diffusion in the extracellular and the

intracellular spaces, respectively.















CHAPTER 4
MULTIEXPONENTIAL DIFFUSION TENSOR
IMAGING OF NORMAL RAT SPINAL CORD


The ability to clearly visualize normal tissue and tissue structure so that clear

comparisons can be made with injury and disease states is important. Although

histological sampling of tissue has given clear insight to both normal and pathological

tissues, such methods cannot give images of the tissue in vivo serially and over the long-

term. Though not in the detail of histology, magnetic resonance imaging can give an

overall picture of the tissue and its structure through TI-, T2-, proton density-, and

diffusion-weighted imaging. Such experiments can be done in vivo, allowing serial

measurements to be done.

The apparent diffusion tensor (ADT) can show an overall picture of tissue

structure making it useful for imaging central nervous system tissues (Basser et al.,

1994a; Basser, 1995; Basser & Pierpaoli, 1996; Chenevert et al., 1990). As we saw in

Chapter 3, however, the diffusion values found by making a single ADT map will depend

on the experimental parameters used to take the data (i.e. TE and diffusion time). This is

due to the fact that there are distinct diffusion pools within the tissue that have different

T2 relaxation rates.

Also in Chapter 3, two unique diffusion and T2 relaxation components were found

in homogeneous samples of excised, fixed human brain tissue, perhaps explaining why a

single ADT map depends on the experimental parameters. Further, evidence was seen









that the two components within the tissue could represent the extracellular and

intracellular compartments. Since the two diffusion components were different enough to

be separable, imaging experiments were done to visualize the two components.


Materials and Methods


Sample Preparation

A Sprague-Dawley rat was euthanized under deep general anesthesia (sodium

pentobarbital, 100 mg/kg, i.p.), exsanguinated, and perfused transcardially with

physiological (0.9%) saline followed by 4% formaldehyde solution. A 3 cm section of

spinal cord was removed from the rat (from the mid-thoracic region through the lumbar

enlargement) following euthanasia and stored in 4% formaldehyde solution.

Approximately 24 hours prior to the NMR measurements the spinal cord was rinsed in a

bath of phosphate buffered saline (PBS). Three times over the 24 hours the cord was

removed from the PBS and rinsed in a fresh bath of PBS. This procedure removed as

much of the free formaldehyde as possible from the cord since, as seen in chapter 2,

formaldehyde dramatically shortens the T2 of the sample.


Diffusion Tensor Measurements and Post Processing

Diffusion tensor measurements and post processing were done almost as

described in the previous chapter. A PGSE imaging pulse sequence was used for ADT

imaging (LeBihan and Breton, 1985). For both spectroscopy and imaging, diffusion-

weighting gradients were aligned along the gradient-winding directions x, y, z, x = y, x =

z, y = z, and x = y = z. DW-images were created used ten different gradient weightings

per direction, and were chosen so that the b values would be logarithmically spaced









between 0 and 10000 s/mm For imaging, acquisition parameters were TR = 3 s, TE =

36 ms, 8 = 9 ms, A = 20 ms, matrix = 128 x 128, and NA = 2. The images were fit

pixelwise using the method described in the previous chapter.


Results

The fast and slow equilibrium images, Sof and Sos, are shown in Figures 4-1a and

4-lb, respectively. In gray matter, the volume fractions for the fast and slow components

are 0.55 and 0.45 respectively. In the white matter, the volume fractions for the fast and

slow components are 0.35 and 0.65, respectively. The sum of these two images gives the

pure relaxation-weighted image (Figure 4-1c). The calculated image in Figure 4-ic looks

like an image taken using the same parameters as the diffusion images but without active

diffusion gradients (Figure 4-1d). Any differences between the two images are due to the

diffusion weighting from the imaging gradients used to make the image in Fig. 4-1d.









h h9

Figure 4-1. Zero diffusion-weighted images.
Calculated images a) Sof image, b) Sos image, and c) sum of the Sof and Sos images gives
the pure relaxation-weighted image. d) An image taken with no diffusion weighting. The
labels a through h are described in table 4-1.


Figures 4-2a and 4-2b show the full diffusion tensors for the fast and slow

diffusion components, respectively, in a rat spinal cord. These were obtained using a

biexponential fit to Eq. 1-39. Note that Dyx = Dxy, D = Dx, and Dzy = Dyz. The image






























b




















Figure 4-2. The full biexponential diffusion tensor.
a) Fast component of the diffusion tensor. Thresholds for these images are set between 0
and 2000 s/mm2. b) Slow component of the diffusion tensor. Thresholds for these images
are set between 0 and 200 s/mm2









Dzz describes diffusional water motion along the length of the spinal cord (in and out of

the image plane). The image Dyy describes diffusional water motion left and right in the

image plane. The image Dxx describes diffusional water motion up and down in the

image plane. Table 4-1 contains the diffusion values for several anatomical regions of

the spinal cord. The regions chosen for Table 4-1 are numbered 1 to 8 and overlaid on

Figure 4-1d. A more complete picture of spinal cord anatomy can be found in Appendix

C.

The first noticeable difference between the fast and slow regime tensors is that the

slow regime image does not show any buffer surrounding the cord. This is expected

since free water diffusion, unlike the diffusion of water in tissue, fits a monoexponential

and does not have a slow component. The ring artifacts around the sample, noticeable in

the off-diagonal elements of the fast-diffusion tensor and in all the elements of the slow-

diffusion tensor, arise from a poor fit to regions at boundaries due to partial volume

effects.

The fast diffusion tensor (4-2a) appears as expected from the spinal cord

structure, with the white matter being oriented along the z direction (like long, thin tubes)

and the gray matter being more isotropic. The threshold in the fast diffusion trace images

is set so that the darkest points are 0 pmm2/s and the brightest points are at 2000 Pm2/s.

Though there is some diffusion in these elements, the off-diagonal elements appear

almost uniformly dark. This is because the diffusion rates in the off-diagonal elements

are much slower than the than their corresponding diagonal elements. The uniform

threshold values chosen to show the diagonal elements to their best advantage causes the

off-diagonal elements to disappear.












Table 4-1. Diffusion rates for the regions of rat spinal cord shown in Figure 4-1d.
The biexponential fit was done to b values in the range of 0 to 10000 s/mm2. Then anatomical regions are shown in Figure 4-1d.
Fast Component Diffusion Rates (Pm2/s) Slow Component Diffusion Rates (Pm2/s)
Region Dx, 'Std Dyy Std Dzz Std gTR Std Dx Std Dyy Std Dzz Std gTR Std

'DF 166.1 34.4 79.9 24.8 1590.7 93.3 618.4 45.6 7.5 6.0 16.5 12.5 77.8 9.7 33.4 6.3
2VLF 131.6 35.6 125.2 26.5 1497.1 153.7 586.2 52.2 7.1 5.4 5.8 4.2 47.5 5.8 19.8 4.2
'VF 201.0 38.8 98.2 23.9 1477.0 154.1 594.2 57.2 3.7 2.8 4.1 3.5 39.5 5.0 15.2 2.5
4DLF 119.0 42.5 120.5 24.4 1505.7 121.5 582.2 46.9 9.4 13.2 8.6 4.7 55.3 5.5 23.9 3.8
'SG 181.6 80.8 115.6 47.2 632.8 322.4 309.5 147.9 5.2 8.2 8.1 12.3 23.6 35.4 12.2 18.2
'DH 493.5 53.9 268.2 32.9 1165.7 106.2 642.1 58.4 60.5 14.8 45.3 10.3 140.6 11.3 83.0 12.3
SVH 561.4 55.5 443.0 54.1 1074.2 122.9 692.4 60.7 77.5 12.4 65.7 12.2 132.5 15.4 92.0 11.1


307.3


69.1


389.1


79.0 870.2 264.3 521.7


128.8 25.5 27.6


42.9 45.2 73.9


75.4 49.7 51.8


1 Dorsal Funiculus
2 Ventral Lateral Funiculus
3 Ventral Funiculus
4 Dorsal Lateral Funiculus
5 Substantia Gelatinosa
6 Dorsal Horn
7 Ventral Horn
8 Gray Commissure
i Standard deviation over the pixels in the region of interest


GC









The slow diffusion tensor (Fig. 4-2b) has the threshold set such that the darkest

points are at 0 pmm2/s and the brightest points are at 200 Pm2/s, a factor of 10 less than

used in the fast diffusion tensor. The diffusion elements Dx and Dyy have a similar

contrast to the fast tensor. The Dzz element, however, has contrast opposite to that seen in

the fast tensor (i.e. the GM is brighter than the WM). Table 4-1 shows explicitly that in

the fast regime, the white matter Dzz is approximately 1.4 times larger than the gray

matter Dzz, whereas in the slow regime, the gray matter Dzz is approximately 2.5 times

larger than the white matter Dzz. The relative decrease of Dzz from fast to slow is much

larger for WM than for GM. The off-diagonal elements are more obvious in the slow

diffusion tensor, but the high amount of noise in these images makes in doubtful that they

are any more significant.

Color diffusion trace (cTR) images are one method to quickly see the structural

information contained within the diffusion tensor. cTR images are not independent of the

relative orientation of the gradients to the sample, so care must be taken in orienting the

spinal cord tissue samples similarly in the magnet. The cord is placed in the gradients

such that the length of the cord (the rostral-caudal extent) is aligned with the z-axis

gradients, the lateral extent of the cord is aligned with the y-axis gradients, and the

anterior-posterior extent is aligned with the x-axis gradients. Therefore, water diffusing

in the rostral-caudal extent (i.e. in and out of the imaged plane) is defined by Dzz, water

The slow diffusion tensor (Fig. 4-2b) has the threshold set such that the darkest

points are at 0 pmm2/s and the brightest points are at 200 Pm2/s, a factor of 10 less than

used in the fast diffusion tensor. The diffusion elements Dx and Dyy have a similar

contrast to the fast tensor. The Dzz element, however, has contrast opposite to that seen in









the fast tensor (i.e. the GM is brighter than the WM). Table 4-1 shows explicitly that in

the fast regime, the white matter Dzz is approximately 1.4 times larger than the gray

matter Dzz, whereas in the slow regime, the gray matter Dzz is approximately 2.5 times

larger than the white matter Dzz. The relative decrease of Dzz from fast to slow is much

larger for WM than for GM. The off-diagonal elements are more obvious in the slow

diffusion tensor due to the difference in the threshold. The signal intensity in these

images is approximately equivalent to the signal intensity seen in the diagonal elements

of the fast diffusion tensor.

Color diffusion trace (cTR) images are one method to quickly see the structural

information contained within the diffusion tensor. cTR images are not independent of the

relative orientation of the gradients to the sample, so care must be taken in orienting the

spinal cord tissue samples similarly in the magnet. The cord is placed in the gradients

such that the length of the cord (the rostral-caudal extent) is aligned with the z-axis

gradients, the lateral extent of the cord is aligned with the y-axis gradients, and the

anterior-posterior extent is aligned with the x-axis gradients. Therefore, water diffusing

in the rostral-caudal extent (i.e. in and out of the imaged plane) is defined by Dzz, water

diffusing laterally (i.e. left and right in the image plane) is defined by Dyy, and water

diffusing anterior-posterior (i.e. up and down in the image plane) is defined by Dxx.

Figures 4-3a and 4-3b show the fast and slow cTR images, respectively. Although these

images do not give different information that the full diffusion tensor, the information is

presented in a way that can be understood much more quickly. For example, in the cTR

images it is immediately obvious that the WM has a bias towards the z direction from the









red coloring present. It is also clear that the GM is much more isotropic. Variations in

color can be seen throughout the gray matter, especially in the slow diffusion cTR.


Fast Slow













Figure 4-3. The color diffusion tensor trace.
a) The fast component of the cTR. b) the slow component of the cTR..


Three parameters, invariant to the relative orientation of the gradient and sample

axes (PJ Basser, 1995), are available from the full tensor: i) the grayscale trace of the

tensor, where gTR = (Dxx + Dyy + Dzz)/3; ii) the fractional anisotropy index (FA) given by


I I [Dij (TR(D))Iij]2
FA = 3 1i=x,y,zj=x,y,z
SiA

1i=x,y,z j=x,y,z
where Iij is the identity matrix; and iii) the volume ratio (VR) given by

Deter min ant(D)
VR=
[TR(D) / 3]3

The fast and slow grayscale diffusion trace (gTR) images are shown in Figs. 4-4a and 4-

4b at display scales identical to the ones used for the fast and slow diffusion tensors in

Fig. 4-2. The fast diffusion trace (gTRf) appears almost uniform across the spinal cord,

indicating that, on average, there is very little differentiation between GM and WM for









the fast diffusing species. In the slow diffusion trace (gTRs), the GM and WM are

completely differentiated, showing there are innate structural differences between the

GM and WM. The ratio of the diffusion rate in the gray matter to the diffusion rate in the

white matter is 1.10 and 3.80 for gTRf and gTRs, respectively.



Fast Slow













Figure 4-4. The grayscale diffusion tensor trace.
a) The fast component of the gTR. b) the slow component of the gTR.


The fractional anisotropy and volume ratio give measures of the anisotropy or

isotropy of the tensors, respectively. Although the FA and VR are complementary, at

times more subtle variations appear more clearly in one than the other. One example of

this is the brightened outline around the gray matter in the slow FA image appears more

clearly than in the slow VR image. Also, the variations of isotropy across the gray matter

from dorsal to ventral stand out more readily in the VR than in the FA images. The fast

and slow FA images are displayed in Figures 4-5a and 4-5b. Overall, the average FA for

the fast component (FAf) is 0.44 for the gray matter and 0.74 for the white matter, i.e. the

white matter is more anisotropic than the gray matter. The FA for the slow component








(FAs) is 0.40 for the gray matter and 0.71 for the white matter. Overall, the fast

component of diffusion is marginally more anisotropic than the slow component.


Fractional Anisotropy
Fast


Volume Ratio
Fast


Slow


Slow


Figure 4-5. The anisotropy/isotropy images.
a) The fast and b) the slow FA images. c) The fast and d) the slow VR images.


The fast and slow VR images are displayed in Figures 4-5c and 4-5d. These

images are complimentary to the FA images displayed in Figures 4-5a and 4-5b. On

average, the VR for the fast component (VRf) is 0.68 for the gray matter and 0.11 for the

white matter. The VR for the slow component (VRs) is 0.74 in the gray matter and 0.15









in the white matter. The VR results imply that the gray matter is more isotropic (or less

anisotropic) than the white matter, consistent with the previous result for the FA. Also,

the slow component of diffusion is marginally more isotropic than the fast component,

which is also constant with the previous FA result.


Discussion

As stated in Chapter 3, if the fast and slow diffusion rates are the extracellular and

intracellular components, the fractional contributions to the signal should be compared to

the physiological values for the extracellular and intracellular volume fractions (fex ~ 20%

and fin 80%) (Nicholson & Sykova, 1998; Sykova, 1997). Although the volume

fractions detected were not the same as the physiological values, they were much closer

to the physiological values than those observed by Neindorf, et al. (1996). They found

the relative magnitudes of the volume fractions were reversed compared to physiological

values, though these volume fractions are effected by other NMR considerations, such as

the T2 and exchange between components discussed in the previous chapter.

As shown in the previous chapter, differences between these values and the

physiological values may be largely due to the effects of multi-compartment T2 (Buckley

et al., 1999; Li et al., 1998; Stanisz et al., 1998; Stanisz & Henkelman, 1998; van

Dusschoten et al., 1995). As observed with the brain tissue samples in Chapter 3, the

shorter T2 intracellular relaxation rate would mean more signal loss for that volume

fraction. Other factors could contribute to the differences observed. Exchange of water

between the compartments could also contribute to the observed differences in fractional

contribution due to mixing between compartments. Schoeninger, et al. (1994) showed

that in Aplysia neurons the nucleus has a much larger diffusion rate than the surrounding









cytoplasm. The spinal cord GM has more cell bodies in it than the WM, perhaps causing

the volume fractions to be significantly changed by the nuclei or other subcellular

organelles having a faster diffusion rate than the surrounding material. Also, Sykova

(1997) observed that white matter is approximately 18% extracellular space, whereas

gray matter is approximately 22% extracellular space which could also explain part of the

difference between the fractional contributions.

The fast component of the diffusion tensor appears as expected from what is

known about spinal cord structure. That is to say, the axons in white matter are oriented

predominantly along z whereas gray matter parenchyma is more isotropic. The slow

component of the diffusion tensor has some unexpected features. The slow Dzz

component exhibits a very slow diffusion rate for WM compared to GM. This implies

that the apparent barriers to diffusion are further apart for the gray matter, or there are

perhaps other restrictions to free diffusion, e.g. macromolecular interactions, giving rise

to the differences between the gray and white matter at this level. Structures such as

myelin, microtubules or neurofilaments, which are much more prevalent in white matter,

could account for the slower white matter diffusion rates.

So the differences between the fast and the slow component of the diffusion

tensor could be largely due to the difference in the type of restriction seen by intracellular

and extracellular water. The fast and slow diffusion coefficients appear to be the average

components of the extracellular (fast diffusing) water and the intracellular (slow

diffusing) water, respectively (Norris & Neindorf, 1995; Neindorf et al., 1996; van Zijl et

al., 1991). The homogeneity of gTRf indicates that the average diffusivity of the

extracellular water fraction is similar in WM and GM, in spite of very different diffusion









anisotropies. gTRs shows that the intracellular water fraction is much more restricted for

WM than for GM, although the anisotropies are very similar to the fast diffusion regime.

These results seem due to similarities in external architecture (at least for tissue fixed

with 4% formaldehyde) for cells in each tissue type, and differences in internal cellular

architecture in each tissue type. It must be kept in mind, however, that the data was taken

at fairly long diffusion times (> 10 ms) and the two components likely cannot be

completely separated into intracellular and extracellular water due to exchange between

the compartments (Karger et al., 1988; Norris & Neindorf, 1995; Neindorf et al., 1996;

van Zijl et al., 1991).















CHAPTER 5
MULTIEXPONENTIAL DIFFUSION TENSOR IMAGING
OF NORMAL AND 1-MONTH POST INJURY
RAT SPINAL CORDS


In all stages of trauma and disease in the brain and spinal cord, it is important to

know the current amount of the physical damage, how far the damage will extend, and

how the structural changes relate to the final amount of functionality. Though it is fairly

straightforward to measure the extent of internal damage ex vivo through histological

sectioning, assessment of internal physical damage in vivo has been difficult. The

innovation of magnetic resonance (MR) imaging has been an important step towards

quantifying structural changes in living systems. One MR contrast mechanism that has

proved useful for the study of nervous tissue is water translational self-diffusion

(Chenevert et al., 1990; Ford et al., 1994; Gulani et al., 1997; Inglis et al., 1997; Kirsch et

al., 1991; Le Bihan et al., 1993; Moseley et al., 1990; Ono et al., 1995; Pattany et al.,

1997; Pierpaoli & Basser, 1996; Thompson et al., 1987; van Gelderen et al., 1994). MR

images of water diffusion have been used extensively to aid in the elucidation of

structure. In cases of trauma or ischemic stroke, diffusion studies have been used to

demonstrate the magnitude of the damage to the tissue (Becerra et al., 1995; Ford et al.,

1994; Kirsch et al., 1991; Moseley et al., 1990; van Gelderen et al., 1994).

Water diffusion is usually considered to occur as a simple, single diffusion rate

(or single diffusion rate tensor) process (Stejkal & Tanner 1965; Basser et al. 1994a &

1994b). Only recently, with the availability of much stronger gradients, has it been









discovered that water diffusion in tissue is a multiple diffusion rate processes (Assaf &

Cohan 1998; Karger et al. 1988; Neindorf et al. 1996; Stanisz et al. 1997; van Zijl et al.

1991). To the limits of the gradients available on our instumentation, two unique

diffusion regimes have been measured for fixed CNS tissue: a fast diffusing component

and a slow diffusing component. It has been speculated that the fast and slow diffusing

components in tissue represent diffusion in the extracellular and intracellular spaces,

respectively (Karger et al., 1988; Neindorf et al., 1996; van Zijl et al., 1991).

Using the multiple component diffusion tensor measurement protocol seen in

Chapter 4, we examined normal and injured rat spinal cord ex vivo. The aim of these

studies was to provide a basic understanding of the information contained in the fast and

slow (i.e. proposed extracellular and intracellular) diffusion compartments. The

information found in these ex vivo measurements will provide a background for future in

vivo experiments, allowing a better understanding of the information provided by the fast

and slow diffusion components.


Materials and Methods


Sample Preparation

Five adult female Sprague Dawley rats were used for this study. Under general

anesthesia, three rats were given a moderate contusion injury to the low thoracic region

(T13) of the spinal cord. These rats were allowed to recover for one month before the

spinal cord was excised.

After the one month recovery period, all rats (normal and injured) were

euthanized under deep general anesthesia by exsanguination and transcardial perfusion

with physiological saline solution followed by a 4% paraformaldehyde solution, the same









procedure that was done in Chapter 4. A 3 cm section of spinal cord, centering on the

region of injury, was removed from each rat and stored in a 4% paraformaldehyde

solution. Approximately 24 hours prior to NMR measurement, the spinal cords were

placed in a bath of phosphate buffered saline (PBS). These cords were placed in fresh

baths of PBS three more times before being inserted into the magnet. This procedure was

done to remove as much free paraformaldehyde as possible from the cord since free

paraformaldehyde in the solution surrounding the tissue will dramatically shorten the T2

relaxation rate of the sample as seen in Chapter 2.


NMR Experiments

Magnetic resonance microscopy and diffusion measurements were performed on

all rat spinal cords using a Varian Unity 600 spectrometer (14.1 T magnet, 51 mm bore).

The gradient probe used was a 5 mm radio-frequency coil, three-axis actively-shielded

Varian gradient probe capable of 300 mT m-1 per axis. Sample temperature was

maintained at 200 C through the entire measurement protocol. The microimaging

measurements were performed using a pulsed gradient spin echo (PGSE) sequence.

Images of the spinal cords were taken in contiguous 250 jpm thick transverse slices.

Other acquisition parameters included TR = 8 s, TE = 14 ms, and a matrix of 256 x 256.

Overall measurement time was 1.5 hours.

The ADT imaging procedure used for the spinal cord was adapted from that

described by Basser, et al. (1994a & 1994b), the same procedure that was utilized in

Chapter 4. Diffusion-weighted (DW) images were acquired using a PGSE imaging

sequence with diffusion gradients aligned along the directions x, y, z, x = y, x = z, y = z

and x = y = z. Ten gradient weightings were applied in each direction to give b values









that were approximately logarithmically spaced between 0 and 10000 s/mm2. Other

acquisition parameters included TR = 3 s, TE = 36 ms, 8 = 9 ms, A = 20 ms, matrix = 64

x 64 and NA = 4. The in-plane resolution was 78 jam x 78 jam and the slice thickness

was 1.0 mm. The overall measurement time was 16 hours.

For each cord, three sets of diffusion and microimaging experiments were done.

One set (6 diffusion slices) was at the epicenter of injury. One set was rostral to the

epicenter (with slice 6 of this set being the same as slice 1 of the epicenter set). The third

set was caudal to the epicenter of injury (with slice 1 of this set being the same as slice 6

of the epicenter set). This procedure allowed for 16 diffusion slices to be made through

the spinal cord, allowing the visualization of damage to the cord as much as 7-8 mm

rostrally and caudally.


Results

Figures 5-1 to 5-3 show diffusion trace images for both normal and 1-month post-

injury rat spinal cords. Self-diffusion in the spinal cord is given in the coordinate system

of the gradient axes. The gTR images (b, d, f and h in Figs. 5-1, 5-2 and 5-3) give an

average diffusion rate across the cord that is independent of the cord orientation. As in

Chapter 4, the cTR images (a, c, e and g in Figs. 5-1, 5-2 and 5-3), in which red indicates

Dzz, green indicates Dyy, and blue indicates Dxx are not independent of cord orientation

inside the gradients. Although the cTR is not independent of cord orientation, all the

tissue samples were equivalently aligned within the gradients so that the cTR images

from different cords could be compared. The cTR images show some structural

differences more readily than the gTR images.






Normal Injured
Fast
Color Diffusion Trace




Grayscale Diffusion Trace



L 4 1 4I P
Slow
Color Diffusion Trace




Grayscale Diffusion Trace




Figure 5-1. Diffusion trace images 7 mm rostral to the epicenter of injury.
Fast component of the a) cTR and b) gTR; slow component of the c) cTR and d) gTR for
normal rat spinal cord. Fast component of the e) cTR and f) gTR; slow component of the
g) cTR and h) gTR for a rat spinal cord 1-month post injury.








Normal Injured
Fast
Color Diffusion Trace







Grayscale Diffusion Trace

lrM&I Pr-i


I
U
I
S



u-I
I


Slow
Color Diffusion Trace


Grayscale Diffusion Trace
Grayscale Diffusion Trace


%W;- --


Figure 5-2. Diffusion trace images at the epicenter of injury.
Fast component of the a) cTR and b) gTR; slow component of the c) cTR and d) gTR for
normal rat spinal cord. Fast component of the e) cTR and f) gTR; slow component of the
g) cTR and h) gTR for a rat spinal cord 1-month post injury.








Normal Injured
Fast
Color Diffusion Trace








Grayscale Diffusion Trace








Slow
Color Diffusion Trace








Grayscale Diffusion Trace








Figure 5-3. Diffusion trace images 7 mm caudal to the epicenter of injury.
Fast component of the a) cTR and b) gTR; slow component of the c) cTR and d) gTR for
normal rat spinal cord. Fast component of the e) cTR and f) gTR; slow component of the
g) cTR and h) gTR for a rat spinal cord 1-month post injury.









Figures 5-4 to 5-6 give comparative views of the anisotropy for each of the

images shown in Figures 5-1 to 5-3. The fractional anisotropy (Basser, 1995; FA; a, b, e

and f in Figs. 5-4, 5-5, and 5-6) is a direct view of the anisotropy of the diffusion images

where the white represents highly anisotropic regions and black represents completely

isotropic regions. The volume ratio (Basser, 1995; VR; c, d, g, h in Figs. 5-4, 5-5, and 5-

6) is a compliment to the FA. For the VR, white represents complete isotropy, and black

represents complete anisotropy.


Normal Rat Spinal Cord

In order to discern what is occurring in the injury case, the normal images at

various positions within the spinal cord should be interpreted first. Figures 5-la, c; 5-2a,

c; and 5-3a, c (the left-hand column in each figure) are representations of the cTR for the

normal spinal cord. The dark red/black region immediately surrounding the gray matter

in the slow cTR images (Figs. 5-1c, 5-2c and 5-3c) is a feature that is not apparent in the

fast cTR images (Figs. 5-la, 5-2a and 5-3a). This region of the cord, known as the

fasciculus proprius (or propriospinal) system, consists of short, thin ascending and

descending fibers. Shorter path lengths are available for water in this region as compared

to water in other white matter regions, as the dark red/black color indicates. This means

that the average diffusion rate is slower in this region than in other white matter regions,

a feature that is visible in the grayscale trace (gTR) images (Figs. 5-1d, 5-2d, and 5-3d).

This shortened path along the length of the cord, just outside the gray matter, is not seen

in the fast (or extracellular) diffusing component, indicating that the extracellular

structure is similar to other regions of white matter. This is one piece of evidence that








Normal
Fractional Anisotropy
Fast


Injured


Slow


Volume Ratio
Fast








Slow


Figure 5-4. Anisotropy/isotropy images 7 mm rostral to the epicenter of injury.
FA a) fast and b) slow; and VR c) fast and d) slow for normal rat spinal cord. FA e) fast
and f) slow; and VR g) fast and h) slow for rat spinal cord 1-month post injury.







Normal
Fractional Anisotropy
Fast


Slow


~W)
-Sw --


Volume Ratio
Fast

pF.,


Slow
Slow


Figure 5-5. Anisotropy/isotropy images at the epicenter of injury.
FA a) fast and b) slow; and VR c) fast and d) slow for normal rat spinal cord. FA e) fast
and f) slow; and VR g) fast and h) slow for rat spinal cord 1-month post injury.


Injured


i








Normal
Fractional Anisotropy
Fast


Slow


Volume Ratio
Fast


Slow


Figure 5-6. Anisotropy/isotropy images 7 mm caudal to the epicenter of injury.
FA a) fast and b) slow; and VR c) fast and d) slow for normal rat spinal cord. FA e) fast
and f) slow; and VR g) fast and h) slow for rat spinal cord 1-month post injury.


Injured









seems to confirm the proposition that the two components of diffusion represent the

extracellular (fast) and intracellular (slow) compartments.

For the fast component, the graph of the diffusion trace values vs. slice position

(Fig. 5-7a) shows that the average diffusion rate in the gray matter regions is slightly

higher than the average diffusion rate in the white matter regions. This information leads

to the conclusion that, on average, if the fast component corresponds to water diffusion in

the extracellular space, the rate of diffusion is similar for both gray and white matter.

This would be expected since the extracellular matrix should be similar. For the slow

component, the graph of the diffusion trace values vs. slice position (Fig. 5-7b) shows

that the average diffusion rate in the gray matter regions is approximately two times

faster than the average diffusion rate in the white matter regions. This difference may be

reflective of the difference in internal structure of the gray and white matter, where gray

matter is composed of mostly cell bodies and white matter is composed mostly of axons.

In the fast cTR images (Figs. 5-la, 5-2a and 5-3a), the majority of the gray matter

regions appear to be varying shades of blue/green to yellow/gray, reflecting the more

isotropic nature of the extracellular spaces in the gray matter. Variations in the color

appear to coincide with the variation in the differing cell types occurring in each gray

matter lamina. These variations are enhanced in the slow cTR images (Figs. 5-1c, 5-2c

and 5-3c) where the gray matter appears in more distinct shades of green, blue and red,

reflecting the orientation of cell bodies and fibers, as well as different internal cell

structure, for each lamina.

From the FA and VR images (a, b, c and d in Figs. 5-4, 5-5, and 5-6), as well as

the graphical representations of each (a and b in Figs. 5-8 and 5-9), gray matter is much














a. Fast
1600
1500
1400
w 1300
.1200
1100
Q 1000
C900
o 900


a
I,I
0=


800
700
600
500
400 -

b. S
I An


Diffusion Trace vs Slice position
Normal Rat Spinal Cord


1 2 3 4 5 6 7 8 9 1011 1213141516
< Rostral Caudal >
low Diffusion Trace vs Slice Position
Normal Rat Spinal Cord


1 2 3 4 5 6 7 8 9 10111213141516
< Rostral Caudal >


c. Fast Diffusion Trace vs Slice Position
.. Rat Spinal Cord One Month Post Injury


1500
1400
1300
1200
1100
1000
900
800
700
600
500
A rfr


1 2 3 4 5 6 7 8 9 10111213141516
< Rostral Caudal >
d. Slow Diffusion Trace vs Slice Position
Rat Spinal Cord One Month Post Injury


1 2 3 4 5 6 7 8 9 1011 1213141516
< Rostral Caudal >


*--* Dorsal Funiculus
.--. Lateral Funiculus
,--, Ventral Funiculus
*-. Dorsal Horn
-A Ventral Horn


Figure 5-7. Graphs showing the fast and slow diffusion rate trace vs. slice position for normal and injured rat spinal cord.


- *













Fractional Anisotropy vs Slice Position
Normal Rat Spinal Cord


2 3 4 5 6 7 8 9 10111213141516
< Rostral Caudal >
Fractional Anisotropy vs Slice Position
Normal Rat Spinal Cord


. .


0.5
0.4
0.3
0.2
0.1
0.0

b. Slow
1.0
0.9
0.8
0.7
0.6
0.5
0.4
i1-
0.3
0.2
0.1
0.0
1


c. Fast Fractional Anisotropy vs Slice Position
1.0 Rat Spinal Cord One Month Post Injury


0.81


1 2 3 4 5 6 7 8 9 10111213141516
< Rostral Caudal >
d. Slow Fractional Anisotropy vs Slice Position
Rat Spinal Cord One Month Post Injury
1.0
0.9
0.8
0.7
0.6
0.5

0.3 '
0.2
0.1


1 2 3 4 5 6 7 8 9 1011 1213141516
< Rostral Caudal >


--* Dorsal Funiculus
H-- Dorsal Horn
*--* Lateral Funiculus
--> Ventral Funiculus
A-. Ventral Horn


Figure 5-8. Graphs showing the fast and slow fractional anisotropy vs. slice position for normal and injured rat spinal cord.


a. Fast
1.0.


2 3 4 5 6 7 8 9 1011 1213141516
< Rostral Caudal >














a. Fast Volume Ratio vs Slice Position
Normal Rat Spinal Cord




.7
.6
.5
4





1 2 3 4 5 6 7 8 9 1011 1213141516
< Rostral Caudal >
b. Slow Volume Ratio vs Slice Position
Normal Rat Spinal Cord

.9 .

-7


c. Fast Volume Ratio vs Slice Position


1 2 3 4 5 6 7 8 9 10111213141516
< Rostral Caudal >
d. Slow Volume Ratio vs Slice Position
, Rat Spinal Cord One Month Post Injury


*--* Dorsal Funiculus
u-- Dorsal Horn
--* Lateral Funiculus
--> Ventral Funiculus
Ak- Ventral Horn


1 2 3 4 5 6 7 8 9 10111213141516
< Rostral Caudal >


< Rostral Caudal >


Figure 5-9. Graphs showing the fast and slow volume ratios vs. slice position for normal and injured rat spinal cord.









more isotropic than white matter in all regions of the cord for both the fast and the slow

diffusing components. Rostral to caudal in the sixteen slices of the rat spinal cord, the

fast diffusing species in the gray matter becomes slightly more isotropic in all regions.

Rostral to caudal in the sixteen slices of the rat spinal cord, the slow diffusing species in

the dorsal gray matter becomes slightly more isotropic down the length of the cord, but

ventral gray matter becomes slightly more anisotropic. These variations probably reflect

the changes in structure of the gray matter in various parts of the spinal cord. However,

the white matter has almost no variation in its diffusion isotropy across these sixteen

slices. This is seen in the graphs of FA and VR, as well as in the images in the three

regions: for FA the white matter always appears almost white, and in the VR it appears

the same shade of dark gray. Moving rostral to caudal, the major differences in white

matter are the relative proportions of ascending to descending fibers, but there are few, if

any, differences between the structure of ascending and descending fibers beyond the

location of the main cell body. Therefore, it seems reasonable that the diffusion isotropy

in white matter would not change significantly, but that the diffusion isotropy in gray

matter might change along the length of a normal rat spinal cord.


Rat Spinal Cord 1-Month Post Injury

With a basic understanding of the structures and structural differences seen with

diffusion tensor imaging of the normal cord, the injured cord data can be interpreted.

First, the fasciculus proprius may no longer be easily discerned in the cTR and gTR

images of the slowly diffusing component (Figs. 5-1g, 5-1h, 5-2g, 5-2h, 5-3g and 5-3h).

It has become less differentiated from the surrounding white matter because the

surrounding white matter has, in general, become more isotropic and exhibits slower









diffusion rates. There should be some amount of disruptions inside the axons due to

degeneration and apoptosis, where internal cellular structures are breaking apart; or cell

survival strategies, where cells produce more organelles in an effort to survive. These

changes would cause slower diffusion rates to occur in the long white matter axons,

making them indistinguishable from the propriospinal regions of the cord.


Epicenter of injury

At the epicenter of injury, it is clear that there are major changes (Figs. 5-2e-h and

5-5e-h). A fluid filled cavity has appeared in the cord. Diffusion in the remaining white

matter tissue is much more isotropic, particularly in the dorsal and lateral sections of the

cord. This is seen in the FA (Figs. 5-5e, f) and VR images (Figs. 5-5g, h) as well as in

the FA or VR vs. slice position graphs (Figs 5-8 and 5-9). In the most ventral portion of

the cord, the fast component appears to be more anisotropic, and thus the tissue appears

more structured than the rest of the cord. This is indicative of spared white matter in this

region. The slow component of diffusion in that same region appears more isotropic,

which is more consistent with the rest of the cord. Gray matter regions are, on average,

slightly more anisotropic than normal for the fast diffusing species and slightly more

isotropic than normal for the slow diffusing species. Slices 5-8 and 5-9 (epicenter of the

injury) in the graphs of the diffusion trace vs. slice position (Fig. 5-7) show that the fast

diffusion rate is faster than in normal tissue, approaching that of free water, for all

regions of the cord. The slow diffusion rate, however, is slower than in normal tissue for

the gray matter regions, but appears almost normal for the white matter regions. The

quicker than normal rate of diffusion for the fast compartment could indicate a rising

amount of free space due to surrounding cellular damage and death, dissolution of the




University of Florida Home Page
© 2004 - 2010 University of Florida George A. Smathers Libraries.
All rights reserved.

Acceptable Use, Copyright, and Disclaimer Statement
Last updated October 10, 2010 - - mvs