University of Cincinnati
Date: 2/17/2011
I, Ahmed D Shereen , hereby submit this original work as part of the requirements for the degree of Doctor of Philosophy in Physics.
It is entitled: Diffusion Tensor Magnetic Resonance Imaging Applications to Neurological Disease
Student's name: Ahmed D Shereen
This work and its defense approved by:
Committee chair: Scott Holland, PhD
Committee member: Robert Endorf, PhD
Committee member: Diana Lindquist, PhD
Committee member: David Mast, PhD
Committee member: Weihong Yuan, PhD
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Last Printed:3/17/2011 Document Of Defense Form Diffusion Tensor Magnetic Resonance Imaging Applications to
Neurological Disease
A dissertation submitted to the
Graduate School
of the University of Cincinnati
in partial fulfillment of the
requirements for the degree of
Doctor of Philosophy
in the Department of Physics
of the College of Arts and Sciences
by
Ahmed Shereen
B.A. Philosophy, University of Dayton
B.S. Physics, University of Dayton
Committee Chair: Scott K. Holland, PhD Abstract
Diffusion tensor magnetic resonance (DTMR) imaging is a novel imaging
technique capable of indirectly measuring the cellular environment of cerebral tissues.
Its use for the clinical assessment of neurological health is increasing, yet the relation
between the DTMR metrics and the integrity, type, severity, and salvageability of
damaged tissue is still an area of active research. The work presented in this dissertation
aims to elucidate underlying cellular architecture of damaged tissues from patterns in
DTMR metrics. Experiments involving neonatal hydrocephalus, neonatal hypoxia- ischemia, and adult acute stroke models were performed wherein DTMR metrics were compared between disease and control specimens, as well as with histological and electron microscopy analyses.
Initial investigations in an experimental neonatal hydrocephalus model showed
significant differences of DTMR metrics between in vivo subjects and controls in the
white, but not gray, matter structures. Imaging resolution was improved in a subsequent
study of a neonatal hypoxia-ischemia model and the results compared to microscopic
histological assays. Decreases in the apparent diffusion coefficient and increases in T2
values in the gray matter correlated to the formation of brain edema, whereas decreases in
the fractional anisotropy of diffusion within the white matter corresponded to
demyelination as observed by histology. Furthermore, the efficacy of a novel drug
treatment for neonatal hypoxia-ischemia was tested. DTMR metrics of the gray and
white matter tissue appeared normal after treatment, and histology confirmed that the
tissue was preserved. However, the DTMR imaging resolution and brain volume
coverage remained the limiting factors in a complete brain imaging analysis that could
ii include some of the finer white matter structure of clinical relevance. Therefore, a third set of experiments was performed using an adult acute stroke model with substantial increases in resolution covering the entire brain volume. Interestingly, while the fractional anisotropy of diffusion was not significantly changed in the damaged white matter tissue in most of the structures measured, additional DTMR metrics, axial and radial diffusivities, showed significant changes. By combining these parameters, various patterns in DTMR quantities, together with electron micrographs from the tissue structures of interest, corresponded and appeared to distinguish between compression of the axoplasma, separation of intact myelin sheaths, and demyelination. While the initial results are promising, further work is necessary to validate these claims. Future studies and methodologies to improve techniques presented in this dissertation are presented in the final chapter.
iii
iv Acknowledgments
The research in this thesis would not have been accomplished without the help of many people. I owe a debt of gratitude to all those who made it possible. I would like to thank first my committee members: Dr. Robert Endorf for accepting me as his formal advisee; Dr. Scott Holland for allowing me to work with the Imaging Research Center, for serving as my committee chair, and for helping me from beginning to end—from conversations where we discovered the source of the majority of initial problems in the diffusion sequence (stimulated echoes) to insightful comments in revising this dissertation; Dr. David Mast for letting a “pre” first year graduate student work in his laboratory—the practical lessons in analogue and digital electronics and the training in high vacuum cryostat systems he gave me have no doubt been useful in understanding and operating MRI hardware and will continue to benefit me in the future; Dr. Weihong
Yuan for teaching me how to use DTI studio and for introducing me to the HCP club, which made possible the first application of diffusion imaging immediately after my first successful image acquisitions; and Dr. Diana Lindquist for being my mentor and allowing me to choose my own research topic—despite her busy schedule she maintained a constant “open door policy,” and always found time to discuss the various parts of my research.
Much of the work in this dissertation results from collaborative efforts with several talented scientists. The first application of diffusion magnetic resonance imaging, presented in Chapter 4, was to an experimental neonatal hydrocephalic model. Many thanks to the cross-disciplinary, cross-institutional efforts of: Dr. Francesco Mangano from Cincinnati Children’s Hospital, Department of Neurosurgery and Pediatrics for his
v expertise as a neurosurgeon and time devoted to performing the necessary surgery to invoke hydrocephalus in the murine model; and to Dr. James P McAllister and Kelley
Deren from the University of Utah, Department of Bioengineering for providing the first hydrocephalic samples and for sharing their insightful knowledge in the area. The work in Chapters 5 and 6 also results from collaborative efforts. Many thanks to Dr. Chia-Yi
Kuan, Dr. Dianer Yang, and Niza Nemkul from Cincinnati Children’s Research Center,
Department of Developmental Biology for providing the hypoxia-ischemia models and for performing the histological analyses; and to Dr. Gang Ning, director of the Electron
Microscopy Laboratory at the Pennsylvania University for performing the electron microscopy analysis.
I would also like to thank Scott Dunn and Dr. Ron Pratt from the 7T laboratory.
Thank you, Scott, for teaching me how to use the 7T Bruker, for the countless conversations we had while the scanner was acquiring data, and for your contagious laughter. Thank you, Ron, for teaching me how to build and test MRI RF coils, for having confidence in my abilities, and for reminding me to follow my dreams.
Above all I must thank my family. To my parents, I am extremely grateful for the warm, nurturing environment in which they raised me. I could not have chosen a better pair. They have been the best of teachers. All the words from all the languages are not enough to encapsulate the magnitude to which I appreciate what they have done for me.
To my siblings: Laila, Yasmine, Peri Hanne, and Rafik—although age helps, it’s nice to know I beat you all to the PhD! Thank you for being not only great siblings, but also the dearest of friends. I also would like to thank Brian Beckham, Joanne Benton, Joseph
Carr, Matt Eulberg, Mohammed El Gazaar, Barbara Liphardt, Roman Petrenko, and
vi Romain Picasso for their kind friendship over the years and for reminding me there is more to life than school. Lastly, I would like to thank my fiancée, Esmat Genaidy.
Without her warmth, compassion, patience, support, and humor I would not have been able to complete this milestone. I dedicate this dissertation to her.
vii Preface
The bulk of this dissertation may be divided into two sections: 1) theory and principles (Chapters 1 and 2) and 2) practice and experiments (Chapters 3-6). Chapter 1 begins with a brief history of the physical discoveries and innovations leading to the invention of nuclear magnetic resonance (NMR). The historical timeline also serves as an outline of the following sections of Chapter 1. These sections elaborate, in terms of technical details, the physical concepts described in the historical account. By the end of
Chapter 1 the chief parameters that influence the NMR signal are related in the Torrey-
Bloch equations, and the dependence of the signal on diffusion is first made apparent.
Chapter 2 derives from a simple one dimensional lattice hopping model the basic diffusion equations: Fick’s first law, the diffusion equation (also known as Fick’s second law), and the continuity equation. An experimental NMR method to measure the diffusion coefficient, the Stejskal-Tanner pulsed gradient spin echo sequence, is then described. The relationship between the NMR signal intensities, the pulse sequence parameters, and the diffusion coefficient is derived. Chapter 2 concludes with a description of the diffusion tensor magnetic resonance (DTMR) metrics: axial, radial, and mean (or apparent) diffusivities, and fractional anisotropy.
Chapters 3-6 form the “practice and experiments” section. Chapter 3 lists the specifications for the hardware used in the experiments. It also describes the optimization of the experimental methods. Preliminary data from three varieties of
DTMR acquisition methods: conventional spin echo, multiple spin echo, and multiple gradient and spin echo pulse sequences are presented. While the second two methods acquire data more rapidly, they suffer from persistent artifacts. For this reason, the
viii conventional spin echo sequence is used for all further experiments. Chapter 4 presents
results of DTMR applied to a neonatal murine model for hydrocephalus. Limitations of
this experiment are the coarse resolution, partial brain coverage, and lack of histological
data to validate or reject the DTMR interpretations. This motivates the work in Chapter
5, where DTMR is applied to a different disease model (neonatal hypoxia-ischemia). The
resolution is improved and the results compared to histological stains. However, the
experimental data is still limited by partial brain coverage and the resolution, although improved from the previous chapter, remains too coarse to distinguish the more interesting, and disease-pertinent, tissue structures. These issues are addressed in the
final experimental chapter, Chapter 6. Here mice from an adult acute stroke model are
imaged in vivo using the same imaging parameters as those in Chapter 5. However, the
animals are then sacrificed and subjected to a lengthy ex vivo (approximately 18 hours),
three dimensional, full brain coverage, high resolution (125 microns isotropic), DTMR
microimaging sequence. In order to investigate the sub-cellular architecture which gives
rise to the DTMR signal, electron micrographs of the brain tissue are acquired and
compared to the DTMR data. The results suggest that patterns in changes in the DTMR
metrics may elucidate specific stages of cellular damage due to acute hypoxia-ischemia,
which is indeed a promising possibility. Outside of these two conceptual divisions of the
thesis resides the concluding chapter. Chapter 7, after a summary of the experiments,
describes possible avenues for future work: directions for improving the methods
employed within this thesis. They are left as a roadmap for anyone wishing to go down
the randomly twisting and ricocheting road which is diffusion tensor magnetic resonance
imaging.
ix Table of Contents
List of Figures……………………………………………………………………………xv
List of Tables…………………………………………………………………………...xvii
Chapter One MRI General Background………………………………………………..1
1.1 A Brief History………………………………………………………………..1
1.2 Quantum Spin Nature of Protons……………………………………………...3
1.3 Proton in a Magnetic Field: the Zeeman Effect………………………………4
1.4 The Magnetic Moment in an External Field: A Classical Approach…………7
1.5 Resonance Condition and Bloch Equations of Motion………………………..9
1.6 From Signal Measurement Techniques to Imaging………………………….13
Chapter Two Diffusion Theory and Application to MRI……………………………..22
2.1 The Basic Equations: The Diffusion Equation, Fick’s Laws, and the
Continuity Equation……………………………………………………………...22
2.2 Diffusion Weighted Pulse Sequences………………………………………..26
2.3 The Diffusion Metrics: ADC, FA, MD, λax, and λrad……………………....30
Chapter Three Imaging Hardware and Optimization……………………………….....33
3.1 Scanner Specifications……………………………………………………….33
3.2 RF Coils: Design, SNR, and B1 Homogeneity……………………………...36
3.3 Optimization of Pulsed Gradient Spin Echo Diffusion Imaging Sequence….38
3.4 Diffusion Weighted Fast Spin Echo and GRASE Pulse Program
Development……………………………………………………………………..43
3.5 Applications of DTMR imaging……………………………………………..50
Chapter Four Quantification of DTMR Metrics in a Murine Model of Hydrocephalus
x (HCP)…………………………………………………………………………….53
4.1 Abstract………………………………………………………………………53
4.2 Background…………………………………………………………………..53
4.3 Methods………………………………………………………………………56
4.3.1 Animals Procedures………………………………………………..56
4.3.2 MRI/DTMR………………………………………………………..57
4.3.3 DTI Data Processing and Analysis………………………………...58
4.3.4 Statistical Analysis…………………………………………………59
4.4 Results………………………………………………………………………..59
4.5 Discussion……………………………………………………………………65
Chapter Five Comparison of Quantitative DTI and Qualitative Histological Staining in a Murine Model for Neonatal Hypoxia-Ischemia………………………………………..68
5.1 Abstract………………………………………………………………………68
5.2 Background…………………………………………………………………..69
5.3 Materials and Methods……………………………………………………….72
5.3.1 Animal surgery …………………………………………………….72
5.3.2 Magnetic resonance imaging………………………………………73
5.3.3 Histological Staining……………………………………………….75
5.3.4 Statistical analysis………………………………………………….75
5.4 Results………………………………………………………………………..75
5.4.1 Magnetic Resonance Imaging: Quantitative T2, ADC, and FA
Imaging…………………………………………………………………..75
5.4.2 Histological Staining……………………………………………….78
xi 5.5 Discussion……………………………………………………………………81
Chapter Six Correlations between Diffusion Tensor Imaging and Electromicroscopy in a Murine Model for Acute Adult Stroke…………………………………………………85
6.1 Abstract………………………………………………………………………85
6.2 Background…………………………………………………………………..85
6.3 Methods………………………………………………………………………87
6.3.1 Animal Surgery…………………………………………………….87
6.3.2 in-vivo MRI………………………………………………………...88
6.3.3 ex-vivo MRI………………………………………………………..89
6.3.4 Electron Microscopy……………………………………………….91
6.3.5 Statistical Analyses………………………………………………...91
6.4 Results………………………………………………………………………..92
6.4.1 in-vivo gray matter T2 and ADC…………………………………..92
6.4.2 in-vivo white matter diffusion anisotropy………………………….94
6.4.3 ex-vivo DTMR micro imaging……………………………………..99
6.4.4 Cellular resolution electron microscopy………………………….103
6.5 Discussion…………………………………………………………………..105
Chapter 7 Summary and Future Directions………………………………………….107
7.1 Summary of experiments: applications of DTMR to disease………………107
7.1.1 HCP……………………………………………………………………….107
7.1.2 Neonatal Stroke…………………………………………………………...107
7.1.3 Adult Acute Stroke……………………………………………………….108
7.2 Future Directions…………………………………………………………...109
xii 7.2.1 Improve scan time and image quality…………………………………….109
a) Pulse sequences………………………………………………………109
b) Customized coils……………………………………………………..110
7.2.2 Streamline post-processing workflow…………………………………….111
7.2.3 Calculate higher order terms to Stejskal-Tanner equation: Diffusion
Kurtosis Imaging………………………………………………………..112
7.2.4 White matter segmentation using fiber tracking………………………….115
7.2.5 DTMR outside the brain: fiber tracking of the heart……………………..117
References………………………………………………………………………………119
xiii List of Figures
Figure 1.1 Moment in external magnetic field……………………………………….7
Figure 1.2 Magnetization nutation in rotating frame………………………………..14
Figure 1.3 Globally Induced FID……………………………………………………15
Figure 1.4 The 90-180 Global Spin Echo……………………………………………16
Figure 1.5 Spin Echo Imaging Pulse Diagram………………………………………17
Figure 1.6 Slice Excitation…………………………………………………………..18
Figure 2.1 Lattice Hopping………………………………………………………….22
Figure 2.2 Pulsed gradient spin echo Stejskal-Tanner experiment………………….27
Figure 2.3 Diffusion ellipsoid……………………………………………………….31
Figure 3.1 7T Bruker Avance magnet……………………………………………….34
Figure 3.2 Bruker integrated components……………...……………………………35
Figure 3.3 The STS RF coil…………………………………………………………36
Figure 3.4 The solenoid coil…………………………………………………………37
Figure 3.5 Anisotropic phantom diffusion images…………………………………..40
Figure 3.6 DTI of a celery phantom…………………………………………………41
Figure 3.7 Ex vivo mouse brain……………………………………………………...42
Figure 3.8 In vivo mouse brain………………………………………………………42
Figure 3.9 Diffusion weighted fast spin echo………………………………………..43
Figure 3.10 Water phantom results from fast spin echo diffusion sequence…………45
Figure 3.11 Three eigenvalues and DEC calculated from images in Figure 3.10…….46
Figure 3.12 DRARE data from a glass capillary phantom……………………………47
Figure 3.13 Three eigenvalues and DEC calculated from images in Figure 3.12…….48
xiv Figure 3.14 GRASE diffusion sequence……………………………………………...49
Figure 3.15 GRASE diffusion imaging of water phantom……………………………50
Figure 4.1 HCP DTMR images……………………………………………………...60
Figure 4.2 DTMR metrics comparison between HCP and controls…………………61
Figure 4.3 Three dimensional T2 weighted fast spin echo images………………….64
Figure 5.1 Regions of interest……………………………………………………….73
Figure 5.2 Quantitative T2 map of PAI treated mice………………………………..74
Figure 5.3 T2 and diffusion MRI 24 h after HI injury………………………………76
Figure 5.4 IgG staining………………………………………………………………77
Figure 5.5 Histology…………………………………………………………………79
Figure 6.1 Sample images from 6 hour HI mouse…………………………………..88
Figure 6.2 In vivo T2 and ADC images……………………………………………...91
Figure 6.3 In vivo diffusion anisotropy……………………………………………...92
Figure 6.4 Linear best fits of the FA data……………………………………………93
Figure 6.5 Linear best fits of the MD data…………………………………………..94
Figure 6.6 Linear best fits of the axial diffusivity data……………………………...95
Figure 6.7 Linear best fits of the radial diffusivity data……………………………..96
Figure 6.8 ADC, FA, and DEC maps compared to a Nissl stained slide……………98
Figure 6.9 Ex vivo DTMR…………………………………………………………...99
Figure 6.10 EM of external capsule…………………………………………………102
Figure 7.1 Comparison of diffusion tensor and diffusion kurtosis imaging……….114
Figure 7.2 Fiber tracking of mouse brain………………………………………….116
Figure 7.3 Global fiber tracking of mouse heart…………………………………..118
xv List of Tables
Table 3.1: Gradient imaging and shim system specifications…………………………...33
Table 4.1: p-values for comparison of HCP DTMR metrics with controls……………..63
Table 5.1: T2, ADC, and FA values for PAI-1 and saline injected controls……………75
Table 6.1: DTMR statistic of fm, ic, and ec at 6, 15, and 24 hrs post HI……………...100
xvi
Chapter One
MRI General Background
1.1 A Brief History
The roots of magnetic resonance imaging (MRI) can be traced to the initial discovery of the proton’s magnetic moment by Otto Stern in 1922 (Gerlach and Stern
1922 ). Stern is awarded the Nobel Prize in 1943 for discovering the proton’s magnetic moment and for developing the molecular ray technology that makes possible its observation. The famous Stern-Gerlach experiment verifies the moment’s existence by direct measurement and finds its value to be twice that calculated from theory. Later,
Isidor Rabi uses the concept of magnetic resonance to probe the quantum spin states of the atomic nucleus. His work opens the door to many scientific developments, including nuclear magnetic resonance (NMR).
In 1946 scientists led by Felix Bloch from Stanford and Edward Purcell from
Harvard independently observe the NMR signal (Bloch, Hansen et al. 1946; Purcell,
Torrey et al. 1946). Using different methods, the two groups excite nuclear spins with radiofrequency (RF) electromagnetic fields. Knowing which frequencies are absorbed and reemitted, i.e. the resonant frequencies, allows them to detect the transition between nuclear magnetic energy levels. For their pioneering work in the field of NMR, Bloch and Purcell share the Nobel Prize in 1952.
In 1973, Paul Lauterbur produces the first images using gradients to spatially encode the NMR signal (Lauterbur 1973). He terms his method “zeugmatography” based on the Greek word “zeugmo,” meaning “that which joins.” Zeugmatography creates
1
images using back projection in the same manner as computerized tomography scans. In
1975, Richard Ernst shows that the nature of the MRI signal has mathematical properties of a Fourier transformation, and he proposes using both frequency and phase encoding to generate data that produce superior images (Ernst, Kumar et al. 1975). One major reason for the better images is that the data may be sampled uniformly, using three orthogonal gradients. In the zeugmatography method, the sample must be subjected to gradients in several directions (accomplished with several different gradient vectors, or, when practical, rotating the sample). Doing so oversamples the origin of frequency data, which results in inhomogenous error distributions and coarser image quality.
In 1977, Sir Peter Mansfield is able to shorten dramatically the lengthy zeugmatography process by implementing the Fourier method for image processing proposed by Richard Ernst. He is credited for using this concept to develop the fast imaging technique, echo planar imaging (Mansfield 1977). All of the above scientists receive Nobel Prizes for their work. Scientists from many fields continue to improve
MRI. Parallel imaging techniques, radio frequency coil fabrication, pulse sequence design; functional, diffusion, perfusion, and angiographic imaging; and image-guided surgery are but a few of the areas of development underway in the field of MRI.
In summary, although the first MRI clinical scanners are not available until the early 1980s, MRI technology represents a culmination of several physical discoveries spanning the twentieth century. An understanding of the quantum mechanical spin nature of subatomic particles, the ability to manipulate the proton’s spin behavior with sophisticated apparatuses, the experimental designs necessary to gain meaningful information from those manipulations, and the development of mathematical frameworks
2
to process the NMR signal all contribute to the success of MRI. The following sections
in this chapter elaborate each of these vital components that make MRI possible.
1.2 Quantum Spin Nature of Protons
Detailed descriptions of the theory of spin physics can be found in quantum
mechanics textbooks (Sakurai 1994; Griffiths 1995). The following description of spin is
restricted to that of a spin ½ proton for pedagogical and practical purposes: the physics is
simpler, and the spin ½ hydrogen proton is the element measured in this thesis.
A central postulate of quantum mechanics is that the spin eigenvalue, s, of an
elementary particle has only discrete, positive, and half-integer values:
s = 0, ½, 1, 3/2, …
The particle has spin momentum along three dimensions denoted by the states: Sx, Sy, and
Sz, with S equal to the sum momentum. If we measure the spin of a proton (s= ½) along
the z-axis, there are two allowed possibilities:
m = - ½ , ½ where m is the z component magnetic quantum number, and the positive (negative) sign denotes a particle with spin pointing “up” (“down”) with respect to z. The magnetic quantum number and spin state are related by the eigenvalue-eigenvector equation:
z ,, msmmsS
where
01 S z 2 10
The wave function is just a superposition of the two possible states:
3
2/1 aa 2/1 with
1 representing spin up, and 0
0 representing spin down, 1
The square of the coefficients, a1/2 and a-1/2, represents the probability of finding the particle in the spin up or down configuration.
The discrete nature of a particle’s spin is what the Stern-Gerlach experiment demonstrates. By passing a beam of spin particles through a magnetic field, the particle beam’s trajectory is bent due to the interaction of the magnetic field with the magnetic moment associated with the particle. Had the particle spin not been quantized, then a continuous range of possible values for m would lead to a continuous range of deflection angles after particles exit the magnetic field. Instead, what Stern observes is that the particle beam splits into two distinct paths, one associated with the spin up particles, the other with the spin down particles. The ability to manipulate spin based on its quantization properties leads to numerous technological advances, not the least of which is NMR.
1.3 Proton in a Magnetic Field: the Zeeman Effect
In thermal equilibrium, and in the absence of any energy fields, the spin up and spin down states are degenerate. Both states correspond to the same energy level, and there is an equal chance of finding a particle in either of the two states. However, placing an ensemble of spin particles in an external magnetic field breaks this degeneracy,
4
resulting in two separate energy levels with different occupational probabilities. This is
known as the Zeeman effect and is described below.
By definition, a spinning charged particle has an associated magnetic moment, µ.
Experimentally, the moment is directly proportional to S:
S
where the constant, γ, is called the gyromagnetic ratio. (It is classically defined as γ =
q/2m where q is the charge of a particle, and m is its mass. However, using this definition
to calculate the gyromagnetic ratio for proton will give the wrong answer. A more exact
derivation of γ requires relativistic quantum field theory and a model of the proton as
being comprised of three quarks, a discussion that is outside the scope of this thesis.)
Imagine a proton at rest placed in a uniform magnetic field pointing in the z
direction, B=B0 z. The Hamiltonian, neglecting gravity and kinetic energy, is then given
by (Sakurai 1994):
01 B0 0 SBSBBH z 2 10
The solutions to EH are therefore:
Eigenstate Ψ+ with energy, E+ = -(γB0 )/2, and
Eigenstate Ψ- with energy, E- = +(γB0 )/2
The degeneracy in energy levels is now broken and two distinct levels exist. The lower of the two corresponds to the moment oriented along the main field, as expected from classical electromagnetism.
The Hamiltonian for this system is time independent, therefore the solution to
Schrodinger’s equation:
5
i H t is given in terms of the stationary states:
ea 0tBi 2/ tiE / tiE / 2/1 )( 2/1 2/1 eaeat 0tBi 2/ 2/1 ea
The coefficients are set by initial conditions. The normalization condition at t = 0 force
2 2 2/1 aa 2/1 1
A solution for the general case is (aside from an imaginary constant whose meaning is irrelevant here):
a )2/cos( 2/1 a 2/1 )2/sin(
The reason for choosing a half angle for the argument in cosine and sine will become clear soon. The importance of the time dependent considerations to the Hamiltonian become obvious with the solutions of the expectation values for Sx, Sy, and Sz.
S tB )cos(sin x 2 0 S tB )sin(sin y 2 0 S cos z 2
These solutions imply that the spin moment is tilted at an angle, θ, to the z axis and is precessing in the x-y plane at a frequency:
B00
known as the Larmor frequency. This is one of the most important relationships in
NMR. The same result would be obtained from classical considerations. Before
6
continuing this discussion, it helps to have a visual model of what the spin experiences.
Hence, a classical rederivation of the Larmor frequency is presented next.
1.4 The Magnetic Moment in an External Field: A Classical Approach
Detailed, classical descriptions of the electromagnetic dynamics of protons in magnetic fields are found in the literature (Jackson 1999). Briefly, in classical physics, the proton is modeled as a spinning sphere of charge. The symmetry between electric and magnetic fields in Maxwell’s equations makes this sphere equivalent to a magnetic dipole moment, µ. In the absence of an external magnetic field, the moments in a bulk material are randomly oriented, and so the net magnetization is zero. However, when immersed in an external magnetic field, B0, the moments will tend to align along or opposite the field. To illustrate the dynamic behavior of the magnetic moment with the field, a simple exercise in classical mechanics is presented below.
dφ B0
dµ
µ θ
Figure 1.1: Moment in external magnetic field. A magnetic moment, μ, immersed in a magnetic field, B0, rotates about the field at an angle, θ.
7
Imagine the dynamic behavior of a proton’s moment when placed in a magnetic field as shown by Figure 1. Recall the magnetic moment is proportionate to the spin angular moment, S, via the gyromagnetic ratio, γ: (1.2) S
Since we are dealing with moments interacting with magnetic fields, there is a magnetic torque:
(1.3) BN 0 which implies a time dependent angular moment, Sd (1.4) N dt
Taking the time derivative of (1.2) and substituting the result into first (1.4) and then
(1.3) yields:
d (1.5) B dt 0
This is the simplified Bloch equation.
From the figure, dµ is defined as:
(1.6) d sind
From the definition of the cross product, (1.5) can be rewritten as
(1.7) 0 sindtBd
d Dividing (1.6) by (1.7) and solving for , i.e. the angular frequency ω, gives: dt
(1.8) B00
8
which is the Larmor equation for precession of a moment in a magnetic field. This is the same result as that derived from a quantum mechanical perspective.
1.5 Resonance Condition and Bloch Equations of Motion
The quantum mechanical nature of protons and the precession characteristics of individual proton moments about a main magnetic field form the basis of MRI.
However, the quantum character of individual protons is not measured directly by MRI experiment since the smallest detectable MRI signal arises from a number of protons on the order of Avogadro’s number. Therefore, it is convenient at this point to define the macroscopic quantity ) ,( trM , the magnetic moment per unit volume of an ensemble of proton spins large enough for Boltzmann statistics, yet sufficiently small to experience a constant magnetic field. Such a spin packet is termed a spin isochromat. It is explicitly defined as
1 (1.9) M i V N where N is the number of spins in a volume, V. The macroscopic analogy to (1.5) neglecting the spin-spin, spin-lattice, and self-diffusion interactions, is Md (1.10) BM dt 0
Assume for the moment the magnetic field is due only to the main external field pointing in the z direction. We then have, in orthogonal components: Md (1.11.a) z 0 dt
9
Md y (1.11.b) BM dt x 0 Md (1.11.c) x BM dt y 0
Manipulation of the magnetic moments’ orientation is accomplished by applying RF magnetic pulses perpendicular to the main field, effectively tipping the net magnetization away from the z axis. Since the magnetization vector is rotating, an efficient way to tip the vector is to use a left-circularly polarized RF field. In practice, the field is created by superimposing two linearly polarized, oscillating RF fields 90 degrees out of phase:
cir 11 ( ˆ cos ˆ tytxBB )sin
Manipulating spins with the circularly polarized field is referred to as operating in quadrature mode. A linearly oscillating field would also tip the spins, however it is not as power efficient. Consequently, quadrature mode results in higher signal to noise.
It simplifies matters to define two reference frames. The first is the laboratory frame, labeled byxˆ and yˆ . The second is a frame rotating at the laboratory controlled
RF frequency, ω, and is labeled by xˆ ’ and yˆ ’ The z axis from both frames are made to coincide, and the unit vectors are related by:
' ˆˆ cos ˆ sin tytxx ' ˆˆ sin ˆ cos tytxy ˆ' zz ˆ which implies that in the rotating frame the RF field is constant and directed along xˆ ’.
Eq. 1.10 in the rotating frame, modified to include the RF magnetic field, becomes:
' Md [zM ˆ ' )( ˆ ' ] BMx 0 1 eff dt
10
cir Here ω1 is the spin-precession frequency due to B1 . From the standpoint of the magnetization vector, the effective magnetic field is given explicitly as:
' ' eff [zB ˆ 0 )( xˆ 1 /]
So far this is what we would expect. Because an RF field has been superimposed on the main external field, the magnetization vector now precesses about a new axis due to the combination of the strong main external field with the relatively weak RF field. One would expect further that this causes merely a slight deviation of the magnetization vector from the z axis. However, when the RF field oscillates at the Larmor frequency, i.e. ω = ω0, the z component of the effective B field vanishes, and the magnetization precesses only about xˆ ' . This extremely important result is what is meant by resonance in the context of NMR. It is what makes nuclear magnetic resonance experiments possible.
Because the z component of the effective magnetic field disappears when a resonant RF field is applied to the magnetization vector, the experimenter has total control over the tip angle generated by the RF field. The tip angle is Δθ = γB1Δt = ω1Δt, where ∆t is the duration of the RF pulse. Timed correctly, the magnetization vector is brought into the transverse plane. When the RF pulse ends, the longitudinal magnetization will grow as the transverse magnetization created by the RF pulse shrinks.
During the return trip to equilibrium, the changing magnetic flux induces a voltage which is measured by a pick up coil tuned to the appropriate frequency. Because the time rate of change of the magnetic flux caused by rotating about the z axis (in the laboratory frame) is much greater than the flux caused by the moment’s return to equilibrium (in the rotating frame), RF receivers are positioned to measure signals from the first type of flux.
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Let the main field and RF field be denoted by B0 and B1. Equations (1.11) are then modified to include the time dependent RF field: Md (1.12.a) z sin( tBMtBM )cos dt x 1 y 1 Md y (1.12.b) ( cos BMtBM ) dt z 1 x 0 Md (1.12.c) x sin( BMtBM ) dt z 1 y 0
The equation for M0 can be obtained easily from Boltzmann statistics [Landau, Lifshitz
2001]. In the large N limit, it reduces to:
2 B0 (1.13) 0 NM 2 BTk
The time it takes for the magnetization to return to thermal equilibrium, M0, is also a function of two basic, and extremely important, parameters: spin-lattice and spin-spin relaxation times. Bloch is the first to incorporate the relaxation terms into Eqs 1.12.
(Bloch, Hansen et al. 1946) He finds that the interaction of the proton with the lattice modifies the changing longitudinal magnetization, while the interaction of the proton with the local fields of their spin neighbors accounts for the decay (i.e. dephasing) in transverse magnetization. The results are named, fittingly, the Bloch equations: Md z 0 MM z )( (1.14.a) x 1 sin( y 1 tBMtBM )cos dt T1
Md y M y (1.14.b) ( z 1 cos x BMtBM 0 ) dt T2
Md x M x (1.14.c) z 1 sin( y BMtBM 0 ) dt T2
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T1 is the spin-lattice relaxation constant and is defined as the time it takes for regrowth of longitudinal magnetization to reach 1-1/e ~ 63% of M0 after excitation by an RF pulse, and T2 is the spin-spin relaxation constant. It is equal to the time for the transverse magnetization to decay to 1/e the value it gained immediately after the end of an RF excitation pulse. When the RF pulse is turned off, the magnetization vector evolves according to the following equations:
/ Tt 1 (1.15.a) z 0 1( eMM )
/ Tt 2 (1.15.b) , , yxyx )0( eMM
* In practice T2 is replaced with T2 which takes into account the other local magnetic interactions besides that of the neighboring spins’ fields that can cause transverse magnetization dephasing, i.e. local field inhomogeneities.
1.6 From Signal Measurement Techniques to Imaging
We are now in a position to describe an essential NMR experiment: the free induction decay (FID) experiment. Imagine a bulk sample at thermal equilibrium with magnetization M0. An RF pulse, B1 of appropriate frequency, power, and duration is applied to the sample such that it tips the net magnetization into the transverse plane
(Figure 1.2).
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z
M(t)
y
B1 x
Figure 1.2 Magnetization nutation in rotating frame: The net magnetization vector is brought into the transverse plane by absorbing resonant RF energy. In the laboratory frame, its rapidly oscillating behavior can be spatially encoded and measured to produce an image.
Once the RF pulse ends, the transverse magnetization begins to decay and the longitudinal magnetization regrows according to equations (1.15), disregarding any diffusion, bulk flow, or magnetization transfer effects. In the laboratory reference frame, the magnetization vector carves a helical path of diminishing radius as it returns to the z axis. If, as is the case in practice, an RF antenna is positioned to receive the induced voltage from the rapidly changing magnetic flux, a signal containing information about the relative number of protons and the relaxation parameters of the sample is obtained.
Figure 1.3 illustrates the events outlined above, and serves as an introduction to pulse sequence diagrams that will be used further in the text.
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RF
ADC ON
Signal
Sampled Data ……………
Figure 1.3 Globally Induced FID: An example of a pulse sequence diagram. The horizontal axis represents time. After an RF pulse excites spins in a bulk sample, an analogue to digital convertor (ADC) captures the decaying signal as a series of voltage values in discretely sampled time points.
In this example of a globally induced FID, the signal results from the conglomerate effect of all the spins within some sample. The key to differentiating between signals from spin populations at various areas within the sample, i.e. to being able to image, is the addition of magnetic field gradients and RF pulses to the diagram in Fig. 3. Although there exist numerous types of pulse sequences, with newer ones being developed continuously, they all rely on the formation and sampling of echoes (Hahn 1950). Creating an echo is a method to refocus temporarily the FID signal. There are two ways to produce an echo.
One uses gradients and is named a gradient echo. The other applies RF pulses and is named a spin echo. Sequences based on gradient echoes are faster, however, spin echo sequences usually result in superior image quality. A diagram of a common spin echo sequence, the 90-180 pulsed sequence, is shown in Figure 1.4.
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π/2 π
RF
Signal
TE
Figure 1.4: The 90-180 Global Spin Echo: A spin echo FID is created by the application of a 90 degree excitation RF pulse followed by a 180 degree refocusing RF pulse. The center of the echo occurs at a time, TE, after the initial pulse where TE is equal to twice the time between the first and second RF pulses. ADC and sampled points are omitted from this sequence diagram for simplicity.
The echo in Figure 1.4 is created after the 180 degree pulse flips the spins about the axis into which they initially are nutated (in the rotational frame). Dephasing after the 90 degree pulse occurs because some spins precess faster than others, and so the magnitude of the net phase direction decreases as individual spin phase vectors begin to fan out.
Flipping the spins allows the slower precessing spins to “catch up” with the spins initially of higher frequency, since the refocusing pulse reverses the phase of the “slower”
(smaller phase angle) and “faster” (larger phase angle) spins. Thus the ensemble begins rephasing until some peak coherence is reached at which point the spins begin dephasing again. (One main reason for manipulating the spins this way is to acquire the data points that correspond to the negative and positive k space elements necessary for Fourier analysis). With the addition of slice selective, frequency encoding, and phase encoding
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gradients the 90-180 spin echo sequence in Figure 1.4 becomes a conventional single spin echo imaging sequence.
π/2 π
RF
Gs
Gφ
Gr
ON ADC TR
Figure 1.5 Spin Echo Imaging Pulse Diagram: A pulse sequence timing diagram illustrating the essential components of a spin echo imaging experiment: 90 and 180 degree RF pulses; slice, phase, and read out gradients; and ADC duration. The dotted line signifies where the sequence is repeated for each consecutive step of Gφ.
Figure 1.5 represents a conventional spin echo imaging pulse sequence. Slice selection is accomplished by simultaneously applying a small magnetic field gradient along the direction of the slice’s area vector and an RF pulse of the appropriate bandwidth, frequency, and shape. Since the RF energy couples to the nuclear spin when
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the resonance condition is satisfied, only those spins which precess within the range of the RF bandwidth are excited into the transverse plane.
B BW
0 z zGBz )()(
Figure 1.6: Slice Excitation: The application of a linear magnetic field gradient results in a uniform spread of frequencies as a function of position. An RF excitation pulse will excite spins in a position interval that corresponds to the bandwidth of the RF pulse, thus only a slice of spins is brought into the transverse plane. The thickness of the slice is adjusted, in principle, by changing the RF bandwidth and/or the magnetic gradient.
The slice gradient induces differing amounts of phase for spins at different positions along the thickness of the slice, thereby decreasing the net signal. Therefore, a refocusing slice gradient is placed after the slice dephasing gradient. To a fair approximation, the spins are tipped instantaneously into the transverse plane at the center of the RF pulse, so dephasing of excited spins occurs only for the second half of the RF duration. For this reason, the refocusing gradient lobe is half that of the dephasing lobe in Figure 5. The bipolar slice gradient pair is repeated during the second 180 degree RF pulse to ensure that only spins within the desired slice are refocused.
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During acquisition, when the ADC is turned on, the read out gradient, Gr, is applied, for example, along the x direction. The FID now contains frequency information from all the spins along x, with each frequency representing a position along x—the spins are spatially encoded as a function of frequency. However, just as in the slice selection case, the readout gradient dephases the spins along x. Therefore, a predephasing x gradient is placed so that spins are maximally rephased at the center of the echo which is made to coincide with the center of the acquisition window. In Figure 1.5 this gradient occurs before the RF refocusing pulse, although in principle it could occur, with opposite polarity, after the refocusing pulse. This would result in a longer TE, which is often undesirable since it reduces signal strength due to intrinsic T2 decay.
In order to distinguish spins along the third dimension, y in the present notation, a gradient along y is turned on and off prior to when the ADC acquires the signal, imparting different phase angles to spins located at different y positions. The FID spectrum now contains both frequency (encoding spins along the x direction) and phase angle (encoding spins along the y direction) information. This process is repeated
(represented in Figure 1.5 by the dotted line) Nφ times, with each repetition corresponding to a step in the phase encode direction by adjusting the phase encode gradient magnitude.
The phase encode gradients could have been placed after the refocusing RF pulse and prior to the acquisition window. As with the read dephase gradient, it is shown here to occur earlier to minimize TE.
At this point we are missing one piece of the puzzle as to what makes imaging possible from what essentially is a series of oscillating voltage measurements arising from the changing magnetic flux of ensembles of nuclear spins. It has been shown how
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to encode spatial information from a series of FID signals by slice select, phase encode, and readout gradients, but this information is only useful for making images if there is a way to decode it. The last step towards understanding how an MR image is formed comes from inspecting the equation for the signal intensity. The observed signal from
Figure 5 takes the form:
t t (1.16) ))((exp))((exp),()( dxdyydGixdGiyxts x y ,0yx 0
With the definition of the k vector:
t (1.17) )( )( dGtk 2 0
Eq. 1.16 simplifies to:
(1.18) ),()( eyxks x y ytkxtki ])()([2 dxdy , yx
Eq. 1.18 is an extremely important result. It illustrates that s(k) and ρ(x,y) are a Fourier transform pair. In other words, although what is measured directly in MRI are the signal intensities of a spatially encoded FID, a proton density weighted image can be reconstructed by taking the inverse Fourier transformation:
(1.19) )(),( eksyx x y ytkxtki ])()([2 dkdk yx kk yx
In biological systems, the most prevalent source of hydrogen protons is found in water. For this reason, MRI is the image modality of choice when it comes to soft tissue contrast, since the water molecules are found with varying density between tissue types.
Additional contrasts between tissues in MR images are made by adjusting pulse sequence parameters to be sensitive to differences in the spin-spin and spin-lattice constants which
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often vary more greatly between certain tissues than the water density. However, the
MRI signal is not just a function of proton density, spin-spin, and spin-lattice relaxation parameters, although these three parameters do provide various and important imaging contrast. Amongst other parameters, the self-diffusion of water molecules influences the
MRI signal. Probing the diffusion characteristics of water in biological tissue and understanding what insight these characteristics can provide in addition to more traditional imaging modalities is the subject of this thesis.
In 1956 HC Torrey expanded the Bloch equations to include the diffusion effects
(Torrey 1956). The modification takes the form:
M x M x BM )( x MMD xx 0 )( t T2
M y M y BM )( y MMD yy 0 )( t T2
M z 0 MM z BM )( z MMD zz 0 )( t T1
Where D is the diffusion coefficient and the differentials refer to a specific point in space and so are partial. These equations are called the Torrey-Bloch equations. Just as pulse sequences can be designed to measure T1 and T2, and therefore create images containing information additional to proton densities, so too can pulse sequences be designed to measure D. Not only is this capability an enormous advantage of NMR in terms of accurately measuring diffusion (it is a difficult measurement in general), but it also is an advantage for medical imaging in terms of assessing pathology in a clinical setting. The second chapter outlines the basic theoretical considerations for an understanding of diffusion contrast magnetic resonance imaging.
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Chapter Two
Diffusion Theory and Application to MRI
Chapter One demonstrates the MRI signal’s sensitivity to proton density and relaxation effects, and it ends acknowledging that the signal intensity is a function of other variables also, i.e. the self- diffusion of moment bearing nuclei. The focus of this chapter is to develop the mathematical tools to understand how diffusion affects, and can be measured by, the MRI signal.
2.1 The Basic Equations: The Diffusion Equation, Fick’s Laws, and the Continuity equation
X =(i-1)a X =ia X =(i+1)a i-1 i i+1
Figure 2.1: Lattice Hopping. One dimensional lattice representing hopping sites.
Imagine a one dimensional, nearest neighbor, discrete random walk where a particle, initially situated at xi, has an equal probability of hopping one lattice spacing to the left or right. There are Ni such particles at site i, with a frequency of transition Γ.
The rate equation is then:
dN 1 1 (2.1) i NNN dt 2 i1 2 i1 i
For reasons that will be made clear, it is convenient to define two functions:
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1 (2.2a) J NN )( i 2/1 2 ii 1
1 (2.2b) J NN )( i 2/1 2 1 ii
The J i 2/1 functions represent the net flux between nearest neighbors. Upon substituting these functions, Eq. 2.1 can be rewritten as:
dN (2.3) i ( JJ ) dt i i 2/12/1
So far we have dealt with discrete functions. The exercise that follows will lead to a derivation of Fick’s first two laws and a continuity equation. But first, we must interpolate the discrete distribution Ni by a continuous function so we can use legitimately properties of calculus in the derivation. Hence, the continuous and differentiable function, ˆ t)(x,N is defined. Its only requirement is that
ˆ (2.4) i t),(xN i (t)N
while it can take any value when xx i .
We can now perform a Taylor series expansion on ˆ t)(x,N about xi. For nearest neighbors, the expansion is expressed as:
Nˆ 1 2 Nˆ (2.5) ˆ )( ˆ )( axNxN a 2 aO 3 )( i1 i x 2 x 2 xi xi which, because of Eq. 2.4, can be written in terms of the discrete counterpart:
N 1 2 N (2.5) aNN a 2 aO 3 )( 1 ii x 2 x 2 xi xi
Substituting the expansion into Eq. 2.1 yields
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N 1 2 N (2.6) a 2 aO 4 )( t 2 x 2 xi xi
Notice the O(a3) vanish, so truncating all but the first term is a fair approximation. If we also assume the equation valid at all points in x, not just discrete sites, then we replace a possibly infinite coupled system of difference-differential equations, Eq. 2.1, with a single partial differential equation for N. It is important to note that Eq. 2.6 is valid for any time evolving property of the system, for example, the probability for any given particle to be found at an arbitrary distance away from an initial position after an arbitrary time has elapsed, i.e., the probability distribution function.
Let us try to extend an analogue of the above derivation to the flux functions. We begin by substituting Eq. 2.5 into Eqs. 2.2
1 N 1 2 N (2.7) J a a 2 aO 3 )( i 2/1 2 x 2 x 2 xi
However, if we were to insert Eq. 2.7 into Eq 2.3 in analogy to the step taken to achieve
Eq. 2.6, we would get
N (2.8) aO 2 )(0 t xi which means we do not have a continuous analogue for Eq. 2.3. It has been shown that if a continuous flux function is defined as
1 N (2.9) ( ), atxJ 2 x
then expanding ( i JJ i 2/12/1 ) about site xi and continuing steps similar to the derivation of Eq. (2.6) leads to the desirable solution. (Ghez 2001) Taking the partial with respect to position of Eq. 2.9:
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1 2 N (2.10) ),( atxJ x 2 x2 and substituting the left hand side of Eq.2.10 into the right hand side of Eq. 2.6 gives
N J (2.11) a aO 4 )( t x
The last step before attaining the basic equations for diffusive processes is to declare the following two definitions
Nˆ (2.12) C a
1 (2.13) aD 2 2
Here C is the concentration per unit cell, and D is the diffusion constant. It is now obvious that Eqs. 2.9-2.13 lead directly to:
C (2.14) (), DtxJ x
C J (2.15) t x
C 2C (2.16) D t x2
Eqs. 2.14 and 2.16 are Fick’s first and second laws. Eq. 2.15 is the continuity equation.
Fick’s second law is also known as the diffusion equation. A very important caveat of the diffusion equation is that it applies not only to C, the concentration gradient, but also to the probability distribution function. Also, although these results are obtained from a one dimensional example with only nearest neighbor transitions; they can be generalized, somewhat tediously, to three dimensions and further hopping transitions while yielding the same results (Eqs. 2.14-2.16).
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2.2 Diffusion Weighted Pulse Sequences
In one of the seminal papers in NMR history, Edwin Hahn outlines the underlying principles of the spin echo experiment, including an explanation of the reduction in the spin echo signal intensity (Hahn 1950). Aside from providing an accurate method for measuring T1 and T2 from a series of echo amplitudes, he also details the effect of diffusion on the NMR signal. Building on his results, Carr and Purcell show how
Hahn’s spin echo experiment can be used to measure diffusion if a constant gradient is applied during the entire experiment (Carr and Purcell 1954). If the gradient area before and after the 180 degree refocusing pulse is equal and the spins stationary, the gradient should have no effect on the signal amplitude (aside from, of course, gradient field inhomogeneities). However, if spins diffuse during the experiment, the phase change will not be equal and opposite before and after the 180 pulse. The additional dephasing attributed to diffusion is calculated for spin echo experiments, and a method to measure very accurately the diffusion coefficient from signal intensity losses is described. Since its inception diffusion NMR has remained the “gold standard” for measurements of diffusion coefficients, with a roughly 1% error margin.
Stejskal and Tanner take the experiment developed by Carr and Purcell further by using two diffusion sensing gradients, one before and one after the refocusing pulse, rather than a single constant gradient (Stejskal and Tanner 1964). This modification leads to a distinction between encoding time and the diffusion time which gives scientists the ability to adjust timing parameters and thus explore diffusion at various length scales more accurately. The experiment is named the pulsed gradient spin echo (PGSE)
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sequence, and the fundamental equation relating the signal intensities of PGSE to the diffusion coefficient is named, aptly, the Stejskal-Tanner equation:
GS ),,( 222 (2.17) ln G D S )0( 3 where the ratio in the logarithm is that of the diffusion weighted signal to the non diffusion weighted signal, γ is the gyromagnetic ratio, G is the diffusion gradient strength, δ is the duration the diffusion gradient is on (encoding time), Δ is the time separation between diffusion gradients (diffusion time), and D is the diffusion constant.
The terms multiplying D are commonly set to “b.” The following derives Eq. 2.17.
Figure 2.2: Pulsed gradient spin echo Stejskal-Tanner experiment (Thomas et al
2000)
Figure 2.2 shows the classic PGSE Stejskal-Tanner experiment neglecting imaging gradients. For simplicity, imagine a system of only 2 spins, originally separate by distance a. Immediately after the 90 degree pulse, the spins are in phase (i). The first diffusing gradient imparts a phase difference between spins as a function of their spatial
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separation (ii). Let the gradient point in direction z. Then the general expression for a spin’s phase evolution is:
(2.18) GzGzdt 0
Assuming the gradient duration is much shorter than the gradient separation (δ<<Δ), to the extent that translation due to diffusion can be considered zero during δ, then the phase dispersion after the first gradient is:
aGaG )( (2.19) aG A 12 2 2
where 2,1 is the phase of spin 1,2 relative to the initial phase prior to the diffusion gradient. A 180 degree pulse followed by a second and equal diffusion gradient would bring the two spins completely back into phase at time TE (Figure 2.2) in the absence of motion. However, the experiment is designed such that the interlude, Δ, is long enough to permit significant diffusion displacements. During this time, the spins move a small
distance denoted in Figure 2.2 by 2,1 . The phase dispersion after the second diffusion gradient is then:
' ' a a (2.20) B 2 1 G 2 G 1 aG 12 )( 2 2
The net dephasing during the entire experiment is:
(2.21) AB G 12 )(
Obviously, the signal is not dephased by the bipolar gradient pair unless the molecules move during the time interval between gradients. In diffusion MR, it is the sum of
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several magnetic moments which is measured, each having its own motion history. The magnetization loss due to diffusion of these many moments is expressed by:
N M i )( (2.22) e j M 0 j1 where N is the number of molecules and Φj is the phase of the jth molecule relative to the phase prior to the first diffusion gradient being turned on. If we know the net phase distribution, then the sum in Eq. 2.22 can be evaluated. Recall that Fick’s second law, the diffusion equation, applies not just for the concentration gradient, but also to the probability distribution function (PDF). Using this knowledge, we can write:
tP 2 tP ),,(),,( (2.23) 12 D 12 t x 2
Assuming the PDF is Gaussian, the solution to Eq. 2.23 is:
2 1 21 )( (2.24) P 12 ),,( exp D)4( 3 4D
P 12 ),,( dε2 is the conditional probability of finding a spin initially situated at ε1 between ε2 and dε2 after a time, Δ. Eq. 2.22 can be rewritten to include this information:
M Gi 21 )( 12 ),,( ddPe (2.25) 21 M 0
Combining Eqs. 2.24 and 2.25 and carrying out the integral yields:
M 2 DG )3/()( (2.26) e M 0
Noting that the magnetization is directly proportional to the signal strength, this is equivalent to the Stjeskal-Tanner equation 2.17
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2.3 The Diffusion Metrics: ADC, FA, MD, λax, and λrad
The terms multiplying D in Eq. 2.26 are commonly set equal to “b.” Adjusting its value allows the experimenter to explore diffusion at different length scales. Linear fits of the log of the signal data versus “b” yield D, usually referred to as the apparent diffusion constant (ADC). The term “apparent” is added to signify that the diffusion coefficient that is calculated is less than that for free water and varies according to location.
If the diffusion is anisotropic, then Eq. 2.17 has to be rewritten in matrix form:
3 3 (2.27) bS )( ln Db ijij S )0( i 1 j 1
D is now a 3x3, second order tensor; it is symmetric with six independent elements, so signal intensities from at least 6 different b weighted gradient directions, in addition to one origin reference, b=0, are needed to solve for it. Diagonalizing the diffusion tensor yields 3 eigenvalues and eigenvectors. They represent the magnitude of diffusion along each of the 3 orthogonal directions.
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Figure 2.3: Diffusion ellipsoid. The first eigenvector represents the direction of greatest diffusion mobility, while the second and third represent the diffusion in descending order and orthogonal to the first eigenvector.
Figure 2.3 illustrates the information contained within one voxel of a diffusion tensor image (DTI). The first eigenvector is often named the axial diffusivity. Its orientation depends on the direction of greatest diffusion, and so will likely vary from voxel to voxel. The average of the second and third eigenvalues is called the radial diffusivity. The highly anisotropic organization of brain axons gives rise to large differences in axial and radial diffusivity, which are explitied in DTMR neuroimaging.
Furthermore, as will be discussed in later chapters, these values reflect the status of underlying cellular architecture. If the architecture is disrupted, for example in the case of cerebral disease, that disruption may be measured directly by changes in the diffusivities. Another important diffusion metric which is used often to characterize the degree of anisotropy of proton diffusion about cellular structures is the fractional anisotropy (FA) measure:
2 2 2 2.28 21 32 13 FA 222 2 321 31
Possible values of FA range from zero to one. Zero implies the three eigenvectors are equal, representing completely isotropic diffusion. At the other extreme, an FA value of one represents completely anisotropic diffusion. In analogy to the ADC, there is the mean diffusivity (MD), which is simply the average of the three eigenvalues. Having an array of diffusion measures makes DTMR a robust imaging technique. However, an exact understanding of what these measures mean in the clinical setting in terms of tissue health is still unclear. Chapters 4-6 discuss experiments designed to clarify this uncertainty. First, the hardware and optimization of experimental methods are presented in the following chapter.
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Chapter Three Imaging Hardware and Optimization
3.1 Scanner Specifications
All MRI experiments in this thesis are performed on a 7.05 Tesla Bruker Biospec
70/30 Avance running Paravision 4.0 software. The Bruker is equipped with several state of the art hardware systems. It houses two NbTi superconducting coils—one to produce the main magnetic field, and the second to reduce the outside stray magnetic field. The superconducting system is contained in a cryostat with liquid helium as the coolant.
Aside from the superconducting coils, the Bruker BGA12-S has electromagnets to produce field gradients in three dimensions. In addition to the coils that control the magnetic field gradient in the three dimensions necessary for gaining slice, read, and phase information for imaging, a set of nine “shim” coils are embedded in the system.
Their purpose is to correct for inhomogeneities to the main field caused by the introduction of the sample’s induced magnetization. Table 3.1 lists the specifications for the gradient and shim system. Figure 3.1 depicts the magnetic.
BGA12-S
Outer diameter (mm) 206 Inner diameter (mm) 116 Strength* (mT/m) at Imax 660 Slew rate* (T/m/s) at Umax 4570 Gradient linearity/DSV (+/- %/mm) 4/80
Number of RT Shims 9 Max. cont. gradient all axis (mT/m) 230 Max. cont. gradient one axis (mT/m) 180 Umax (V)/Imax (A) 500/300
Table 3.1: Gradient imaging and shim system specifications.
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Figure 3.1: 7T Bruker Avance magnet. The magnet is enclosed in an RF shielded room to minimize noise from outside RF electromagnetic fields.
Radio frequency (RF) coils are used for signal excitation and reception, and connect to a set of amplifiers that adjust transmit power levels for RF pulse shape and duration via a digital frequency synthesizer, as well as amplify the minute voltage signals received from the sample to voltage levels suitable for the analogue to digital convertor (ADC).
According to the parameters set by the particular pulse sequence program being executed, the computer sends commands to the frequency, timing, gradient, and receiver control units in the acquisition processor to control and measure the magnetic gradient field dynamics. Simultaneously, it sends commands to the transmitter array which controls the
RF excitation pulses. It also receives input from the ADC, performs discrete Fourier
34
transforms on the data, and organizes the information into the final image files. The block diagram in Figure 3.2 illustrates how these subsystems are integrated into the
Bruker 7.05 Tesla Avance system.
Figure 3.2: Bruker integrated components. Schematic illustrating all hardware components exterior to magnet and the chain of command that takes user input and provides output in the form of image data (Courtesy of Bruker, Inc.).
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3.2 RF Coils: Design, SNR, and B1 Homogeneity
Two RF coils are used for signal excitation and reception in the experiments
(Chapters 4-6). The first coil is a slightly larger, single-turn-solenoid (STS) (Figure 3.3).
It has a diameter of 25 mm and length of 30 mm. The STS transceiver consists of a volume coil—two sections of 50 micron thick copper sheet connected by evenly distributed tuning capacitors inductively coupled to a matching circuit—a loop of 16 gauge wire and 25 mm in diameter connected to variable capacitors to maximize the coupling efficiency. The volume coil transmits magnetic energy to the sample for excitation, receives energy from the sample, and transfers this energy to the matching circuitry. Its signal and contrast to noise characteristics, and B1 field homogeneity are described in great detail elsewhere (DiFrancesco et al, 2008).
Figure 3.3: The STS RF coil. The fixed capacitors can be seen joining the two halves of the volume coil. There is also a variable balancing capacitor on top of the volume coil.
The two other variable capacitors to the right match the loop’s impedance to the loaded volume coil and input impedance of the transmitter/receiver.
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The second coil is a smaller, solenoid coil. It consists of 14 gauge copper wire, wound 5 times about an inner diameter of 14 mm, with a winding spacing of 4 mm, and length 21 mm (Figure 3.4). Signal to noise (SNR) measurements using a multi-spin- multi-echo pulse sequence with a slice thickness of 1 mm, 200 micron in plane resolution, TE=15ms, TR=1000, and FOV=2.56 cm by 2.56 cm yield an SNR value of
193 from a sample of water doped with Cu2SO4.
Figure 3.4: The solenoid coil. The solenoid coil has one fixed capacitor placed in the center of the windings and variable capacitors to match and tune the coil. The geometry of the solenoid coil provides greater SNR, however the field is less uniform than the STS.
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3.3 Optimization of Pulsed Gradient Spin Echo Diffusion Imaging Sequence
During a diffusion imaging experiment, the experimenter has control over several imaging parameters, these include: diffusion time (Δ), diffusion gradient duration (δ), and the number and direction of diffusion gradients. Ideally δ << Δ so that all appreciable diffusion occurs when the diffusion gradients are turned off, and therefore the assumption leading to Eq. 2.19 is satisfied. In practice, δ must be sufficiently long to allow the gradients to ramp up to their maximum value, hold that value long enough to obtain the desired b value (which is also dependent on Δ), and ramp back down to zero gradient strength. The minimum allowable time for the S116 gradients on the Bruker to ramp up and down is 0.4 ms (0.2 ms each way). On the other hand, to achieve practical b-values with such a short δ would require increasing Δ which would in turn increase TE to a point where the majority of the signal is lost to T2 decay. Therefore, a compromise must be met which optimizes these three timing parameters.
Likewise, choosing the number and direction of diffusion gradients forces one to compromise and optimize. Although six uniform diffusion gradients directions are needed to fill the six independent elements in the diffusion tensor, sampling more directions results in a better fit, theoretically increases SNR, and reduces directional biases that may arise from eddy currents, hardware considerations, etc. (Le Bihan et al,
2001). However, there is debate concerning what the optimum number of directions is, and whether it is more advantageous to signal average to improve SNR than to increase the number of diffusion gradient directions. Investigations based on empirical studies,
Monte Carlo simulations and theoretical analysis provide different answers as to what strategy to use in selecting the number of diffusion encoding gradient directions. The
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literature reports a range from 6-30 directions necessary for obtaining robust estimations of the diffusion tensor (Ni, H. et al, 2006; Hasan et al, 2001; Jones et al, 2004;
Poonawalla et al, 2004). Each additional direction increases scan time by a factor of TR x NΦ for 2D imaging and by a factor of TR x NΦx x NΦy for 3D imaging. NΦ represents the number of phase encoding lines of k space orthogonal to the read and slice directions, and NΦx and NΦy represent the number of phase encoding lines of k space in the two directions orthogonal to the read gradient direction. In agreement with previous empirical studies, no appreciable advantage is observed in using more than six directions, especially considering the extra scan time more directions incur (Ni et al, 2005; Hasan et al, 2001). This is particularly true of the standard spin echo sequence which already suffers from long acquisition times, but is less prone to artifacts from sequences like EPI.
For the experiments in the following sections, we employ the timing parameters that optimize the SNR in terms of reduced TE for a specific b value while minimizing δ.
Empirically, these are found to be δ = 4 milliseconds and Δ = 12 milliseconds. 12 milliseconds diffusing time is chosen since it corresponds to a root mean square displacement of approximately 10 microns, which is on the order of the scale of cellular compartments in the central nervous system. In agreement with the previous empirical results of Ni et al and Hasan et al, we conclude that six directions are not only time efficient but also result in insignificant differences in FA and MD (as compared to 15 directions). We use a direction scheme for the six diffusion directions based on an electrostatic repulsion model (Jones et al, 1999). Prior to using these parameters in our studies (Chapters 4-6), experiments to test the image quality based on the optimized parameters are conducted. Three imaging phantoms are used. The first (Figure 3.5) is an
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inorganic sample consisting of an array of glass capillaries bound by a layer of heat shrink surrounded by foam, all of which is immersed in CSF mimicking fluid. The second is a section of celery stalk, and the third is a fixed ex vivo mouse brain preserved in phosphate buffered saline solution (Figure 3.6, 3.7). Finally, a live mouse is imaged
(Figure 3.8). Images in Figures 3.5, 3.6, and 3.8 are obtained using the STS coil, while images in Figure 3.7 are obtained using the solenoid coil.
TE/TR=17/1500 TE/TR=20/1000 B=400 B=800 Res=156x156x2000 Res=156x156x2000 Averages=4 Averages=4 Tacq=3hrs Tacq=2hrs
Figure 3.5: Anisotropic phantom diffusion images. A phantom consisting of glass capillaries bundled in heat shrink, surrounded by foam and immersed in CSF mimicking fluid is used to test the DTMR imaging sequence. Two different sets of TE, TR, and b- values produce very similar images.
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TE/TR=18.7/500 B=500 Res=156x156x1000 Averages=1 Tacq=15 MIN!
Figure 3.6: DTMR image of a celery phantom. The purpose of this experiment is to find minimum acquisition time for acceptable image quality.
TE/TR=22/1000 Ex Vivo Mouse Brain B=1200 Res=106x106x500/327 ax/sag Averages=4 Tacq=2hrs
Figure 3.7: Ex vivo mouse brain. Using the solenoid coil and an ex vivo mouse brain results in a high filling factor and therefore provides a significant increase in signal to noise. These images represent a reasonable limit in resolution for 2D DTMR that produce high quality images (106 x 106 x 500/327 μm3). Increasing the in plane
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resolution further introduces B1 inhomogeneity artifacts, while decreasing the slice thickness introduces significant noise.
In Vivo Mouse
TE/TR=28/2000 B=100, 800 Res=150x150x500 Averages=3 Tacq=2hrs 45min
Figure 3.8: In Vivo mouse brain. Preliminary in vivo results: the imaging parameters from these images are further optimized in the results sections of Chapters 4-6.
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3.4 Diffusion Weighted Fast Spin Echo and GRASE Pulse Program Development
The pulsed gradient spin echo diffusion weighted experiment is capable of producing high quality, artifact-free images at the expense of long scan times. To reduce scan time, one must either sacrifice resolution or implement different pulse sequence methods. In this section, efforts to acquire diffusion data using a fast spin echo (RARE) and combined gradient recalled and spin echo (GRASE) pulse sequences are described.
Figure 3.9: Diffusion weighted fast spin echo. This pulse sequence acquires multiple lines of k space from echoes produced by repetitively refocusing pulses within each TR.
The large blue bars represent the diffusion sensitizing gradients. The dotted line indicates the loop structure in the pulse sequence program. It is within this loop that multiple echoes at different phase encode steps are collected. The loop structures
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responsible for incrementing the diffusion gradient direction table, the b values, and the slice location are omitted for simplicity.
Adding diffusion gradients to a fast spin echo sequence is not trivial. It is an active area of research, and is not yet used in the clinical setting. Indeed, few groups publish diffusion imaging based on this sequence. The addition of diffusion weighting gradients introduces inconsistent phase errors and stimulated echoes. Different techniques have been developed to address these issues (Aslop, 1997; Schick, 1997;
Williams et al, 1999; Mori et al, 1998). Many of these techniques employ complicated methods which require acquiring additional information to correct for phase artifacts— thereby increasing the scan time that should be saved using multiple echoes. A fast spin echo sequence based on Figure 3.9 is programmed in the ParaVision 4.0 pulse programming environment. Images acquired on the Bruker system using this relatively simple flavor of fast spin echo diffusion imaging are shown in Figures 3.9-3.12. The sequence employs large spoiler gradients to destroy (dephase) the stimulated echo so that it does not appear in the acquisition window.
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A B C D
E F G H
I J K L
M N OP
Figure 3.10: Water phantom results from fast spin echo diffusion sequence. A) is the b0 image, B)-G) are diffusion weighted images from six different directions. H)-N) are the corresponding k-space data for A)-G). O) is the FA map, and P) is the tensor trace image. Relevant scan parameters are: number of echo excitations = 2, b = 200 s/mm2,
TE/TR=24/1000 ms, resolution = 234 μm in plane, and slice thickness = 2 mm.
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A B
C D
Figure 3.11 Three eigenvalues and directionally encoded color (DEC) map calculated from images in Figure 3.10. A), B), and C) represent eigenvalues 1, 2, and
3. D) is the DEC map. Interestingly, whereas eigenvalue 1 (A)) should represent the direction of greatest diffusion, it is the least bright.
A B C D
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A B C D
E F G H
I J K L
M N O P
Figure 3.12: Diffusion weighted fast spin echo data from a glass capillary phantom.
A) is the b0 image, B)-G) are diffusion weighted images from six different directions. H)-
N) are the corresponding k-space data for A)-G). O) is the FA map, and P) is the tensor trace image. Relevant scan parameters are: number of echo excitations = 2, b = 200 s/mm2, TE/TR=24/1000 ms, resolution = 234 μm in plane, and slice thickness = 2 mm.
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A B
C D
Figure 3.13: Three eigenvalues and DEC calculated from images in Figure 3.12. A),
B), and C) represent eigenvalues 1, 2, and 3. D) is the directionally encoded color
(DEC) map. Interestingly, whereas eigenvalue 1(A)) should represent the direction of greatest diffusion, it is the least bright.
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Figure 3.14: GRASE diffusion sequence. A more complicated extension of the diffusion weighted fast spin echo, this sequence employs gradient recalled echoes in addition to the RF spin echoes. Furthermore, sinusoidal gradients (to minimize eddy currents) and navigator echoes are used (Courtesy of Susumu Mori).
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A B
Figure 3.15: GRASE diffusion imaging of water phantom. A) Reconstructed b0 image shows severe artifacts. B) Apparently, there are multiple echoes being collected within one acquisition window which seem to correspond to the three echoes in the inset in
Figure 3.12.
Both the fast spin echo and GRASE diffusion pulse sequences are prone to severe artifacts. Although progress is made to reduce them, the artifacts persist and these projects are abandoned in favor of the conventional spin echo sequence. Possible areas of improvement for fast spin echo and GRASE diffusion imaging are discussed in the future directions section of Chapter 7.
3.5 Applications of DTMR imaging
Having discussed the theoretical background to magnetic resonance and diffusion tensor magnetic resonance imaging, as well as the practical considerations for producing image data, one may ask: “for what purpose(s) is this imaging technique used?” Since its invention in the middle 1990s (Basser, Mattiello et al. 1994) the answer to this
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question continues to grow as the technique continues to improve. From a materials science perspective, DTMR provides useful information in characterizing porous substances. In general, diffusion measurements are extremely difficult, and until the advent of NMR, were impossible to measure non-destructively and non-perturbatively.
From a clinical perspective, DTMR imaging provides a unique window into cellular structures which is not possible with other imaging techniques. DTMR is applied to neuropsychiatric applications such as schizophrenia, bi-polar disease, alcoholism, geriatric depression; developmental studies of neural synoptic connectivity; and other neurological disorders such as multiple sclerosis, hydrocephalus, stroke, and traumatic brain injury.
With approximately 100 billion neurons connected by a series of axonal pathways, the neural network which comprises the human brain is arguably the most complicated of organs, and surely the least understood. DTMR remains one of the most powerful tools for exploring these synaptic connections. Recently, DTMR is applied to organs other than the brain, where muscle orientation, not nerve fiber orientation, provides the anisotropic contrast. Despite the organ of interest, DTMR is a difficult imaging technique to perform. This is because it inherently suffers from low signal to noise ratios (DTMR measures diffusion indirectly by measuring signal attenuation) and long acquisition times (many images are required to calculate the diffusion metrics).
Therefore collecting high resolution and high SNR images in a timely fashion becomes a challenging task, above and beyond the normal challenge for doing so in traditional MR.
The goals of the following three chapters are to surmount these challenges and collect high resolution images from disease animal models, provide robust DTMR data,
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compliment this data with a series of histological assays, and finally to provide insight into what the DTMR metrics reflect on the cellular scale from the analyses.
The following chapter contains results from the first set of experiments aimed at accomplishing some of these goals—experiments which apply high resolution DTMR imaging to a neonatal model for hydrocephalus. The work presented results from a productive collaboration between Dr. James P McAllister and Kelley Deren from the
University of Utah, Department of Bioengineering, Dr. Francesco Mangano from
Cincinnati Children’s Hospital, Department of Neurosurgery and Pediatrics, and Dr.
Weihong Yuan from Cincinnati Children’s Hospital, Imaging Research Center. More information including histological assays and correlation analysis can be found in Yuan et al, 2010.
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Chapter Four
Quantification of DTMR Metrics in a Murine Model of Hydrocephalus (HCP)
4.1 Abstract
DTMR data is collected from a sample of 8 rats from 1 litter (5 rats with hydrocephalus and 3 controls) between postnatal days 8 (P8) and P10. Significant differences between populations from the DTMR data are found in the corpus callosum, external capsule, and internal capsule, but not in the cerebral cortex. This study demonstrates the feasibility of DTMR imaging of neonatal rat models of hydrocephalus.
Further research is required to correlate these findings to their causes, i.e. stretching, shearing, and compression of tissue, partial volume effects, demyelination, tissue scarring, etc.
4.2 Background
Affecting nearly 700,000 Americans, HCP occurs at all ages, can be congenital or acquired, and incurs neurological and motor skill deficits if left untreated. It is a condition characterized by abnormally large amounts of cerebrospinal fluid (CSF) collecting in, and enlarging, the ventricles. This results in an elevation of intra-cranial pressure and a distortion of normal brain anatomy. The effect of HCP on the developing brain often delays behavioral and cognitive abilities. Shunt surgery to redirect excessive
CSF out of the hydrocephalic brain is one of the most common types of neurosurgery in the clinical pediatric setting (Hirsch, 1992). Despite the prevalence of HCP, the pathophysiology associated with it remains unclear.
DTMR is applied to clinical studies of HCP to investigate the mechanisms of injuries that cause poor behavioral and cognitive performance in HCP patients. Results
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in FA measurements from these studies are mixed. Several studies reveal an increase in
FA in the internal capsule and a decrease in FA in the genu of the corpus callosum in patients with HCP as compared to controls (Assaf 2006, Yuan 2009, and Hattingen
2010). A similar investigation discovers only decreases in WM FA values of HCP children relative to controls (Hasan 2008). In that study, four WM tracts are chosen based on their association with cognitive functions typically impaired in HCP cases: speech and language, visuospatial skills, attention, and verbal and visual memory.
Generally, increases in FA are attributed to compression of the WM tracts, while decreases in FA due to increases in transverse diffusivity are explained as disintegration of myelin sheaths enclosing the WM tracts. However, without histology to back these claims, inferences as to the cellular environment reflected by diffusivity metrics are questionable.
Few diffusion MRI animal studies are performed to assist interpretation of the diffusivity abnormalities found in the clinical setting, and all of the previous diffusion studies are limited imaging to diffusion weighting which yields scalar ADC values without the full, directional information provided by DTMR. For example, one investigation measures ADC in gray matter and observes ADC in the white matter
(corpus callosum) (Braun et al, 1998). The study concludes that edema occurs in the white, but not gray matter in their experimental HCP model. Although gray matter ADC values are calculated and found to be insignificantly different between groups, the assessment of white matter edema is based on qualitative analysis of the images only.
Collecting reliable diffusion data from the WM in HCP animal models is difficult.
A main reason for this is that the diameter of most fiber tracts is on the order of an
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imaging voxel. The problem is further exacerbated by the fact that WM is typically surrounded by enlarged HCP ventricles, i.e. water. The high density of very mobile protons partially occupying voxels that also contain WM leads to a large bias in the diffusion data. Nonetheless, a handful of groups report quantitative diffusion data of the
WM in HCP animal models. One study measures the ADC in the corpus callosum and finds it significantly larger in HCP than in controls (Tourdias et al 2009). The result has a strong correlation (R=0.85, p<0.0001) with periventruicular AQP4 expression, the primary channel for water flow across cell membranes, further reinforcing the relationship between increased ADC and edema.
Although no DTMR from HCP animal models are reported in the literature, one study does investigate diffusion as a function of direction in the gray and white matter
(Massicotte 2000). The study uses diffusion sensing gradients in two directions (left- right, up-down) to calculate ADCs in the cortex, striatum, and corpus callosum at 1 and 8 days post HCP induction. Significant differences with respect to controls in all regions and time points in the ADCs in the vertical direction (except white matter at 1 day post induction) are found. In the horizontal direction, significant differences only in the striatum and corpus callosum at eight days are discovered. Interestingly, there is a general pattern, most prominent in the corpus callosum, of reduction at 1 day followed by increase beyond control baseline of the ADC by 8 days.
The above studies motivate an investigation into the cellular changes that occur alongside these radiological findings, and suggest the usefulness of applying DTMR to
HCP animal models. Like their clinical counterparts, animal studies of hydrocephalus would benefit from quantitative DTMR. Unlike clinical studies, animal studies of
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hydrocephalus would have the added benefit of being able to definitively remark on the cellular structure of HCP WM through histological analysis. Interpretations of WM integrity from DTMR data could therefore be validated, not speculative. The objective of the material presented in this chapter is to provide imaging information in the first, to our knowledge, DTMR study of HCP in an animal model.
4.3 Methods
4.3.1 Animals Procedures
All animal procedures are in accordance with the guidelines of the Institutional
Animal Care and Use Committees at the Cincinnati Children’s Hospital Research
Foundation. Two groups of neonatal Sprague-Dawley rat pups from a single litter are used in the study. In the first group, hydrocephalus is induced in 8 rat pups at P2. The method to induce obstructive HCP is described in a previous publication (McAllister et al, 1985). First, animals are immersed in an ice bath for four minutes, which anesthetized the pups long enough for surgery. The pups are placed on a sterile sheet, and an incision is made at the base of the skull. A 100 microliter dose of kaolin solution is delivered to the cistern magna (a cavity in the brain through which CSF drains) by a 30 gauge needle.
The result is an accumulation of CSF in the ventricular cavities, and the eventual compression, shearing, and stretching of various white/gray matter structures. The kaolin solution consists of 250 mg powdered kaolin per ml of saline; the solution is sterilized by an autoclave along with all surgical tools. After kaolin injection, the skin is sutured, and the pups warmed until they gain consciousness at which point they return to their mother.
For the second group, two control rat pups receive a sham injection of saline solution,
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while a third is anesthetized but not injected. Three HCP animals die soon after the procedure and are not included in the results.
4.3.2 MRI/DTMR
MRI/DTMR scans are performed between P8 and P10 at Cincinnati Children’s
Hospital Medical Center (CCHMC). Prior to scanning, the rats are anesthetized with 4% isoflurane, placed in the supine position in the magnet, and sedated with a mixture of 1-
1.5% isoflurane and oxygen for the duration of the experiment. They are kept warm, at approximately 37°C, with circulating heated air. An inflatable pillow and/or foam material are used to secure the head inside the coil. The respiratory rate is monitored closely and maintained at 50 breaths/minute (±10/minute).
All MRI/DTMR imaging data are acquired on a 7T Bruker MRI scanner (Bruker
Biospec 70/30, Karlsruhe, Germany) equipped with an actively shielded 400 mT/m gradient set. The diameter of the gradient set is 20 cm. A custom-designed single-turn- solenoid (STS) RF coil is used in this study (Chapter 3).
All the DTMR images are acquired in the coronal plane with a 6-direction diffusion weighted multi-slice spin-echo imaging protocol: TR= 2500 ms, TE= 21 ms, 5 slices, slice thickness = 1.5 mm, inter-slice gap = 0.25 mm, b-value = 1200 s/mm2, diffusion gradient duration δ = 4 ms, and gradient separation Δ = 12 ms. The animals are scanned with an in-plane resolution of 200x200 μm with four different field of views
(FOV) between 16x16 mm and 25.6x25.6 mm. The time for acquisition ranges between
23:20 minutes to 37:20 minutes. Two of the rats are scanned at slightly different in-plane resolutions (resolution = 196x196 μm, TA = 26:50 min., and resolution = 200x225 μm
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TA = 23:20 min.). The reason for the discrepancy in resolution is human error for the
196x196 μm scan and time constraints for the 200x225 μm scan.
A whole brain T2 weighted 3D volume scan is obtained using a rapid acquisition with relaxation enhancement (RARE) sequence with the following parameters: TR=1000 ms; effective TE=70.56 ms; FOV=32x19.2x19.2 mm; acquisition matrix = 256x128x128; spatial resolution = 0.125x0.150x0.150 mm; scanning time = 17:04 min. The T2 weighted RARE anatomical images are used to assess the ventricle size and also as a reference for anatomical structures.
4.3.3 DTMR Data Processing and Analysis
Image reconstructions, post-processing, and ROI-based DTMR imaging parameter calculations are performed with the software DTIStudio 2.4 (Jiang et al, 2006).
The color-coded FA maps are used to identify regions of interest (ROI). DTMR imaging parameters are calculated and averaged for all voxels contained per ROI. On a voxel by voxel basis, the six elements (Dxx, Dyy, Dzz, Dxy, Dxz, and Dyz) are calculated and
diagonalized to compute the three eigenvalues (λ1, λ2, λ3) corresponding to the three eigenvectors in the diffusion tensor matrix. Mean diffusivity (MD) is calculated as the mean of the three eigenvalues. Fractional anisotropy (FA) is calculated using the
definition from Chapter 2. Following convention, λ1 is renamed the axial diffusivity, and the average of the second and third eigenvalues is labeled radial diffusivity. The ROIs for each subject are manually determined. The following ROIs are defined: corpus callosum (CC), internal capsule (IC), external capsule (EC), cortex (Cx).
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4.3.4 Statistical Analysis
Statistical analysis is performed Microsoft Excel. The unpaired Student’s t-Test is used to compare the DTMR imaging parameters between HCP rats and controls for respective ROIs in the brain.
4.4 Results
Sample MD, FA, and DEC images of the HCP and control are shown in Figure
4.1. Comparisons of the fractional anisotropy, mean diffusivity, and axial and radial diffusivities for regions of interest taken from the cerebral cortex, external capsule, corpus callosum, and internal capsule are illustrated in Figure 4.2. Statistical comparisons between HCP and control gray and white matter areas are presented in
Table 4.1, and they include the second and third eigenvalues of the diffusion tensor in addition to those metrics that appear in Figure 4.2. DTMR analysis shows no significant differences between groups in the grey matter of the cerebral cortex. However, in the white matter, several metrics are significantly different between groups in the external capsule and the corpus callosum. Specifically, the external capsule has increases in all three diffusion directions, resulting in an increased mean diffusivity. However, the overall fractional anisotropy is insignificantly altered. On the other hand, the corpus callosum does have a significantly lower fractional anisotropy as is evidenced in the decreased axial, and increased radial, diffusivity. Interestingly, for the internal capsule only the fractional anisotropy has significantly different values between groups.
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Saline Control Hydrocephalic
CX EC
IC
CC DEC FA MD Figure 4.1: HCP DTMR images. The HCP animals clearly show extreme enlargement of the ventricular space. The cortex is severely compressed. The cortex (CX) corpus callosum (CC), external capsule
(EC), and internal capsule (IC) are identifiable.
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Fractional Anisotropy Comparison
HYDRO NORMAL 0.6
0.5
0.4 FA FA 0.3
0.2
0.1
0.0 cortex external capsule corpus callosum internal capsule
Mean Diffusivity Comparison HYDRO NORMAL 0.0025
0.0020
0.0015 /sec) 2
0.0010 MD (mm MD
0.0005
0.0000 cortex external capsule corpus callosum internal capsule
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Axial Diffusivity Comparison HYDRO NORMAL 0.0030
0.0025
0.0020
/sec) 0.0015 2 (mm 1
0.0010
0.0005
0.0000 cortex external capsule corpus callosum internal capsule
Radial Diffusivity Comparison HYDRO NORMAL 0.0020
0.0016
0.0012 /sec) 2
0.0008 (mm r
0.0004
0.0000 cortex external capsule corpus callosum internal capsule
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Figure 4.2: DTMR metrics comparison between HCP and controls. Although the
DTMR values in the cortex do not differ significantly between groups, several white
matter tracts have significant changes.
FA MD L1 L2 L3 LRADIAL
cx 0.0695 0.0817 0.3018 0.1969 0.1054 0.3947 ec 0.1016 <0.0001 < 0.0001 0.0004 <.0001 <.0001 cc 0.0011 0.8239 0.003 0.0807 0.005 0.0779 ic 0.017 0.4281 0.2182 0.6318 0.7687 0.7787
Table 4.1: p-values for comparison of HCP DTMR metrics with controls. Although
the cortex (cx) shows no significant difference between groups, all white matter
structures measured do, with the external capsule (ec) having more pronounced
difference than the corpus callosum (cc) or the internal capsule (ic). N=3 for controls
and N=5 for HCP pups.
B
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Figure 4.3 Three dimensional T2 weighted fast spin echo images. A) and B) are taken from control animals at 8 and 15 days post-saline injection. C), D), and E) are taken from HCP animals at 4, 8, and 17 days post-kaolin injection. The ventricles enlarge at an accelerated rate.
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4.5 Discussion
This chapter presents data from the first, to our knowledge, DTMR application to a neonatal rat model of HCP. However, there are limitations to the methods in this study.
First, the imaging resolution of 0.25 by 0.25 by 1.5 mm3 is quite coarse compared to the average size of the white matter tracts investigated here. For example, the external capsule in the HCP animals stretches and thins to as little as 0.2 mm in diameter in some areas. Second, the procedure for inducing HCP in this study accelerates ventricle enlargement at an alarming rate (Figure 4.3). These two methodological limitations may explain some of our observations, or lack thereof.
Having too large an imaging resolution would increase the bias in data due to partial volume effects. In the case of the external capsule, which in the HCP animals is surrounded by CSF, this would result in an overall increase in diffusivity (Figure 4.1).
The large density of highly mobile protons in the CSF partially occupying the volume of an imaging voxel would have an appreciable effect on the diffusivity measurements.
Indeed, the mean diffusivity, axial diffusivity, and radial diffusivity for the external capsule is about twice that in HCP animals compared to controls.
The rapid rate of ventricular enlargement in this model may also explain the lack of observation of a change in gray matter DTMR values. Previous literature demonstrated that ADC values in the cortex first decrease, then return toward normal in the HCP brain (Braun et al, 1998). One possible explanation for this phenomenon is that the cortex is initially compressed; however, the skull reacts to the intracranial pressure it is subject to by expanding, thereby relieving the pressure which results in a renormalization of the gray matter ADC values. The significant expansion of the
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animal’s skulls prior to DTMR imaging in our study is evident in Figure 4.4, and may explain the insignificant change in cortical gray matter. Regardless of the causes of our observations, the experiments in this chapter demonstrate for the first time the feasibility, albeit technically difficult, of DTMR as applied to murine HCP models.
A possible solution to these limitations/technical difficulties would be to image animals sooner after HCP induction. The first limitation of imaging resolution may be circumvented since imaging them at a younger age and before their skulls expand would allow the use of smaller RF coils which provide superior signal to noise and filling factor.
The gain in SNR and reduced field of view could then be used to increase spatial resolution. Furthermore, imaging earlier after HCP induction would decrease the chance of partial volume effects since there would be less stretched and thinned white matter engulfed by CSF fluid to bias the data. Finally, imaging between 4 and 8 days post kaolin injection would preclude the significant skull expansion and may affect the diffusivity in the cortical gray matter (Figure 4.3).
Aside from the interpretations of the data presented above, several injury mechanisms have been proposed to account for changes in diffusion metrics. Recent studies show that axial and radial diffusion coefficients can potentially serve as differentiating biomarkers for axonal and myelin damage (Budde et al, 2007; Song et al,
2003; Song et al, 2005). Disintegration of the myelin sheaths allows water to diffuse more readily perpendicular to the axon, and thus leads to increased radial diffusivity. The formation of scarred tissue along the axon is one possible mechanism that would decrease the axial diffusivity. Perhaps the single most accurate way to validate or formulate interpretations of the DTMR data is collecting and comparing histological tissue data to
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DTMR data. The next chapter focuses on the use of histological staining to help explain
DTMR observations in a neonatal stroke model. The work in that chapter results from a collaboration between Dr. Chia-Yi Kuan, Dr. Dianer Yang, and Niza Nemkul from
Cincinnati Children’s Research Center, Department of Developmental Biology. This group provided the neonatal stroke model and performed the histological analysis. The investigation resulted in a publication where one can find additional information to that provided in Chapter 5 (Yang et al, 2009).
In conclusion, the benefit to HCP human patients from these animal studies lies in translating the knowledge gained in our experiments to a clinical setting by comparing the common characteristic changes in DTMR abnormalities in the context of the developing CNS. Better understanding of the tissue characteristics and mechanisms underlying DTMR data will undoubtedly lead to a more accurate interpretation of
DTMR, which in turn will lead to more effective treatment decisions in the pediatric patient population.
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Chapter Five
Comparison of Quantitative DTMR Imaging and Qualitative Histological Staining
in a Murine Model for Neonatal Hypoxia-Ischemia
5.1 Abstract
Quantitative DTMR imaging is a useful clinical tool for assessing the degree and localization of damage from neurovascular disease. However, it lacks the resolution to make definitive statements concerning what processes occur at the cellular level. In this study, quantitative MRI/DTMR and qualitative histological staining is applied to a murine model of neonatal cerebral hypoxia-ischemia (HI). T2 MRI detects edema in the gray matter. ADC values show a significant drop in the damaged cortical gray matter, and
FA values decrease significantly in the corpus callosum white matter. Qualitative histological staining suggests that tissue-type plasminogen activator (tPA) proteases cause a breakdown in the blood-brain-barrier that eventually lead to the formation of edema. Once the BBB becomes leaky, pathogens and foreign material penetrate the BBB and infiltrate the brain parenchyma, which signals antibodies to crowd the brain matter.
The increase in these micro sized obstacles may explain the increase in restricted diffusivity in the cortex, as measured by decreased ADC. Results from myelin basic protein and Nissl staining strongly suggest fragmentation of the myelin and axonal swelling as the cause in FA reduction.
In addition to determining the underlying cellular causes behind changes in
DTMR metrics in this specific model, another aim of the study is to validate the utility of
DTMR in measuring the treatment effectiveness of a novel drug for neonatal HI: plaminogen activator inhibitor-1 (PAI-1). Traditional adult HI drugs target matrix
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metalloproteases (MMP), a type of protease that degrades proteins in the extracellular matrix and appears soon after adult HI insult. However, in neonatal HI, the presence of
MMP occurs much later, after irreversible brain damage. This suggests that the biophysical mechanisms in neonatal HI differ from adult HI. We hypothesize that another protease, tissue-type plasminogen activator (tPA), which directly breaks down the BBB, is responsible for initiating brain damage and setting off a chain of events that releases MMP downstream of the ischemic cascade. To test this, a series of MRI and histological assays are performed on neonatal HI rats administered with PAI-1 and sham saline injections. Saline injected controls show the changes in T2, ADC, and FA as described in the above paragraph, however, animals injected with PAI-1 show full recovery from the HI injury as measured by DTMR and validated by histology. These findings demonstrate the ability of DTMR to quantify drug treatment efficacy in this neonatal HI model, and highlight the importance of knowing what biophysical pathways are responsible for a particular stroke injury in order to make optimum decisions in drug therapy.
5.2 Background
Stroke is the third leading cause of death in the United States, affects 700,000 people annually, and results in 160,000 deaths (Jantzie et al, 2008). It is particularly devastating when it occurs as neonatal ischemic stroke. This is not only because of child mortality, but also because many lifetime debilitating diseases (cerebral palsy, seizure disorders, hearing and vision loss, mental retardation, learning disabilities, schizophrenia, etc) are linked to neonatal stroke. Imaging is an integral part of the evaluation for stroke
(Srinivasan et al, 2006; Xue et al, 2001). Challenges in imaging evaluations include:
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identifying salvageable tissue, determining whether a patient is suitable for a particular treatment, and establishing a measure to determine treatment effect (Sotak, 2002).
Because of its superior soft tissue contrast, MRI is well suited for stroke diagnosis.
Advances in diffusion imaging prove it to be extremely useful for quantitative assessment of both the gray and white matter. Specifically, quantitative analysis of FA shows great promise in detecting the integrity of synaptic connections in the brain after stroke injury and assessing the degree of recovery after therapy, while ADC analysis aids in detecting gray matter damage.
Previous studies demonstrate the usefulness of diffusion imaging in terms of identifying gray matter lesions not visible on T2 images, discriminating between old and new lesions, and detecting lesions earlier (less than 48 hours after stroke episode) than T2 imaging (Lutsep et al., 1997, Van Everdingen et al., 1998). Additional results from
Gonzales et al. indicate that diffusion imaging is superior compared to conventional MR in terms of sensitivity in detecting stroke legions. The study calculates specificity and sensitivity for the three modalities and finds diffusion MR to be 100% specific and sensitive in a group of 22 (14 diagnosed with acute stroke) individuals scanned six hours after suspected stroke. While conventional MR is also 100% specific, it is only 18% sensitive in this investigation (Gonzales 1999).
The generalization of scalar diffusion weighted magnetic resonance to diffusion tensor magnetic resonance opens the door to applications to white matter investigations
(Basser et al, 1994). Several groups attempt to connect changes in DTMR values with white matter damage information: axonal and myelin degeneration, time since injury, and WM remyelination (Song et al, 2003; MacDonald et al, 2007; Harsan et al, 2006).
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However, the specific cellular environments that give rise to the diffusion signal are not easily inferred. Often, multiple causes can yield similar changes in diffusion metrics.
For example, deterioration of myelin and axonal degeneration both tend to manifest as decreases in FA. When myelin, an electrically insulating sheath that covers the axons, disintegrates water molecules are free to diffuse more readily in the direction transverse to the axon’s length. The increase in radial diffusivity leads to a decrease in FA.
Likewise, no change in the myelin structure, but an introduction of foreign obstacles along the inside length of the axon would tend to decrease the axial diffusivity, thereby also decreasing FA. The situation is further complicated as multiple processes often occur simultaneously during neurological damage. One goal of this study is to elucidate what changes occur at the cellular level to cause changes in the DTMR metrics after a neonatal HI attack.
Another goal is to determine the efficacy of drug treatment using DTMR as an imaging tool for assessing white and gray matter recovery following ischemic stroke injury. The series of events leading to irreversible cell damage following ischemic stroke is known as the ischemic cascade. Briefly, the oxygen supply to the brain is reduced, and
ATP production is temporarily halted. This causes the sodium-potassium ionic transport cellular pumps to fail. Calcium begins to build up within the cells, triggering a host of events eventually leading to cell necrosis. Once oxygen levels return to normal, the body’s defenses engage an inflammatory response that releases antibodies, phagocytes, and proteases to break down and remove the dead cells. In the process, they destroy viable tissue. The BBB is disrupted, allowing water to flow into the brain through osmosis, leading to an excess accumulation of water, i.e., edema. The water carries with
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it various foreign material such as bacteria, which accelerate the body’s inflammatory response. Although described in a linear fashion, these processes are often intertwined and cyclical.
Identifying which stage in the cascade a stroke victim is in provides invaluable knowledge for determining optimum treatment options. This is often an extremely difficult task. However, neonatal HI has unique characteristics that may help in choosing treatment options. For example, in neonatal HI, it appears that tPA precedes MMP formation in neonatal HI, opposite the order in most adult stroke. Unfortunately, tPA directly breaks down the BBB which promotes all levels of the ischemic cascade.
Developing drugs that target tPA specifically may provide the key in future neonatal HI treatment. In this study, we examine what clinical role DTMR can play in assessing recovery from neonatal HI after administration of tPA targeted drug therapy.
5.3 Materials and Methods
5.3.1 Animal surgery
The Institutional Animal Care and Use Committee approved all procedures.
Seven-day-old Wistar rat pups for the Vannucci cerebral ischemia– hypoxia (HI) model are used in this study. The pups are provided to the IRC for imaging from Dr. Kuan’s laboratory at Cincinnati Children’s Hospital Medical Center in the Department of
Developmental Biology. The method for inducing HI is described previously (Rice et al.,
1981; Adhami et al., 2008). Briefly, the pups are anesthetized with 3% isoflurane. Then, the right common carotid artery is pinched to reduce blood flow to the brain, causing ischemia. After recovering in ambient air for one hour, the animals are placed in glass chambers containing 10% oxygen, 90% nitrogen for the hypoxia portion of HI. They
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remain in this environment, while submerged in a 37˚ C water bath for one and a half hours.
5.3.2 Magnetic resonance imaging
All data are acquired on a Bruker BioSpec 7T system with 40 G/cm gradients using the custom-built 25 mm single-turn transmit/receive solenoid coil described in
Chapter 3. Animals are grouped in two cohorts, with two each saline-treated or PAI-1- treated animals in the first cohort and three each saline- or PAI-1-treated animals in the second cohort. Animals are taken to the scanner 24 h after HI, where they are anesthetized and maintained with 1% isoflurane in air and kept warm with heated air circulating through the magnet bore. T2- weighted anatomical images are acquired using a two-dimensional RARE (rapid acquisition and relaxation enhancement) sequence with an effective echo time of 76.96 ms, repetition time of 1000 ms, field-of-view (FOV) of
19.2 x 19.2 mm2, and a 256 x 192 matrix size, and slice thickness of 0.75 mm.
Diffusion tensor images are acquired with a spin echo sequence using an echo time of 21 ms, repetition time of 1100 ms, b-value of 800, six diffusion directions, FOV of 19.2 x 19.2 mm2, a matrix of 128 x 128, and a slice thickness of 0.75 mm. ADC and
FA maps are calculated using the Bruker online processing software, Paravision 4. From the ADC maps, left versus right hemisphere areas of the cortex are chosen as regions of interest (ROIs) and pixels are chosen manually from which ADC values averaged over five slices are calculated. From the FA maps, the left and right portions of the corpus callosum are chosen for comparison. Figure 5.1 illustrates these ROIs.
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A A B
Figure 5.1: Regions of interest (ROI). (A) the cortex is divided into two ROIs for analysis from a trace-weighted image (B) an FA map shows strong white matter contrast, as evidenced by the yellow ROI around the left section of the corpus callosum. A and B are calculated from the same data set.
For the second cohort, T2 maps are calculated from data acquired with a spin echo sequence using echo times of 20, 40, 60, 80, and 100 ms at a repetition time of 1800 ms with the same FOV and matrix as used for the diffusion scan. The T2 maps are processed offline using Cincinnati Children’s Hospital Image Processing Software
(CCHIPS) developed at the IRC, which calculates T2 by fitting the signal intensities from different echo times to equation 1.15b. The average values of T2 in the left hemisphere are compared to the right by manually drawing ROIs using CCHIPS as shown in Figure
5.2.
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A B
Figure 5.2: Quantitative T2 map of PAI treated. (A) and PBS B at 24 h.
Hyperintensities in (B) are due to increased water content in the cerebral edema. ROIs are drawn to encompass entire hemispheres and are averaged over 5 slices.
5.3.3 Histological Staining
Nissl, myelin basic protein (MBP), and terminal deoxynucleotidyl transferase dUTP nick end labeling (TUNEL), and immunoglobulin staining are performed as described previously (Adhami et al., 2008). Dissection and staining are performed by Dr.
Kuan’s lab.
5.3.4 Statistical analysis
Values are represented as the mean ± SD or SEM as indicated. ROIs such as those in Figures 5.1 and 5.2 are used for statistical analysis. Quantitative data are compared between different groups using Microsoft Excel two-sample (unpaired) t test assuming equal variance. The p-values are incorporated into Figure 5.3.
5.4 Results
5.4.1 Magnetic Resonance Imaging: Quantitative T2, ADC, and FA imaging
MRI data clearly detects brain edema at 24 h in the saline treated animals, but not in the PAI-1 treated animals (Figure 5.3). The ipsilateral hemisphere appears
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hyperintense in the T2 image of the saline treated animal (Figure 5.3 A,B). From the saline group, average percent increase of T2 relaxation times of the ipsilateral compared to contralateral side is 39.7% (68 to 95 ms), whereas for the PAI-1 treated group it is
15.1% (71 to 82 ms). The T2 increases are significantly different between groups
(p=0.009, n=3 from each group, Figure 5.3 C).
In the ADC images of the saline group, the ipsilateral hemisphere is hypointense compared to the contralateral (Figure 5.3 D, E). In contrast, the PAI-1 treated group has no observable difference between hemispheres. Analysis of the cortical gray matter show an average ADC of 1.005 μm2/ms on the contralateral side as compared to 0.775
μm2/ms on the ipsilateral side of the saline-injected animals (p<0.005, n=3). In comparison, the PAI-1 group shows insignificant changes in ADC values between hemispheres (1.032 μm2 /ms on contralateral versus 1.026 μm2 /ms, n=3, Figure 5.3 F).
FA data analysis from the corpus callosum shows decreased anisotropy in these white matter tracts on the HI injured hemisphere of the saline-treated animals (Figure 5.3
G, H). At 24 h, the saline injected rats had an approximate 10% reduction in FA in the corpus callosum (p=0.005, n=5). The reduction of FA in the PAI-1 treated animals is insignificant (Figure 5.3 I). MRI results are summarized in the table.
TABLE 5.1 Metric T2(ms) ADC(µm2/ms) FA
ROI Global Cortex CC
Saline Injected Contralateral 68 ± 5.2 1.005 ± 0.047 0.347 ± 0.018
Ipsilateral 95 ± 9.1 0.755 ± 0.064 0.314 ± 0.017
PAI-1 Injected Contralateral 72 ± 3.3 1.032 ± 0.047 0.383 ± 0.018
Ipsilateral 83 ± 1.9 1.026 ± 0.051 0.378 ± 0.020
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Figure 5.3: T2 and diffusion MRI 24 h after HI injury. (A, B) T2 weighted images detect edema in the gray matter (GM) on the lesion side (R) reflected by significant changes in the T2 times (C). (D, E) ADC maps detect edema as a decrease in diffusivity in GM. Analysis shows significant reduction in ADC in the cortical GM of saline treated animals, (F). (G, H): directionally encoded color maps of the FA illustrate significant damage (I) to corpus callosum (CC).
To clarify the underlying cellular activity responsible for our observed changes in the diffusion data, histological staining results are shown next.
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5.4.2 Histological Staining
As mentioned above, one of the dangers of disruption of the BBB is the extravasation of pathogens into the neuronal body and bundles which may cause infection. Furthermore, the antibodies that are sent to destroy these pathogens often will also destroy healthy cell “stand bys.” The main antibody, or immunoglobulin, IgG is present in 75% of serum immunoglobulins in the human body. It is the only antibody capable of passing from the mother to the fetus through the placenta. Staining for IgG shows a large area of the antibody on the HI insulted hemisphere of saline injected animals, and a much smaller, but still visible, amount on the HI side of PAI-1 injected animals (Figure 5.4).
Figure 5.4: IgG staining. IgG
immunoglobulin is markedly present in
the cortex (Ctx) and hippocampus (Hip)
in the saline HI area, and much less
present in the PAI-1 treated HI side at 24
h post HI insult.
Additional staining: Nissl, TUNEL, and MBP further illuminate our DTMR findings.
Nissl staining shows swollen defasciculated CC in the ipsilateral side of the saline treated animals (Figure 5.5 B). TUNEL staining, which tags broken DNA, shows brain damage ranging from massive cystic degeneration to multiple columnar lesions in the cortex
(Figure 5.5 E). MBP staining demonstrates a much more fragmented deterioration of the myelin structure in the saline treated animals (Figure 5.5 H) and less obvious soma
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(Figure 5.5 K) than in either the contralateral side or the HI injury side of PAI-1 treated animals (Figure 5.5 G, J, I, L).
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Figure 5.5: Histology. (B) the CC has expanded in the ipsilateral hemisphere of the saline injected animal compared to the contralateral side and the PAI-1 treated animal (A, C) as labeled by the red line. Saline treated animals also showed increased TUNEL staining which corresponds to DNA breakdown, (E). Fragmentation of MBP-positive processes, (H), and reduced MBP staining in the soma, (K).
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5.5 Discussion
In this study, we first aim to connect the underlying cellular processes that occur due to neonatal HI to quantitative diffusion data through the use of qualitative immunohistological staining. Second, we test the hypothesis that the effects of anti-tPA treatment would inhibit the injury processes, and that the integrity of protected tissue can be validated through DTMR measurements. Indeed, histology corroborated our DTMR interpretations and confirmed the efficacy of the anti-tPA treatment.
Although the T2 increase among the saline controls is a classic sign of water accumulation in edematous lesions, DTMR analysis provides additional information related to the age of lesion and cellular integrity of synaptic connections (Qiao et al.,
2001). While there is a degree of consensus as to the interpretation of various changes in
DTMR metrics, the exact mechanisms underlying the imaging results is a matter of lively debate. Different theories to explain the decrease in ADC in gray matter after stroke include: 1) tortuous and diminished diffusion path in the extracellular compartment, 2) failure of the sodium-potassium ionic pump resulting in water uptake to the more viscous intracellular compartment, and 3) transition of water from solution to gel state (van der
Toorn et al, 1996; Mosley et al, 1990; Mintrorovitch et al, 1994; and Branco, 2000).
In our study, IgG staining demonstrates a large increase in the presence of antibodies in the cortex. The presence of antibodies implies the presence of pathogens.
DTMR images of the cortex show a decrease in ADC, which may be explained as a restriction in diffusion lengths due to water molecules encountering and scattering off micro sized obstacles (i.e., the antibodies, pathogens, and whatever else may have leaked
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through the BBB). This interpretation may seem additional to, but is arguably congruent with, at least the first two different theories mentioned in the previous paragraph.
Specifically, 1) the increase in micro sized objects would inevitably lead to a tortuous and diminished diffusion path in the extracellular compartment, and 2) as mentioned in
Section 5.2, failure of the sodium-potassium ionic pump precludes the body’s inflammatory response. Therefore, the failure of the ionic pump reduces ADC and results in additional micro sized diffusion obstacles that compound the reduction in ADC.
In the white matter, interpretations of decreases in the fractional anisotropy also vary as they do in interpretations of ADC decreases in the gray matter. Although many state that FA reduction in the white matter is a sign of demyelination, other factors such as obstructions within the axonal tracts may contribute to a reduction in FA (Horsfield et al, 2002; Smith et al, 2006; Mazziota et al, 1995). In our study, FA reduction in the CC has a two fold explanation as gleaned from histology. First, fragmentation of the myelin sheets, as illustrated by MMP staining, reduces the organization of axon anisotropy that is found in the healthy tissue. Second, the axonal bodies themselves swell, which increases the diameter of the CC, and in turn increases the radial diffusivity. The swelling demonstrated on the Nissl staining (Figure 5.5 B) supports the second part of this interpretation of reduced FA. However, care must be taken in assuming that reduction in
FA or ADC necessarily implies the biophysical mechanisms we discover through histology. Further work must be done to determine if various patterns in FA, ADC, axial and radial diffusivity can provide more definitive interpretations as to the cellular environment DTMR imaging represents.
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Our second major aim in this study is to test the hypothesis that tPA is the primary proteases responsible for edema due to its early instigation of BBB damage in this neonatal stroke model. To test this hypothesis, histology was performed on PAI-1 drug
(anti-tPA therapy) treated HI animals, and compared to controls. Of course, in the clinical setting histology is of no benefit to the patient. Therefore, we first performed
DTMR analysis of treated versus not treated tissue to assess the tissue integrity of both the gray and white matter (CC), and then compared the DTMR findings with the gold standard of histology.
The T2 and ADC results show that the gray matter remains intact in PAI-1 drug administered animals, which suggests that PAI-1 treatment successfully reduced BBB damage by inhibiting the activation of MMP. Histological MBP staining supports this claim as observed by the less severe changes in the PAI-1 treated versus controls (Figure
5.5). The downstream effects of BBB disruption are alleviated after PAI-1 treatment, as depicted by less abnormalities in the histological stains. IgG staining illustrates lower levels of antibodies; Nissl staining shows little or no swelling of the CC, and TUNEL staining shows very little change in the cortex and hippocampus (Figures 5.4 and 5.5).
A common injury among prenatal and newborn HI is periventricular leukomalacia, which is death of white-matter near the ventricles (Volpe, 2008). The decrease in the degree of diffusion anisotropy in the corpus callosum in our prenatal HI model supports this finding. Death of white-matter involves several stages which comprise Wallerian degeneration. Destruction of the myelin, infiltration of the tissue by antibodies, and axoplasmic swelling resulting from ionic pump failure are a few stages in
Wallerian degeneration. As mentioned above, we observed all of these aspects of
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degeneration in the histological stains and DTMR images. When compared with PAI-1 treated animals, DTMR images appeared normal, and the histological staining confirmed the integrity of the tissue (Figures 5.3-5.5).
In conclusion, we find DTMR to be sensitive to pathology in this murine model of neonatal HI. Explanations of the changes in diffusion metrics are given through careful histological observations. Finally, the novel drug therapy for neonatal HI PAI-1 shows great promise as a neuroprotective agent for pediatric health care. However, our
DTMR imaging technique is limited in both scope and resolution. As a result, only one large white matter structure was analyzed, and the data came from only one imaging slice of the entire axonal tract. The next chapter presents data from a higher resolution and larger scope DTMR microimaging technique applied to an adult stroke model. The work results from a collaboration between Dr. Chia-Yi Kuan, Dr. Dianer Yang, and Niza
Nemkul from Cincinnati Children’s Research Center, Department of Developmental
Biology and Dr. Gang Ning, director of the Electron Microscopy Laboratory at the
Pennsylvania University. More details can be found in Shereen et al, 2010.
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Chapter Six Correlations between Diffusion Tensor Imaging and Electromicroscopy in a Murine Model for Acute Adult Stroke.
6.1 Abstract In this study, we combine DTMR and electromicroscopy analyses of a murine model for acute adult thrombotic stroke to determine whether DTMR can distinguish characteristics unique to this pathology. Animals are imaged at 6, 15, and 24 h post HI injury. DTMR detects significant changes in WM as early as 6 hours post hypoxia- ischemia (HI). Contrary to the common finding of decreased FA due to decreased λ\\ and increased λ┴ in stroke studies, we observe a trend toward decreased λ\\ and λ┴ in all three analyzed WM structures (Wang et al, 2008). This has the effect of an almost insignificant change in FA values as illustrated most dramatically in the internal capsule.
In previous HI studies, demyelination causes an increase in λ┴ (Harsan et al, 2006).
However, in our model, electron microscopy reveals that HI causes separation of myelin sheaths and protrusion of vesicles from the myelin, which compresses the axon plasma and creates multiple diffusion confining compartments leading to a reduced λ┴. These results highlight the importance of considering changes in all diffusion metrics in the diagnosis of WM injury.
6.2 Background
The severity of stroke-induced damage to brain parenchyma is outlined in Chapter
5, where it is important to note that the structural cerebral damage that occurs due to stroke in general varies greatly. Because different drug therapies address the different biomechanistic damages, correlating DTMR to specific types of underlying cellular damage plays a vital role for advances in utility of clinical imaging. Furthermore,
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detecting at risk patients prior to stroke attack would increase both the likelihood of preventing HI injury, as well as the preparedness to act quickly in the unfortunate event a stroke occurs. This is particularly important since the therapeutic window for effective treatment is but a few hours.
Of particular importance in stroke is white matter injury, since it comprises half the human brain, but receives far less of the blood supply and circulation (Dewar, Yam et al. 1999). However, it is difficult to distinguish white from gray matter damage and determine the point of irreversible white matter injury in acute stroke. The imaging modality best suited for the task is DTMR. Previous studies attempt to correlate DTMR metrics with underlying biophysical structures and neurophysical diseases. Theoretical modeling shows that the structural breakdown of focal enlargement-constriction of the neurites will result in reduced axial diffusivity (Beaulieu 2002; Budde and Frank 2010).
DTMR studies of Wallerian (trauma or axotomy induced) degeneration disease demonstrate a steady decline of axial diffusivity and increase in radial diffusivity which results in a dramatic decrease in fractional anisotropy (Mac Donald, Dikranian et al.
2007; Zhang, Jones et al. 2009). On the other hand, DTMR studies of patients with acute stoke have shown a reduction in both axial and radial diffusivity, but little initial change
(<24 hrs) in fractional anisotropy (Yang, Tress et al. 1999; Bhagat, Hussain et al. 2008;
Sakai, Yamada et al. 2009). In Bhagat, Hussain et al., appreciable reduction of fractional anisotropy 24 hours post stroke signified irreversible white matter damage. The ability to identify at risk white matter injury before this point of no return is of crucial importance in clinical applications, however, to date there are no DTMR-neuropathology correlation data in patients with acute ischemic stroke. This chapter attempts to elucidate patterns of
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DTMR changes specific to acute adult HI to aid in the diagnosis of this disease and in understanding the relation between patterns of change of DTMR metrics and the underlying cellular integrity.
6.3 Methods
The work presented in this chapter is derived mainly from a collaborative study between the Imaging Research Center, Department of Radiology; Division of
Developmental Biology; Division of Neurology, Cincinnati Children’s Hospital Medical
Center, and Department of Biology, The Pennsylvania State University.
6.3.1 Animal Surgery
Animal surgery, biochemistry and histology procedures and analysis are performed by Dr. Kuan’s group in the Department of Developmental Biology at
Cincinnati Children’s Hospital Medical Center. 8-12 week-old male CD-1 mice (Charles
River) are used in this study. Details of the temperature-controlled cerebral HI model are described elsewhere (Adhami et al., 2008). Briefly, animals are anesthetized using 0.5-
2% isoflurane while maintaining respiration at 80-120 breathes per minute. Partial cerebral ischemia is established by permanent unilateral (right) common carotid artery occlusion. Following this, hypoxia is initiated by administering 7.5% O2/92.5% N2 through a gas mask for 50 minutes under anesthesia. The body temperature of mice is maintained at 37 ± 0.5°C with a thermocontroller connected to a rectal probe and heating light. At the end of hypoxia, mice are returned to the animal care facility. The animals are then sent to MRI imaging lab in three cohorts: one group of four at six hours, a second at 15 hours, and a third at 24 hours post HI. These animal procedures are
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approved by the Institutional Animal Care and Use Committee and conform to the NIH
Guide for Care and Use of Laboratory Animals.
6.3.2 in-vivo MRI
All data is collected on a Bruker BioSpec 7 Tesla system equipped with 400 mT/m actively shielded gradients. Animals are scanned with the custom-built, single-turn radio frequency coil described in Chapter 3. Anatomical data are acquired with a three dimensional, fast spin echo sequence using the following parameters: echo train length =
16, TEeff/TR = 70.56/1000ms, FOV = 32x19.2x19.2 mm3, matrix size = 256x96x96, and one average, resulting in a resolution of 125x200x200 μm3 with a total acquisition time of under ten minutes. The anatomical data are used as a reference for the subsequent diffusion weighted images. Two dimensional diffusion tensor imaging data are collected using a conventional Stejskal-Tanner single spin echo sequence with diffusion gradients along six directions in both coronal and axial planes. The diffusion imaging parameters are: b=800 sec/mm2 with gradient separation/duration of Δ/δ = 12/4 ms, FOV =
51.2x19.2 mm2, TE/TR = 22/1000 ms, two averages, matrix = 256 x 96, slice thickness =
0.6 mm (5 coronal and 1 axial), and resolution = 200 x 200 μm2 in plane. Acquisition time is approximately 20 minutes for each orientation. Analysis is performed using the
ParaVision 4.0 software package. Regions of interest are prescribed in the striatum, hippocampus, and the cortex. Apparent diffusion coefficients (ADC) from each cohort of animals are averaged separately for the ipsilateral and contralateral sides at each time point.
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6.3.3 ex-vivo MRI
Due to the relatively higher noise and lower resolution of the in vivo DTMR, ex vivo imaging is performed to assess the damage in the white matter structures. One animal from each time point from the in vivo scans is sacrificed immediately after in vivo scanning by transcardial perfusion of formalin. The brains are excised and flushed with phosphate buffered saline solution. All ex vivo images are acquired with a custom-built solenoid transmit/receive coil (Chapter 3). The coil has five turns, a diameter of 14 mm, and a length of 21 mm. Whole brain data are collected using a three dimensional, conventional spin echo DTMR imaging sequence with the same parameters as the in vivo scans except for: FOV = 32 x 12 x 12 mm3, matrix = 256 x 96 x 96, and therefore resolution = 125 μm isotropic. Total scan time is approximately 18 hours. Quantification of DTMR metrics including fractional anisotropy (FA), axial diffusivity, and radial diffusivity is performed using DTIstudio software (Jiang et al., 2006). The FA value is calculated using the formula from Chapter 2. The DTMR metrics are obtained from manually ascribing ROIs to the fimbria, external capsule, and internal capsule. Data from the ROIs come from 15 transverse slices and 35 coronal slices per animal in order to capture the majority of the WM structures. An illustration from a subset of the total slices is depicted in Figure 6.1.
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DEC FA λ1 λ 2 λ 3 MD
Figure 6.1: Sample images from 6 hour ex vivo HI mouse. Rows 1-3 are consecutive
125 micron transverse slices illustrating the external capsule (pink, brown) and fimbria
(peach, green) and the last five rows are 125 micron slices spaced every 500 microns illustrating the external capsule, fimbria, and internal capsule (magenta, yellow).
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6.3.4 Electron Microscopy
Samples are sent to Dr. Ning’s Laboratory at the Pennsylvania State University for analysis by electron microscope. At indicated times after HI, animals are perfused transcardially with 4% paraformaldehyde and 1% glutaraldehyde in 0.1M phosphate buffer. The brains are removed and horizontal 100 μm thick sections are cut with a vibratome. Areas of the indicated tissues from the HI challenged and contralateral hemispheres are dissected and post-fixed with 1%OsO4. The tissues are dehydrated and embedded in epoxy resin (Ted Pella, CA). Then, sections of 70 nm thick are cut with a
Leica UC6 ultramicrotome (Deerfield, IL) and stained with uranyl acetate and lead citrate. The sections are analyzed in a JEM 1200 EXII electron microscope (JEOL,
Peabody, MA).
6.3.5 Statistical Analyses
All statistics are performed using SPSS for Windows version 12.0. Data are first analyzed using a general linear model analysis with time, side (contralateral and ipsilateral), and location as factors. Side and time are significant factors for all locations, but there are no significant side x location effect. There is a significant time x side effect for axial diffusivity and a significant location x time effect for FA. To determine the specific interactions, all data are analyzed separately for each side using a one-way
ANOVA with time as the factor. Contrasts are defined in this analysis comparing the 6 and 15 hr time points and the 6 and 24 hr time points. Following that analysis, each time point is analyzed comparing the contra- and ipsilateral sides using Student’s t-test.
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6.4 Results
6.4.1 in-vivo gray matter T2 and ADC
T2-weighted MRI shows a gradual accumulation of water on the HI-challenged side of the brain and T2-hyperintensities along some axonal tracts at 15-24 hrs of recovery (Fig. 6.2e, see increased signals in the external capsule, molecular layer of dentate gyrus, the alveus and stratum oriens in T2 images). At almost all time points and gray matter regions, there are significant and progressive decreases in the ADC values
(Figure 6.2g-i).
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Figure 6.2: In vivo T2 and ADC images. At 6 hours post HI, differences between hemispheres is unnoticeable in T2 images a, but is evident in ADC map, b. Quantitative
ADC values were significantly lower in the damaged side at all time points and regions except the hippocampus at 6 hours post HI and the cerebral cortex at 15 hours, although they approached significant difference g-i. T2-MRI hyperintensities in WM, is obvious only at the 24 hour time point, e. Ctx=cortex, Th=thalamus, St=striatum,
Hip=hippocampus, CB=cerebellum, ec=external capsule, alv/Or=alveus stratum oriens,
Rad=stratum radiatum, and MoDG=molecular layer of dentate gyrus.
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6.4.2 in vivo white matter diffusion anisotropy
DTMR images contrast some white matter structures, most notably the external capsule and the fimbria (Figure 6.3).
Figure 6.3: In vivo diffusion anisotropy. Although the fimbria (purple structure referred by arrow in 6hr DEC) and external capsule (green structure referred by arrow in 15hr DEC) are visible, the image quality is overall noisy and the voxel size large compared to the WM structures.
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Fractional Anisotropy
Fimbria MCAO Fimbria Contra EC MCAO EC Contra Linear (Fimbria MCAO) Linear (Fimbria Contra) Linear (EC Contra) Linear (EC MCAO)
0.7
0.6
0.5
0.4 FA FA
0.3
0.2
0.1
0 0 5 10 15 20 25 30 Hours Post Occlusion
Figure 6.4: Linear best fits of the FA data. The dotted lines represent the FA values from the damaged fimbria (black) and external capsule (red).
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Mean Diffusivity
Fimbria MCAO Fimbria Contra EC MCAO EC Contra Linear (Fimbria Contra) Linear (Fimbria MCAO) Linear (EC MCAO) Linear (EC Contra)
1.2
1
0.8
0.6
0.4 Diffusivity (1000*mm^2/sec)
0.2
0 0 5 10 15 20 25 30 Hours Post Occlusion
Figure 6.5: Linear best fits of the MD data. The dotted lines represent the MD values from the damaged fimbria (black) and external capsule (red).
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Axial Diffusivity
Fimbria MCAO Fimbria Contra EC MCAO EC Contra Linear (Fimbria Contra) Linear (Fimbria MCAO) Linear (EC Contra) Linear (EC MCAO)
2
1.8
1.6
1.4
1.2
1
0.8
Diffusivity (1000*mm^2/sec) 0.6
0.4
0.2
0 0 5 10 15 20 25 30 Hours Post Occlusion
Figure 6.6: Linear best fits of the axial diffusivity data. The dotted lines represent the axial diffusivity values from the damaged fimbria (black) and external capsule (red).
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Radial Diffusivity
Fimbria MCAO Fimbria Contra EC MCAO EC Contra Linear (Fimbria Contra) Linear (EC Contra) Linear (Fimbria MCAO) Linear (EC MCAO)
0.9
0.8
0.7
0.6
0.5
0.4
0.3 Diffusivity (1000*mm^2/sec)
0.2
0.1
0 0 5 10 15 20 25 30 Hours Post Occlusion
Figure 6.7 Linear best fits of the radial diffusivity data. The dotted lines represent the radial diffusivity values from the damaged fimbria (black) and external capsule (red).
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Figures 6.4-6.7 depict in vivo WM DTMR data from two animals from each time point. The DTMR data for the other animals are too noisy to delineate accurately the
WM tracts, and so are not included. Trends towards decreased axial, radial, and therefore mean, diffusivities are observed in both the fimbria and external capsule. This unique and interesting result warrants further investigation.
6.4.3 ex vivo DTMR micro imaging
In order to characterize accurately the diffusion properties of the smaller white matter structures, ex vivo DTMR microimaging is performed. The directionally encoded color (DEC) maps clearly delineate all major nerve fiber tracts and some hippocampal substructures (Figure 6.8). ROIs are drawn in the fimbria (fm), internal capsule (ic), and external capsule (ec) to quantify axial diffusivity, radial diffusivity, and fractional anisotropy (FA). Analysis shows no significant changes of DTMR metrics in the contralateral side of brain, but ipsilaterally, axial diffusivity progressively decreases 27-
40% and is significantly different from the 6-hour time point in all three WM structures both at 15 and 24 hours post HI based on one way ANOVA statistical analysis. The radial diffusivity decreases 17-22% in all three axon tracts within 24 hrs after HI, however the decrease is not significant in the ec at the 15 or 24 time point. In only the ec, the significant decrease in axial diffusivity, but insignificant change in radial diffusivity led to the significant decrease of more than 30% in FA by 24 hours (Figure 6.9b). In contrast, FA insignificantly reduces by less than 5% in the fm and ic. Our observed HI- induced alterations of diffusion metrics in the WM are in contrast to the patterns in traumatic axonal injury or axotomy-induced Wallerian degeneration where radial diffusivity is either unchanged or increases over time (Mac Donald, Dikranian et al.
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2007; Zhang, Jones et al. 2009). The disparity suggests that our model for acute cerebral
HI may produce unique axonal pathology. In order to gain more insight into these discrepancies, electron microscopy is performed.
Figure 6.8: ADC, FA, and DEC maps compared to a Nissl stained slide. The DTMR
can discern several subhippocampal structures. CA1, CA2, C3, and DG anatomy is well contrasted in the ADC, but is nearly invisible in the FA map. Color contrast in the DEC
aids tremendously in delineating compact, crowded WM.
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Figure 6.9: Ex vivo DTMR. Although at much lesser resolution, DEC images distinguish WM with greater contrast than Nissl staining (a). The more internal WM structures (the fm and ic) demonstrate marked decline in axial and radial diffusivity, but not FA (b). However, the ec showed significant decreases in both FA and axial, but not radial, diffusivity. * represents p<0.05.
Table 6.1: DTMR statistics of fm, ic, and ec at 6, 15, and 24 hrs post HI. Ipsi/Cont represent ipsilateral/contralateral side of HI. The p values are determined using a one- way ANOVA with time as the factor with respect to the 6 hr time point.
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6.4.4 Cellular resolution electron microscopy
Results from electron microscopy show several interesting phenomena which may explain our unusual DTMR findings. The most striking anomaly is the separation of both myelin sheaths and the myelin-axoplasma interface (Fig. 6.10: A, B). Other structural alterations include mitochondrial swelling (colored in green) and multiple empty zones between axons. We also observe many large vesicles containing myelin on the surface
(arrows in Fig. 6.5D), which compress the axoplasma (colored in pink in Fig. 6.5: C, D).
These characteristics suggest that the vesicles are protrusions of the myelin sheaths or oligodendrocyte processes, which could restrict transverse water diffusion (i.e. radial diffusivity) in the WM. The EM analysis also detects many pyknotic nuclei in the external capsule at 15 hrs after HI (Fig. 6.5: E, F).
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Contralesional Ipsilesional
A B
C D
E F
Figure 6.10: EM of external capsule. The myelin is still intact, however, at 24 hours the innermost myelin sheet layers separate (arrows) and mitochondria swell, creating multicompartmented intercellular spaces (*) that compress on the axoplasma (pink) which may explain the reduction in λ┴. Scale bar = 1μm.
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6.5 Discussion
It is interesting to note that our adult acute HI model contains many features
characteristic of Leukoaraiosis (LK). LK is a unique subset of chronic ischemic
damage in that it originally is defined based on radiological findings alone
(Hachinski et al., 1987). It is identified by diffuse areas of low attenuation on CT or
hyperintense T2 MR in the periventricular deep white matter (note the hyperintense
external capsule in Figure 6.2 e). Whether LK is an independent risk factor or an
intermediate surrogate of stroke is unclear (Inzitari, 2003). It is statistically
associated with a specific stroke type, lunar infarction, caused by occlusion of the
arteries that supply blood to the deeper brain regions (Leyes et al, 1999). Indeed, this
agrees with our findings of the less severely damaged exterior white matter, i.e.
external capsule, but more severely damage deep white matter of the fimbria and
internal capsule. Also, the method used to induce injury starves the deeper regions
of the brain from oxygen, further aligning our adult stroke model with LK
characteristics.
One can imagine that although hyperintense T2 white matter may be the
traditional indicator of LK, different patients with hyperintense T2 white matter may
have different cellular damages from the same T2 findings. This is where DTMR
may provide additional, clinically useful information to traditional T2 weighted
clinical scans. Since the cellular affects that result from HI insult vary in type and
severity it is important to correlate DTMR metrics precisely with cellular damage
type. We have shown that in our model of acute adult HI, patterns in DTMR metrics
may potentially serve as biomarkers for specific cellular damage, i.e. separation of
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the myelin sheaths and compression of the axoplasma, as elucidated by significant decreases in axial and radial diffusivity, but modest changes in FA. Although further investigation is required to support these claims, the initial results are promising. A more rigorous study where cellular resolution EM (such as that shown in Figure
6.10) correlates with DTMR on a pixel by pixel basis along the white matter tracts would allow for stronger connections to be made between various DTMR patterns and the underlying cellular environment. Although seemingly a daunting task, it is conceivable that ex vivo brains could be imaged while encased within a medium with uniform markings every 100 microns. DTMR imaging could be made to coincide slices with these markings, and subsequently the ex vivo brain would be physically sliced along the same planes as used for imaging slices. These slices could then be imaged with an electron microscope, and fitted to a grid that aligned with the imaging pixels. Although tedious, quantitative data such as the axonal caliber, number of myelin healthy versus damaged axons, etc. could be correlated to the
DTMR metrics, on a pixel by pixel basis. The obvious benefit to clinical radiology would be enormous.
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Chapter 7 Summary and Future Directions
7.1 Summary of experiments: applications of DTMR to disease
7.1.1 Neonatal Hydrocephalus
Chapter 4 presented results from DTMR experiments applied to a neonatal hydrocephalic murine model. Fractional anisotropy, axial, radial, and mean diffusivities were measured in the external capsule, internal capsule, corpus callosum, and cortex.
Except for the cortex, every structure measured had at least one significantly different diffusion metric as compared to controls. However, since the cortex is also a much larger structure than the other three white matter tissues, it is questionable whether neurophysical damage or partial volume effects contribute more to the observed differences. In order to separate these possible causes to the DTMR signal changes, higher resolution imaging and correlation studies with histopathological gold standards are required.
7.1.2 Neonatal Stroke
Chapter 5 presented results from DTMR and histological experiments applied to a neonatal hypoxic-ischemia murine model. The previous hydrocephalic experiments stressed the importance of higher resolution for accurately quantifying the minute white matter and the need for confirming DTMR interpretations with the gold standard of histological data. Consequently, imaging techniques were improved and histological staining performed. DTMR imaging resolution was increased from 0.2 x 0.2 x 1.5 mm3 in the HCP experiments to 0.15 x 0.15 x 0.75 mm3 (voxel reduced by a factor of 3.56) while reducing scan time from approximately 37 minutes to 16 minutes. The extra scan
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time for experiments was used to collect T2 maps for quantitative comparison with the
DTMR and histological data. T2 values increased in the lesion hemisphere, reflecting the edema. Histological staining confirmed the DTMR interpretation of reduced FA as a result of demyelination as previously observed (Harsan, Poulet et al. 2006). Also, the novel drug, PAI-1 was shown to be highly effective in preventing WM damage as indicated by DTMR findings and confirmed by histological data. Despite the increased resolution, anisotropic tissue in the hippocampus (which is often the first area damaged during HI) was barely discernible. This motivated the experiments in chapter 6.
7.1.3 Adult Acute Stroke
In chapter 6, in vivo DTMR imaging of an adult murine model of acute stroke was performed following the imaging protocols developed in Chapter 5. Next, the protocol was improved from a 2D sequence with relatively low resolution and minimum brain coverage to a 3D full brain coverage DTMR microimaging protocol with resolution of
125 isotropic microns. This resolution corresponded to a voxel reduction factor of 8.64 as compared to the data from Chapter 5 and a 30.75 reduction as compared to the data in
Chapter 4. DTMR microimaging was performed on ex vivo samples and the data was compared to electron micrographs (EM). The EM elucidated the subcellular architecture that affected the DTMR signal, yet was invisible to even the highest DTMR microimaging capabilities (Zhang, van Zijl et al. 2002; Zhang, Richards et al. 2003;
Aggarwal, Mori et al. 2010). Thorough DTMR imaging evaluation of white matter regions was performed. Quantification of the fractional anisotropy, axial diffusivity, and radial diffusivity revealed unique patterns in DTMR changes. Combined with the EM data, the DTMR findings suggested the possibility of distinguishing between various
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types and degrees of white matter damage including: demyelinated versus damaged but intact myelin, axoplama compression, swelling of oligodendrocytes, degeneration of hippocampal dendrites, and structural breakdown of axons (Shereen, Nemkul et al. 2010).
Our findings indicated that DTMR may be a useful tool for early diagnosis of vascular dementia in the acute hypoxia-ischemia population.
7.2 Future Directions
7.2.1 Improve scan time and image quality a) Pulse sequences
Although DTMR imaging provides useful, quantifiable information in addition to that of traditional T1 or T2 weighted MRI, a major disadvantage of the technique is its inherently long acquisition time and low signal to noise ratio. Signal averaging will increase the signal to noise ratio, however this is at the expense of further increasing acquisition time. For a given set of relevant imaging parameters (i.e. matrix size, repetition time, number of diffusion directions, b values and averages) the only way to reduce scan time is to employ different pulse sequence or data acquisition strategies.
Such strategies would either collect multiple k-space read out lines within one repetition time (i.e. fast spin echo, echo planar, or sequences that combine the two), acquire less data for reconstruction (i.e. partial-Fourier imaging, or compressed sensing as in sparse
MRI), or utilize parallel imaging hardware (i.e. multiple receivers connected to a phase array coil). In this section, a method to collect more diffusion weighted data
(specifically, more b-values) in less time by combining a diffusion weighted fast spin echo with partial-Fourier reconstruction is described.
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In Chapter 3 the results from one type of diffusion weighted fast spin echo are illustrated (Figures 3.9-3.13). The method is based on a rapid acquisition with relaxed enhancement (RARE) fast spin echo technique, where the additional spin echoes within each repetition time are used to acquire different phase encoded lines of k-space.
However, the addition of diffusion gradients to the traditional RARE sequence leads to phase inconsistencies between the different echoes. This issue may be avoided by using the different echoes for different diffusion weightings (b-values). Further motivation for acquiring data in this manner is that signals from different echoes inherently correspond to different b-values since they occur at different points in time (i.e., increase in diffusion time leads to an increase in b-value). The additional b-values acquired this way make such a diffusion fast spin echo sequence applicable to bi-exponential, kurtosis, or q space diffusion models. Combined with a partial Fourier imaging technique, wherein at least half of k – space is acquired, this pulse sequence has the possibility of acquiring 3-4 times as much diffusion weighted data in half the time of a conventional spin echo experiment. The partial Fourier technique takes advantage of the symmetry in k space.
Ideally, the half of the k space plane above the x = 0 line is a mirror image of the lower half, thus a full image can be reconstructed from only have the data. In practice this increases noise, but generally the time payoff is worth the drop in SNR. b) Customized coils
Perhaps the most straightforward, simple, and effective way to improve image quality and possibly scan time for DTMR protocol on the 7T Bruker is customizing coils for each application. Because the Bruker is routinely used to image different animals which come in a variety of body and head shapes and sizes, customizing coils to fit
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specific geometric dimensions would greatly enhance the quality of DTMR images.
DTMR imaging inherently suffers from low signal to noise, therefore creating coils with the large filling factors is quick way to boost SNR.
7.2.2 Streamline post-processing workflow
Data processing of DTMR data manually on a subject by subject basis is extremely time consuming. This is particularly true of high resolution, three dimensional data such as that presented in Chapter 6. The 125 micron isotropic data from these experiments contains 2,359,296 voxels per brain, accessible from 448 imaging slices from the three spatial orientations. In addition, the processed image data produces a variety of maps: fractional anisotropy, mean, axial, and radial diffusivities being the most commonly used. Many anatomical structures are only visible in some of the different maps (Figure 6.8), forcing one to compare different maps in order to confidently separate tissue structures. Therefore, even a skilled DTMR data analyst with strong experience recognizing and delineating white matter structures from the various DTMR maps requires extensive time per brain simply to segment DTMR metrics from several regions of interest and compile the data into meaningful graphs. When a large number of brains are imaged for statistical comparison, the task not only becomes extremely tedious, but also the results less precise since the affinity of regions of interest between data sets is subject to the propagation of human error. A method to substantially decrease data post- processing time and error is proposed below wherein: 1) a detailed template is created manually which segments the various white and gray matter structures, 2) DTMR software packages are used to co register the image data to the template, and 3) the data
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collected from 2) is automatically processed into graphs by a second software package,
Standard Analysis Software System (SASS).
Making a 3D template with delineated anatomical structures is relatively straightforward and can be performed using DTI Studio Landmark software. Essentially, image data like that found in Figure 6.1 would contain manually drawn ROIs for all discernable tissue structures from all relevant image slices from one (or an average of several) healthy brain. Because animal studies often use mice and rats of different types, and from ages spanning birth to adulthood, depending on demand a template should be designed for each geometrically unique brain, i.e., one for neonatal rat, another for adult mouse, etc. Once a detailed template is constructed, automated image registration (AIR) software would transform the next set of data to align with the template. Regions of interest are overlaid from the template onto the new data set, and the numerical data exported to SASS. At this stage, SASS compiles the numerical data into graphs for user friendly representation of the data. Automated statistical analysis can be incorporated for comparisons within studies. Although completing the tasks to automate the post- processing analysis as mentioned above may take several months, the result would be a net time savings after approximately a few dozen subject analyses. This is of huge benefit to any study requiring large N.
7.2.3 Calculate higher order moments to Stejskal-Tanner equation: Diffusion Kurtosis
Imaging
In Chapter Two the Stejskal-Tanner equation was derived from a random walk model in one dimension. It was assumed that the probability distribution function (PDF) was Gaussian. A Gaussian PDF is appropriate if the diffusive medium is unrestricted
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and unbound, which is not true of biological structures. There are several imaging techniques that do not assume a Gaussian PDF, but these methods are time consuming and therefore not useful in a clinical setting (Tuch et al, 2003; Tuch 2004). Diffusion kurtosis imaging is a new technique that measures the deviation from Gaussian behavior
(or kurtosis) of the diffusion coefficient. To quantify this deviation, Equation 2.27 is expanded:
bS )( 1 22 3 ln app app app bOKDbDb )( S )0( 6
Kapp is the apparent kurtosis coefficient (AKC). Like the ADC, it is a scalar and is directionally dependent. In analogy to the diffusion tensor, there is also a kurtosis tensor:
Wi.j.k.l. It is a rank 4, 3 x 3 x 3 x 3 fully symmetric tensor with 15 independent elements.
Therefore, diffusion gradients in at least 15 non-coplanar directions are needed to solve for the kurtosis tensor. Because Kapp appears in the second order term, at least two b values for each direction in addition to the b = 0 data are also required. This makes DKI more demanding on the hardware and more time consuming.
Literature on DKI is extremely limited, and research in the area is performed by only a few groups (Lu, Jensen et al. 2006; Minati, Aquino et al. 2007; Cheung, Hui et al.
2009). In some cases, the full kurtosis tensor is not calculated explicitly, but instead mean kurtosis (MK) maps are generated from averaging AKC from 3 orthogonal directions, which reduces scanning time. AKC maps from these studies show superior gray matter contrast as compared to their ADC counterparts. However, further work is necessary before the importance of DKI in the clinical field can be determined.
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One expected application of DKI is in stroke. To investigate the utility of DKI to stroke imaging, a 15 hour post occlusion, hypoxic-ischemic ex vivo mouse brain from
Chapter 6 was subjected to an additional scan suitable for performing kurtosis calculations. Imaging parameters were: field of view = 10 x 10 x 16 mm3, resolution =
250 microns isotropic, b values = 0, 1000, 2000 s/mm2, TE/TR = 24/1000 ms, and 30 diffusion sensing directions. To improve the kurtosis estimation, five b0 images were acquired for a total scan time of approximately 29 hours. An example comparison of the fractional anisotropy, mean diffusivity, and mean kurtosis images from one slice are shown in Figure 7.1.
Fractional Anisotropy Mean Diffusivity Mean Kurtosis
1.6 Damaged Healthy 1.4
1.2
1
0.8
0.6
0.4
0.2
0 FA MD MK
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Figure 7.1: Comparison of diffusion tensor imaging fractional anisotropy and mean diffusivity maps with diffusion kurtosis imaging mean kurtosis map. Regions of interest enclose the superior portion of the hippocampus.
Although the preliminary results illustrated in Figure 7.1 are based on one sample, they are nonetheless extremely promising. All three images are calculated from the same data set, allowing for a direct comparison of the three metrics. It is clear from the histograms that the mean kurtosis is more sensitive to hypoxic-ischemic lesions than fractional anisotropy or mean diffusivity. It is important to note that the bars represent the standard deviation of pixel values within each ROI and are not a measure of error.
The larger spread in mean kurtosis values may indicate that kurtosis imaging supplies greater gray matter contrast than traditional diffusion tensor imaging.
The “holy grail” of stroke imaging is to be able to determine the time since injury onset. This is essential since the therapeutic window for drug treatment is limited to a few hours. Mean kurtosis imaging appears to be more sensitive than mean diffusivity in detecting legions at 15 hours post insult in this animal model. Therefore, it is plausible that diffusion kurtosis imaging may provide a rubric for determining the time course of hypoxic-ischemic injury. This extremely important possibility is worth pursuing in future investigations.
7.2.4 White matter segmentation using fiber tracking
Soon after the first DTMR imaging data was processed, it was proposed to use the data to track the axonal fibers pathways (Mori S, Crain BJ et al 1998). Such fiber tracking methods provide highly illustrative information of the geometry of synaptic connections. However, several limitations exist in fiber tracking. It is a subjective
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technique—user input dictates what FA thresholds and turning angles to use for initiating and terminating a fiber tract. Often, several fictitious fibers will branch from a main, true axonal fiber bundle. In cases where multiple fibers cross within a voxel, the net anisotropy is reduced, thereby making it difficult to resolve crossing fibers. Higher order tensor techniques are being developed, however, that can distinguish multiple fiber orientation within a voxel (Tournier, Calamante et al. 2004; Tuch 2004). Kurtosis imaging is one such example (Lazar, Jensen et al. 2008). Figure 7.2 shows examples of fiber tracking performed on the 6 hour post insult ex vivo imaging data first presented in
Figure 6.9 a.
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Figure 7.2: Fiber tracking of mouse brain. Four perspectives of a mouse brain illustrating the: corpus callosum (red), fimbria (yellow), and anterior commissure
(green).
The different orientations in Figure 7.2 correspond to the following points of view: above and at a sideways angle (top left), directly overhead (top right), sagittal profile (bottom left), and from below (bottom right). The next section covers the application of fiber tracking to another organ: the heart.
7.2.5 DTMR outside the brain: fiber tracking of the heart
DTMR has found its main application in neuroscience as a consequence that the brain contains two types of tissue: the more isotropic gray matter and the anisotropic white matter. Because DTMR is sensitive to the degree of anisotropy, it provides excellent contrast between the gray and white matter. Since the information contains both the magnitude and direction of diffusion, it can be used to identify fiber tracks in the manner illustrated in the previous section.
However, other tissue types also have directionality to their structure besides the white matter. One example is muscle tissue. In the case of the heart, the muscle fibers have a twisting pattern that allows the contraction of the heart to pump and circulate blood. Fiber tracking of muscle tissue, such as that shown for the heart in Figure 7.3, may be a more suitable application than brain tissue. One reason for this is that fiber tracking of the brain relies on subjectively picking and choosing which fibers to include as representative of actual synaptic pathways. However, for the fiber tracking illustrated in Figure 7.3, all fibers are included, giving a global picture of the orientation of the
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muscle fibers. Since the entire heart is made of directional tissue, there is no need for subjectively separating fibers based on FA values and turning angles. Also, because the muscle fibers smoothly change directions, inter-voxel fiber crossing is not an issue, as is the case in fiber tracking of the brain.
Figure 7.3: Global fiber tracking of mouse heart. Two perspectives of the mouse heart both show the changing muscle fiber orientation that is characteristic of this organ.
In conclusion, although the main experiments in this dissertation involve traditional diffusion tensor magnetic resonance imaging of various neurological diseases, there is plenty of room for growth—both inside and outside of the brain.
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